text stringlengths 14 5.77M | meta dict | __index_level_0__ int64 0 9.97k ⌀ |
|---|---|---|
FROM clipper/py-rpc:latest
MAINTAINER Dan Crankshaw <dscrankshaw@gmail.com>
COPY containers/python/noop_container.py /container/
CMD ["python", "/container/noop_container.py"]
# vim: set filetype=dockerfile:
| {
"redpajama_set_name": "RedPajamaGithub"
} | 5,173 |
Can VisaCentral obtain additional documents required to apply for my travel visa, such as a Russian Invitation?
Russian Invitations are documents approved by the Foreign Ministry of Russia. These documents authorize you to visit their country and are required for all travellers. VisaCentral is able to acquire invitations for travel to Russia on your behalf. Go to Russian Invitations to learn more.
To track the status of your order, go to Order Status where you can get up-to-date information on your order. You can track your order by using either the VisaCentral order code or itinerary number and traveller's last name or the traveller's date of birth and last name. If you are the account manager for a VisaCentral account, you can log in to your account to see all of the orders you are managing.
Some countries require you to show proof of vaccination for certain diseases in order to apply for a visa. Any vaccinations required to obtain a visa will be clearly listed in the VisaCentral Application Kit. However, additional vaccinations may be recommended for you. To determine if vaccinations are recommended for your travel itinerary, please contact your local physician or consult Immunisations. | {
"redpajama_set_name": "RedPajamaC4"
} | 9,752 |
Q: Physical interpretation of single layer potential in the plane Let $\Omega\subset\mathbb{R}^2$ be a bounded domain with smooth boundary $\partial\Omega$. The single layer potential with charge density $f$ sitting on $\partial\Omega$ is defined by $u(z)=\displaystyle\int_{\partial\Omega}f(w)\ln|z-w|ds_w.$ What is a physical interpretation of the single-layer potential in the plane? (For $\mathbb{R}^3$ this matter is discussed e.g here)
A: This is just the line integral which gives you the electric potential in two dimensions due to a charge distribution of one or more closed loops, i.e. closed charged wires.
The logarithm is coming from the solution of laplace equation in two dimensions, replacing the $\frac{1}{|\vec{x} - \vec{x}'|}$ of three dimensions, and $f(w)$ is just the charge density along the wire (loop). For $ds_w$, this is just the line element, which is the differential length along the charged wire (loop).
I think a notationally more transparent expression would be
$$
\phi(\vec{x}) = \sum_i\oint_{\mathcal{C}_i}dl' \,\rho(\vec{x}') \text{ln }|\vec{x} - \vec{x}'|
$$
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 1,851 |
package rules
import (
"context"
"fmt"
"io/ioutil"
"math"
"os"
"sort"
"testing"
"time"
"github.com/go-kit/kit/log"
"github.com/prometheus/client_golang/prometheus"
"github.com/prometheus/common/model"
yaml "gopkg.in/yaml.v2"
"github.com/prometheus/prometheus/pkg/labels"
"github.com/prometheus/prometheus/pkg/rulefmt"
"github.com/prometheus/prometheus/pkg/timestamp"
"github.com/prometheus/prometheus/pkg/value"
"github.com/prometheus/prometheus/promql"
"github.com/prometheus/prometheus/promql/parser"
"github.com/prometheus/prometheus/storage"
"github.com/prometheus/prometheus/util/teststorage"
"github.com/prometheus/prometheus/util/testutil"
)
func TestAlertingRule(t *testing.T) {
suite, err := promql.NewTest(t, `
load 5m
http_requests{job="app-server", instance="0", group="canary", severity="overwrite-me"} 75 85 95 105 105 95 85
http_requests{job="app-server", instance="1", group="canary", severity="overwrite-me"} 80 90 100 110 120 130 140
`)
testutil.Ok(t, err)
defer suite.Close()
err = suite.Run()
testutil.Ok(t, err)
expr, err := parser.ParseExpr(`http_requests{group="canary", job="app-server"} < 100`)
testutil.Ok(t, err)
rule := NewAlertingRule(
"HTTPRequestRateLow",
expr,
time.Minute,
labels.FromStrings("severity", "{{\"c\"}}ritical"),
nil, nil, true, nil,
)
result := promql.Vector{
{
Metric: labels.FromStrings(
"__name__", "ALERTS",
"alertname", "HTTPRequestRateLow",
"alertstate", "pending",
"group", "canary",
"instance", "0",
"job", "app-server",
"severity", "critical",
),
Point: promql.Point{V: 1},
},
{
Metric: labels.FromStrings(
"__name__", "ALERTS",
"alertname", "HTTPRequestRateLow",
"alertstate", "pending",
"group", "canary",
"instance", "1",
"job", "app-server",
"severity", "critical",
),
Point: promql.Point{V: 1},
},
{
Metric: labels.FromStrings(
"__name__", "ALERTS",
"alertname", "HTTPRequestRateLow",
"alertstate", "firing",
"group", "canary",
"instance", "0",
"job", "app-server",
"severity", "critical",
),
Point: promql.Point{V: 1},
},
{
Metric: labels.FromStrings(
"__name__", "ALERTS",
"alertname", "HTTPRequestRateLow",
"alertstate", "firing",
"group", "canary",
"instance", "1",
"job", "app-server",
"severity", "critical",
),
Point: promql.Point{V: 1},
},
}
baseTime := time.Unix(0, 0)
var tests = []struct {
time time.Duration
result promql.Vector
}{
{
time: 0,
result: result[:2],
}, {
time: 5 * time.Minute,
result: result[2:],
}, {
time: 10 * time.Minute,
result: result[2:3],
},
{
time: 15 * time.Minute,
result: nil,
},
{
time: 20 * time.Minute,
result: nil,
},
{
time: 25 * time.Minute,
result: result[:1],
},
{
time: 30 * time.Minute,
result: result[2:3],
},
}
for i, test := range tests {
t.Logf("case %d", i)
evalTime := baseTime.Add(test.time)
res, err := rule.Eval(suite.Context(), evalTime, EngineQueryFunc(suite.QueryEngine(), suite.Storage()), nil)
testutil.Ok(t, err)
var filteredRes promql.Vector // After removing 'ALERTS_FOR_STATE' samples.
for _, smpl := range res {
smplName := smpl.Metric.Get("__name__")
if smplName == "ALERTS" {
filteredRes = append(filteredRes, smpl)
} else {
// If not 'ALERTS', it has to be 'ALERTS_FOR_STATE'.
testutil.Equals(t, smplName, "ALERTS_FOR_STATE")
}
}
for i := range test.result {
test.result[i].T = timestamp.FromTime(evalTime)
}
testutil.Assert(t, len(test.result) == len(filteredRes), "%d. Number of samples in expected and actual output don't match (%d vs. %d)", i, len(test.result), len(res))
sort.Slice(filteredRes, func(i, j int) bool {
return labels.Compare(filteredRes[i].Metric, filteredRes[j].Metric) < 0
})
testutil.Equals(t, test.result, filteredRes)
for _, aa := range rule.ActiveAlerts() {
testutil.Assert(t, aa.Labels.Get(model.MetricNameLabel) == "", "%s label set on active alert: %s", model.MetricNameLabel, aa.Labels)
}
}
}
func TestForStateAddSamples(t *testing.T) {
suite, err := promql.NewTest(t, `
load 5m
http_requests{job="app-server", instance="0", group="canary", severity="overwrite-me"} 75 85 95 105 105 95 85
http_requests{job="app-server", instance="1", group="canary", severity="overwrite-me"} 80 90 100 110 120 130 140
`)
testutil.Ok(t, err)
defer suite.Close()
err = suite.Run()
testutil.Ok(t, err)
expr, err := parser.ParseExpr(`http_requests{group="canary", job="app-server"} < 100`)
testutil.Ok(t, err)
rule := NewAlertingRule(
"HTTPRequestRateLow",
expr,
time.Minute,
labels.FromStrings("severity", "{{\"c\"}}ritical"),
nil, nil, true, nil,
)
result := promql.Vector{
{
Metric: labels.FromStrings(
"__name__", "ALERTS_FOR_STATE",
"alertname", "HTTPRequestRateLow",
"group", "canary",
"instance", "0",
"job", "app-server",
"severity", "critical",
),
Point: promql.Point{V: 1},
},
{
Metric: labels.FromStrings(
"__name__", "ALERTS_FOR_STATE",
"alertname", "HTTPRequestRateLow",
"group", "canary",
"instance", "1",
"job", "app-server",
"severity", "critical",
),
Point: promql.Point{V: 1},
},
{
Metric: labels.FromStrings(
"__name__", "ALERTS_FOR_STATE",
"alertname", "HTTPRequestRateLow",
"group", "canary",
"instance", "0",
"job", "app-server",
"severity", "critical",
),
Point: promql.Point{V: 1},
},
{
Metric: labels.FromStrings(
"__name__", "ALERTS_FOR_STATE",
"alertname", "HTTPRequestRateLow",
"group", "canary",
"instance", "1",
"job", "app-server",
"severity", "critical",
),
Point: promql.Point{V: 1},
},
}
baseTime := time.Unix(0, 0)
var tests = []struct {
time time.Duration
result promql.Vector
persistThisTime bool // If true, it means this 'time' is persisted for 'for'.
}{
{
time: 0,
result: append(promql.Vector{}, result[:2]...),
persistThisTime: true,
},
{
time: 5 * time.Minute,
result: append(promql.Vector{}, result[2:]...),
},
{
time: 10 * time.Minute,
result: append(promql.Vector{}, result[2:3]...),
},
{
time: 15 * time.Minute,
result: nil,
},
{
time: 20 * time.Minute,
result: nil,
},
{
time: 25 * time.Minute,
result: append(promql.Vector{}, result[:1]...),
persistThisTime: true,
},
{
time: 30 * time.Minute,
result: append(promql.Vector{}, result[2:3]...),
},
}
var forState float64
for i, test := range tests {
t.Logf("case %d", i)
evalTime := baseTime.Add(test.time)
if test.persistThisTime {
forState = float64(evalTime.Unix())
}
if test.result == nil {
forState = float64(value.StaleNaN)
}
res, err := rule.Eval(suite.Context(), evalTime, EngineQueryFunc(suite.QueryEngine(), suite.Storage()), nil)
testutil.Ok(t, err)
var filteredRes promql.Vector // After removing 'ALERTS' samples.
for _, smpl := range res {
smplName := smpl.Metric.Get("__name__")
if smplName == "ALERTS_FOR_STATE" {
filteredRes = append(filteredRes, smpl)
} else {
// If not 'ALERTS_FOR_STATE', it has to be 'ALERTS'.
testutil.Equals(t, smplName, "ALERTS")
}
}
for i := range test.result {
test.result[i].T = timestamp.FromTime(evalTime)
// Updating the expected 'for' state.
if test.result[i].V >= 0 {
test.result[i].V = forState
}
}
testutil.Assert(t, len(test.result) == len(filteredRes), "%d. Number of samples in expected and actual output don't match (%d vs. %d)", i, len(test.result), len(res))
sort.Slice(filteredRes, func(i, j int) bool {
return labels.Compare(filteredRes[i].Metric, filteredRes[j].Metric) < 0
})
testutil.Equals(t, test.result, filteredRes)
for _, aa := range rule.ActiveAlerts() {
testutil.Assert(t, aa.Labels.Get(model.MetricNameLabel) == "", "%s label set on active alert: %s", model.MetricNameLabel, aa.Labels)
}
}
}
// sortAlerts sorts `[]*Alert` w.r.t. the Labels.
func sortAlerts(items []*Alert) {
sort.Slice(items, func(i, j int) bool {
return labels.Compare(items[i].Labels, items[j].Labels) <= 0
})
}
func TestForStateRestore(t *testing.T) {
suite, err := promql.NewTest(t, `
load 5m
http_requests{job="app-server", instance="0", group="canary", severity="overwrite-me"} 75 85 50 0 0 25 0 0 40 0 120
http_requests{job="app-server", instance="1", group="canary", severity="overwrite-me"} 125 90 60 0 0 25 0 0 40 0 130
`)
testutil.Ok(t, err)
defer suite.Close()
err = suite.Run()
testutil.Ok(t, err)
expr, err := parser.ParseExpr(`http_requests{group="canary", job="app-server"} < 100`)
testutil.Ok(t, err)
opts := &ManagerOptions{
QueryFunc: EngineQueryFunc(suite.QueryEngine(), suite.Storage()),
Appendable: suite.Storage(),
TSDB: suite.Storage(),
Context: context.Background(),
Logger: log.NewNopLogger(),
NotifyFunc: func(ctx context.Context, expr string, alerts ...*Alert) {},
OutageTolerance: 30 * time.Minute,
ForGracePeriod: 10 * time.Minute,
}
alertForDuration := 25 * time.Minute
// Initial run before prometheus goes down.
rule := NewAlertingRule(
"HTTPRequestRateLow",
expr,
alertForDuration,
labels.FromStrings("severity", "critical"),
nil, nil, true, nil,
)
group := NewGroup(GroupOptions{
Name: "default",
Interval: time.Second,
Rules: []Rule{rule},
ShouldRestore: true,
Opts: opts,
})
groups := make(map[string]*Group)
groups["default;"] = group
initialRuns := []time.Duration{0, 5 * time.Minute}
baseTime := time.Unix(0, 0)
for _, duration := range initialRuns {
evalTime := baseTime.Add(duration)
group.Eval(suite.Context(), evalTime)
}
exp := rule.ActiveAlerts()
for _, aa := range exp {
testutil.Assert(t, aa.Labels.Get(model.MetricNameLabel) == "", "%s label set on active alert: %s", model.MetricNameLabel, aa.Labels)
}
sort.Slice(exp, func(i, j int) bool {
return labels.Compare(exp[i].Labels, exp[j].Labels) < 0
})
// Prometheus goes down here. We create new rules and groups.
type testInput struct {
restoreDuration time.Duration
alerts []*Alert
num int
noRestore bool
gracePeriod bool
downDuration time.Duration
}
tests := []testInput{
{
// Normal restore (alerts were not firing).
restoreDuration: 15 * time.Minute,
alerts: rule.ActiveAlerts(),
downDuration: 10 * time.Minute,
},
{
// Testing Outage Tolerance.
restoreDuration: 40 * time.Minute,
noRestore: true,
num: 2,
},
{
// No active alerts.
restoreDuration: 50 * time.Minute,
alerts: []*Alert{},
},
}
testFunc := func(tst testInput) {
newRule := NewAlertingRule(
"HTTPRequestRateLow",
expr,
alertForDuration,
labels.FromStrings("severity", "critical"),
nil, nil, false, nil,
)
newGroup := NewGroup(GroupOptions{
Name: "default",
Interval: time.Second,
Rules: []Rule{newRule},
ShouldRestore: true,
Opts: opts,
})
newGroups := make(map[string]*Group)
newGroups["default;"] = newGroup
restoreTime := baseTime.Add(tst.restoreDuration)
// First eval before restoration.
newGroup.Eval(suite.Context(), restoreTime)
// Restore happens here.
newGroup.RestoreForState(restoreTime)
got := newRule.ActiveAlerts()
for _, aa := range got {
testutil.Assert(t, aa.Labels.Get(model.MetricNameLabel) == "", "%s label set on active alert: %s", model.MetricNameLabel, aa.Labels)
}
sort.Slice(got, func(i, j int) bool {
return labels.Compare(got[i].Labels, got[j].Labels) < 0
})
// Checking if we have restored it correctly.
if tst.noRestore {
testutil.Equals(t, tst.num, len(got))
for _, e := range got {
testutil.Equals(t, e.ActiveAt, restoreTime)
}
} else if tst.gracePeriod {
testutil.Equals(t, tst.num, len(got))
for _, e := range got {
testutil.Equals(t, opts.ForGracePeriod, e.ActiveAt.Add(alertForDuration).Sub(restoreTime))
}
} else {
exp := tst.alerts
testutil.Equals(t, len(exp), len(got))
sortAlerts(exp)
sortAlerts(got)
for i, e := range exp {
testutil.Equals(t, e.Labels, got[i].Labels)
// Difference in time should be within 1e6 ns, i.e. 1ms
// (due to conversion between ns & ms, float64 & int64).
activeAtDiff := float64(e.ActiveAt.Unix() + int64(tst.downDuration/time.Second) - got[i].ActiveAt.Unix())
testutil.Assert(t, math.Abs(activeAtDiff) == 0, "'for' state restored time is wrong")
}
}
}
for _, tst := range tests {
testFunc(tst)
}
// Testing the grace period.
for _, duration := range []time.Duration{10 * time.Minute, 15 * time.Minute, 20 * time.Minute} {
evalTime := baseTime.Add(duration)
group.Eval(suite.Context(), evalTime)
}
testFunc(testInput{
restoreDuration: 25 * time.Minute,
alerts: []*Alert{},
gracePeriod: true,
num: 2,
})
}
func TestStaleness(t *testing.T) {
st := teststorage.New(t)
defer st.Close()
engineOpts := promql.EngineOpts{
Logger: nil,
Reg: nil,
MaxSamples: 10,
Timeout: 10 * time.Second,
}
engine := promql.NewEngine(engineOpts)
opts := &ManagerOptions{
QueryFunc: EngineQueryFunc(engine, st),
Appendable: st,
TSDB: st,
Context: context.Background(),
Logger: log.NewNopLogger(),
}
expr, err := parser.ParseExpr("a + 1")
testutil.Ok(t, err)
rule := NewRecordingRule("a_plus_one", expr, labels.Labels{})
group := NewGroup(GroupOptions{
Name: "default",
Interval: time.Second,
Rules: []Rule{rule},
ShouldRestore: true,
Opts: opts,
})
// A time series that has two samples and then goes stale.
app := st.Appender()
app.Add(labels.FromStrings(model.MetricNameLabel, "a"), 0, 1)
app.Add(labels.FromStrings(model.MetricNameLabel, "a"), 1000, 2)
app.Add(labels.FromStrings(model.MetricNameLabel, "a"), 2000, math.Float64frombits(value.StaleNaN))
err = app.Commit()
testutil.Ok(t, err)
ctx := context.Background()
// Execute 3 times, 1 second apart.
group.Eval(ctx, time.Unix(0, 0))
group.Eval(ctx, time.Unix(1, 0))
group.Eval(ctx, time.Unix(2, 0))
querier, err := st.Querier(context.Background(), 0, 2000)
testutil.Ok(t, err)
defer querier.Close()
matcher, err := labels.NewMatcher(labels.MatchEqual, model.MetricNameLabel, "a_plus_one")
testutil.Ok(t, err)
set, _, err := querier.Select(false, nil, matcher)
testutil.Ok(t, err)
samples, err := readSeriesSet(set)
testutil.Ok(t, err)
metric := labels.FromStrings(model.MetricNameLabel, "a_plus_one").String()
metricSample, ok := samples[metric]
testutil.Assert(t, ok, "Series %s not returned.", metric)
testutil.Assert(t, value.IsStaleNaN(metricSample[2].V), "Appended second sample not as expected. Wanted: stale NaN Got: %x", math.Float64bits(metricSample[2].V))
metricSample[2].V = 42 // reflect.DeepEqual cannot handle NaN.
want := map[string][]promql.Point{
metric: {{T: 0, V: 2}, {T: 1000, V: 3}, {T: 2000, V: 42}},
}
testutil.Equals(t, want, samples)
}
// Convert a SeriesSet into a form usable with reflect.DeepEqual.
func readSeriesSet(ss storage.SeriesSet) (map[string][]promql.Point, error) {
result := map[string][]promql.Point{}
for ss.Next() {
series := ss.At()
points := []promql.Point{}
it := series.Iterator()
for it.Next() {
t, v := it.At()
points = append(points, promql.Point{T: t, V: v})
}
name := series.Labels().String()
result[name] = points
}
return result, ss.Err()
}
func TestCopyState(t *testing.T) {
oldGroup := &Group{
rules: []Rule{
NewAlertingRule("alert", nil, 0, nil, nil, nil, true, nil),
NewRecordingRule("rule1", nil, nil),
NewRecordingRule("rule2", nil, nil),
NewRecordingRule("rule3", nil, labels.Labels{{Name: "l1", Value: "v1"}}),
NewRecordingRule("rule3", nil, labels.Labels{{Name: "l1", Value: "v2"}}),
NewRecordingRule("rule3", nil, labels.Labels{{Name: "l1", Value: "v3"}}),
NewAlertingRule("alert2", nil, 0, labels.Labels{{Name: "l2", Value: "v1"}}, nil, nil, true, nil),
},
seriesInPreviousEval: []map[string]labels.Labels{
{},
{},
{},
{"r3a": labels.Labels{{Name: "l1", Value: "v1"}}},
{"r3b": labels.Labels{{Name: "l1", Value: "v2"}}},
{"r3c": labels.Labels{{Name: "l1", Value: "v3"}}},
{"a2": labels.Labels{{Name: "l2", Value: "v1"}}},
},
evaluationDuration: time.Second,
}
oldGroup.rules[0].(*AlertingRule).active[42] = nil
newGroup := &Group{
rules: []Rule{
NewRecordingRule("rule3", nil, labels.Labels{{Name: "l1", Value: "v0"}}),
NewRecordingRule("rule3", nil, labels.Labels{{Name: "l1", Value: "v1"}}),
NewRecordingRule("rule3", nil, labels.Labels{{Name: "l1", Value: "v2"}}),
NewAlertingRule("alert", nil, 0, nil, nil, nil, true, nil),
NewRecordingRule("rule1", nil, nil),
NewAlertingRule("alert2", nil, 0, labels.Labels{{Name: "l2", Value: "v0"}}, nil, nil, true, nil),
NewAlertingRule("alert2", nil, 0, labels.Labels{{Name: "l2", Value: "v1"}}, nil, nil, true, nil),
NewRecordingRule("rule4", nil, nil),
},
seriesInPreviousEval: make([]map[string]labels.Labels, 8),
}
newGroup.CopyState(oldGroup)
want := []map[string]labels.Labels{
nil,
{"r3a": labels.Labels{{Name: "l1", Value: "v1"}}},
{"r3b": labels.Labels{{Name: "l1", Value: "v2"}}},
{},
{},
nil,
{"a2": labels.Labels{{Name: "l2", Value: "v1"}}},
nil,
}
testutil.Equals(t, want, newGroup.seriesInPreviousEval)
testutil.Equals(t, oldGroup.rules[0], newGroup.rules[3])
testutil.Equals(t, oldGroup.evaluationDuration, newGroup.evaluationDuration)
testutil.Equals(t, []labels.Labels{{{Name: "l1", Value: "v3"}}}, newGroup.staleSeries)
}
func TestDeletedRuleMarkedStale(t *testing.T) {
st := teststorage.New(t)
defer st.Close()
oldGroup := &Group{
rules: []Rule{
NewRecordingRule("rule1", nil, labels.Labels{{Name: "l1", Value: "v1"}}),
},
seriesInPreviousEval: []map[string]labels.Labels{
{"r1": labels.Labels{{Name: "l1", Value: "v1"}}},
},
}
newGroup := &Group{
rules: []Rule{},
seriesInPreviousEval: []map[string]labels.Labels{},
opts: &ManagerOptions{
Appendable: st,
},
}
newGroup.CopyState(oldGroup)
newGroup.Eval(context.Background(), time.Unix(0, 0))
querier, err := st.Querier(context.Background(), 0, 2000)
testutil.Ok(t, err)
defer querier.Close()
matcher, err := labels.NewMatcher(labels.MatchEqual, "l1", "v1")
testutil.Ok(t, err)
set, _, err := querier.Select(false, nil, matcher)
testutil.Ok(t, err)
samples, err := readSeriesSet(set)
testutil.Ok(t, err)
metric := labels.FromStrings("l1", "v1").String()
metricSample, ok := samples[metric]
testutil.Assert(t, ok, "Series %s not returned.", metric)
testutil.Assert(t, value.IsStaleNaN(metricSample[0].V), "Appended sample not as expected. Wanted: stale NaN Got: %x", math.Float64bits(metricSample[0].V))
}
func TestUpdate(t *testing.T) {
files := []string{"fixtures/rules.yaml"}
expected := map[string]labels.Labels{
"test": labels.FromStrings("name", "value"),
}
st := teststorage.New(t)
defer st.Close()
opts := promql.EngineOpts{
Logger: nil,
Reg: nil,
MaxSamples: 10,
Timeout: 10 * time.Second,
}
engine := promql.NewEngine(opts)
ruleManager := NewManager(&ManagerOptions{
Appendable: st,
TSDB: st,
QueryFunc: EngineQueryFunc(engine, st),
Context: context.Background(),
Logger: log.NewNopLogger(),
})
ruleManager.Run()
defer ruleManager.Stop()
err := ruleManager.Update(10*time.Second, files, nil)
testutil.Ok(t, err)
testutil.Assert(t, len(ruleManager.groups) > 0, "expected non-empty rule groups")
ogs := map[string]*Group{}
for h, g := range ruleManager.groups {
g.seriesInPreviousEval = []map[string]labels.Labels{
expected,
}
ogs[h] = g
}
err = ruleManager.Update(10*time.Second, files, nil)
testutil.Ok(t, err)
for h, g := range ruleManager.groups {
for _, actual := range g.seriesInPreviousEval {
testutil.Equals(t, expected, actual)
}
// Groups are the same because of no updates.
testutil.Equals(t, ogs[h], g)
}
// Groups will be recreated if updated.
rgs, errs := rulefmt.ParseFile("fixtures/rules.yaml")
testutil.Assert(t, len(errs) == 0, "file parsing failures")
tmpFile, err := ioutil.TempFile("", "rules.test.*.yaml")
testutil.Ok(t, err)
defer os.Remove(tmpFile.Name())
defer tmpFile.Close()
err = ruleManager.Update(10*time.Second, []string{tmpFile.Name()}, nil)
testutil.Ok(t, err)
for h, g := range ruleManager.groups {
ogs[h] = g
}
// Update interval and reload.
for i, g := range rgs.Groups {
if g.Interval != 0 {
rgs.Groups[i].Interval = g.Interval * 2
} else {
rgs.Groups[i].Interval = model.Duration(10)
}
}
reloadAndValidate(rgs, t, tmpFile, ruleManager, expected, ogs)
// Change group rules and reload.
for i, g := range rgs.Groups {
for j, r := range g.Rules {
rgs.Groups[i].Rules[j].Expr.SetString(fmt.Sprintf("%s * 0", r.Expr.Value))
}
}
reloadAndValidate(rgs, t, tmpFile, ruleManager, expected, ogs)
}
// ruleGroupsTest for running tests over rules.
type ruleGroupsTest struct {
Groups []ruleGroupTest `yaml:"groups"`
}
// ruleGroupTest forms a testing struct for running tests over rules.
type ruleGroupTest struct {
Name string `yaml:"name"`
Interval model.Duration `yaml:"interval,omitempty"`
Rules []rulefmt.Rule `yaml:"rules"`
}
func formatRules(r *rulefmt.RuleGroups) ruleGroupsTest {
grps := r.Groups
tmp := []ruleGroupTest{}
for _, g := range grps {
rtmp := []rulefmt.Rule{}
for _, r := range g.Rules {
rtmp = append(rtmp, rulefmt.Rule{
Record: r.Record.Value,
Alert: r.Alert.Value,
Expr: r.Expr.Value,
For: r.For,
Labels: r.Labels,
Annotations: r.Annotations,
})
}
tmp = append(tmp, ruleGroupTest{
Name: g.Name,
Interval: g.Interval,
Rules: rtmp,
})
}
return ruleGroupsTest{
Groups: tmp,
}
}
func reloadAndValidate(rgs *rulefmt.RuleGroups, t *testing.T, tmpFile *os.File, ruleManager *Manager, expected map[string]labels.Labels, ogs map[string]*Group) {
bs, err := yaml.Marshal(formatRules(rgs))
testutil.Ok(t, err)
tmpFile.Seek(0, 0)
_, err = tmpFile.Write(bs)
testutil.Ok(t, err)
err = ruleManager.Update(10*time.Second, []string{tmpFile.Name()}, nil)
testutil.Ok(t, err)
for h, g := range ruleManager.groups {
if ogs[h] == g {
t.Fail()
}
ogs[h] = g
}
}
func TestNotify(t *testing.T) {
storage := teststorage.New(t)
defer storage.Close()
engineOpts := promql.EngineOpts{
Logger: nil,
Reg: nil,
MaxSamples: 10,
Timeout: 10 * time.Second,
}
engine := promql.NewEngine(engineOpts)
var lastNotified []*Alert
notifyFunc := func(ctx context.Context, expr string, alerts ...*Alert) {
lastNotified = alerts
}
opts := &ManagerOptions{
QueryFunc: EngineQueryFunc(engine, storage),
Appendable: storage,
TSDB: storage,
Context: context.Background(),
Logger: log.NewNopLogger(),
NotifyFunc: notifyFunc,
ResendDelay: 2 * time.Second,
}
expr, err := parser.ParseExpr("a > 1")
testutil.Ok(t, err)
rule := NewAlertingRule("aTooHigh", expr, 0, labels.Labels{}, labels.Labels{}, nil, true, log.NewNopLogger())
group := NewGroup(GroupOptions{
Name: "alert",
Interval: time.Second,
Rules: []Rule{rule},
ShouldRestore: true,
Opts: opts,
})
app := storage.Appender()
app.Add(labels.FromStrings(model.MetricNameLabel, "a"), 1000, 2)
app.Add(labels.FromStrings(model.MetricNameLabel, "a"), 2000, 3)
app.Add(labels.FromStrings(model.MetricNameLabel, "a"), 5000, 3)
app.Add(labels.FromStrings(model.MetricNameLabel, "a"), 6000, 0)
err = app.Commit()
testutil.Ok(t, err)
ctx := context.Background()
// Alert sent right away
group.Eval(ctx, time.Unix(1, 0))
testutil.Equals(t, 1, len(lastNotified))
testutil.Assert(t, !lastNotified[0].ValidUntil.IsZero(), "ValidUntil should not be zero")
// Alert is not sent 1s later
group.Eval(ctx, time.Unix(2, 0))
testutil.Equals(t, 0, len(lastNotified))
// Alert is resent at t=5s
group.Eval(ctx, time.Unix(5, 0))
testutil.Equals(t, 1, len(lastNotified))
// Resolution alert sent right away
group.Eval(ctx, time.Unix(6, 0))
testutil.Equals(t, 1, len(lastNotified))
}
func TestMetricsUpdate(t *testing.T) {
files := []string{"fixtures/rules.yaml", "fixtures/rules2.yaml"}
metricNames := []string{
"prometheus_rule_evaluations_total",
"prometheus_rule_evaluation_failures_total",
"prometheus_rule_group_interval_seconds",
"prometheus_rule_group_last_duration_seconds",
"prometheus_rule_group_last_evaluation_timestamp_seconds",
"prometheus_rule_group_rules",
}
storage := teststorage.New(t)
registry := prometheus.NewRegistry()
defer storage.Close()
opts := promql.EngineOpts{
Logger: nil,
Reg: nil,
MaxSamples: 10,
Timeout: 10 * time.Second,
}
engine := promql.NewEngine(opts)
ruleManager := NewManager(&ManagerOptions{
Appendable: storage,
TSDB: storage,
QueryFunc: EngineQueryFunc(engine, storage),
Context: context.Background(),
Logger: log.NewNopLogger(),
Registerer: registry,
})
ruleManager.Run()
defer ruleManager.Stop()
countMetrics := func() int {
ms, err := registry.Gather()
testutil.Ok(t, err)
var metrics int
for _, m := range ms {
s := m.GetName()
for _, n := range metricNames {
if s == n {
metrics += len(m.Metric)
break
}
}
}
return metrics
}
cases := []struct {
files []string
metrics int
}{
{
files: files,
metrics: 12,
},
{
files: files[:1],
metrics: 6,
},
{
files: files[:0],
metrics: 0,
},
{
files: files[1:],
metrics: 6,
},
}
for i, c := range cases {
err := ruleManager.Update(time.Second, c.files, nil)
testutil.Ok(t, err)
time.Sleep(2 * time.Second)
testutil.Equals(t, c.metrics, countMetrics(), "test %d: invalid count of metrics", i)
}
}
func TestGroupStalenessOnRemoval(t *testing.T) {
if testing.Short() {
t.Skip("skipping test in short mode.")
}
files := []string{"fixtures/rules2.yaml"}
sameFiles := []string{"fixtures/rules2_copy.yaml"}
storage := teststorage.New(t)
defer storage.Close()
opts := promql.EngineOpts{
Logger: nil,
Reg: nil,
MaxSamples: 10,
Timeout: 10 * time.Second,
}
engine := promql.NewEngine(opts)
ruleManager := NewManager(&ManagerOptions{
Appendable: storage,
TSDB: storage,
QueryFunc: EngineQueryFunc(engine, storage),
Context: context.Background(),
Logger: log.NewNopLogger(),
})
var stopped bool
ruleManager.Run()
defer func() {
if !stopped {
ruleManager.Stop()
}
}()
cases := []struct {
files []string
staleNaN int
}{
{
files: files,
staleNaN: 0,
},
{
// When we remove the files, it should produce a staleness marker.
files: files[:0],
staleNaN: 1,
},
{
// Rules that produce the same metrics but in a different file
// should not produce staleness marker.
files: sameFiles,
staleNaN: 0,
},
{
// Staleness marker should be present as we don't have any rules
// loaded anymore.
files: files[:0],
staleNaN: 1,
},
{
// Add rules back so we have rules loaded when we stop the manager
// and check for the absence of staleness markers.
files: sameFiles,
staleNaN: 0,
},
}
var totalStaleNaN int
for i, c := range cases {
err := ruleManager.Update(time.Second, c.files, nil)
testutil.Ok(t, err)
time.Sleep(3 * time.Second)
totalStaleNaN += c.staleNaN
testutil.Equals(t, totalStaleNaN, countStaleNaN(t, storage), "test %d/%q: invalid count of staleness markers", i, c.files)
}
ruleManager.Stop()
stopped = true
testutil.Equals(t, totalStaleNaN, countStaleNaN(t, storage), "invalid count of staleness markers after stopping the engine")
}
func TestMetricsStalenessOnManagerShutdown(t *testing.T) {
if testing.Short() {
t.Skip("skipping test in short mode.")
}
files := []string{"fixtures/rules2.yaml"}
storage := teststorage.New(t)
defer storage.Close()
opts := promql.EngineOpts{
Logger: nil,
Reg: nil,
MaxSamples: 10,
Timeout: 10 * time.Second,
}
engine := promql.NewEngine(opts)
ruleManager := NewManager(&ManagerOptions{
Appendable: storage,
TSDB: storage,
QueryFunc: EngineQueryFunc(engine, storage),
Context: context.Background(),
Logger: log.NewNopLogger(),
})
var stopped bool
ruleManager.Run()
defer func() {
if !stopped {
ruleManager.Stop()
}
}()
err := ruleManager.Update(2*time.Second, files, nil)
time.Sleep(4 * time.Second)
testutil.Ok(t, err)
start := time.Now()
err = ruleManager.Update(3*time.Second, files[:0], nil)
testutil.Ok(t, err)
ruleManager.Stop()
stopped = true
testutil.Assert(t, time.Since(start) < 1*time.Second, "rule manager does not stop early")
time.Sleep(5 * time.Second)
testutil.Equals(t, 0, countStaleNaN(t, storage), "invalid count of staleness markers after stopping the engine")
}
func countStaleNaN(t *testing.T, st storage.Storage) int {
var c int
querier, err := st.Querier(context.Background(), 0, time.Now().Unix()*1000)
testutil.Ok(t, err)
defer querier.Close()
matcher, err := labels.NewMatcher(labels.MatchEqual, model.MetricNameLabel, "test_2")
testutil.Ok(t, err)
set, _, err := querier.Select(false, nil, matcher)
testutil.Ok(t, err)
samples, err := readSeriesSet(set)
testutil.Ok(t, err)
metric := labels.FromStrings(model.MetricNameLabel, "test_2").String()
metricSample, ok := samples[metric]
testutil.Assert(t, ok, "Series %s not returned.", metric)
for _, s := range metricSample {
if value.IsStaleNaN(s.V) {
c++
}
}
return c
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 7,874 |
Nuova Pallacanestro Gorizia fue un club de baloncesto con sede en la ciudad de Gorizia, en Friuli-Venecia Julia, que disputó 27 temporadas en la Serie A, la máxima categoría del baloncesto italiano. Fue fundada en 1934, y tras su desaparición en 1999, se refundó ese mismo año, desapareciendo definitivamente en 2010.
Historia
La Unione Ginnastica Goriziana fue fundada en 1868 cuando Gorizia pertenecía todavía al Imperio de los Habsburgo. El primer partido oficial de baloncesto (según los archivos) se jugó en la ciudad el 24 de mayo de 1920, y desde entonces el baloncesto se convirtió en una actividad recreativa al aire libre. En 1934 nacía oficialmente la sección de baloncesto de la U.G.G., disputando 10 años después su primer campeonato nacional, mientras que al año siguiente tendría plaza en la Serie A, que entonces se encontraba dividida en grupos regionales.
El equipo llegaría a la primera división, la Serie A, en 1952, permaneciendo allí durante dos temporadas. Goriziana jugó cinco temporadas de la Serie A en los años 60 (1961-62, 1963-65, 1966-67, 1969-70). Alternó entre el nivel superior y el segundo nivel (Serie A2) entre 1975 a 1984, después de lo cual permaneció en la Serie A2 hasta 1998. Una temporada solitaria de vuelta en la Serie A vería el club escapar del descenso en la cancha, para posteriormente vender los derechos deportivos a Scavolini Pesaro y bajar a la tercera división de la Serie B1.
El equipo comenzó de nuevo desde la Serie B1 como Nuova Pallacanestro Gorizia. Sin embargo, siguió luchando dentro y fuera de la pista y estaba en la Serie C dilettanti cuando se retiró de la liga en septiembre de 2010, debido a que el propietario se negó a financiar el club por su cuenta. El club no participó en otra liga y dejó de funcionar ese año.
Trayectoria
Patrocinadores
Zoppas Gorizia (1961–1962)
Unione Ginnastica Goriziana (1962-1964)
Splugen Brau Gorizia (1966-1970)
Patriarca Gorizia(1975–1976)
Pagnossin Gorizia (1976-1980)
Tai Ginseng Gorizia (1980-1981)
San Benedetto Gorizia (1981–1984)
Segafredo Gorizia (1984-1988)
San Benedetto Gorizia (1988–1990)
Brescialat Gorizia (1994-1996)
Dinamica Gorizia (1996-1997)
S.D.A.G. Gorizia (1998-1999)
Referencias
Enlaces externos
Resultados históricos en Serie A
Clubes de baloncesto desaparecidos de Italia
Deporte en Friuli-Venecia Julia | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 9,866 |
package org.apache.camel.builder.component.dsl;
import javax.annotation.Generated;
import org.apache.camel.Component;
import org.apache.camel.builder.component.AbstractComponentBuilder;
import org.apache.camel.builder.component.ComponentBuilder;
import org.apache.camel.component.aws2.msk.MSK2Component;
/**
* Manage AWS MSK instances using AWS SDK version 2.x.
*
* Generated by camel-package-maven-plugin - do not edit this file!
*/
@Generated("org.apache.camel.maven.packaging.ComponentDslMojo")
public interface Aws2MskComponentBuilderFactory {
/**
* AWS 2 Managed Streaming for Apache Kafka (MSK) (camel-aws2-msk)
* Manage AWS MSK instances using AWS SDK version 2.x.
*
* Category: cloud,management
* Since: 3.1
* Maven coordinates: org.apache.camel:camel-aws2-msk
*/
static Aws2MskComponentBuilder aws2Msk() {
return new Aws2MskComponentBuilderImpl();
}
/**
* Builder for the AWS 2 Managed Streaming for Apache Kafka (MSK) component.
*/
interface Aws2MskComponentBuilder extends ComponentBuilder<MSK2Component> {
/**
* Setting the autoDiscoverClient mechanism, if true, the component will
* look for a client instance in the registry automatically otherwise it
* will skip that checking.
*
* The option is a: <code>boolean</code> type.
*
* Default: true
* Group: common
*/
default Aws2MskComponentBuilder autoDiscoverClient(
boolean autoDiscoverClient) {
doSetProperty("autoDiscoverClient", autoDiscoverClient);
return this;
}
/**
* Component configuration.
*
* The option is a:
* <code>org.apache.camel.component.aws2.msk.MSK2Configuration</code>
* type.
*
* Group: producer
*/
default Aws2MskComponentBuilder configuration(
org.apache.camel.component.aws2.msk.MSK2Configuration configuration) {
doSetProperty("configuration", configuration);
return this;
}
/**
* Whether the producer should be started lazy (on the first message).
* By starting lazy you can use this to allow CamelContext and routes to
* startup in situations where a producer may otherwise fail during
* starting and cause the route to fail being started. By deferring this
* startup to be lazy then the startup failure can be handled during
* routing messages via Camel's routing error handlers. Beware that when
* the first message is processed then creating and starting the
* producer may take a little time and prolong the total processing time
* of the processing.
*
* The option is a: <code>boolean</code> type.
*
* Default: false
* Group: producer
*/
default Aws2MskComponentBuilder lazyStartProducer(
boolean lazyStartProducer) {
doSetProperty("lazyStartProducer", lazyStartProducer);
return this;
}
/**
* To use a existing configured AWS MSK as client.
*
* The option is a:
* <code>software.amazon.awssdk.services.kafka.KafkaClient</code> type.
*
* Group: producer
*/
default Aws2MskComponentBuilder mskClient(
software.amazon.awssdk.services.kafka.KafkaClient mskClient) {
doSetProperty("mskClient", mskClient);
return this;
}
/**
* The operation to perform.
*
* The option is a:
* <code>org.apache.camel.component.aws2.msk.MSK2Operations</code> type.
*
* Group: producer
*/
default Aws2MskComponentBuilder operation(
org.apache.camel.component.aws2.msk.MSK2Operations operation) {
doSetProperty("operation", operation);
return this;
}
/**
* If we want to use a POJO request as body or not.
*
* The option is a: <code>boolean</code> type.
*
* Default: false
* Group: producer
*/
default Aws2MskComponentBuilder pojoRequest(boolean pojoRequest) {
doSetProperty("pojoRequest", pojoRequest);
return this;
}
/**
* To define a proxy host when instantiating the MSK client.
*
* The option is a: <code>java.lang.String</code> type.
*
* Group: producer
*/
default Aws2MskComponentBuilder proxyHost(java.lang.String proxyHost) {
doSetProperty("proxyHost", proxyHost);
return this;
}
/**
* To define a proxy port when instantiating the MSK client.
*
* The option is a: <code>java.lang.Integer</code> type.
*
* Group: producer
*/
default Aws2MskComponentBuilder proxyPort(java.lang.Integer proxyPort) {
doSetProperty("proxyPort", proxyPort);
return this;
}
/**
* To define a proxy protocol when instantiating the MSK client.
*
* The option is a: <code>software.amazon.awssdk.core.Protocol</code>
* type.
*
* Default: HTTPS
* Group: producer
*/
default Aws2MskComponentBuilder proxyProtocol(
software.amazon.awssdk.core.Protocol proxyProtocol) {
doSetProperty("proxyProtocol", proxyProtocol);
return this;
}
/**
* The region in which MSK client needs to work. When using this
* parameter, the configuration will expect the lowercase name of the
* region (for example ap-east-1) You'll need to use the name
* Region.EU_WEST_1.id().
*
* The option is a: <code>java.lang.String</code> type.
*
* Group: producer
*/
default Aws2MskComponentBuilder region(java.lang.String region) {
doSetProperty("region", region);
return this;
}
/**
* If we want to trust all certificates in case of overriding the
* endpoint.
*
* The option is a: <code>boolean</code> type.
*
* Default: false
* Group: producer
*/
default Aws2MskComponentBuilder trustAllCertificates(
boolean trustAllCertificates) {
doSetProperty("trustAllCertificates", trustAllCertificates);
return this;
}
/**
* Whether the component should use basic property binding (Camel 2.x)
* or the newer property binding with additional capabilities.
*
* The option is a: <code>boolean</code> type.
*
* Default: false
* Group: advanced
*/
@Deprecated
default Aws2MskComponentBuilder basicPropertyBinding(
boolean basicPropertyBinding) {
doSetProperty("basicPropertyBinding", basicPropertyBinding);
return this;
}
/**
* Amazon AWS Access Key.
*
* The option is a: <code>java.lang.String</code> type.
*
* Group: security
*/
default Aws2MskComponentBuilder accessKey(java.lang.String accessKey) {
doSetProperty("accessKey", accessKey);
return this;
}
/**
* Amazon AWS Secret Key.
*
* The option is a: <code>java.lang.String</code> type.
*
* Group: security
*/
default Aws2MskComponentBuilder secretKey(java.lang.String secretKey) {
doSetProperty("secretKey", secretKey);
return this;
}
}
class Aws2MskComponentBuilderImpl
extends
AbstractComponentBuilder<MSK2Component>
implements
Aws2MskComponentBuilder {
@Override
protected MSK2Component buildConcreteComponent() {
return new MSK2Component();
}
private org.apache.camel.component.aws2.msk.MSK2Configuration getOrCreateConfiguration(
org.apache.camel.component.aws2.msk.MSK2Component component) {
if (component.getConfiguration() == null) {
component.setConfiguration(new org.apache.camel.component.aws2.msk.MSK2Configuration());
}
return component.getConfiguration();
}
@Override
protected boolean setPropertyOnComponent(
Component component,
String name,
Object value) {
switch (name) {
case "autoDiscoverClient": getOrCreateConfiguration((MSK2Component) component).setAutoDiscoverClient((boolean) value); return true;
case "configuration": ((MSK2Component) component).setConfiguration((org.apache.camel.component.aws2.msk.MSK2Configuration) value); return true;
case "lazyStartProducer": ((MSK2Component) component).setLazyStartProducer((boolean) value); return true;
case "mskClient": getOrCreateConfiguration((MSK2Component) component).setMskClient((software.amazon.awssdk.services.kafka.KafkaClient) value); return true;
case "operation": getOrCreateConfiguration((MSK2Component) component).setOperation((org.apache.camel.component.aws2.msk.MSK2Operations) value); return true;
case "pojoRequest": getOrCreateConfiguration((MSK2Component) component).setPojoRequest((boolean) value); return true;
case "proxyHost": getOrCreateConfiguration((MSK2Component) component).setProxyHost((java.lang.String) value); return true;
case "proxyPort": getOrCreateConfiguration((MSK2Component) component).setProxyPort((java.lang.Integer) value); return true;
case "proxyProtocol": getOrCreateConfiguration((MSK2Component) component).setProxyProtocol((software.amazon.awssdk.core.Protocol) value); return true;
case "region": getOrCreateConfiguration((MSK2Component) component).setRegion((java.lang.String) value); return true;
case "trustAllCertificates": getOrCreateConfiguration((MSK2Component) component).setTrustAllCertificates((boolean) value); return true;
case "basicPropertyBinding": ((MSK2Component) component).setBasicPropertyBinding((boolean) value); return true;
case "accessKey": getOrCreateConfiguration((MSK2Component) component).setAccessKey((java.lang.String) value); return true;
case "secretKey": getOrCreateConfiguration((MSK2Component) component).setSecretKey((java.lang.String) value); return true;
default: return false;
}
}
}
} | {
"redpajama_set_name": "RedPajamaGithub"
} | 8,732 |
'use strict';
/**
* Producer
* @author Chen Liang [code@chen.technology]
*/
/*!
* Module dependencies.
*/
var Promise = require('bluebird');
var Exchange = require('./exchange');
// var Connection = require('./connection');
var Message = require('./message');
var _ = require('lodash');
var debug = require('debug')('broker:Producer');
var Router = require('./router');
/**
* Message Producer.
*
* @param {Object} options [description]
* @param {Channel} options.channel Connection or channel.
* @param {Exchange} options.exchange Optional default exchange.
* @param {String} options.routingKey Optional default routing key.
* @param {Boolean} options.autoDeclare Automatically declare the default
* exchange at instantiation.
* @default true
*
*/
var Producer = function(options) {
options = options || {};
this.channel = options.channel;
this.exchange = options.exchange;
this.routingKey = options.routingKey;
this.autoDeclare = _.isBoolean(options.autoDeclare) ? options.autoDeclare : true;
if (!this.exchange) {
this.exchange = new Exchange();
}
// debug('.constructor.autoDeclare', this.autoDeclare);
if (this.autoDeclare) {
this.exchange = this.exchange.use(this.channel);
}
// debug('.constructor.exchange', this.exchange);
};
/**
* Declare `exchange` for this producer
* @return {[type]} [description]
*/
Producer.prototype.declare = Promise.method(function() {
if (!_.isEmpty(this.exchange.name)) {
return this.exchange.declare();
}
});
/**
* Publish message to the specified exchange.
* Use `Channel_Model.publish(exchange, routingKey, content, options)`
*
* @param {Message} message Message body.
* @param {String} routingKey Message routing key.
*
* @param {Object} options [description]
* @param {Object} options.headers Mapping of arbitrary headers to pass
* along with the message body.
* @param {String} options.routingKey Override default routingKey
* @param {Exchange} options.exchange Override the exchange.
* Note that this exchange must have
* been declared.
*
* @return {[type]} [description]
*/
Producer.prototype.publish = function(message, options) {
options = options || {};
var exchange = options.exchange || this.exchange.name;
var routingKey = options.routingKey || this.routingKey;
var headers = options.headers;
if (exchange instanceof Exchange) {
exchange = exchange.name;
}
if (!(message instanceof Message)) {
message = new Message({
body: message,
headers: headers,
});
}
if (_.isNull(message.deliveryMode) || _.isUndefined(message.deliveryMode)) {
message.deliveryMode = this.deliveryMode;
}
return this.channel.getChannel()
.then(function(channel) {
return channel.publish(
exchange, routingKey,
message.encode(), message.getPublishOptions());
});
};
/**
* Use `Channel_Model.publish(exchange, routingKey, content, options)
*
* @param {[type]} exchange [description]
* @param {[type]} routingKey [description]
* @param {[type]} content [description]
* @param {[type]} options [description]
* @return {[type]} [description]
*/
Producer.prototype._publish = function(exchange, routingKey, content, options) {
return this.channel.getChannel()
.then(function(channel) {
return channel.publish(exchange, routingKey, content, options);
});
};
/**
* Return a `Router` instance with `this` as the producer
*
* @param {[type]} options options will be passed to `Router`
* @param {[type]} options.headers [description]
* @param {[type]} options.routingKey [description]
* @param {[type]} options.exchange [description]
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cover
# Copyright
Copyright © 2018 by Nathan Schneider
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First Edition: September 2018
Published by Nation Books, an imprint of Perseus Books, LLC, a subsidiary of Hachette Book Group, Inc.
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Library of Congress Cataloging-in-Publication Data
Names: Schneider, Nathan, 1984–author.
Title: Everything for everyone: the radical tradition that is shaping the next economy / Nathan Schneider.
Description: First Edition. | New York: Nation Books, [2018] | Includes bibliographical references and index.
Identifiers: LCCN 2018007566| ISBN 9781568589596 (hardcover) | ISBN 9781568589602 (ebook)
Subjects: LCSH: Cooperative societies—History—21st century. | Capitalism—Social aspects. | Political participation.
Classification: LCC HD2956 .S465 2018 | DDC 334—dc23
LC record available at https://lccn.loc.gov/2018007566
ISBNs: 978-1-56858-959-6 (hardcover); 978-1-56858-960-2 (ebook)
E3-20180726-JV-NF
# Contents
Cover
Title Page
Copyright
Epigraph
**Introduction:** Equitable Pioneers
**1 All Things in Common:** Prehistory
**2 The Lovely Principle:** Formation
**3 The Clock of the World:** Disruption
**4 Gold Rush:** Money
**5 Slow Computing:** Platforms
**6 Free the Land:** Power
**7 Phase Transition:** Commonwealth
Acknowledgments
About the Author
Illustration Credits
Notes
Index
I bow to the economic miracle, but what I want to show you are the neighborhood celebrations.
—Chris Marker, _Sans Soleil_
# Introduction
## Equitable Pioneers
My maternal grandfather came into the world just north of Johnstown, Colorado, in 1916. It's a place of high, dry plains under the Rocky Mountains, which stretch far off along the western horizon. On cassette tapes recorded a few years before his death, he and my grandmother bicker about those days. She'd come from Lincoln, Nebraska, and, like my grandfather, was the child of German-speaking migrants whose ancestors had lived for centuries in Russia's Ukrainian conquests. She complains that his parents were hard and cruel for not keeping him in school longer than it took to learn reading and some math. He fires back, not kindly—saying you can't apply "modern standards" to the way it was then and there, when he slept with his brothers year-round in an open lean-to on the sugar-beet farm where the family tenanted, no heat or light at night except what scarce wood could provide. My grandparents were about the same age, and of the same peculiar ethnicity, but town and country then were two entirely distinct worlds.
Modern standards eventually came to the farms around Johnstown, but not inevitably. Although cities like Lincoln had electric lights by the time my grandmother was born there, electric companies had no interest in stringing power lines to dispersed farmhouses. Electricity arrived only in the 1940s with the expansion of the Poudre Valley Rural Electric Association—a company organized and owned by its customers, set up with financing through the Rural Electrification Act, which President Franklin Roosevelt steered through Congress in 1936. Poudre Valley REA is still running, still a cooperative, and is an aggressive adopter of solar farms. It's part of a resident-owned grid that delivers power to about 75 percent of the territory of the United States.
As a teenager, my grandfather moved in with his older brother in Greeley, where he started working at an auto-parts store. He made extra money connecting power lines to German-speakers' farms and selling them their first washing machines. After a wartime spell in the army, he began a career as a roving hardware-store manager, then as an executive, and finally, as the director of Liberty Distributors, which became one of the larger hardware firms in the country during his tenure.
Liberty's members, and my grandfather's bosses, were regional hardware wholesale companies; together, they bought saws and sandpaper and other goods that would be sold in local stores and lumberyards. Each member company held one share and one vote, and members split any surpluses. It was a co-op. Since the onslaught of big-box chains, it's mostly thanks to co-ops like this that the small hardware stores my grandfather loved can persist at all. Perhaps the co-op model helps solve a family mystery, too—how Grandpa managed to build a national company without becoming especially rich.
Liberty did about $2 billion in business annually in today's dollars during the early 1980s, serving three thousand or so stores. The company's mission, according to the company handbook, was to fulfill its members' "continued desire through a cooperative effort to meet with the economic pressures facing each business." It also allowed a more flexible arrangement than the conformity expected by other co-ops such as Ace Hardware. But, like them, its job was survival.
Liberty is not the only co-op I've encountered in my family's past. When I take a ride in a nearly automated tractor with one of my grandfather's nephews, who still farms near Greeley, he tells me about how he brings his sugar beets to Fort Morgan for processing. He is a member of the Western Sugar Cooperative, a descendant of the same Great Western Sugar Company that brought our ancestors to Colorado after they arrived at Ellis Island in 1907. Thanks to the co-op, he keeps up the old family crop.
_A map of Liberty Distributors' member wholesalers, from the 1980 company directory._
Nobody told me when I was growing up that this particular way of doing business had so much to do with our family history. Why should they? Why would the kind of company matter?
More than a century later, here I am. I was raised back east, lived on both coasts, and then wound up moving—returning—from New York City to Colorado with my wife and our unborn son, who would enter the world an hour's drive from the nameless spot where my grandfather did. Compared to what it was in his time, Colorado is another kind of place, a land of ski resorts and hydraulic fracturing and tech startups. Cooperative business shores up the area's burgeoning affluence—the mortgage-lending credit unions, the babysitting time-banks, the consumer-owned REI stores for skiwear and climbing gear. High-country electric co-ops helped plan out some of the famous resort towns. But Colorado is still a place where people have to create an economy of their own to get by. When I take a ride with an East African driver-owner of Green Taxi or meet a child-care co-op member who speaks only Spanish, I remember my grandfather's immigrant parents a century earlier.
It wasn't investigating my family history that put me on the lookout for cooperatives. I started looking because of stirrings I noticed as a reporter among veterans of the protests that began in 2011, such as Occupy Wall Street and Spain's 15M movement. Once their uprisings simmered, the protesters had to figure out how to make a living in the economy they hadn't yet transformed, and they started creating co-ops. Some were doing it with software—cooperative social media, cloud data, music streaming, digital currencies, gig markets, and more. But this generation was not all lost to the digital; others used cooperation to live by dirt and soil.
The young radicals turned to the same kind of business that my buttoned-up, old-world, conservative grandfather did. Following them, I began following in my grandfather's footsteps before I even knew it.
Both he and the protesters professed principles derived from a small group of neighbors in mid-nineteenth-century Britain—the Rochdale Society of Equitable Pioneers. These Equitable Pioneers were mostly weavers working too hard for too little in textile mills, and they set up a store where they could buy flour and candles on their own terms. Equitable co-ownership and co-governance were practical tools for accomplishing this task. Through their democracy, they cut costs, ensured quality, and spun the threads that would help stitch together a global movement. But any movement can fray with time. Each generation has needed its own equitable pioneers. And these pioneers, I've learned, can leave marks far beyond their neighborhood stores.
Co-ops tend to take hold when the order of things is in flux, when people have to figure out how to do what no one will do for them. Farmers had to get their own electricity when investors wouldn't bring it; small hardware stores organized co-ops to compete with big boxes before buying local was in fashion. Before employers and governments offered insurance, people set it up for themselves. Co-ops have served as test runs for the social contracts that may later be taken for granted, and they're doing so again.
This book is a sojourn among the frontiers of cooperation, past and present— _cooperation_ not in the general sense of playing nice, but in the particular sense of businesses truly accountable to those they claim to serve. It's about the long history and present revival of an economy in which people can own and govern the businesses where they work, shop, bank, or meet, sharing the risk and the rewards. These represent a parallel and neglected tradition that runs alongside the usual stories we tell ourselves about how the world as we know it came to be and what is possible there. New cooperators are rearranging this tradition into inventive, networked guises, as if the future depends on it.
Cooperative enterprise can be as old as you want it to be, and a lot of the basic ideas go back as long and far as human economies in general. I'll offer a partial history in the coming chapters, told through the eyes of those reliving pieces of it now. This history carries evidence, from one century to another, that people can govern their own lives, if we give ourselves the chance. Cooperation is tradition and innovation, homegrown yet foreign to the ways of the world around it. It's part of my family's story, and it's a new generation of equitable pioneers. It's like the French peasant-prophet Peter Maurin used to say about things of this sort: "A philosophy so old that it looks like new." It's a philosophy whose discreet return I've had the chance to witness and document, a philosophy of utopian trouble and dull practicality, a philosophy carried out over and over, yet one that we habitually forget or outright deny we are capable of fulfilling. Well, we are.
It's really not so surprising that I didn't grow up knowing of my grandfather as a cooperator. After World War II, in a United States still reeling from the labor struggles of the 1930s and fearful of communist revolutions abroad, an implicit deal was struck: democracy would be for the voting booth alone, not the boardroom. Law and culture concurred. Most large co-ops that persisted—Liberty Distributors among them—did their best to blend into the corporate order. Vulnerable as they were to Red-baiting, democratic businesses cast themselves as good-old American capitalism.
This strategy, however, meant forgetting part of why those co-ops were created in the first place. The social reformers at work during my grandparents' youth had a habit of invoking the vision of a "cooperative commonwealth," an economy made up of interlocking but self-governing enterprises, which put control over production and consumption in the hands of the people most involved in them. Those people would choose what to produce, how to do it, and what to do with the profits. The commonwealth, and the gradual, evolutionary process of getting there, offered an antidote to the authoritarian tendencies then ascending on the right and the left; for six-time Socialist Party presidential candidate Norman Thomas, writing in 1934, "the only effective answer to the totalitarian state of fascism is the cooperative commonwealth." Farmers had been setting up purchasing and marketing co-ops for decades to counteract the power of urban industrialists. W. E. B. Du Bois, meanwhile, was documenting and celebrating the commonwealth among the "communal souls" in African American cooperative businesses.
All this rested on a faith that ordinary people could choose their destinies. One of the most memorable slogans from the labor struggles in those days was a saying of child-laborer-turned-organizer Rose Schneiderman: "The worker must have bread, but she must have roses, too." If "bread" was the buying power of wages, "roses" was the right to the free time that came from reasonable working hours—time for enjoyment and self-management. Schneiderman said those words in a 1912 speech to a room of a few hundred wealthy women in Cleveland. Women's suffrage was the immediate subject and crusade of Schneiderman's speech, but to her, the ballot meant more than voting for politicians every few years. It was the key to a commonwealth. Her organization during that period, the Women's Trade Union League, regarded "self-government in the workshop" as an overriding demand; the momentary struggles over hours and wages and suffrage were a means to that end. The International Ladies' Garment Workers' Union, for which she had also worked, pursued the commonwealth by organizing co-owned apartments for its members.
Serious businesspeople nowadays tend to regard any alternative to the investor-owned corporation as aberrant or impossible. But the alternatives actually preceded the models that prevail today. In Britain, the first legislation for co-ops passed four years before joint-stock companies got their own law in 1856. Legal scholar Henry Hansmann has suggested that we regard investor-owned companies as a distorted kind of cooperative, bent in service of investor interests over anyone else's. The kind of business that now seems normal was once strange; someday it might seem strange again. Perhaps the strangeness is creeping back.
Surveys suggest that something like 85 percent of workers worldwide don't feel engaged in their jobs. As a stopgap, consultants teach corporate managers to instill the fictional "sense of ownership" that so many people want to experience in their economic lives—for employees, and consumers as well. The internal website for Walmart "associates" is MyWalmart.com; "It's _your_ store," Albertsons supermarkets used to tell their customers. Harvard Business School's Francesca Gino, among others, has documented productivity benefits when employees experience "psychological ownership." A pair of former Navy SEALs turned executive coaches preach "extreme ownership." But keeping up this facade is hard work, especially when it has no relationship to reality. It could be more efficient to set up at least a partial ESOP, or employee stock-ownership plan. Partial employee ownership, as at Southwest Airlines or W. L. Gore, is a long-standing tradition in US business, but even that rarely comes up in the management lit. Strange indeed. Why does it seem so hard to take the desire for genuine participation seriously?
As I began encountering the new cooperative frontiers, I learned to notice remnants of past and partial commonwealths still at work around me. When I travel now, I see them fly by everywhere, points of interest missing their commemorative plaques. In the most drab of parking lots, I look around and there they are, dotting the strip malls. These traces of commonwealth have begun to seem like a secret society, an inverted reality lurking inside what claims to be reality, economies that reject the rules by which the economy supposedly plays. In these traces, even tucked within competitive markets, cooperative advantage holds its ground.
Each example pokes a hole in the usual story about how the world came to be as it is, challenging tall tales about progress made from competition and the pursuit of profit. No, there have been other principles at work.
Pass a Best Western hotel or a Dairy Queen or a Carpet One on the highway—can you see the purchasing co-ops built into their franchise models? How about in an antique store that doubles as a sales office for State Farm, still a cooperative-like mutual owned by its car-insurance policyholders? In a Whole Foods Market, and even its adopted parent, Amazon, perhaps there are still ghosts of the organic food co-ops that helped create the demand Whole Foods feeds on, and that it then swallowed. Are there traces left in Burley bike trailers, passing by on the shoulder, of the days when that company was worker owned? As I've driven by the King Arthur Flour factory in Vermont, or Publix grocery stores in Florida, or the New Belgium brewery in northern Colorado, I see some of the more than fourteen million US workers who benefit from an ESOP. Pass a cluster of solar panels in farm country, and chances are it delivers power to members of the area's cooperative electric utility, financed by a hundred-billion-dollar cooperative bank in a city many miles away. Pick up a local newspaper in a diner, and half its heft is wire stories from the Associated Press, a co-op since its founding before the Civil War. The rusty grain silo in a farming town, the laundry service for my region's hospitals, a brutalist credit union building I pass every day—co-op, co-op, co-op.
The International Cooperative Alliance calculates that the largest cooperatives globally generate about $2.2 trillion in turnover and employ about 12 percent of the employed population in G20 countries. As much as 10 percent of the world's total employment happens through co-ops. According to the United Nations, the world's 2.6 million co-ops count over 1 billion members and clients among them, plus $20 trillion in assets, with revenue that adds up to 4.3 percent of the global GDP. The country with the largest total number of co-op memberships—though many members don't know themselves as such—is the United States, home to more than forty thousand cooperative businesses. A national survey found that nearly 80 percent of consumers would choose co-ops over other options if they knew they had a choice. I'm still learning where and how to notice them.
Portions of the commonwealth have trouble noticing each other, too. The worker-owners of an urban house-cleaning co-op might not recognize the cowboy cooperation of ranchers buying feed together, or the hackers sharing cooperative servers while pounding away at their code. A fair-trade spice distributor and a worker-owned mental-health center have offices next door to each other in my town, but they've never talked with each other about being co-ops. With practice, the commonwealth appears. Some of the big, older co-ops have even started displaying their cooperative identity again, as something to be claimed rather than hidden. Whether they admit it or not, they've each turned to democracy out of need.
Economist Brent Hueth finds that cooperatives arise most often when there are "missing markets," when the reigning businesses fail to serve an unmet demand or utilize latent supply. While coffee companies ran a race to the bottom in environmental and labor practices, co-ops engineered a fair-trade movement that went the other way, from the worker-owned roaster Equal Exchange to consumer-owned grocery stores and countless grower co-ops around the world. When competing banks needed to collaborate with each other more reliably, they formed Visa and the SWIFT network as cooperatives. Democracy can be creative and flexible where top-down models fear to tread.
Still, cooperation remains a minority logic in the global economy, and the kinds of hopes that today's equitable pioneers stumble toward are anything but inevitable. Authoritarian, neo-feudal tendencies have found fresh appeal in many quarters; surveys suggest that, worldwide, the desire for democratic politics is on the decline. Young people in the United States increasingly consider democracy—as they know it, at least—a poor way to run a country. Cooperatives themselves have fallen victim to this. Many large credit unions, electric co-ops, mutual insurance giants, and the like have lost the kind of member involvement that they had at their founding, and managers find it just as well not to remind their members that they are, in fact, co-owners. The result is stagnation, usually, or sometimes outright graft. If the world is forgetting its capacity for democracy, the co-ops are, too.
When politicians talk about spreading democracy, they typically have in mind an expansion to more and more countries, forcibly or otherwise, of representative governments and accompanying political rights. But democracy might spread in forms other than ballot boxes. It can spread like Schneiderman's roses into ever more hours of our days, into our workplaces and markets and neighborhoods, and into what becomes of the wealth we generate. It can start to take root in levels of the social order where it was previously absent. Otherwise, democracy becomes a spectator sport—as real, and yet as out of reach, as reality TV.
When tech people talk about "democratizing" something, like driving directions or online banking, what they really mean is _access_. Access is fine, but it's just access. It's a drive-through window, not a door. Access is only part of what democracy has always entailed—alongside real ownership, governance, and accountability. Democracy is a process, not a product.
Apple's Orwell-themed 1984 Super Bowl commercial presented the personal computer as a hammer in the face of Big Brother; later that year, after Election Day, the company printed an ad in _Newsweek_ that proposed "the principle of democracy as it applies to technology": "One person, one computer." The best-selling futurist handbook of the same period, John Naisbitt's _Megatrends_ , likewise promised that "the computer will smash the pyramid," and with its networks "we can restructure our institutions horizontally." What we've gotten instead are apps from online monopolies accountable to their almighty stock tickers. The companies we allow to manage our relationships expect that we pay with our personal data. The internet's so-called sharing economy requires its permanently part-time delivery drivers and content moderators to relinquish rights that used to be part of the social contracts workers could expect. Yet a real sharing economy has been at work all along.
During the 2016 International Summit of Cooperatives in Quebec, I attended a dinner at the Château Frontenac, a palatial hotel that casts its glow across the old city. Quebec City has an especially well-developed commonwealth; many residents can recount a typical day with a litany of one co-op after another—child care, grocery stores, workplaces, and so on. We heard from Monique Leroux, then president of the International Cooperative Alliance, the sector's global umbrella organization. A selection of Canada's legislators, government ministers, and foreign emissaries rose in turn as the emcee announced their names and titles. Among them were cooperative managers from every corner of the world, dressed the way the establishment was supposed to dress before the rise of startup bros and hedge funders, enjoying a meal worthy of the lavish benefit dinners I used to attend as a freeloading guest in New York City. Their credit unions and farm co-ops and wholesalers represented a non-negligible chunk of the global economic order. And though these cooperative titans personally claimed spoils lower than those of their peers in investor-owned conglomerates—maybe a few hundred thousand dollars a year rather than many millions—the ironies of any establishmentarian gathering were present there, too.
Keith Taylor, a co-op researcher at the University of California–Davis, texted me from the United States: "i imagine youre seeing a lot of lip service for members and communities... w/no representation." Pretty much.
Ironies and all, the fact of that elegant dinner bore a revelation. Most of the younger cooperators I'd been among the past few years, working in isolation and starting from scratch, didn't know a gathering like this was possible. The scene in Quebec was a reminder that the cooperative movement—even its most bureaucratic participants refer to it as a "movement"—is no theoretical or utopian phenomenon. I met directors of co-ops from around the world owned by their workers, their farmers, their depositors, their residents, and their policyholders. They brought many languages and many sorts of formal dress. As a group, they had little in common except a set of agreements held and honed over time about how to make cooperation work in an acquisitive world.
The International Cooperative Alliance first met in 1895 in London. The principles it would adopt to define and guide the international movement derived from the rules that the Rochdale Pioneers set out for themselves in 1844. These principles have evolved over the years. The most recent list, approved in 1995 by the ICA and framed on the wall in the boardrooms and kitchens of co-ops the world over, are these:
1. Voluntary and open membership
2. Democratic member control
3. Member economic participation
4. Autonomy and independence
5. Education, training, and information
6. Cooperation among cooperatives
7. Concern for community
Alongside the principles, in its materials on "cooperative identity," the ICA promulgates a list of values that inform the principles' meaning: self-help, self-responsibility, democracy, equality, equity, and solidarity. Much resides in these principles and values; their meanings will unfurl in the pages to come. I'll refer to them again. They're a monument as much as they're a method. They're violated as systematically as they're followed across the ever-partial global commonwealth. And yet they're a moving, beating heart.
The arteries and veins of the cooperative idea are participation and control. Those who use an enterprise should be those who own and govern it. It's not just a vessel for absentee speculators. When participants are owners, the firm becomes worth more than what an owner can extract from it. A co-op's members might be individuals, or businesses, or other co-ops, but in any case the model invites them to come as their whole selves. They have the freedom to seek more than profit.
Co-ops of any substantial size hire staff to manage the day-to-day, but for big decisions or board elections, the rule is one member, one vote. Investor-owned companies give greater control to those who own more shares, but a cooperative counts its members according to their solidarity, not their investment. As co-owners, they're all on the hook for how they govern. The enterprise stands or falls by how they direct it. Thus the fifth principle—the part about education.
This kind of responsibility calls for a lifetime of learning about the particulars of the business at hand, toward the wisdom that self-management requires. Co-ops are supposed to constantly equip their members with the knowledge and skills they need to be good stewards; they are also expected to broadcast their mission and model to the public beyond. In this and much else, co-ops can team up. The sixth principle enjoins them to align their efforts through federation and collaboration, turning their cooperation into an advantage in competitive markets. Finally, because a co-op's owners are the people who live where it operates, they have every reason to care how it affects their communities. The community is not an externality, it's part of the business.
These principles are a series of feedback loops. Each is meant to reinforce the others to produce viable businesses that serve their members and the common good. But they're not a guarantee of anything.
The commonwealth has stalled in areas and industries where it once thrived. A gulf separates the generations that built much of its past and the newcomers trying to reinvent a commonwealth for themselves. The newcomers conjure up experiments with Bitcoin but don't bother voting in their local credit union's election. And the credit union's management may actually prefer it that way; when I asked my own credit union's CEO if he would like to see more than the handful of members who come to the annual meeting, he said credit unions aren't like that anymore. To vote in my mutual car-insurance company's annual meeting, I still have to send in a request by physical, mailed letter to an address tucked away in fine print.
For people to use their power, they have to remember, or be reminded, that they have it or could have it in the first place. As much as co-ops arise out of economics, they depend on a supportive, nourishing culture from below and enabling policy from on high. They depend on a democracy that is dexterous, not fixed and frozen in time. Their lifeblood is participation and commitment. Yet the values and principles amount to nothing if there isn't a solid basis in business.
Does cooperation count as capitalism, or something else? Some co-op directors have insisted to me it is. If capitalism means freely associating in the economy, or ingenuity and innovation, or the rough-and-tumble of setting up a business, or price-based reasoning—then, yes, cooperation overlaps with it. But if capitalism means a system in which the pursuit of profit for investors is the overriding concern, cooperation is an intrusion. Participation is what co-ops are accountable to, not just wealth. It's an inversion of that capitalist order, but one that can nevertheless persist in that order's midst.
Sure, many people invest in the stock of companies with which they shop, work, bank, or insure. But that kind of ownership isn't the same as co-op membership. The rules surrounding stock markets presume that owners want only financial gain. For instance, after the 2017 Grenfell Tower fire killed seventy-one people in London, the shareholders of a complicit supplier sued their company—not for the loss of life or the moral negligence, but for shareholder losses; ExxonMobil employees similarly sued the company over its climate-change deceptions—in pursuit of lost value in their stock options. Nothing else would hold up in court. This kind of system contorts the actual people involved. It sees only a tiny sliver of their humanity. These capital markets have created a machine, a kind of profit-sniffing artificial intelligence, in whose service its subjects work, buy, invent, and even rest. If we're to take on existential market externalities such as poverty and climate change, we need companies capable of seeing the world in the way people do.
Just as cooperatives co-created the industrial world, they are at work on what comes next. They're vying among other candidate regimes, from the easy money of venture capitalists to the corporate darlings of authoritarian governments. And the prospects for a cooperative commonwealth may never have been better. When the Wharton School business guru Jeremy Rifkin spoke to the International Summit of Cooperatives in Quebec, he assured his listeners that their tradition was the way of the future. "Co-ops will be the ideal venue to scale this new digital revolution," he said. "Even if you didn't exist, you're the model we'd have to create."
Social movements are betting on the model, too. Some beleaguered labor unions in the United States and Europe are devising a new vocation and a new strategy through unionized co-ops—recovering a union-cooperative symbiosis that was more prevalent a century ago. Defenders of the environment, from indigenous tribes to Pope Francis, have turned to cooperation in pursuit of what has come to be called climate justice. So it appears also in struggles for racial justice; the Movement for Black Lives, for instance, uses cognates of _cooperative_ forty-two times in the Economic Justice portion of its official platform, which insists on "collective ownership" of the economy, "not merely access." Upstart politicians, such as Jeremy Corbyn of the United Kingdom's Labour Party and Bernie Sanders in the United States, have put co-ops in their platforms as well.
This isn't new. The Scandinavian social democracies grew from the root of widespread co-ops and folk schools. The US civil rights struggle of the 1960s mobilized the self-sufficiency black farmers had already built through their co-ops. Although best known for his obstructive resistance against British rule of India, Mohandas K. Gandhi viewed the "constructive program" of spinning wheels and village communes as the real center of his strategy. Cooperation, however, cannot be claimed as the purview of any one political outlook or party—neither in my grandfather's time nor today. Electric co-ops and credit unions may have found their early advocates in Washington, DC, among progressives, but they now find more affinity with right-wing lawmakers willing to roll back cumbersome regulations. The 2016 party platforms of both Democrats and Republicans encouraged employee ownership. Among younger cooperators, one frequently encounters devotees of the right-libertarian Ron Paul.
Yet the commonwealth is anything but inevitable; I would give more credit to capitalism than Rifkin did. As much as digital networks empower peer producers, they are furnishing unprecedented global monopolies and previously unimaginable feats of surveillance. There's no guarantee that the equitable pioneers will win out. But taking cues from the shreds of past cooperation they encounter, they're devising futures that challenge both the co-op configurations of my grandfather's era and the imperatives that capital imposes now. The stories I'll be telling are not about cooperation-the-venerable-achievement but cooperation-the-work-in-progress.
These newer co-ops aspire to reach further and encompass more than their predecessors. Cooperators want to confront the intersectional dividing lines of identity that too easily determine the economy's winners and losers, including in co-ops. They exhibit a tendency that has come to be called open cooperativism, an extra emphasis on the first cooperative principle's openness for a network-enabled age. They venture to the radical edges of transparency. They adopt complex, multi-stakeholder ownership structures to account for these complex challenges; I know of at least one co-op that reserves a board seat for the Earth itself. Rather than merely serving their members and their members' surroundings, these cooperators want to do good in the world beyond. They secure B Corp certifications, based on metrics of social impact, to prove it. They share common property in ways that seek to dispense with property altogether.
If this is where the cutting edge points, it's toward a kind of paradox: employing the method of cooperative ownership so as to wither ownership away. The new equitable pioneers have bold ideas, as their predecessors did, but they also run the risk of capriciousness, of neglecting sturdy institutional forms on behalf of a specious liberation.
Among the enigmatic utterances of the philosopher Jacques Derrida was a habit of referring to "democracy to come." Democracy can never be a static or stable condition, he believed, because its most basic commitments are forever in tension with one another—equality and diversity, freedom and accountability. We never quite possess democracy in any full sense, except to the degree that we strive toward it, attempting to reconcile its tensions by kneading them over and over into our lives. These are the tensions, for instance, between the dignitaries' dinner in Quebec and the wry text messages of my friend Keith, or between data-sharing over cloud servers and old-fashioned property. Without continual striving, what once seemed like democracy becomes ossified and unresponsive. What we discover from this striving today will shape the social contracts to come.
One can't know when or where the breakthroughs might occur. A commonwealth arises from the persistent hope that more and fuller democracy is possible, and through the persistent risk that human beings might trust themselves and each other with their destinies. In this book I've attempted to compose a portrait of that risk, and of that hope.
#
# All Things in Common
## _Prehistory_
Gregorian chant and free jazz are two kinds of music that sound nothing alike. One came from the monasteries of medieval Europe, where nuns and monks intoned scriptural verses in unison. The other was an invention of African Americans who were in but not of the white monoculture of the 1950s and early 1960s, discarding fixed melodies and rhythms for cacophonous liberty. It is hard to imagine forms more different. Both, however, are the sounds of self-governance.
The band plays in the dark. People onstage and off go about their business. The percussionist pounds out one beat for a while, then changes to another. The upright bassist thumps along to that same beat, until venturing elsewhere, then reconverging some minutes later. Same with the piano, the sax, and whatever else is in that session. A lot of the time they're each in their own tempo and key, if any, working something out for themselves. And then they come together—when they feel like it—and it's a relief to a listener used to more dictatorial orchestration. Harmony becomes precious when it's not a given, and soon the discord obtains a beauty of its own. That's the sound of freedom and free association, of living by choice and not coercion.
Sun Ra, an Afrofuturist composer with free-jazz influences, proposes playing a song, in his 1974 film _Space Is the Place_ , so as to "teleportate the whole planet": "Then we'd have a multiplicity of other types of destinies. That's the only way." These sounds are accompaniments to surviving by improvised economies, to living in a world whose rules aren't for you.
The monks sing to the dark. It's before dawn between the cold stone walls of the chapel. Every morning of their lives, they utter first the same words: "Lord, open my lips, and my mouth will proclaim your praise." Their voices are one, as much as is possible for fallen, sinful beings with only the aid of grace. This is work; they call it the Divine Office. Soon the sun will rise. After more prayers, the monks go out into the fields and barns that surround the cloister and begin the manual work that helps maintain the monastery, with the same lockstep as that of their prayers in the chapel.
In the chapel many of them are tired, but they stay awake for each other like fellow soldiers on a battlefield. A short monastic poem, found in a twelfth-century French manuscript, reports the responses of God, the devil, and the abbot to a young monk who falls asleep during prayers. The devil is optimistic about winning the monk's soul for himself. The abbot asks for help from God, who declines to intervene in such a minor incident. No one takes the matter as seriously as the monk himself, who expresses his regret in gruesome form: "Sooner would I have my head cut off than fall asleep again."
This is the music of mutual accountability—whether in the stinging shame of sleep or in the slow finding of a common beat. This is _ora et labora_ , the ancient mixture of prayer and work that goes back to the apostle Paul making tent pegs to support his preaching. This is _kujichagulia_ and _ujamaa_ , the Swahili notions of autonomy and cooperation, adopted by descendants of slaves. The music is part of these. And it's part of a usable history for those turning to cooperativism again.
There's a temptation, in the course of a book such as this, to abuse our ignorance of the prehistoric past by claiming it as a time in which we all cooperated. One could begin even before there was a human _we_ —enter tales of evolutionary history that stress the survival value of symbiosis and sociality among organisms instead of ruthless, solitary competition. Picture the blobs in primordial goo feeding each other useful enzymes, or bonobos licking filth off their young. In the long, grand story of the universe, cooperation has been a fact of nature. But resist the easy way out: it is not the only fact. The friendly and the cutthroat have each contributed to our mysterious origins, and it's at least partly true to emphasize either one.
I will not dwell much, either, on the early human side of what museums consider natural history—our mythologies of tribal, "primitive" societies, which rest on an assumption that general facts hold consistent for a tremendous range of groupings of human beings across ages and biomes, societies either too remote or too extinct to talk back. Even Margaret Mead, an anthropologist not shy of drawing strong conclusions, could conclude little more from her editorship of a volume titled _Cooperation and Competition Among Primitive Peoples_ than that "competitive and cooperative behavior on the part of individual members of a society is fundamentally conditioned by the total emphasis of that society"—that is, _it depends_. But suffice it to say that in societies without stockbrokers, where survival is a daily activity carried out among a smallish number of interdependent people, economy ends up being a more egalitarian affair than the rest of us are probably used to. It's no accident that some newfound cooperators today have taken to calling their transnational affinity groupings "neo-tribes."
The Nobel-laureate political economist Elinor Ostrom spent decades studying how various communities the world over manage what she termed "common-pool resources"—the stuff they share and use together. These systems might govern fisheries or forests or waterways or bodies of knowledge through strategies formed over centuries. Ostrom found that such systems exhibit certain features. As if echoing the cooperative principles listed earlier, she identified seven main "design principles":
1. Clearly defined boundaries
2. Local rules adapted to local conditions and needs
3. Mechanisms for those affected by the rules to change them
4. Monitoring of participant behavior
5. Appropriate consequences for rule violators
6. Processes for conflict resolution
7. Free and flexible self-organization
To these Ostrom added an eighth principle, for larger systems: a pattern of nesting, so that smaller decisions happen in smaller groupings, which in turn defer to larger institutions for larger challenges—the principle of federation. This, like Ostrom's other principles, overlaps plentifully with modern cooperation. Her findings point toward a vast prehistory for this subject matter.
Cooperative precedents appear around the world, from lending circles referred to in Confucian texts to African merchants' caravans. But the lineage that I will dwell on here is one that happened to achieve particular influence in the global economic order, starting with the civilizations that formed around the Mediterranean Sea. There were the ancient Jewish Essene communes, which in some respects prefigured the farming-village _kibbutzim_ that helped build modern Israel. Islam likewise instituted the principle of the _waqf_ , a set of shared property held in perpetuity for the common good, and _takaful_ , a system of mutual insurance. Such institutions existed throughout the region, from Greek secret cults to Roman burial societies. They could be subversive enough that Julius Caesar tried to ban them.
Traces of a commonwealth appeared with particular vividness in the Christian church's first days. Twice in the Book of Acts, soon after Jesus leaves his followers to their own devices, they begin pooling property. Here is the first time, in Chapter 2:
Awe came upon everyone, and many wonders and signs were done through the apostles. All who believed were together and had all things in common; they would sell their property and possessions and divide them among all according to each one's need.
The same practice reappears in Chapter 4, where, just after another experience of "signs and wonders," we read that "the community of believers was of one heart and mind, and no one claimed that any of his possessions was his own, but they had everything in common." The next chapter tells the story of Ananias and Sapphira, who die sudden deaths after attempting to withhold from the community part of their earnings from a sale of land. When their story ends, again, "Many signs and wonders were done among the people at the hands of the apostles." Evidently, there is a link between the experience of divine activity in the world and the sharing of property among members of the Christian community; dishonest dealing in this arrangement has dire consequences. The lesson of Ananias and Sapphira casts its warning from St. Peter's Basilica in Rome, where a depiction of it appears on the canvas over the Altar of the Lie.
A chapter later, the apostolic commune experiences more growing pains. The original apostles find the task of resource management beyond their ken; the needs of widows are being neglected. They ask the community to select seven trusted representatives to carry out the distributions. Their cooperation, as in modern cooperatives of any significant scale, required electing a board.
This cooperative imprint in its scriptures keeps coming back to haunt Christendom, despite its most imperial pretensions. Monasteries first appeared in the fourth century, just after the emperor Constantine made Jesus Christ the official god of Rome. Strenuous believers fled to the desert, where they could practice their faith in solitude and simple communities, away from the corruptions of empire. The economic spirit of the apostles reappeared among them. Citing Acts, the North African, early fifth-century Rule of St. Augustine instructs monastics, "Call nothing your own, but let everything be yours in common." About a century later in Italy, Benedict of Nursia went further in his rule, stipulating, "As often as anything important is to be done in the monastery, the abbot shall call the whole community together," discussing the matter with everyone before making a decision. The Rule of St. Benedict prescribes election of the abbot by the community and expects the community to support itself through shared businesses. Both rules emphasize obedience to the abbot or abbess over democratic deliberation. But they also enjoin an egalitarian spirit and a collaborative economy.
The spirit of Acts returned in force during the thirteenth-century mendicant movement, when barefoot preachers spread across Europe, contrasting their poverty with the lavish lifestyles among church officials and in wealthy monasteries. Clare of Assisi, Francis of Assisi's friend and colleague, enshrined in her rule for Franciscan sisters a particular measure of countercultural self-governance. The draft of the rule that Pope Innocent IV proposed for her order required that the sisters' elected abbess gain the approval of the male friars' minister general, a provision St. Clare struck from the final version. She also added the practice of a weekly meeting—which apparently the pope deemed unnecessary for women—in which the sisters would gather to confess their offenses and discuss "the welfare and good of the monastery." She stressed the inclusion of all community members in this process, noting, "the Lord often reveals what is best to the lesser among us."
As Clare and Francis's movement grew in influence, church leaders sought to manage it. The most contested question was that of whether Franciscan communities would have to hold property or retain radical poverty. Some early Franciscan scholars developed sophisticated legal arguments to insist that the friars could have _use_ of goods like food and clothing without actually _owning_ them. They cited the economy of the Garden of Eden to this effect, a state of nature in which the first people shared stewardship of the whole world. But this strategy foundered, and church law would require their order to hold its own property. Rome deemed ownership necessary to protect the Franciscans' poverty and communalism from an acquisitive outside world.
If possession for the sake of sharing seems like a contradiction, it wasn't a new one. Gratian's twelfth-century _Decretum_ , the compendium of canon law that thereafter steered governance in the church for eight hundred years, held that "all things are common to everyone." By the lights of natural law, at least, private property is an aberration, though under the conditions of fallen human society it's a necessary arrangement. This paradox has come to be called, including in the current Catholic catechism, the universal destination of goods.
What a strange phrase: _the universal destination of goods_. It holds that everything—in the final analysis, even if we can barely act this way here and now—is somehow everyone's. This doesn't pretend to offer a practical business model, yet it asks that any provisional, proprietary business somehow reflect the communal reality beneath. And as impossible an expectation as this seems, it keeps coming back.
The cave dwellings in Matera, Italy—the Sassi—are said to have been inhabited for nine thousand years. Staggered terraces of masonry facades line ragged cliffs that fall into canyons. After World War II, the Sassi became the country's most notorious slum, and the government emptied residents into modern apartments on the plateau above. For decades the ancient caves lay empty. Pier Paolo Pasolini and Mel Gibson both filmed movies about Jesus there. In the 1990s, a band of cultured squatters began to move in and renovate, leading the way for a tourist industry in the otherwise sleepy city. UNESCO declared the caves a World Heritage Site; the sides of Matera's police cars now boast "Cittá dei Sassi." Most of Matera's sixty thousand residents, however, live not in that romantic past but in a present where it's not altogether clear what they have to offer in the global economy. Decent work is hard to find, and the city is hemorrhaging its youth.
In early 2014, the ancient caves of Matera became home to an experiment: an unMonastery, the first of its kind. For the dozen or so unMonks who moved there from across Europe and North America, plus the hundreds following their progress online, it carried the quixotic hope of an underemployed generation regaining control of the technology that increasingly commodifies and surveils their lives. Monasteries ushered civilization through the Dark Ages, harboring scholars and inventors and the technology of writing; perhaps unMonasteries, sparing the dogma and self-flagellation, could keep alive the promise of a liberating internet.
The unMonastery's gestation began in 2011. The Council of Europe's ominous-sounding Social Cohesion Research and Early Warning Division sought, in the words of its chief, "to have a better idea of the extent of insecurity in society." The international body sponsored the invention of what came to be called Edgeryders, "an open and distributed think tank" of people working through an online social network and a series of conferences. Anyone could join, but those who did ended up being mostly young, tech-savvy, and entrepreneurial, and mostly from Western Europe. What united them was not a political ideology, but the dead-end conditions of austerity and the hope of figuring out better ways forward. They produced a report about the economic crisis, which they called a "guide to the future." Soon the council's funding ended, but Edgeryders pressed on as an online network with more than two thousand members and an incorporated entity. The group began presenting itself as a company in the business of "open consulting."
At the end of their first meeting in June 2012, a small circle of Edgeryders, with glasses of wine in their hands and under the shadow of a Strasbourg church, dreamed up the unMonastery. The idea was this: find a place with unmet needs and unused space that could lend a building to a group of young hackers. Live together cheaply, building open-source infrastructure with the locals. Repeat until it becomes a network.
The unMonastery vision went viral among the Edgeryders. It fit into a widely felt longing at the time, evident in many parts of Europe and North America where protest had been breaking out, to start figuring out practical alternatives to the failed order. This was the period, too, of National Security Agency whistleblower Edward Snowden's leaks, of persecuted hacker Aaron Swartz's suicide, of blockades against techie commuter buses in San Francisco. Google became one of the world's leading lobbyists, and Amazon CEO Jeff Bezos bought the _Washington Post_. The internet could no longer claim to be a postpolitical subculture; it had become the empire.
As tech achieved its Constantinian apotheosis, old religious tropes seemed to offer a return to lost purity, a desert in which to flee, the stark opposite of Silicon Valley. A bonneted "Amish Futurist" began appearing at tech conferences, asking the luminaries about ultimate meaning, as if she came from a world without the internet. Ariana Huffington cashed in with her mobile app, GPS for the Soul.
For a year and a half, the unMonastery idea developed and grew. Edgeryders brought their favorite conceptual vocabularies to bear: social innovation, network analysis, open source. They also brought their experience with hackerspaces, makerspaces, and co-working. Alberto Cottica, an Italian open-data advocate and leading Edgeryder, perused the Rule of St. Benedict and discovered its author to be a network-savvy, evidence-based social innovator.
"Each monastery is a sovereign institution, with no hierarchy among them," Cottica explained in the Edgeryders' online discussions. "The Rule acts as a communication protocol across monasteries." He compared Benedict to Jimmy Wales, the founder of Wikipedia, and Linus Torvalds, creator of the open-source operating system Linux. "The rule was—still is—good, solid, open-source software."
In Brussels, Cottica learned about Matera's bid to be declared a European Capital of Culture by the European Union and saw an opportunity for his fellow Edgeryders. The bid proposal centered around the theme of "ancient futures"—"in order," it said, "to give voice to forgotten places, areas often pushed to the outskirts of modernity, yet which remain the bearers of deep values that remain essential." The committee in charge of the bid came to recognize the unMonastery concept, with its supporters throughout the continent, as a useful addition to Matera's portfolio. The city agreed to provide a small cave complex, as well as €35,000 for travel and expenses for four months, which stretched to six.
_Dinner outside the unMonastery's caves._
The presiding unAbbot was Ben Vickers, twenty-seven years old, with patches of gray on either side of his well-trimmed hair and a hooded black coat worn over his banded-collar black shirt. While also more or less retaining his post as "curator of digital" for London's Serpentine Galleries, Vickers was the unMonastery's theorist and coordinator; the others generally praised his ability to digest and summarize their various points of view, and to document them on the online platforms they used to communicate. He blasted George Michael songs while setting up breakfast and found a certain glee in the prospect of failure—a turn of mind probably honed during his days in doomed anarchist squats. Documentation, he believed, can trump even failure; others can study the attempt, tweak it, and try again.
Visible from what became the unMonastery's patio, down one cliff and up another, were dark abscesses in the rock, their interiors still bearing remnants of paintings from past use as churches and hermitages. Where the monks and nuns who once lived there had hours of structured prayer each day, the unMonastery had documentation—the basic act of piety in any open-source project. Before an algorithm can be copied, adapted, and redeployed, it must be radically transparent. Monks expose themselves to God through prayer; unMonks publish their activities on the internet.
Some of the documentation looked outward. Maria Juliana Byck, a videographer from the United States, was working on a project to map common resources in town, to help Matera residents—the Materani—connect with each other and collaborate. There was an "unTransit" app in the works for local timetables and workshops on the gospel of open data. Also underway on the Materanis' behalf were an open-source solar tracker, an open-source wind turbine, and coding classes in the unMonastery caves for adults and kids.
As in real monasteries, much of the unMonastery's piety went toward scrutinizing the minutiae of daily life. This was of particular concern to a pony-tailed, thirty-one-year-old software developer named elf Pavlik, who had been living for five years without touching money or government IDs. With nearly pure reason, he implored the others to document more and more precisely what came and went, from food to tampons, so they'd learn to budget not by cost but in terms of the resources themselves. Using a software package called Open Energy Monitor, they kept track of the unMonastery's electricity usage minute by minute, room by room.
Keeping track of the longer view was the job of Bembo Davies, a Canadian-turned-Norwegian widower and grandfather, a veteran of the circus and stage who updated his WordPress chronicle in august prose. Accompanying material evidence—skeletal floor plans, a mannequin's headless torso—came from Katalin Hausel, an artist who once helped rewrite the official history in her native Hungary. They talked about the unMonastery, even in its first months, as at the beginning of a two-hundred-year history. It didn't seem like so much time to ask for in a place that has been around for millennia.
The unMonastery sat on more precipices than one: it was an emissary of the hubristic tech culture it represented, but also a patient attempt at redemption. While planning ahead for centuries, the unMonks practiced the one-step-at-a-time philosophy of Agile software development; if breakfast wasn't on the table on time, or when they worried about whether they'd done any good for Matera whatsoever, they reminded each other, "Everything's a prototype."
The days and nights I spent embedded in those caves were manic with the spectrum of old and new realities that my informant-hosts were trying to stuff into their experience: tech culture, monk culture, nonprofit culture, local culture, art culture, protest culture, entrepreneurial culture, recession culture—all in the space of a few months and a finite budget. They might have called themselves a cooperative were it all not so ephemeral. The want of clarity wasn't so different from what one reads in the sayings of the early Desert Fathers and Mothers, the progenitors of Christian monasticism; none of them knew what they were really up to. Those possibly lunatic ancient hermits kept going around asking each other, in every way they could think of, "What are we doing here?"
Monastic rules, like company bylaws, establish a discipline. They take raw, human material and provide a form into which we can proceed and persist, by which we can tolerate the inevitable coming and going of inspiration. But discipline is no good, either, without the grappling. This is why I don't think we can understand the cooperative past or imagine a cooperative future without these errant, fumbling stories. Like most stories, you don't get to know the end until you get there, if there is an end at all.
On a windy day in May, gusts swelled through the unMonastery's first-floor caves, blowing from the walls various colored sticky notes and hand-drawn posters made in meetings heady with excitement and hope. They were schedules, sets of principles, slogans to remember, lists of things to do. A maxim for the Edgeryders' doctrine of do-ocracy, for instance: "Who does the work calls the shots." These relics remained on the floor for hours, apparently provoking insufficient motivation to pick them up.
There had been a kind of monastic routine at the unMonastery in the first weeks. At specified times, the group would sit in circles to share feelings and discuss concerns. A flying drone once captured footage of the theatrical morning exercises that Bembo Davies led. But by May, the circles and the exercises were on indefinite hiatus.
After the seven o'clock wake-up bell rang half an hour late one morning, Davies groaned, on the way to the shower in his underwear, "We're sliding into a prehistoric condition." He lamented on his blog that people had been reverting to talking about the laptops they'd brought as "mine." Benedict's rule has harsh words for private property: "Above all, this evil practice must be uprooted and removed from the monastery."
A few months in, the unMonastery's communications had become a jungle of platforms, many of them proprietary, with few clear lines between inward and outward: the public Edgeryders website, public Trello boards, a closed Google Group, and public folders full of Google Docs. The "ideologically coded" unMonastery website that elf Pavlik had designed was badly out of date and difficult to use, so a Facebook page had become the main means of sharing information with the world. Before, one unMonk had always refused to use Facebook on principle; it was only after coming to this supposedly open-source hacker commune that he felt compelled to start an account. The unMonastery's vision of an open-source way of life seemed at risk of becoming a wholly owned subsidiary of the status quo.
_Software developer elf Pavlik in the unMonastery kitchen._
Back and forth, they debated what the real problem was: The decline of ritual? Attempts to revive the morning exercises kept failing. The lack of ties with people in Matera? They knew there were grumblings among locals about why the city was spending money to support a bunch of foreigners. Too much software, or not enough? Alberto Cottica warned from afar over the Edgeryders platform about fixating on technology rather than on actual social interactions. They disagreed about the rules that governed them, as well as whether there were any in the first place. Losing patience in a tendentious meeting, Rita Orlando, one of the unMonastery's Materan allies, begged, "Let's try to think like a company, even though we are not a company—please!" A company, at least, has to concern itself with doing something of value for someone else.
The last two months of the experiment proved eventful, at least. "Most of the demons have scurried off and work ethic is buzzing away at a good clip," Bembo Davies reported in the last days, with his usual obscurity. Pavlik brought a new cadre of hackers in for a spell, and dozens of local children attended coding classes. A video of a "co-napping" experiment on the streets of Matera went viral online, though it made some Materani cringe. The wind turbine and unTransit projects came closer to having prototypes of their own; they would carry on even though the unMonastery prototype would be closing. A pack of young locals got to work editing their documentary about it. Ben Vickers scrambled to assemble the unMonks' fervent documentation into the "unMonastery BIOS," named after the initialization firmware in a computer—a box full of lessons and design patterns for the iterations to come. He alternated between grandiosity and humility. Vickers wrote, on a thread on the Edgeryders website, that the "unMonastery for me is not a utopian project designed to solve the woes of the world, it operates at the scale of the invention of the fire hydrant."
Rita Orlando lived in Matera before the unMonastery came and remained after it left. She felt frustrated with the aftermath. People in town mostly just saw the project's foreignness and naïveté, not its promise or vision. "We've been too short on time," Orlando said.
Before the end of 2014, at least in part thanks to the visibility the unMonastery lent it, the European Union named Matera one of the 2019 European Capitals of Culture. A few of the unMonks stayed in town; others tried to open a new unMonastery in Greece. They're still trying to see whether the unMonastery is a protocol that can travel, that can go to other places with unused spaces and unused people who want to do good. A lot of aging religious communities are meanwhile trying to figure out how to put their empty buildings to use these days, while preserving some kernel of their traditions.
The prefix "un" has its uses—for marking a new beginning, for putting aside certain inadequacies of the past—and yet one cannot go on negating and reinventing everything forever. Ancient monks had to learn this, too. First the desert hermits, then the Benedictines, then the Franciscans—each fled the world but then became part of its ongoing reality. A time may come when spiritual-social-technological institutions with features such as those of the prototype in Matera will be content to drop the "un" and call themselves, simply, monasteries.
Metaphors have their usefulness, in the meantime, and the distant Middle Ages offer new cooperators an ample supply of them. While monasteries sought to keep souls apart from the world, another set of institutions served those in the midst of it, where other strategies were needed for imitating the Book of Acts.
Some months after my time in Matera, I joined Chris Chavez, Jerone Hsu, and Dan Taeyoung as they splayed themselves out along a suspended I-beam and stray ladder on a roof in the Hell's Kitchen neighborhood of Manhattan. We talked about their new co-working space and the history of the world. The three of them, in their late twenties and early thirties, were overseeing a renovation of the structure beneath them. First built in 1919 as a garage, it was being transformed to include an art studio in the basement, an open-plan office and café at the ground level, and a room for workshops and meditation on the second floor. Chavez greeted construction workers by name as they passed by.
The three began to tell me where they situated their plans, world-historically speaking. "It took a few hundred years to get over the hangover of the Industrial Revolution," Chavez said. He explained that this hangover has lasted well into the digital age, manifesting most recently in the instability wrought by ever-looming waves of automation. It was now time, they believed, to restore a preindustrial template to prominence. They'd decided to reinvent Prime Produce, a small nonprofit that Hsu had founded some years earlier, by modeling it after a medieval guild.
The idea came to them the previous spring, when they organized a retreat for entrepreneurs on the grounds of Bluestone Farm, a community of eco-feminist Episcopal nuns in Brewster, about an hour upstate on the Metro-North Railroad. After some years engaged in varied forms of entrepreneurship, the three were trying to figure out what forms of organization would best suit their peers' shifting work conditions. Neither unions nor chambers of commerce seemed suited to a generation that can't count on having a fixed place of work. The Reverend Leng Lim, a minister and executive coach who lived across the street from the nuns, suggested that Chavez and his compatriots look into guilds.
From roughly the turn of the first millennium to the French Revolution, guilds organized Europe's urban economies. They were associations of independent craftspeople, setting standards for their lines of work and cultivating lively subcultures around their labor. They typically held legal monopolies over crafts in particular jurisdictions; one guild's members might be responsible for all of a town's stone carving, while another would control the market for blacksmithing. Members were also expected to have each other's backs. In _Wage Labor and Guilds in Medieval Europe_ , Steven A. Epstein, a historian at the University of Kansas, cites a tenth-century guild that obliged members to rally for mutual defense and vengeance against clients who failed to pay up. "The members also swore an oath of loyalty to each other," Epstein writes, "promising to bring the body of a deceased member to a chosen burial site and supply half the food for the funeral feast." One of Prime Produce's initial members told me that Chavez recruited him with a copy of Epstein's book in hand.
This guild's dozen or so members didn't have plans for funeral insurance just yet, and they weren't defining themselves around a particular trade or industry. They included an architect, an accountant, a food-and-beverage vendor, and a painter. The typical co-working space is run by a company that workers pay for use; by contrast, Prime Produce would make many of its members co-owners of a cooperative, which would manage the proceeds of their dues and pay rent to the sympathetic investors who owned the buildings. Chavez explained that co-ownership can be a way to opt out of the broader economy's pressures—and to reclaim the former meanings of words from before they were conscripted to capitalism.
"The word 'company' doesn't need to exist in a market logic," he said.
Members of medieval guilds typically progressed in rank from apprentice to journeyman to master craftsman—distinctions still used by some trade associations today. Prime Produce would also incorporate three tiers, but based on levels of commitment rather than on experience and proficiency. As a rite of passage, new members would each receive a pair of slippers to wear while inside the space—a "differentiating mechanism," Chavez said, between members and visitors.
Prime Produce wasn't alone in looking to old guilds as the way of the future. Some see a model for organizing freelancers in Hollywood's guild-like set-worker unions, which establish industrywide standards as their members bounce from production to production. Jay Z's Tidal streaming platform sold itself to consumers as a kind of guild for musicians; a group of Silicon Valley business writers has organized itself into the Silicon Guild to help amplify each member's networks; some gig-economy workers have an Indy Workers Guild to distribute portable benefits. In the twentieth century, Charlie Chaplin and his friends formed United Artists to produce their own films, and photographers such as Henri Cartier-Bresson and Robert Capra formed Magnum, a cooperative syndication guild. Less glamorously, the professional organizations for doctors, lawyers, real estate agents, and hairdressers have clung to the guild model, complete with monopoly powers recognized by governments and peers.
As we talked on the rooftop, Prime Produce's founders freely mixed medieval idiom with that of Silicon Alley. Taeyoung cited the computer programming guru Donald Knuth's dictum, "Premature optimization is the root of all evil." That is, if they decided too much ahead of time and in too much detail, they wouldn't be as flexible or as iterative. Hsu described what Prime Produce was doing as "crafted social innovation," a form of "slow entrepreneurship." The guild's appeal wasn't just nostalgic to them but was a means of navigating an often lonely, attention-deficient economy, by cultivating habits of excellence and communizing resources like office space, companionship, and broadband. Adding to the stew of anachronism, Chavez referred to the old guilds as "catalysts" for a better kind of technological progress. "They blocked innovation that dehumanized work," he said. "Guilds were always responsible to people first."
Others might object. Adam Smith referred to the guilds' price-fixing practices as "a conspiracy against the public," and at the start of the French Revolution, they were among the first features of the _ancien régime_ dispatched to the institutional guillotine. The usual story since has held that guilds in fact stymied efficiency and technological innovation. Epstein's book sought to correct this narrative, as does the work of the Dutch social historian Maarten Prak. Guilds, Prak told me, "were not opposed to innovation per se; they were opposed to machines taking over." When factory production replaced craft guilds, "work was transformed from rather boring to hopelessly boring." Products became cheaper and more uniform, with fewer workers required to make them. But gone, too, was the fingerprint of the craftsperson. Prak also stresses the importance of what he calls "formal anchoring" for medieval guilds—establishing arrangements with local governments—to sustain themselves "for a longer period than the enthusiasm of the founding members."
Politics meant legitimacy, but it also meant collusion. "It was a sort of deal between small businessmen and the authorities," says Sheilagh Ogilvie, an economic historian at the University of Cambridge who is more critical of the guilds' legacy than Epstein or Prak. Ogilvie believes that guilds enforced an exclusionary economy, barring from their trades whomever they happened not to like, which often meant women, Jews, and immigrants. It was only in the last gasps of the guilds, after they'd lost most of their monopolies and had their most discriminatory habits banned, that Ogilvie thinks their nuisance was minimized.
Thus far, at least, Prime Produce's membership had considerable ethnic, gender, and occupational diversity. And rather than making political deals, the founders seemed content with the synergy of their slippers and their good works. Despite various delays and hitches, no one had yet dropped out. "The ingredient that plays a central role in all this is trust," Qinza Najm, an artist who planned to work in the basement studio, told me. After a burglary and a lousy contractor delayed the opening more, they held events about prepackaged culture and participatory design in their construction site.
_Qinza Najm, Saks Afridi, and Jerone Hsu on the roof of the Prime Produce building._
Before the afternoon on the rooftop was over, another master-member, Marcos Salazar, came to visit. He was taller than the others, his attire less laid-back. Salazar worked as a consultant for cultivating "purpose-driven careers, businesses, and lives." He also organized events for social entrepreneurs in the city and planned to hold some at the Prime Produce space when it became ready.
"I've heard a lot about guilds," he said, as if he'd heard about enough. But when I asked about the slippers, he shrugged and looked at the founders uneasily. They smiled. They hadn't mentioned that part yet.
The practical guilds worked alongside the mystics in the monasteries. Each arranged a sort of business meant to put property and commoning into balance. But as the signs and wonders of modern progress began to appear, spreading by printing presses and colonial expeditions, the scales tipped squarely to the side of property. It was a change noticed well enough to merit bloody resistance.
During the torture that preceded his beheading in 1525, the German preacher Thomas Müntzer reportedly confessed to believing that _omnia sunt communia_ —all things are common. Perhaps it matters little whether this report from the torturers was truly the position of Müntzer and the popular revolt that he helped lead, or merely a concoction they devised in order to hasten his demise; in either case, they deemed professing this teaching of the apostles and principle of canon law as evidence justifying his execution. The torturers' account went on to say that he believed property "should be distributed to each according to his needs, as the occasion required. Any prince, count, or lord who did not want to do this, after first being warned about it, should be beheaded or hanged."
Müntzer was a contemporary of Martin Luther's who was less adept at siding with the ascendant elites. His movement fell under the swords of princes, as did Müntzer himself. But remnants of the "radical Reformation" of which he was a part persist today in the intentional economies of such Anabaptist sects as the Amish and Mennonites. The Calvinist variant of the Reformation's communal impulses, too, found expression among the Puritans who settled in New England. Although the Puritans' initial experiment in shared farmland and produce was short-lived, their legacy has lived on in New England's town meetings and the congregationalist governance structure that still holds sway in much of US Protestantism. It appears, too, in the medical cost-sharing organizations that offer a faith-based alternative to the corporate health insurance system.
None of these old communards exactly correspond with cooperative enterprise in the modern sense. In certain respects they challenge cooperative principles; expressly religious communes have tended to privilege poverty over ownership and obedience over autonomy. But such precursors do suggest that when modern cooperation did arise, it did not do so as a rude break with the past, but in continuity with customs of commoning and cooperation that people had lived by for ages.
In the Magna Carta and its sister document, the Charter of the Forest, a thirteenth-century English king had to acknowledge the ancient rights of commoners to co-manage and live in the thickest, wildest regions of the realm. One provision protected, for instance, the right of a widow to her "reasonable estovers of the common"—access to supplies that she needed to survive from common land. But during the same centuries in which the Reformation dismantled Rome's spiritual hegemony across Europe, an economy of corporations and capital began to decimate the guilds and the commons. The cataclysm of this process is difficult to appreciate now, centuries later—unless we compare it to the mix of splendor and squalor in the global economic cataclysms now underway. Land that had long been available for shared use became a patchwork of fenced-off enclosures; work that before had been obviously communal started to be regimented into firms.
Among the squeaks in this engine of progress were those who called themselves the Diggers, or the True Levellers—a short-lived and peaceable insurgency in the midst of the English Civil War, led by a drifter named Gerrard Winstanley. Within weeks of occupying a site called St. George's Hill, they declared their intentions in terms that were spiritual, social, and scatological:
In that we begin to Digge upon _George-Hill_ , to eate our Bread together by righteous labour, and sweat of our browes, It was shewed us by Vision in Dreams, and out of Dreams, That that should be the Place we should begin upon; And though that Earth in view of Flesh, be very barren, yet we should trust the Spirit for a blessing. And that not only this Common, or Heath should be taken in and Manured by the People, but all the Commons and waste Ground in _England_ , and in the whole World, shall be taken in by the People in righteousness, not owning any Propriety; but taking the Earth to be a Common Treasury, as it was first made for all.
As in the monasteries, the Digger cosmology presumed a God who created everything for everyone; while the Diggers waited for the world to recognize this, they began practicing it in microcosm, through a cooperative community of their own on a pathetic piece of land. Before long they'd be driven from it by goons working for the reigning order, which deemed their views obnoxious and their commoning of land to be trespassing.
Like Müntzer's, the Diggers' position would not carry sway among the contenders groping for control over a shifting world. The feudal commons was up for grabs, and the proposal to replace it with even more commoning, on the model of the first Christians, was inadequately convenient for those who commanded armies. The radical Reformers' ideas have lived on mainly among the partisans of other lost causes who have periodically rediscovered them, from Marxists in interwar Germany to the late 1960s San Francisco counterculture. Müntzer and the Diggers tempt nostalgia, even if what they called for never fully existed. Yet their declarations carry in them, at least, the memory of a world in which habits of commoning were more familiar, in which land was not a commodity, in which work was a shared enterprise. Theirs was a hard world, one that for many reasons we're better off having left behind. But for those now trying to imagine and carry out an economic future more equitably shared among all who inherit and contribute to it, some nostalgia has value. It can remind us of forgotten achievements, of capacities latent among us that may be of use once again.
#
# The Lovely Principle
## _Formation_
The Great Depression is not frequently regarded as a time of triumph. But in the 1936 edition of his treatise _Cooperative Democracy_ , James Peter Warbasse wrote, "The years since 1929 have seen the greatest advancement in cooperation the country has ever seen." Warbasse, a surgeon, became the first president of the Cooperative League of the United States of America in 1916 and served until 1941. The league was the national umbrella organization for the US cooperative movement, and it lives on today as the National Cooperative Business Association—that is, NCBA CLUSA. It keeps its headquarters in the lobbying district of Washington, DC, and has become a prolific purveyor of international aid. In the early 1920s, the league created the cooperative logo of two pines side by side in a circle, still widely used; in 2000, the NCBA helped secure the creation of the ".coop" top-level domain for co-ops' websites. It has been the US sector's official evangelist.
Warbasse's successor as Cooperative League president, Murray Lincoln, referred to the founder in his memoirs as "a fine, sincere man" and a "crackerjack when it came to expounding theory." Yet Warbasse's enthusiasm in the 1930s was understandable. The conditions of the Depression had spurred people to form cooperatives across the country. New Deal programs were promoting co-ops, and Congress passed the Credit Union Act in 1934. _Cooperative Democracy_ includes a chapter titled "Cooperation Throughout the World" that details a lengthy catalog of cooperative achievements, from French worker-owned factories, Germany's famous consumer-owned banks, and Russia's early Soviet co-ops to parallel achievements as far-flung as China and Japan, with occasional references to the co-ops' run-ins with the ascendant fascist regimes. (The motto of the German movement, whose storefronts became Nazi targets after Kristallnacht: "Cooperation Is Peace.") The book's frontispiece, opposite the title page, is an artist's rendition of twenty-five impressive buildings owned by the British Cooperative Wholesale Society piled on top of each other like a pyramid, a monument to the organized consumer, that pharaoh of the cooperative commonwealth on the rise. By this time, the old tradition of shared ownership and enterprise had found a distinctly modern, industrial expression.
_The frontispiece of James Peter Warbasse's_ Cooperative Democracy _._
As geopolitical as Warbasse's vision gets, it's also a vision of what kinds of people we might become. In the book's final words, he concludes that the point of it all is "the development of superior individuals, appreciative of cultural values, and with a passion for beauty, truth, and justice." He's talking about cooperation as a school, just as the earlier monks regarded their monasteries—not only a better society in which human beings might live, but a means of forming them, forming us, into better human beings. It couldn't be otherwise. The very possibility of such enterprise in the industrial age was not a given but became evident through lessons that had to be learned. This kind of business, with effort and error, had to be formed.
By the time of Warbasse's optimism, the cooperative movement was already a century old, more or less. It was a movement of movements, appearing in many countries and languages, including capitalism's Anglophone cradles.
One of the first workers' strikes on record in what would become the United States, among New York City tailors in 1768, birthed a cooperative workshop when the tailors went into business for themselves. Free blacks in New Orleans formed a Perseverance Benevolent and Mutual Aid Association in 1783. As secretary of state under President George Washington, Thomas Jefferson helped craft a tax-relief package for cod fishing that encouraged profit-sharing among workers—a maritime version of his commitment to an economy based on small family farms. A cooperative-like business model undergirded Benjamin Franklin's prototypical public library and fire department in Philadelphia. And the federated democracy of the Iroquois Confederacy, which Franklin and others observed in their dealings with native tribes, likely informed the structure of the Continental Congress through which the colonists organized to shed themselves of British rule. When Alexis de Tocqueville wrote home to France about the young United States, he marveled at its people's talent for association.
The pre–Civil War period saw the blossoming of utopian communities throughout the country, involving interesting religious, sexual, racial, and dietary experimentation—attempts, perhaps, to reclaim the innocence beginning to be lost with the rise of industry. Among these were sects such as the Shakers, Oneidans, and Mormons. Joseph Davis, the brother of Confederate president Jefferson Davis, organized an alleged model community of slaves at Davis Bend in Mississippi, cooperative to the degree that outright bondage would allow. In Massachusetts, the interracial Northampton Association of Education and Industry became home to the prophet Sojourner Truth. Frederick Douglass visited from time to time, and he would later write, "The place and the people struck me as the most democratic I had ever met."
With the first fits and starts of modern industrialism came the beginnings of modern cooperation. The National Trades Union, which arose out of early skirmishes between industrial labor and capital, professed a worker-governed economy as its objective. The 1830s occasioned the first "building societies"—essentially joint lending clubs that enabled working families to become homeowners—as well as early co-ops for agricultural marketing and processing. For the rest of the nineteenth century, cooperation and worker organizing went hand in hand. The cooperative workshops and benevolent societies and communes reflected assumptions that have become long lost today.
In 1859, a year before winning the presidential election, Abraham Lincoln made a speech in Wisconsin that outlined a kind of American dream based on " _free_ labor." Some people might need to hire themselves out for a little while to get started, he allowed, but all in order to one day own and control the manner and fruits of their labors—a farm, a store, an office, whatever. "If any continue through life in the condition of the hired laborer," Lincoln said, "it is not the fault of the system, but because of either a dependent nature which prefers it, or improvidence, folly, or singular misfortune." Ownership is the path to realizing one's selfhood. Pity the job-holders.
These words, at that time, could not be separated from the question of slavery—labor at its least free. The implication was that working a job for wages lay on a spectrum not far from outright enslavement. The absurd notion of spending one's whole career in jobs, with no ownership over one's work, could illustrate for Lincoln's audiences the injustice of that more extreme version of the same thing. Yet his efforts to secure abolition also helped secure the rise of the job-based industrial economy; the North's victory in the Civil War was a victory of factory capital over plantation capital, and factory owners wanted wage workers.
Lincoln was not the first to imply a continuity between jobs and slavery. It's part of a long legal and philosophical tradition, from the Emperor Justinian and John Locke to Nobel-winning economists, that has regarded the sale of one's labor in an employment contract as akin to being sold into a life of slavery. (Locke described employment as mere "drudgery," just shy enough of slavery to be permissible; the economists refer to it as a kind of self-rental.) In times of legal slavery, even paid work for others could seem too close for comfort. It was obvious to Lincoln, at least, that a prerequisite for economic self-respect was owning and directing the means of one's own livelihood. And when women in the textile mills of Lowell, Massachusetts, went on strike in 1836, a favorite marching song ended:
_For I'm so fond of liberty_
_That I cannot be a slave._ 7
The prevailing ideology nowadays regards getting a job as a celebration-worthy accomplishment and a free choice. It is now the politician's ultimate conversation-stopper; nobody in Washington can get away with arguing against more jobs. A decent job, or a string of them, promises at least the possibility of a decent life. Humane and rewarding jobs surely deserve more credit than Lincoln and Locke allowed them. But how much choice is there, really? Most people feel they need to get a job to secure material necessities, so the choice is already not a matter of _whether_ , but _which_. A common criterion for a successful work-life is having made excellent contributions to an undertaking whose purpose and benefits are somebody else's. This would sound altruistic if the path had been chosen without coercion, which is not usually the case. We've forgotten the search for something better, a search that in Lincoln's time was producing remarkable discoveries.
Slave-picked cotton from the Southern states, combined with new weaving machines, furnished a profitable and brutal textile industry in England. Charles Dickens recorded the horrors. But the cooperators' favorite chronicler of this period is surely George Jacob Holyoake. In addition to his participant-observer histories of British cooperative enterprise, Holyoake coined the terms _secularism_ and _jingoism_ and held the distinction of being the last Briton convicted of blasphemy for a public lecture, for which he spent several months in prison.
The catalyst of Holyoake's tale was misused technology. "The rise of machinery was the circumstance that filled the working class with despair," he wrote in his _History of Cooperation_. "The capitalist able to use machinery grew rich, the poor who were displaced by it were brought in great numbers to the poor-house." This was machinery that could have been labor saving and life improving. But the early industrial free-for-all brought about such conditions as fourteen-hour workdays, child labor, and wages conducive to little more than permanent indebtedness. Holyoake held this condition up against the order that preceded it:
The capitalist was a new feudal lord more cruel than the king who reigned by conquest. The old feudal lord had some care for his vassal, and provided him with sustenance and dwelling. The new lord of capital charges himself with no duty of the kind, and does not even acknowledge the laborer's right to live.
Yet from this capitalist class arose Robert Owen, Holyoake's first hero of British cooperation and its first great dead end. A fellow religious skeptic (who frequented spiritualist seances in his later years), Owen spent his early life fulfilling the mythic promise of the self-made industrialist. He was the son of a Welsh saddler, with education only until age ten, and he worked his way into the management of Manchester textile mills. After marrying into wealth, he arranged for the purchase of a mill in New Lanark, Scotland, which he gained substantial control over by 1813. This became the ground of his experimentation.
On New Year's Day in 1816, Owen opened his Institute for the Formation of Character. It took on the education of the millworkers' children, starting from when they were old enough to walk—unusually early schooling for the period, and soon to be replicated widely. The curriculum avoided books and formal instruction, instead relying on the children's innate curiosity and self-direction. "Thus it came to pass," explains Holyoake, "that the education of members has always been deemed a part of the cooperative scheme among those who understood it."
This was only one of the ways New Lanark modeled an industrialism that served its workers, not just the owners, eschewing private profit for the common good. While mill workers across England and the United States agitated for a ten-hour workday, Owen instituted eight hours. And yet the mill prospered; it seemed to demonstrate that other kinds of industrial orders were possible, attracting visitors as eminent as the tsar of Russia. Owen also established a store where the workers could buy their necessities without the usual markup, together with a system of exchange wherein people could trade an hour of one kind of work for that of another. There was a system for arbitrating conflicts among workers. Today, the New Lanark complex is a UNESCO World Heritage Site.
The crucial component that held this remarkable artifice together, it turned out, was Owen himself. In addition to his entrepreneurial prowess, he proved an effective propagandist, inspiring many imitators but not nearly as much actual replication. In 1825, he relocated to the United States to found a new New Lanark on the southern tip of Indiana with a settlement called New Harmony—on the grounds of an earlier utopian community of German extraction, Harmonie—but it collapsed upon his departure two years later. His was a kind of cooperation that relied on a skilled paternalist. Yet it helped circulate the notion of cooperative industrialism, even if its reality was so far-fleeting. Attempts to test and perfect variants of Owenism began to spread.
The earliest explicit mention of _cooperation_ as an economic system that Holyoake could find was from the period of Owenist enthusiasm. The first issue of a short-lived periodical called the _Economist_ declared, on August 27, 1821, "The SECRET IS OUT," and "it is unrestrained COOPERATION, on the part of ALL the members, for EVERY purpose of social life."
After decades of Anglophone experiments and dead ends in the wake of Owen, the fervor began to coalesce around a more or less common model that worked. Disparate groups arrived at similar conclusions on their own with the simultaneous isomorphism that tends to occur around consequential discoveries. The most famous site of this discovery was Rochdale, an English town ten miles north of Manchester. To Holyoake, this was the great focal point and turning point for the whole history of cooperation—perhaps because of his own role in it.
Holyoake recounts a speech on cooperation he delivered to Rochdale textile workers in 1843—a year after his blasphemy trouble, a year before the start of the famous store. He spoke about Chartism, a movement by which workers were seeking the vote and other political rights, and he railed against the scourge of debt. Rochdale was a town through which these and other ideas, including Owen's, had long been circulating. It had been home to cooperative experiments already. But the year after Holyoake's visit, a group of twenty-eight workers there—weavers and others associated with the textile trade—arranged to establish a small store on Toad Lane where they could buy decent groceries, clothing, and other goods at reasonable prices. They were the Rochdale Society of Equitable Pioneers. The store opened before the end of 1844 for a few hours a week.
The Rochdale store implemented a specific concoction of the cooperative practices that had been swirling around in different combinations for years. Its member-owners were its customers. They would invest a weekly subscription of two pence, with each member entitled to an equal vote in decision-making. Perhaps the critical innovation was that, as co-owners, they were each entitled to a dividend from the store's profits, proportional to how much they had spent—a system that would come to be called the patronage dividend, or simply the divi. If a member collected it, this could be a windfall; if not, it became a mechanism for savings. There was a strict rule, too, that the store would neither extend nor expect credit. All cash, no debtors.
When compared to Owen's feat, the significance of Rochdale was that it put the beneficiaries—the ones in need—in charge. It wouldn't have happened without them. This system depended on no patriarch for either wisdom or capital. The store's early success spread simply because of the visible effect it had on its members, who "appeared better fed, which was not likely to escape notice among hungry weavers," according to Holyoake. "The children had cleaner faces, and new pinafores or new jackets, and they propagated the source of their new comforts in their little way, and other little children communicated to their parents what they had seen." Whereas Owen wanted to abandon private property to a paternalistic commons, the Rochdale store was a commons that put its members in better stead for a world of property.
At a time, too, when unscrupulous dealers might adulterate flour and soap to the point of danger, the co-op was a means of ensuring quality sourcing—quality of the product itself and the labor practices that produced it. In this, Rochdale prefigured how co-ops would later pioneer the organic and free-trade movements. My earliest memory of a co-op is of a store my mother shopped at when I was little, where she could get the boxes of organic soy milk that were not yet available in supermarkets.
The mighty Rochdale store, even by Holyoake's cheerful account, had its troubles. Rochdale included its share of "social porcupines, whose quills eternally stick out," "who know that every word has two meanings, and who take always the one you do not intend," "who predict to everybody that the thing must fail, until they make it impossible that it can succeed, and then take credit for their treacherous foresight." And yet. Perhaps the chronicler's most lyric phrases come while meditating on a table that listed the society's quantities of members, funds, revenue, and profits each year, from
to
"Every figure glows with a light unknown to chemists," he writes. "Every column is a pillar of fire in the night of industry, guiding other wanderers than Israelites out of the wilderness of helplessness from their Egyptian bondage."
Even with such growth, the Rochdale organization would be little better than Owenism if it were yet another impressive but solely historical exception. The difference is that it lives on in one of the ways that mortal cooperators can: institutionally. The Rochdale store began producing offspring within a few years of its founding. New branches opened around town, with services from shoemaking to housing, and copycat co-ops appeared elsewhere. The British Parliament helped clear the legal pathway for this with the Industrial and Provident Societies Act of 1852—again, before the 1856 Joint Stock Companies Act, the founding legislation for public, investor-owned corporations. But, as a cooperative, the Rochdale store wasn't set up to become a rapacious conglomerate, as investor-owners would demand. It would have to grow differently.
What came to be called the Cooperative Wholesale Society began in Manchester, in 1863, through a conspiracy of several hundred local co-ops across northern England, with several Rochdale Pioneers among its leadership. Cooperative wholesales like this had been tried before, but now they had the firm foundation of the Rochdale model to build on. The wholesale's job would be to furnish products for the local co-ops, whether by bulk purchase or through its own factories. It would also aid them with marketing, putting the strength of a national brand behind them. And the wholesale was a co-op, too. Its member-owners were the local cooperative stores that patronized it, and its management was responsible to them, just as the stores were responsible to their own patrons.
This kind of structure is called a federation, or a confederation, or a secondary cooperative—a co-op of co-ops. It's how cooperative endeavors around the world since then have met the challenge of scale, while retaining units small and autonomous enough to be responsive to their members. It's reflected in that sixth cooperative principle of "cooperation among cooperatives," as well as Elinor Ostrom's eighth design principle of nesting commons within a commons.
It was this same Cooperative Wholesale Society whose buildings boasted their grandeur from Warbasse's frontispiece in 1936. Today, its pile of buildings is even more impressive. The CWS has evolved into the Cooperative Group, or the Co-op, a massive consumer federation that includes grocery stores, the Cooperative Bank, the Phone Co-op for telecommunications, an appliance business, insurance, and funeral services. Since 1917, too, it has been a leading sponsor of the Cooperative Party, a political coalition that pursues policies friendly to co-ops. British cooperation has ultimately accompanied, rather than replaced, the investor-owned corporate order. But the breadth of the Co-op's offerings bears witness to that old and comprehensive idea of local co-ops linking into a commonwealth.
Simply sharing everything with everyone wasn't what made the Rochdale model work. The Pioneers didn't try reenacting the Acts of the Apostles. What's more formidable is that they struck a balance. The mix of cooperative rules at Rochdale hit a spot where human nature, economics, and neighborliness converged to make a certain kind of business work. In the years since, as cooperation of this sort has spread, there has been research—not enough—to explain the competitive advantages of co-op enterprises, especially in markets not designed to support them. The findings go a little something like this:
• Co-ops can _establish missing markets_ by reorganizing supply or demand to meet unmet needs
• _Leaner startup costs_ can result from volunteerism and sweat equity
• _Productivity benefits_ arise when members experience direct benefits from their co-op's success
• Co-ops offer _protection from exploitation_ for members, resulting in greater trust and loyalty
• _Information-sharing_ within an organization becomes easier with shared ownership
• Co-ops face a _lower chance of failure_ , especially after the startup phase, and greater _resilience in downturns_ due to risk adversity and shared sacrifice
• There can be _savings in transaction and contracting costs_ through co-ownership among clients
These competitive advantages come with costs of their own. Doing business this way can present barriers to obtaining capital and more demanding forms of governance. A give-and-take between costs and benefits has steered the course of this story—as with that between pragmatism and purpose.
Horace Greeley, founder of the _New-York Tribune_ , became one of the nineteenth century's most effective propagandists of cooperation in the United States. He served on various co-op boards, introduced Holyoake's writings to American attention in the _Tribune_ , and put the newspaper itself under an employee profit-sharing arrangement. The paper was also an early member of the Associated Press, a co-op for news gathering. Greeley, Colorado, the city where my grandfather got his start in business and where members of my family still live, takes its name from him; the _Tribune_ 's agricultural editor founded the settlement in 1870 as Union Colony, a prohibitionist cooperative. Those decades after the Civil War saw a hardening of the US corporate system along with new varieties of agitation for something else. Co-ops, Greeley predicted, would be "the appointed means of rescuing the Labouring Class from dependence, dissipation, prodigality, and need... conducive at once to its material comfort, its intellectual culture, and moral elevation."
Once again that ambition of holistic human improvement repeats itself like a refrain. Cooperation's boosters proposed it as an antidote to the deterministic, one-dimensional class struggle of Karl Marx. A person is more than any class. They promised this kind of business as a means of overcoming drunkenness and other workingmen's temptations. They talked about "emancipation" from wage labor, extending slave liberation from cotton plantations to the textile factories. The same year the Civil War ended, a group of cooperators in Philadelphia announced their store in terms much like Greeley's: "Cooperation aims at elevating men morally, socially, physically, and politically." The poster enjoins its readers, "Be of one mind in support of the truth; have faith in the lovely principle of Cooperation, and you may cast your mountain of woe into the sea of oblivion."
Some of those who fell for the principle fell hard. In an 1868 union newspaper, an iron molder in Troy, New York, confessed, with respect to cooperation, "I have dreamed about it, thought about it in the shop, on the street, at church, in fact, everywhere." Everywhere, the lovely principle was spreading.
This was the period that saw the birth of the modern insurance industry, first through local fraternal organizations and secret societies that people organized to cobble together a safety net. These evolved into cooperative-like mutuals, owned by their policyholders, such as New York Life and Northwestern Mutual, which are still leaders in the US insurance business. Mired in labor conflicts, industrialists such as Andrew Carnegie, John D. Rockefeller, and J. P. Morgan dabbled in employee ownership and profit-sharing. And as family farmers began to see their power wane compared to the influence of big-city industry, they began to create a cooperative system that remains the basis for a lot of the family farming that has managed to persist today.
One can still find Grange halls scattered across the rural United States, active and otherwise, attesting to the difficulties and salves of that time. There are several still operating within an hour's drive of where I live. The National Grange of the Order of Patrons of Husbandry first appeared in 1867, out of the ashes of war, to unite farmers across North-South lines and among the West's scattered settlements. In those halls, farmers learned skills from each other and shared their economic hardships. Grangers organized co-ops for purchasing, processing, credit, and retail, usually following the Rochdale model. One of their mottos was "cooperation in all things." It was an educational, political, and social movement—and in the West, also a colonial one—but its outcomes and underpinnings were consistently cooperative. More co-ops grew out of the later Farmers' Alliance, a multiracial network whose cooperatives broke from the Rochdale system by allowing its cash-strapped members to buy their supplies on credit.
Meanwhile in the cities, with the 1870s came the rise of the Knights of Labor, a cross-industrial national union for which organizing workers also meant organizing co-ops. Just as the Grange did for farmers, it set up cooperative stores for factory workers, as well as worker-owned businesses—mines, foundries, mills, printers, laundries, lumberyards, and more. These put a Knights of Labor label on their products. During the 1880s, at least three hundred such co-ops formed. The Knights joined with farmers to create the People's Party, which waged an insurgency in national politics to break the capitalist grip on government.
This was a prohibitionist, women's-rights, anti-monopoly populism hard to imagine under the rural-urban, red-blue lines that divide the United States today. The principal demand was for a more flexible monetary system than the gold standard, one that would put the supply of credit under the control of small producers, not big bankers. The People's Party elected a local Knights of Labor secretary to the Colorado governor's seat in 1893, and before the year was out, it became the second state to adopt women's suffrage. The populists' basic premise throughout was that opposing entrenched power and creating co-ops went hand in hand.
That strategy was already well known and well practiced among African Americans. W. E. B. Du Bois, the most prominent black intellectual of the period, organized a conference in 1907 called "Economic Cooperation Among Negro Americans" at Atlanta University. The event's resolutions determined, "From the fact that there is among Negroes, as yet, little of that great inequality of wealth distribution which marks modern life, nearly all their economic effort tends toward true economic cooperation." The almost two-hundred-page report details the many forms of the black cooperative economy, broadly conceived, including churches, schools, insurance, banks, secret societies, and more. Among these are formal cooperative businesses, more than 150 of which are listed by name. Co-op lending circles, insurance pools, and stores were a necessity for people whom white-controlled businesses and governments often declined to serve. Cooperation would be an ongoing fascination for Du Bois; in 1918, he organized a Negro Cooperative Guild to help the co-ops unite their efforts. Even as white society opted for the allures and inequities of capitalism, he believed his people could choose another way.
Mutual education was part of it all along. In her more recent survey, political economist Jessica Gordon Nembhard writes, "Every African American–owned cooperative of the past that I have researched, and almost every contemporary cooperative I have studied, began as the result of a study group or depended on purposive training and orientation of members." Whether an individual business thrived or foundered, the effects of that education shaped its participants.
By the time of Du Bois's conference, the populists' surge was over. The crackdown following the 1886 Haymarket riot was the beginning of the end for the Knights of Labor, and the American Federation of Labor that took its place practiced a kind of unionism friendlier to investor-owners and indifferent to cooperation. The People's Party collapsed after it splintered during the 1896 election. There was an attempt to form a Cooperative Union of America, a predecessor of Warbasse's Cooperative League, but it lasted only until 1899. Yet the lovely principle kept on seducing.
One of its remnants sits just ten miles up the road from me. In 1897, a Colorado mining-equipment supplier, Charles Caryl, composed and self-published a utopian drama outlining a system of worker-managed mines in Boulder County meant to swallow the whole country in a cooperative New Era Union. Despite raising substantial capital from New York investors, however, Caryl's scheme failed; he reestablished himself in a spiritualist sect and fled to California. His office is a museum now, open one day a month, in a mountain gulch with a few neighbors left and the towering ruins of the old gold mill. Meanwhile, Maine department-store owner Bradford Peck penned another cooperative fantasy called _The World a Department Store_ ; he thereafter attempted to form a Cooperative Association of America, which fell short of national reach but which at least managed his store under an employee profit-sharing arrangement from 1900 to 1912. It seemed like the cooperative commonwealth might kick off anywhere, and with time, in pieces, it did.
The populists' organizing built the basis of a system that, in the coming century, would generate cooperative agricultural brands like Cabot Creamery, Land O'Lakes, Ocean Spray, and Organic Valley. (Less visible in grocery stores are CHS, the agricultural supply giant, and Genex, the high-tech purveyor of bull semen.) A revived Grange and the Farm Bureau insurance systems kept the Rochdale idea spreading. The US Department of Agriculture established dedicated co-op programs, and acts of Congress in 1914 and 1922 shielded farmers' co-ops from antitrust law. Immigrant communities—perhaps most energetically, Scandinavians in the Upper Midwest—imported cooperative models from the Old World and innovated new ones. Department-store mogul Edward Filene, who first coined the term _credit union_ , financed the spread of such co-op banks across the country, starting with his own employees, and lobbied for enabling legislation. A cooperative radio network emerged in the 1920s, the Mutual Broadcasting System, which produced such classic radio dramas as _The Lone Ranger_ and _The Shadow_. The more cooperation became a fixture of the economy, the less it drew attention to itself; one could be forgiven for failing to notice that practical, powerful, hardly utopian pockets of a commonwealth had already taken hold.
In 1941, the year Murray Lincoln succeeded Warbasse as its president, the Cooperative League produced a film, _The Co-ops Are Comin'_. It depicted a co-op department store in Columbus, Ohio, a co-op tractor, the co-op hatchery of the Indiana Farm Bureau, and a co-op fertilizer plant challenging a corporate monopoly, all bound together with a map of the forty-eight states blanketed in the twin pines logo. Such universality was aspirational, but it represented the mounting reality of an agricultural heartland more and more bound together in cooperative business, if only the commonwealth's momentum would continue. But this momentum, the film contended, would depend on local, informal, mutual education. "Since a cooperative is a miniature democracy," one title card explains, "its strength lies in its informed members who teach themselves through their study groups." Perhaps without the impending war and the corporate juggernaut that followed, those little groups would have been sufficient. The fate of cooperation, anyway, was not merely a question for one or another constituency in the United States. By the time the International Cooperative Alliance first met in London in 1895, a global movement was already discovering itself.
_A recent—and far from complete—map of cooperatives throughout the United States._
Salinas de Guaranda is an Ecuadorian mountain village most of a day's drive from Quito. It has become a minor destination thanks to its factories that make cheese, chocolate, and textiles. At least part of its appeal is the fact that each of these enterprises is owned by and accountable to Salinas's residents, all through a byzantine organizational structure surrounding their credit union. The village has become an engine for development throughout the region, producing offshoots and replicas. A cooperative hostel hosts visitors. The weekly town meeting takes place in an upper room next to the church on the main square, under the concrete cross mounted on the hill above; the gathering doubles as a prayer meeting. The whole system arose in the 1970s at the instigation of an Italian priest.
Salinas is in some respects an exception—to the usual economic hopelessness of remote mountain towns, to the usual craving for rescue by multinational corporations—and in some respects not. Among impressive co-ops the world over, a story of influence repeats itself, in parallel with the spread of the Rochdale model. The first credit union in the United States, St. Mary's Bank, was born of a New Hampshire parish in 1908 with the help of Alphonse Desjardins, founder of Quebec's vast credit-union federation, who also mentored Edward Filene. Desjardins, in turn, borrowed the idea from Farmers' Bank of Rustico, founded under the guidance of a Jesuit priest on Prince Edward Island. The largest, most renowned worker cooperative on record is the Mondragon Corporation in the Basque Country in Spain, which employs more than seventy thousand people, most of them co-owners—thanks to another enterprising priest, much like the one in Salinas.
_Salinas._
The medieval commons found new expression in modern co-ops. Roman Catholics were not alone in this; secularists, Jews, communists, Buddhists, Protestants, Muslims, and others have formed the cooperative movement as well. But the Catholic contribution has been notably persistent, even if few Catholics know about it. I'm a Catholic myself, and I've never heard this story told in church. One might not expect cooperative democracy from such a monarchic, rigid hierarchy, but it's there. It is a story I had to piece together from inklings in my travels and in books, from stray remarks and unexpected teachers.
When Pope Leo XIII promulgated his 1891 encyclical letter _Rerum Novarum_ (or, _Rights and Duties of Capital and Labor_ ), he regarded his church as standing between a materialist-socialist rock and a robber baron–capitalist hard place. Decades of revolution and class conflict had shaken Europe, cracking many of the church's secular buttresses. Wary of accumulations of power in either business or the state, Leo proposed a third-way solution: double down on private property, but provide for its more widespread distribution. He called for the dispossessed workers of the world to take ownership. "The law," he wrote, "should favor ownership, and its policy should be to induce as many as possible of the people to become owners."
Even while asserting the priority of property, he retained the spirit of that old idea of the universal destination of goods, by which property should be treated somehow as if everything were really everyone's. The encyclical didn't include an explicit embrace of Rochdale-style cooperation but provided a basis for its subsequent adoption. And throughout the Catholic world, in a tremendous variety of ways, people tried to figure out how to put his sketch of a solution into practice. Popularizers of the effort such as Hilaire Belloc and G. K. Chesterton fashioned "distributism" into a subgenre of political philosophy.
At a crowded lunch reception in Melbourne, Australia, a young cooperator working for the local archdiocese pointed me to an elderly man. The man had something he wanted to say. He came close to me and began to speak, and from that noisy scene I recollect only one crucial word: _formation._
The man's name was Race Mathews. And despite his reference to a theological concept, he confessed to being neither a Catholic nor a believer. For most of his career, before retiring to study the origins of the modern cooperative tradition, he was a politician and official in Australia's Labor Party. He wanted to share his latest discovery.
_Formation_ is a word now used frequently in the Catholic vernacular. It refers to a person's ongoing conversion to Christianity—through prayer, study, and experience. The kind of formation one receives depends on one's outside influences and one's interior choices, and economic life is part of formation, too.
Since the 1980s, Mathews had made a series of visits to Mondragon. This remarkable network of worker co-ops emerged under the shadow of Francisco Franco in the 1950s through the guidance of the one-eyed priest José María Arizmendiarrieta, or simply Arizmendi. It's a system of factories, schools, banks, retailers, and more, all owned and governed by people who work in them. It's a beacon of possibility the world over that democratic business can thrive, employing high tech and large scale, though it has yet to be outdone or replicated.
Mathews's 2009 book, _Jobs of Our Own,_ traces Arizmendi's precursors, including _Rerum Novarum_ and the distributists. In Mondragon, Mathews saw a practical manifestation of the ideas earlier Catholics had only alluded to, dubbing it "evolved distributism." But only after publishing that book, while studying the Catholic Action and Young Christian Workers movements that influenced Arizmendi, did Mathews zero in on the concept of formation.
Mondragon, he realized, is a monument not only to a particular way of doing business but to a vision for forming the souls who partake in it. Before the first Mondragon cooperative opened in 1956, Arizmendi started a secondary school, financed and co-governed by students' families, in which he and his students developed their plans together over the course of a decade. They tested their ideas relentlessly and creatively through practice, and then adjusted those ideas accordingly. The reasons for Mondragon's success are complex enough to be infinitely open to interpretation, but among them is the view of participants' spiritual development as an end in itself, rather than simply a means toward enacting an abstract economic system. "It has been said that cooperativism is an economic movement that uses the methods of education," Arizmendi once wrote. "This definition can also be modified to affirm that cooperativism is an educational movement that uses the methods of economics." The centrality of this kind of education for Mondragon is hard to overstate.
Mondragon continues to be a uniquely successful model of cooperative industrialism, but as a cooperative expression of Catholic social teaching it is far from alone. The Knights of Labor's ranks were heavily Catholic, including pro-cooperative leaders such as Terence Powderly, who petitioned Leo XIII for support. Starting in the mid-1930s, through a university extension program, two priests in Nova Scotia seeded the Antigonish movement, which resulted in hundreds of co-ops throughout the region. In the US South, the African American priest Albert J. McKnight became one of the architects of a cooperative system that enabled thousands of black farmers to own land. Meanwhile in New York, the lay-edited Catholic magazine _Jubilee_ , active between 1953 and 1967, organized itself as a consumer cooperative, with shares owned by subscribers; this model took inspiration from journalist and children's book author Clare Hutchet Bishop's _All Things in Common_ , a lyrical dispatch from among the worker-cooperative industries that appeared throughout France after World War II. Around the world, mission agencies have supported co-ops among poor farmers and craftspeople, enabling them to bring products to global markets on terms more of their own choosing. Catholic Relief Services calls this methodology "integral human development." Among the "interfaith partners" of the fair-trade worker cooperative Equal Exchange are not only Catholic Relief Services but also the Quakers' American Friends Service Committee, the Jewish Fair Trade Project, the Mennonite Central Committee, the Presbyterian Church USA, and the Unitarian Universalist Service Committee.
Few places exemplify the odd bedfellows that cooperation brings together like the northern Italian territories of Tuscany, Trentino, and above all Emilia-Romagna. There, cooperatives organize the timbre and tempo of the whole economy. Italy's two largest grocery-store chains are cooperatives—one owned by its consumers, the other by local retailers. Co-ops control Unipol, one of the largest insurers, whose modern skyscraper towers over the terra-cotta rooftops of Emilia-Romagna's capital, Bologna; they carry out activities as varied as construction, garbage collecting, and producing a best-selling brand of boxed wine. Co-ops can look like the trattoria in the Trastevere neighborhood of Rome run by the community of Sant'Egidio, or a monastery-turned-guesthouse along a canal in Venice; both make a point of employing people with disabilities. One can visit a showroom of sophisticated dental chairs at a massive worker-owned factory or buy bonds from a dairy co-op backed by wheels of its Parmesan cheese. Cooperative networks enable small- and medium-size enterprises to remain dominant in a region that exports world-renowned food, automobiles, and packaging equipment. In part because of its culture of cooperatives, Emilia-Romagna has the highest median family income in Italy, with the lowest unemployment rate and the highest participation of women in the workforce. This is the outcome of a curious convergence.
_A showroom of dental chairs at a factory for Cefla, a manufacturing cooperative near Bologna._
Emilia-Romagna was, starting in the late nineteenth century, a leftist stronghold. Communists and socialists dominated the first national cooperative association, Legacoop, founded in 1886. Catholics formed another association, Confcooperative, in 1919. At a time when the Catholic Church preferred monarchies over democracies, and communists were vying for their own absolutist schemes, in northern Italy both opted to back bottom-up businesses. Today, the two organizations have come to regard their ideological differences as negligible. They have initiated a merger. "The Berlin Wall doesn't exist anymore, but we in Italy realized it only recently," says Gianluca Laurini, a Legacoop official in Bologna. "Ideology aside, a co-op is a co-op."
Cooperative formation, it seems, can outlast its original rationales. It works by a distinct logic and imparts its own lessons, assembling a commonwealth among people and places with little else in common.
My flight arrived in Nairobi with the sunrise. It was my first time in the city, my first time in sub-Saharan Africa, and I was still half asleep. But I had an appointment an hour later at a hotel downtown, so I allowed myself no time to come to my senses before getting into a taxi.
In the thick traffic between the airport and the city, I started to look around through the haze of morning. Along the side of the road, buildings came and went among the palm trees and power lines. There were stores, stray hotels, and office buildings that offered no indication of the work done inside. Fashion models watched me go by from billboards, towering over hand-painted mural ads for Safaricom, the telecom company that runs a celebrated text-message payment system called M-Pesa. And then I started seeing storefronts for the Co-operative Bank. As the Nairobi skyline came into view, I saw that name also atop one of the taller buildings. I hadn't come to Kenya because of its cooperatives, nor did I know that I should; I'd come to visit family members who were living at a research station near Mount Kenya. But I had never been to a place where co-ops were so ubiquitous and so vital.
I asked the cab driver about the Co-operative Bank. He told me about _his_ cooperative bank, a kind of small credit union among his fellow drivers called a SACCO, or savings and credit cooperative. For these independent workers fending for themselves, the SACCO is their social-safety net, enabling them to cover medical expenses if they get ill and burial expenses when they die. It's also how he got his start as a business owner; with loans from the SACCO he started buying cars and built a small fleet. He told me about the secrets of his business—turnover, not margins—and about the tricky politics that can arise among a group of drivers trying to manage a pool of swirling capital. He'd been president of the SACCO on and off, so he knew all about conflicts between membership and management. As I listened to him talk, I felt I'd never met someone so expert in the mechanics of democracy—along with its contradictions and limits. Cooperation, for him, was a matter of necessity more than choice. He said, "It's a double-edged sword."
Modern cooperation had come to the country as an instrument of exploitation. By the end of the nineteenth century, after honing cooperative business to uplift their own working poor, the British turned it on their colonies. Even by the time of the 1931 Cooperative Societies Ordinance in colonial Kenya, membership was still open only to white settlers, who used their co-ops to organize the export of cash crops grown with African land and African labor. Meanwhile, British colonists in India encouraged farming co-ops, and in British-Mandate Palestine, Jewish settlers from Europe were establishing collective villages on land Arabs had held for centuries.
In Kenya, the white-only system started to change in the 1940s, when the colonial governors reasoned that a middle class of black cooperators could serve as a bulwark against uprisings. Upon independence in 1963, Kenyans turned this means of exploitation into one of liberation; co-ops became the basis of state-sponsored "African socialism" in the country. The official ideology reinterpreted the cooperative system as a return to a precolonial, communal way of life—the economic expression of the new nation's motto, _harambee_ , meaning "coming together."
_The Cooperative University of Kenya._
Today, nearly half of Kenya's gross domestic product flows through cooperatives, and the International Labour Organization estimates that 63 percent of the population derives a livelihood from them. The historic dominance of farming co-ops is giving way to the finance sector, which ranges from my driver's small SACCO to the Cooperative Bank, the country's fourth-largest financial institution. Kenyan co-ops organize themselves into a series of federations according to sector and region, which in turn join to form an apex federation, the Cooperative Alliance of Kenya. The International Cooperative Alliance also has a regional office in Nairobi.
On my last day in the city, I caught a ride to the Cooperative University of Kenya, a tranquil campus in the western suburbs. The buildings were painted blue and white. It is in most respects an ordinary business school, with better-dressed-than-average students darting along its sidewalks and lawns between classes on marketing, accounting, and finance. But it's more than that, too.
Esther Gicheru, the school's former director, grew up on a coffee farm, the daughter of co-op members. Her own education began by taking part in her family business. "In cooperative training," she told me, as if channeling the likes of Holyoake and Greeley, "we are not just thinking about disseminating business knowledge and skills. We are thinking about the growth and the advancement of people at all levels, in a way that an ordinary stock company will never do." Now she runs the Institute for Cooperative Development, a new arm of the university dedicated to research. She and her colleagues want to help existing businesses do better, as well as to set up business types less common in the country, such as worker co-ops and housing co-ops.
Only since a law passed in 1997 have Kenyan cooperatives been meaningfully independent from government support and control. This was part of a bigger, ambivalent restructuring process at the behest of such institutions as the World Bank, nudging the country away from African socialism and toward global markets. Perhaps only then did Kenya's co-ops have to become true co-ops—truly autonomous and self-managed. Some collapsed under their own unmarketable weight, while others have learned to become more competitive and thrive. The university's job has taken on new significance. "Members used to look at cooperatives as extensions of government," Gicheru said. "Now cooperatives take education very seriously."
_Esther Gicheru._
Back in downtown Nairobi, in a dense complex of bureaucratic concrete, I visited Nyong'a Hyrine Moraa, chief cooperative officer at the government's Ministry of Industrialization and Enterprise Development. Co-ops used to have the privilege of their own ministry; now, the job of her office is to steer the sector toward habits of mind more conducive to survival under globalization. Every co-op in the country still has to submit its accounts to the reorganized ministry, but no longer can they expect state protection as in times past.
"We try to tell the cooperatives it's not business as usual. It's not like the way they used to do things," Moraa said. "There is need to impress entrepreneurship in anything that they are doing."
Moraa's particular priority was for co-ops to invest in the means of adding value to their products, beyond just churning out raw materials. It's an old problem, dating back to the British system of growing cheap crops in the colonies but keeping the most profitable links of the supply chain at home. Moraa talked about leather, about food processing, about textiles. Yet the vexing paradoxes of the postcolonial condition persist there, as in so many parts of the world. Around half of Kenyans live in poverty; their SACCOs don't give them access to the wealth that the political elite skims off the top. Much of the financing for co-op development comes from agencies abroad, often from the same wealthy countries that compel Kenya to conform its policies to the dictates of global markets. But Moraa was also trying to help Kenya's co-ops leverage each other. Her office, for instance, was connecting farmers in the countryside with affordable, flexible loans from SACCOs in the cities.
As I went on asking about the details of these financing schemes, Moraa grew restless and asked if I had noticed that the office was mostly empty that day. I had; it was. She explained this was because the employees' SACCO was having an election. She had to excuse herself, which she did as she showed me back to the elevator. She needed to go vote.
Just as the cooperative idea needed forming by trial and time, cooperators need forming too. Education was among the founding principles of the Rochdale store, and it has remained enshrined in every update of that list. But it is also an easy principle to disregard in the short term, until after a while it is nowhere to be found. The kind of formation I saw available in Nairobi is harder to come by back home. There's no such thing in the United States as a cooperative business school.
Despite representing a sector with significant scale and a distinctive logic, cooperative principles and practices nearly disappeared from economics textbooks after World War II. According to one study, published in 2000, only six of seventeen North American introductory economics texts even mentioned co-ops, and almost always briefly and dismissively. Among twenty leading US MBA programs I polled, not one reported a single course devoted to cooperative enterprise. Several professors of management and economics I queried about cooperative business weren't sure what I was talking about.
This would come as a disappointment to Leland Stanford, the robber-baron founder of Stanford University. Accompanying his 1885 initial endowment were instructions to promote "the right and advantages of association and cooperation." As a US senator, he championed legislation to support worker-owned cooperatives, which he saw as preferable to the investor-owned enterprise that had made him so wealthy. He told the university's first class of students, "Cooperative societies bring forth the best capacities, the best influences of the individual for the benefit of the whole, while the good influences of the many aid the individual." This was guidance that his university, including its elite business school, has almost completely ignored.
The exceptions to this lacuna are generally found not in MBA programs but in the less glamorous discipline of agricultural economics. Since cooperatives are part of US farmers' essential infrastructure, the Department of Agriculture has long supported university research on co-ops, especially at land-grant campuses. Among the most prolific of these programs is the University of Wisconsin–Madison's Center for Cooperatives, established with federal assistance in 1962, whose very existence is required by state law. Yet when the center was running the search for its current faculty director, it had trouble finding qualified candidates. Brent Hueth, the agricultural economist who ended up getting the job, had been studying co-ops largely in isolation. "I pretty much stumbled into it on my own," he says.
What drew him was the recognition that co-ops were uniquely effective in enabling independent farmers to purchase supplies and sell to markets with an economy of scale. "It's not idiosyncratic to the country, it's not one-off," he told me. "There seems to be something fundamental about these sets of markets and these economic environments where the investor-owned model doesn't get the job done."
Keeping the Madison center open and funded hasn't been easy; the co-op sector doesn't have access to the kinds of wealthy benefactors that furnish MBA programs with names and fortunes. "Cooperatives create a lot of wealth, but it doesn't get concentrated in a small number of people," Hueth says. Persuading a democratic co-op to fund university programs can be trickier than luring individual donors with the prospect of leaving a legacy. A co-op MBA program at Canada's St. Mary's University depends on relationships with cooperatives that send their employees to study.
A lot of the co-op business education that does take place nowadays happens in unaccredited academies run by community organizations. The lessons are often experiential and group oriented, evaluated by real-world success. But the formation of a co-op sector of any scale and seriousness will need formal training, too. Melissa Hoover, executive director of the Democracy at Work Institute, a leading promoter of US worker co-ops, can't afford to wait. She needs co-op entrepreneurs, as soon as possible, who know how to work with the nuts and bolts of existing capitalism. "I reject the special-snowflake version of cooperative education," she told me. "Move, people. Go to traditional business schools and politicize your own learning."
The university system itself has origins in cooperation. Europe's early universities emerged from self-governing guilds of scholars, a legacy that lives on in dreaded faculty meetings and committee work. Perhaps this legacy is in need of revival. Some have called for schools to be owned and governed not just by faculty members but by stakeholders ranging from students to custodians. Throughout the United Kingdom in recent years, at pre-university levels, parents and teachers have taken advantage of privatizing reforms to set up cooperative schools that they own and manage together.
When I try to figure out what prompted me to think that the stories of equitable pioneers might be worthy of consideration, I think back to a time in school. My high school math teacher once invited me to chair a committee that would reconsider our public alternative school's admissions policy. This was a touchy subject because our previous policy had been overruled in a big court case. I don't think I'd ever been on a committee before, much less chaired one; who knows why he thought I could. But I did. We met in his classroom in the evenings—including him, parents just out of work, and fellow students. With the school nearly empty and night outside, the building itself seemed to be listening to us. For months, we debated possibilities, then drafted a proposal to better reach underserved neighborhoods in the county. We brought it to the school board. I gave a speech there, and our proposal passed. I guess I got it into my bones then that even a teenager lousy at math, given the chance to help govern, can rise to the occasion.
"With a greater intelligence, and with a better understanding of the principles of cooperation," Leland Stanford said in the 1887 congressional record, "the adoption of them in practice will, in time I imagine, cause most of the industries of the country to be carried on by these cooperative associations." He believed that a bit more of the right kind of research and teaching and forming would usher in a cooperative commonwealth. But despite his best efforts at the university he founded, and those of others since, his supposition remains mainly untested. Those turning to cooperation today have had to rediscover the lovely principles for themselves.
#
# The Clock of the World
## _Disruption_
I went to Detroit looking for the concrete, for the tangible stuff I'd heard was there—guerrilla farms carved into abandoned lots, foreclosed homes turned into communes, peeks into the apocalyptic future that other cities might have coming their way when the American dream abandons them, too. Those were there all right. Pedaling among the empty, stately homes and factory ruins at the speed of a borrowed bike, the possibilities were as visible as the wreckage, and in many cases the two were one and the same. It is as good a place as any to pivot this story from the past to the present and its contending futures.
Detroit has long been a place of pilgrimage. It was Motor City, the engine of American car culture, and it was Motown, where the black middle class built a center for entertainment and art between the coasts. Lately, the country has looked to it for other reasons—for the direness of its postindustrial decay, and for its relative emptiness, which is not in fact emptiness at all, but which looks enough like it to beckon the imaginations of pioneers, equitable and otherwise, all vying to be protagonists of the city's inevitable revival. Detroit understands the disruptions of our time with particular acuity. It also knows especially well the new longing for cooperation.
My excuse for the visit was a conference called New Work New Culture, an oblique celebration of Michigan philosopher Frithjof Bergmann's decades-long quest, amid the rise and fall of the auto industry, to transform work from a dead-end chore into a joy. Also in town that week were the Black Farmers and Urban Gardeners Conference and the United Nations representatives investigating home water shutoffs that were part of the city's ongoing bankruptcy proceedings.
"Ask what 'new work' is," said one of my hosts at the New Work Field Street Collective house, where I slept on the floor, "and everyone will tell you something different." That was the point. Bergmann found the genesis of good work in how each of us probes our most genuine, most particular desires.
The night I arrived, I met the elder member of the Field Street Collective, Blair Evans, not long since out of prison for Black Panther–era activities. He told stories. He loved all the gadgets he'd been missing out on, and he kept a little video camera hanging from his neck to record the police. In the house, he was teaching younger guys how to craft leather goods, which he'd learned to do while incarcerated. The next day, I met Marcia Lee, a younger woman-about-town who worked for the local Franciscan friars. She let me ride along for a strenuous day in her life of organizing, including a stop at a photo shoot for queer activists and a prayer supper. In between, she told me about her study circle with fellow women of color who were dreaming up co-ops.
How much of this was really working? If something works in what remains of Detroit, surely it can work anywhere. I was ready to see models—replicable innovations I could gather up and share elsewhere. To the model-acquiring frame of mind alone, however, the first day of New Work New Culture was an almost total waste of time.
Under the fluorescent lights of a lecture hall at Wayne State University in midtown Detroit, the invocation came as a volley of African drumming. The discussions that followed were on the "new culture" side of things, consisting of fairly general reflections on life and the universe derived from a synthesis of activist idioms, Africana, and plain experience. "If you stand here"—meaning Detroit—"and survive, you learn something about a higher self," said Mama Sandra Simmons, a transfixing woman who introduced herself, among other things, as an ordained minister. "We are warriors, and we are in this together." But the most frequently repeated phrase among speakers was a question: "What time is it on the clock of the world?"
_The population of Detroit since 1900._
These were the words of Grace Lee Boggs, the mentor of many of the event's organizers. She earned her PhD in philosophy just before the United States entered World War II. A Chinese American herself, she married an African American factory worker and labor organizer, Jimmy Boggs, and fell under the influence of the Trinidadian socialist C. L. R. James. She rejected Soviet communism but joined with the Black Panthers and Malcolm X to build a revolution of local economies, by and for marginalized communities of color. She preached the power of "critical connections" over "critical mass." As the conference proceeded, Boggs remained in the basement of her home, while the rooms above were still being used for organizing. She had strength at her advanced age to see only her closest companions, including Marcia Lee. The following year, a century old, she would pass on to join the ancestors.
"The clock of the world" is a call to notice where we are and where we might go next. Boggs had long used Detroit as a clock that could see into the future, that could predict the crises soon to spread elsewhere and the means of surviving them. Automation came to Detroit's factories long before the internet came for travel agents; the housing bubble was already long-popped by 2008. Her disciples invoked the question less because they expected an answer than to provoke further probing. The best hope was "a way out of no way."
As the day's sessions ended, boxes full of percussion instruments appeared and made their way out among the crowd. Thus began a rising cacophony that took several minutes to resolve into a common beat. I received, and proceeded to shake, an old plastic POM juice bottle half full of sand.
The second day was more like what I'd originally had in mind. A bus tour showcased the gardens in abandoned lots. But back at the conference, attendees grilled Bergmann, who wore a black leather cap over restless gray hair, on the features of his theory. Ideas he'd formed decades ago as an antidote to the auto assembly lines—like living your passion and choosing your own hours—sounded suspiciously like a pitch for the gig-economy hustle that younger people in the room knew too well. Bergmann's liberation was their perpetual insecurity. He reveled in the possibilities of 3D printers for localizing production, but groans came from those who were sick of being told that their rescue was only one more contraption away. To Boggs's big question, gender theorist Kathi Weeks won applause when she replied, "It's quitting time." She didn't trust work enough to entrust her passion to it.
That afternoon I found Bergmann sitting alone, feeling frustrated and misunderstood. So much had changed. The factories weren't the starting point anymore. The vision of new work he'd hoped for had been co-opted in capitalism before a better version got a chance to grow.
Around him, breakout groups held nitty-gritty discussions about financing cooperatives and organizing time-banks. I joined a tour of a state-of-the-art fab-lab, in which "at-risk" youth were making everything from coasters to an electric car with precision mills and, yes, 3D printers. Something to write home about, maybe.
To get back to my inflatable mattress that night, I caught a ride with Tawana Petty. She was an organizer of the conference, an activist and mother with a relentless smile that she said she had learned as part of the emotional labor expected of her while serving fast food. Now, she does research and education on "data justice." I listened from the back seat as she, in the passenger seat, caught up with a visiting friend behind the wheel. She described a moment in which she'd been called to speak before UN representatives about the water crisis. She said she'd felt the ancestors speaking through her, in her, with her. Not blood family, necessarily—for instance, she'd felt the presence of Charity Hicks, a woman who had fought with particular tenacity against the water shutoffs until she was killed by a rogue car. "Charity was there," Petty said.
The utopias of Detroit, as best I could judge, were mostly in the process of being steamrollered by capital, or co-opted when doing so was profitable. The tide was raising some boats and sinking others. The only way for the others was no-way. The error on my part was failing to see enough value in the primary tip or trick or model these holdouts of Detroit had to offer: the stubborn cultivation of faith.
There is a simple chart that captures many perils and anxieties of our age in pithy summary. It has come to be called the jaws of the snake. There are two lines. One ventures upward, jagged but steady. That represents the percent increase in US productivity since World War II. The second line follows it almost exactly—at first. This one represents wages, the degree to which most actual producers actually benefit. After rising in unison with the first, around 1970 the second line goes flat; by then private-sector union membership was in freefall. A similar thing happened again in 2000, except this time the line that went flat was total private-sector employment; this time, some say, it was automation by software.
_The jaws of the snake._
The economy keeps getting more efficient and generating more value, but most people are getting a smaller and smaller portion of it. The rest of the value gets siphoned upward to the few and wealthy. More than pleasing customers, more than creating jobs, business keeps getting better at serving the single-minded goal of maximizing shareholder value—the rewards for those who already have excess to invest. Economist Thomas Piketty's best-selling book _Capital in the Twenty-First Century_ argued that the returns to investors are careening the world into a new feudalism; his most celebrated critic, twenty-six-year-old MIT graduate student Matthew Rognlie, differed only in stressing that the major share of the phenomenon was in real estate. An uptick in the minimum wage isn't going to fix this. One way or another, wealth is going to the owners—of where we live, where we work, and what we consume.
In between the jaws sit most of us. The lucky ones could go on being peaceably ignorant until the widening jaws clenched a bit in the 2008 financial crisis. Then the nature of the system revealed itself. High finance got bailouts while millions of people around the world, especially those in already precarious situations, got catastrophic losses. Even the new regulations meant to keep this from happening again were tailor-made for big businesses and further squeezed smaller ones. This laid bare the power relations at work; it demonstrated right out in the open which people and which institutions had the capacity to protect their interests and which didn't. Where jobs have returned to replace the ones that disappeared, they have been less predictable, with fewer benefits, fewer of the guarantees that used to accompany employment. Millions of homeowners lost their homes. It was a crisis, yes, but it was also a symptom of celebrated norms. This was the upshot of something we'd been longing for.
A favorite aspiration for entrepreneurs today, by their own broken-record account, is disruption. The sign of a promising new enterprise is that it disrupts some industry or cultural habit or human-intensive inefficiency. This talk has become so pervasive that we neglect to notice what the word means—what it means and has meant, for instance, in Detroit. There, Jimmy Boggs saw disruption decades ago, when a brew of robots, racism, and imports from Asia shut down the city's factories, and when what remained of the auto industry fled to the whiter suburbs—consigning that capital of black America into decline and collapse.
The jargon of disruption derives from a more precise academic concept. Harvard Business School professor Clayton Christensen began honing what he came to call "disruptive innovation" in the mid-1990s and early 2000s, referring to how a simple development, often from an oblique end of a market, can refashion the rules of the market in which it operates. In this way, the cheaper, less-mighty cars from Japan took on Detroit's Cadillacs. It's how Kodak invented the first digital camera in the 1970s but, by clinging to film, collapsed into bankruptcy by the hand of its own invention. It's how smartphones have replaced everything from alarm clocks and record collections to asking driving directions from a gas-station attendant. The disrupters can win big. Christensen's peers credited him with discovering a motive force in contemporary capitalism, a sunny successor to the "creative destruction" that Karl Marx, and then Joseph Schumpeter, observed in the industrial age. Thus we deify serial disrupters like Steve Jobs and Elon Musk. But what about the disrupted—those who endure the effects?
In centuries past, among St. Clare's nuns and the Diggers, among the Rochdale Pioneers and the Knights of Labor, cooperative economies have tended to take hold on the receiving end of economic upheavals. What cooperators built then became infrastructure for the new order, more or less in tension with it, a lifeline that enabled people who would otherwise be left behind to survive and flourish. It happened with the monasteries that lasted through the collapse of the Roman Empire, with the urban guilds that bore the costs of caskets in plagues, with the cooperative stores and workshops that helped workers endure the sweatshops that disrupted the guilds.
The disruptions of the early third millennium cascade and intersect. Human civilization's exhaust has caused extreme weather events to grow in frequency and force, together with the long, slow devastation of droughts. These combine with a whack-a-mole world war on terrorism to set off waves of mass migration. Globalized markets let capital flow freely but stop the desperate migrants at the borders. The liberal-democratic consensus that some expected to spread everywhere has buckled as voters around the world elect autocrats.
We've also been living through a disruption of networks. For Silicon Valley, the internet has created the favorite case in point of disruptive innovation. It wasn't walking, talking, sci-fi robots that took the place of travel agents or Borders Books, it was apps—new points of connection that replaced incumbent intermediaries. These connections replace physical assets and "human resources" with creative arrangements of users and their data. McKinsey and Company estimates as many as half of all jobs are vulnerable to existing technologies. Rather than industrial production and distribution—now outsourced to other lands—the apps offer postindustrial matching algorithms. But networked connections can do more than endlessly disrupt us.
Behind so many disruptive tech companies lies an innovation that started with collaboration. Before there was Airbnb, travelers stayed in each other's homes for free with Couchsurfing. While Google and Facebook were disrupting the print advertising industry, an Egyptian Google employee used Facebook to help set off the popular uprising that brought down the regime of Hosni Mubarak. Car sharing, crowdfunding, social networks—these are things that people previously turned to co-ops to do. The collaborative possibilities of the internet are cooperative possibilities, too. The trouble is, as finance goes on becoming an ever-larger portion of the economy as a whole, outside investors' money has become easier and cheaper for new companies to access than that of customers or employees. Maverick businesses that a generation or two ago might have had little choice than cooperation now find investors willing to buy in and take over before they bother considering other options. Awash in investor capital, most ambitious entrepreneurs seem oblivious to the prospect of funding and growing businesses grounded in the communities they serve. But not all have.
The new equitable pioneers don't tend to salivate at the thought of disruption the way startup bros do. Disruption sounds great to investors whose money lets them hover above the economic fray. But when you're accountable to fellow members, to others struggling to get by, there's not much to like about wiping away the basis of their livelihoods. Less exposed to risk and less inclined to panic, financial co-ops and credit unions kept up deposits and kept lending after the 2008 crisis hit. While others were disrupting, cooperators have been innovating in their own fashion.
The 1960s counterculture produced famous consumer-owned grocery stores like Brooklyn's Park Slope Food Co-op: by the turn of the millennium, co-ops like these had helped build the global fair-trade movement for goods like coffee and chocolate, a much-needed feat of counterglobalization. The 1960s and 1970s saw a more buttoned-up kind of cooperation as well, such as when Seattle banker Dee Hock convinced Bank of America to spin off its credit-card franchise into a bank-owned cooperative, Visa. The Vanguard Group meanwhile bypassed Wall Street's gatekeepers with a low-cost, consumer-owned mutual fund. In Italy, so-called social cooperatives transformed the care industry through shared ownership by both caregivers and their clients. Social co-ops also specialize in employing people with disabilities and criminal records; when painter Mark Bradford created his installation for the US pavilion at the 2017 Venice Biennale, he partnered with a social co-op through which local inmates grow produce and make crafts. Since it opened in 1985, Cooperative Home Care Associates in the Bronx has become the country's largest worker co-op—signaling promise for more in the fast-growing care sector—and it's now a certified, public-benefit-seeking B Corp on top of that. Japanese housewives in search of decent milk built a consumer co-op conglomerate. Indian sex workers used co-ops to establish more bearable standards in an underground industry. When Argentina's economy collapsed in 2001, workers took over factories that owners tried to close and started running them for themselves. Aided by tax perks, employee-stock ownership plans expanded to transfer corporate profits to millions of US workers. New cooperators are appearing alongside the disruptions, the artificial and natural ones alike.
Hurricane Sandy struck New York City on October 29, 2012—an event ambiguously attributable to climate change, worsened in turn by the city's human inequities. It nearly washed away the Rockaway Peninsula, a narrow strip of land on the southeastern end of Queens, home to over one hundred thousand people. Structures that once stood near the beach could be found in pieces blocks away, alongside overturned cars and other hefty debris. A long strip of storefronts burned down in an electrical fire. Public apartment towers stood dark, without electricity or heat. Because of the mold growing in their flooded basements, residents couldn't return home. Yet thousands of New Yorkers joined in the recovery effort, there and in other coastal areas. The most sudden, remarkable volunteer-wrangling operation was Occupy Sandy, an undertaking of organizers who had been sharing things in common at Occupy Wall Street a year earlier. Within days, they had furnished a complex system of intake forms, trainings, mold-remediation equipment, and distribution centers for donated supplies. Before long they were creating co-ops, too.
The following June, in the cramped upper room of a church building in Far Rockaway, I attended a graduation ceremony for WORCs, or Worker-Owned Rockaway Cooperatives. Occupy veterans had teamed up with five aspiring co-op businesses from the neighborhood for a twelve-week program. In the making were a _panadería_ , a "people's market" for fresh groceries, a _pupuseria_ , an entertainment company, and a construction crew. Among them was Brendan Martin, offering encouragement and footing the bill, young for an executive director and wearing street clothes. After working in high finance, he moved to Argentina and formed the Working World, which began by making hundreds of loans to cooperative businesses there. The organization was beginning to expand back into the United States, starting with disruption zones like this one, with the Occupiers' help.
"We've done a lot of protesting in the last few years, but this has been a way to create alternative structures," one of the volunteers told me at the time. She would soon be among the Occupy veterans to make a pilgrimage to Detroit, searching for guidance on what to do next. When they got back, they could be heard asking each other, "What time is it on the clock of the world?"
Occupy's co-op affinity was only part of a revival in the United States during the Great Recession. Move-your-money campaigns turned disgust with the big banks into new accounts at credit unions. Real estate investment co-ops organized to turn the tide of urban gentrification. But the most fervent hope was reserved for worker co-ops. The New York City Network of Worker Cooperatives was founded in 2009; it became part of the US Federation of Worker Cooperatives, which was itself only five years old then. NYC NOWC, pronounced "nick knock," proved an effective lobbyist, and by 2014, its coalition had convinced the city council to fund $1.2 million in worker co-op development, particularly in immigrant communities—which has since grown to millions more. Former Occupy Sandy organizers joined NYC NOWC's fledgling staff. In Cleveland, a group of local "anchor institutions" like hospitals and universities helped create worker-owned laundry and green-energy co-ops; the allied Democracy Collaborative used this and other examples as the basis for national-scale transition plans. Madison, Wisconsin, voted to fund worker co-ops in late 2014; Oakland, Austin, Minneapolis, Newark, and other cities got on board in various ways. By 2017, Bernie Sanders was leading a group of Democratic senators and representatives to propose federal legislation on behalf of worker-owned businesses. Some embattled labor unions seemed ready to turn back to their roots with a newfound interest in co-ops, too. Alongside the NCBA and other older co-op organizations, these efforts tended to coalesce around the youthful, intersectional, diverse umbrella of the New Economy Coalition—founded around the time of the 2008 crash. They considered themselves part of a wider "solidarity economy."
It was in 2008, too, that Bank of America cut its line of credit to Republic Windows and Doors, a factory on Chicago's Goose Island. Production was set to end, but some of the workers refused to leave, and their occupation became a national totem. President-elect Barack Obama said then, "What's happening to them is reflective of what's happening across this economy." A legal settlement required the bankers to compensate the workers, and another company tried to buy the factory but failed to keep it afloat. Then one of the original worker-occupiers, union-local president Armando Robles, met Brendan Martin and invited the Working World to get involved. It was a case much like those Martin had seen among the recovered factories in Argentina. A group of workers, with the support of their union, formed New Era Windows Cooperative and borrowed more than $1 million through the Working World. Now they have their own factory, and they're making windows at a profit again.
_Armando Robles in the New Era Windows Cooperative office, with the factory floor behind him._
"To me, it's the next step for any union," Robles told me when I visited the new factory. "Instead of losing members, try to help them to maintain their jobs, create co-ops, and give them the tools they need."
New Era is an isolated case, but it's also a scalable model—no lock-ins required. More than half of US employers are businesses owned by baby boomers set to retire in the coming generation. Project Equity, an Oakland nonprofit that assists in such conversions, estimates that 85 percent of those businesses don't have a succession plan, and many will have trouble finding an outside buyer. Selling to their employees might be the best option in a lot of those cases, if only the owners—and the employees—knew that there might be another way.
When I moved to Colorado in the summer of 2015, I found that the cooperative revival was happening there, too. A group called the Community Wealth Building Network was meeting monthly in Denver office buildings, wrangling funders and policymakers to support cooperative models. The Rocky Mountain Employee Ownership Center was targeting retirement-ready business owners for conversion, and the Rocky Mountain Farmers Union started bringing its agricultural co-op experience to urban service workers. But some of the most seismic action was happening on the roads.
On the morning of Labor Day Sunday in 2016, the parking lot behind the Communication Workers of America Local 7777 office filled up with cars. Some already had the black or green paint of Green Taxi Cooperative, its name inscribed in the typeface of a Wild West saloon. But many were unmarked, or bore the branding of one of Denver's other cab companies, for whom their drivers were working even after putting down the $2,000 investment to become member-owners of Green Taxi. Some hadn't yet quit Uber. All eight hundred slots for Green Taxi members had been filled, and there was demand for more, but only around 150 members were driving for the co-op so far. The rest were waiting, working for other companies, keeping their status as co-owners of a competing business quiet and biding their time to see if this would really work. The largest taxi company in the Denver metro area was still mostly secret.
"I've never heard of a meeting on the Sunday before Labor Day," Sheila Lieder, the local's political director, told the assembly of about ninety co-owners, nearly all of whom were born and raised in places where Labor Day does not exist. Green Taxi's drivers came from thirty-seven countries, I was told, especially East African ones. At a time when the taxi industry here and virtually everywhere was facing an existential disruption from Silicon Valley apps, these immigrant workers self-funded a third way. They hoped that without bosses skimming profits they'd be able to take home enough to make driving a decent living in the age of apps, with a company and an app of their own.
"When we talk about the company, that's you," Abdi Buni, the board president, reminded his co-owners, "and when we talk about the drivers, that's also you."
With the backing of Communication Workers of America, including an office Green Taxi rented in the union hall's basement, Buni and his fellow founders had been clearing regulatory hurdles since 2014. The company's slow, quiet start began when the office opened on July 1, 2016; the first cars hit the streets later that month. It was part of an international surge of taxi co-ops trying to turn the industry's disruption-by-app into an opportunity for worker ownership—in suburban Virginia, in Seoul, throughout Europe, and beyond. For the Denver taxi scene, Green Taxi was game changing. For members, it was a better deal.
"I paid extra to use the owners' license before," said Kidist Belayneh, who has been driving taxis about half of the six years since she moved to Denver from Ethiopia. "Now I'm an owner. We don't pay extra." She was one of just a handful of women in the room.
The main business of that Sunday meeting was to vote on a legally inert but rhetorically meaningful amendment to Green Taxi's bylaws, which would emphasize that "members" were indeed "owners." These drivers were sticklers for detail. Some had driven for the two other smaller co-ops formed in recent years, Union Taxi and Mile High Cab, which allowed members to lease cars to nonmembers. Green Taxi set out to be different; all the drivers would be member-owners. "We need documentation of legal ownership," one of them said from among the ranks. "That's why I came from my other company." Another allowed me a glimpse at his stock certificate.
The first shouting match broke out over the books. Green Taxi lost its first bookkeeper, and the board had been slower than it had promised in delivering the financials to members. The hired accountant made excuses, insisting that any profits would go back to the members and that they should be patient, but a few loud voices pressed on. "This is our money and our company," one interjected. "This is not just some job." The uproar was so intense I wondered if some were paid disrupters from other companies they still worked for. Members got up to speak, alternating between declarations of loyalty and surges of defiance, then counteraccusations against the malcontents who wouldn't stop driving for Uber. In exasperation, one man stood up and said to the board what migrant workers aren't supposed to say out loud in America, that America is anything other than the hilltop Promised Land: "I came from Ethiopia sixteen years ago to make money so I can go back to Ethiopia. You're supposed to help me make money so I can go home." At last the board treasurer offered to show anyone who wanted to see it the bank ledger on his phone.
"This is democracy," Buni repeated, attempting to moderate—as if consoling himself, telling himself that the voice of the people will somehow lead to the good.
_One of Green Taxi Cooperative's early member meetings._
Green Taxi's biggest problem, however, was not there in the room. In a car-culture city, the backbone of the taxi industry was the $55.57 flat-rate fare between the airport—nestled in the high prairie, far from everything—and downtown Denver. According to how the airport granted permits, in proportion to market share, Green Taxi's eight hundred members should have entitled the company to about one-third of the 301 available slots. So far, it had received only twenty. But with eight hundred drivers, according to Buni, twenty airport permits wouldn't be enough to keep the business afloat. What's more, the airport was planning to change the whole system, just as Green Taxi organized to claim its market share. The airport's website had a notice about an impending contract bid for taxi companies, replacing the permits. This could reshape the city's taxi business and make or break Green Taxi's plan to cooperativize—and unionize, with CWA—one-third of the market.
The airport's new regime affected only taxi companies, but it had everything to do with the influx of apps. Unlike taxis, Uber and Lyft drivers faced no restrictions on their airport usage. They often drove nicer cars and spoke better English; they were more likely to be white. In December 2014, the app drivers made 10,822 trips through the airport, compared to 30,535 by taxis. A year later, for the first time, app-based airport trips exceeded the taxis, and they'd done so every month since. As taxi companies prepared to fight among themselves under the still-unpublished new rules, Silicon Valley's expansion proceeded unrestrained—even welcomed by the relevant authorities. Rumors were flying about an insider deal, and nobody at Green Taxi seemed to be in on it.
"I have really deep concerns about how this is being done," Lieder told the drivers. She said she'd been trying to reach people all over government about it and not hearing back. "Something stinks about this."
Proceedings continued to the bylaws, and some complained that they'd never seen any. (They were on the internal website, but not where you'd expect.) A debate broke out about whether the members not yet driving for the co-op or paying dues should be allowed to vote. This necessitated a break, five minutes of intermingled talk, shouting, a bit of shoving, and laughter. It wasn't all hard feelings. But it was tense. I heard grumbling that the board might have rigged its own election—which came, it turns out, from a candidate who lost.
Jason Wiener, Green Taxi's counsel and a rising-star lawyer for the region's social-enterprise sector, tried to clarify things. He broke down the provisions of the bylaws about who could vote. The members almost made it to voting on the ownership amendment, but they didn't. They decided to table it for later. That was the closest thing to a decision made all day—for some, their first decision as business owners.
Despite whatever powers come with ownership, so much was out of the drivers' control, and the anxieties of futility seemed to be bearing down on them hard. They were fighting for slots at the all-important airport, and they were only a tiny player in the global scramble for control over the future of logistics. Wiener counseled more patience. "What you're trying to do is not easy," he said. "Try to see the long arc." He fielded more questions about the bylaws. It wasn't much longer before the three-hour meeting ambiguously ended.
A day earlier, I attempted to hail a Green Taxi for a short ride using the company's new mobile app. I was far from downtown Denver, and it took a few minutes before the app found me a driver from the skeleton fleet. While I waited, I scrolled through the Twitter feed of Autocab International, the company that created Green Taxi's app, "the No. 1 largest supplier of taxi booking and dispatch systems in the world." Recent posts included pictures of a workshop held in the United Kingdom about how to beat Uber, as well as links to news articles reporting new tests of self-driving cars, self-driving trucks, self-driving mini-buses. Also, alongside a broken link: "Crisis management is our specialty."
While Green Taxi's drivers scrambled to protect their livelihoods, Uber and Tesla and Google were tooling up to automate them. I asked Buni about this. He said, "We're really trying to feed a family for the next day. When it happens, we'll make a plan"—that is, crisis management, for the foreseeable future. To that end, he and his crisis-ridden co-owners pooled more than $1.5 million to put one-third of Denver's taxi industry under worker control. Self-driving cars hadn't come to the city's roads yet, but Wall Street's anticipation of them was fueling investment in the big apps, which put pressure on the taxi market and motivated so many drivers to set off on their own. The disruption was already happening, and Green Taxi had been born of it.
In the beginning, before Uber and Lyft and even checkered taxicabs, there was sharing. At least that's the story according to Dominik Wind, a German environmental activist with a genial smile and a penchant for conspiracy theories. Years ago, out of curiosity, Wind visited Samoa for half a year; he found that people shared tools, provisions, and sexual partners with their neighbors. Less encumbered by industrial civilization, they appeared to share with an ease and forthrightness long forgotten in the world Wind knew back home.
Wind and I got to know each other in Paris while splitting a stranger's apartment that we found through Airbnb. It was 2014, and thanks to apps like that, such apps were on the rise in urban centers. The internet was making it possible again for people to share resources such as cars, homes, and time—bringing us together, for a price. Capitalism's creative destruction may have ravaged our communities for centuries with salvos of individualism, competition, and mistrust, but now it was ready to sell the benefits of community back to us on our smartphones.
Without owning any guestrooms of its own, Airbnb was by then more valuable than Hyatt; Zipcar, which rents cars by the hour, had been bought by the international car-rental company Avis Budget. The sharing economy was also changing the way at least some people worked. Online labor brokers such as Amazon's Mechanical Turk enticed hundreds of thousands of people to take up digital piecework—data entry, transcribing audio, running errands—without expectation of paid leave, health insurance, or even a minimum wage. But it was also alluringly permissionless—no application process, no fixed hours, no managers. Compared to the rest of the global economy, these companies remained small potatoes, but they seemed like portents of a shift that we'd soon be taking for granted before we had the chance to question it.
The occasion that brought Wind and me to Paris was OuiShare Fest, an annual gathering for the sharing economy held in a red circus tent, on an adjoining strip of AstroTurf, and aboard a boat floating in the nearby Canal Saint-Martin. That year's theme, the Age of Communities, was broad enough to welcome all sides of the sharing phenomenon: venture capitalists alongside black markets, slow foodies alongside big data.
Paris is not Detroit, but here was another conference meant to ascertain the time on the clock of the world, to confront widespread disruption with critical connections.
The first morning of the three-day event began with an invitation for everyone to stand up and hug three people around them. Forms of sharing spread across domains freely; a conversation about startups could quickly pivot to one about polyamory or the universe. The same words came out over and over: _trust_ , _community_ , _network_ , _passion_ , _collaboration_ , and a good deal of _love_. As a Brazilian entrepreneur put it, "Why don't we talk about love in big companies?"
It wasn't so clear, however, how far the sharing economy they were supposed to be building would bend toward justice. This sharing was not the kind of sharing that co-ops had been doing for generations. Cooperative models were alluded to occasionally. But for the moment, challenging corporate control with shared ownership and shared governance wasn't really on the table. When the sharing evangelist and consultant Rachel Botsman showed slides of Arab Spring crowds, those scenes served as an analogy, not a recommended course of action. She described sharers as "insurgents" against old-fashioned hierarchical businesses, engaged in "revolution," "democratizing," and of course "disruption."
_Disruption_ came up at OuiShare Fest a lot. Just as Airbnb disrupted the hotel industry, the sharing startups present were poised to undermine more industries in short order. One could sense a general din of cheerfulness, as the startup boosters and organic farmers alike expected an imminent and inevitable disintegration of the economic establishment and a triumphant future of sharing ready to take its place. We heard little, however, about the effects that disrupting major industries might have on those people less well-equipped than the entrepreneurial class to adapt, about how workers on sharing apps usually lack what used to be standard benefits and rights of employment. At this all-English conference in Paris, the kinds of people most likely to be disrupted were not around to speak.
Surely an economy built on sharing could be for the good. Sharing enables ordinary people to buy less, connect to one another more, and retain the value they generate in their own communities. But sharing could also make us even more reliant on corporate whims, allowing companies to dictate how, why, when, and what we share, extracting the highest fees they can get for themselves in the process. That's what was happening already in Paris. That's why, in Denver, cabbies had to form Green Taxi.
In a network economy, the power lies with whomever controls the points of connection—the web servers and databases and terms of use. The old means of production matter less. A sharing elite was well on the way to establishing itself; by the time I went to OuiShare Fest, the sharing sector built on venture capital and gray-area labor was a multibillion-dollar business. The idea of a real sharing economy based on shared ownership and shared governance remained mostly an afterthought.
Silicon Valley was already giving up on the language of "sharing." The word left companies too vulnerable to criticism, and even they could recognize it wasn't very accurate. Uber became part of the "on demand" economy; Mechanical Turk was mere "crowdsourcing." In the years to come, though, the young organizers behind OuiShare kept on being OuiShare, kept trying to hold the tensions between big business and the hope of business models that might actually be collaborative, that might actually share. They formed partnerships with an older generation of cooperative companies, including a large mutual insurer, to support the upstarts and ground their work in the legacy of pre-digital sharing. They schemed about entering politics.
In the United States I've noticed a particular chasm between the entrepreneurs and the protesters, between those building functional enterprises and those who feel the inadequacy of the status quo in their bones. Maybe it's because, for certain can-do types, there's simply so much investment capital going around that questioning the system would mean giving up too much; we've become victims of our own success, unable to see beyond the particular business models with which we so marvelously disrupt. Maybe it's also because protest becomes a habit that's hard to break.
I remember Grace Lee Boggs warning about this when she spoke to a roomful of New York's activist intelligentsia in late 2013. "Think about the people, not just the system," she said. "If you only look at the crimes of the system, you aren't looking at the people, and you won't meet their needs."
In international circles like OuiShare, I've found this kind of critical-constructive sensibility to be more common than it is at home.
It was through OuiShare, for instance, that I learned about SMart— _Société Mutuelle pour Artistes_ —an organization of more than seventy-five thousand workers in eight European countries. Together they turn the precarity of sharing-economy gig work on its head by creating a support infrastructure of their own. In Belgium, SMart members can process their gig income through the organization, which then pays them as salaried workers, making them eligible for more public services, even while keeping the autonomy and flexibility of freelancing. They share a variety of digital tools for invoicing and collaborating. The organization pays members for their jobs promptly, out of the general cash flow, regardless of when the client pays up. SMart began as a Belgian nonprofit, but as it spread abroad, it found cooperative ownership to be more appropriate, and now the whole network has gone co-op. It binds many thousands of workers into a common enterprise, a togetherness that eases the path to independent, experimental work-lives. Julek Jurowicz, SMart's founder, described it to me as "a solidarity mechanism."
Jurowicz has deep-set eyes and short, gray hair. Between sessions at OuiShare, he explained how SMart got its start with the case of an undocumented immigrant—his wife, who came to Belgium from the Czech Republic to work in the film industry. Jurowicz accumulated enough bureaucratic expertise that artist friends started coming for help, followed by strangers, until he realized he needed to form an organization. That was back in 1998. The problems of an undocumented immigrant have since become a condition of the masses. SMart brought to OuiShare the reminder that precarious, uncertain work is nothing new, although it may be shifting from marginal to ubiquitous. As destabilizing tremors spread with each subsequent disruption, so do the contrivances among those determined to take back control, or at least to take more control over their lives than they could have had before.
Among those who cluster around OuiShare, the corps of elite organizational scientists are the New Zealanders, in particular the members of Enspiral. They're best known for an app called Loomio, a collaboration and decision-making tool initially derived from the assembly process at the Occupy Wellington encampment in 2011. This activist invention is now used by schools, political parties, and businesses around the world. Whereas a discussion in a Facebook group usually just leads to more endless discussion, feeding more data to the algorithms, Loomio's polls and proposals steer discussions toward actual accomplishments.
From 2003 to 2010, Enspiral was just a name used by Joshua Vial, an Australian software developer living in Wellington, for his personal consulting business. By 2010, he was trying to spend less time on paid work and more on volunteer projects; he turned Enspiral into a vessel to help others do the same—sharing gig opportunities and freeing hours for good works. It then grew to more than forty core members, as well as about 250 "contributors" who are participants in the network, and fifteen small companies called "ventures," of which Loomio is one. Many members are techies of some sort, but people of any profession can join, in principle. Vial stepped down from its board. He's now, more or less, just another member.
New Zealand has the world's largest cooperative economy as a percentage of GDP, thanks mostly to hulking dairy co-ops. After incorporating as a worker cooperative, however, the Loomio team discovered it was the country's only one. Enspiral's structure is less easy to categorize—a standard limited-liability company that calls itself a foundation and operates as a co-op.
I visited Wellington expecting to find a group of people bound by managing shared _things_ —for instance, working space and budgets and businesses. And I saw some of that. But Enspiral's power lies less with the stuff it manages than the connections it enables. It links like-minded people and groups, and they pool some of their money for whatever they want to invest in together. Members and contributors spoke about their friendships, their mutual encouragement, and the way the community responds to requests for help. Enspiral is, no more and no less, a network—one that has evolved to meet the needs of an often alienated, isolated network society.
Enspiral serves as a financially lean, but anecdotally essential, connective fiber among its independent workers and small companies. Enspiralites pass jobs around to help stabilize the ups and downs of freelancing, as Vial started the network to do, but now they also fund one another's business experiments and assist one another if things go sour. They hold retreats twice a year. They're relying less and less on the Robin Hood strategy of taking corporate contracts to pay for volunteer time; instead, they're creating their own jobs and companies with do-gooding built in. Enspiral-affiliated ventures, along with Loomio, have included ActionStation, an online organizing tool; Scoop, an alternative-news source; and Chalkle, an education community.
I spent a morning with Vial in a conference room at Enspiral Dev Academy, a web-developer boot camp he opened in 2014. He gave me a tour of the network on his laptop. Enspiralites work at several co-working spaces across town—and, increasingly, outside Wellington—but the space that most unites them is a cluster of online tools. Some are commercial, such as GitHub and Slack; the most important ones had to be custom-built. There's an internal bookkeeping system at my.enspiral.com, and at cobudget.co, they've created a tool that helps contributors and members allocate funds for each other's projects and other worthy causes. Loomio serves as the network's official decision-making mechanism.
As Vial showed me the various tools and tasks, I asked questions about how they prevent bad actors. What if someone wants to rig a decision on Cobudget to get money for his or her project? What if the project is a sham? He replied with a shrug. "It's a high-trust network," he said. "We don't try to optimize for low-trust situations." An almost universal characteristic among the Enspiralites is an enthusiasm for interpersonal processes and a systemic manner of describing them.
A short walk from the Dev Academy and up the elevator of a downtown office building is a drab half-floor of co-working rooms that are the closest thing to Enspiral's headquarters. There I met Alanna Krause, an immigrant from California who encountered Enspiral early in its transition to collectivity. She became, among other things, the "bossless leadership geek" at Loomio and an Enspiral board member. She and some of her co-workers relayed the litany of ways the network works for its members.
"Somebody's laptop gets stolen, we buy them a new one," Krause told me. "Somebody's house burns down, we pay their rent. Somebody's organization has to downsize, the other ones will hire those people." They also cover one another's therapy sessions, when needed. And the result of this safety net, she thinks, is "actual innovation." When you know someone has your back, it's easier to take risks.
From the other side of the world, seeing Enspiral's work-life mix lent some vindication to Frithjof Bergmann's theories, which were so hard to hear in disruption-worn Detroit. When equality is its premise, perhaps work really need not be segregated from life, from the ambitions and needs of our actual selves. Back home in Colorado, I've started to see that kind of vindication as well, again in the form of a real sharing economy.
There's a local talisman around Boulder known as Niwot's Curse—to the effect that the beauty of the place, the gentle weather and soaring rocks, would draw people in and those people would destroy the beauty that drew them. The curse's namesake was a peaceable Arapaho chief from Boulder Valley who died of wounds suffered in the 1864 Sand Creek Massacre, on the east end of Colorado, conducted by an especially genocidal militia of white settlers.
Boulder's present residents interpret his words in a variety of ways. For some, especially the older-timers, it's a rebuke against the plentiful newcomers fleeing from the coasts, along with the traffic and construction projects they bring. For the newcomers, it evokes the discovery that here in flyover country, the cost of living turns out to be no lower than back on the coasts. And thus the curse is also a hypocrisy, one familiar among liberal utopias: the counterculture and inclusivity that attract so many new settlers have priced out any inclusive countercultures to come.
Part of any curse is the curse of forever trying to lift it. Here, we keep at it. That's why, after midnight on the first Wednesday of 2017, the city council passed a measure that enabled housing cooperatives to form in Boulder's neighborhoods.
I first saw the curse at work almost two years earlier, soon after moving to Boulder for a job. It was at another city council meeting, where the subject of debate was an occupancy limit that prevented more than three or four unrelated people from sharing a single house—and in particular, whether the city should start actually, aggressively enforcing it. Angry homeowners, especially from around the student ghetto of University Hill, called for a crackdown. But far outnumbering them was an organized bloc of mainly young, illicit over-occupants, together with allies from the three legal co-op houses.
Almost a hundred people spoke that night in the public comments, but the phrase I remember most vividly was from a woman who pleaded before the council, "You're legislating isolation!"
It was a statement about family. A family of two grandparents, two parents, and six grandkids could, by right of law, share a house that ten people unconnected by blood could not—even if they considered their housemates their family, even if their biological families had turned them out, as was the case for several speakers that night, generally on account of their gender identities. This was a claim to the right of intentional community, the right that so many monastics, artist colonies, friends, and co-workers have shared. Those words rebuked the regime of detached houses with yards and strip malls, which James Howard Kunstler has suggested make America less "worth defending." This system of thought requires each person or couple to consistently earn the money sufficient for a house, a car or two, a lawn, however many batches of child care and higher education they dare to commit themselves to through procreation, and so on. The cooperators, in contrast, shared their calculations of how drastically their electric, gas, and water consumption paled in comparison to the average Coloradan. This enabled them to take risks with their work, to be artists and entrepreneurs and activists. As I listened, I remembered the stories of an old friend (we met in a housing co-op in college) who grew up in the Boulder of another era, raised by the members of his family's Marxist commune.
In the debate about occupancy limits, speakers were beginning to coalesce around co-ops as a solution. The council could create a pathway to legalization for those affordable, over-occupied homes by enabling them to become bona fide, above-ground, registered cooperatives, governed and in many cases owned by their residents. This would mean replacing an existing, decades-old co-op ordinance so cumbersome that the only legal co-ops had to be formed as exceptions to it. By injecting the mutual and community responsibility that cooperative principles require, perhaps the over-occupiers could stem the fears of their neighbors. Boulder would get a cheap and bottom-up way of creating the affordable housing that had otherwise been so elusive.
And so I watched from a cautious newcomer's distance as the organizing took place, a campaign of mobilization and persuasion. A group of cooperators led it, under the aegis of the Boulder Community Housing Association. Some of their neighbors supported them, and packs of retirees, longing for co-ops of their own, joined the cause, too. Together they drafted ordinance proposals, held public events, helped elect friendly city-council candidates, kept saturating council meetings, concocted social-media memes, saturated more meetings, collected public data into spreadsheets and graphs, wrote letters, got their friends to write letters, got me to write letters, invited council members over for visits, and sometimes rested—all the stuff you're supposed to do in a good, local democracy. The opposition formed the Boulder Neighborhood Alliance, led by homeowners intent on preserving their town more or less as-was, despite its actual residents. They took out ads demonizing the young and tried to get some of the illegal co-ops evicted. People lost their homes. Yet the democracy seemed to be working. At the International Summit of Cooperatives in Quebec, I met the head of the Canadian co-op housing association, and when he heard where I lived, he asked about the effort, knowingly, and wanted to hear how things were going. As someone usually drawn to lost causes, I surprised myself by saying that things were going pretty well.
The style of co-op housing then being sought in Boulder—packing big houses with a dozen or so people—is only one form that housing co-ops might take. On the north end of town, there was a group putting together a community land trust, an arrangement that places the land under a home or apartment permanently off the market, reducing the dwelling's speculative value and thus its cost of use. Down in Denver, some Catholic Workers I knew were trying to set up cooperative tiny-house villages for the homeless. In other parts of the country residents of manufactured home parks were organizing to buy and own their parks cooperatively. Some of New York City's most exclusive, expensive apartment buildings are co-ops, but so are many affordable buildings, true to the model's roots among immigrant networks and labor unions. The policy for packed houses on the table in Boulder was just a start, a wedge in the door.
I arrived half an hour early for the final, fateful city council meeting, that January night in 2017, but early was late. There was already a potluck underway in the lobby, full of co-op stir-fries and salvaged baked goods. I ran into a woman I knew from church with her little son and daughter, who unbeknownst to me used to live in one of the co-ops. She told me I shouldn't wait to go upstairs to sign up to speak in the public comment, which I'd been asked to do. There, an enormous line snaked around the stadium seating—enough chairs for most Tuesday nights but not this one. I joined the end of the line and began talking with the man in front of me, a retired sociologist at my university wearing a colorful knit sweater, who turned out to be the uncle of my aforementioned friend, one of whose tasks in the Marxist commune was to take care of that friend, when he was a baby, on Monday mornings.
Before getting to co-ops, the council passed a mainly symbolic measure to declare Boulder a "sanctuary city," defying the tide of deportations that was soon to come under President Donald Trump. This seemed promising; if co-ops thereafter failed to find sanctuary also, the hypocrisy might cause Chief Niwot to strike from his grave.
Eighty-eight people signed up to speak at public comment. We got two minutes each. Some organized so as to pool their time as a continuous presentation of charts and figures in defense of the right density limits and resident caps and square-footage-per-person, so that affordable co-ops would actually be possible. A few residents spoke of fears about their neighborhoods and their property values; some outright demanded fewer people and fewer jobs in town. But the vast majority stood in favor, testifying as residents, neighbors, and experts to the benefits of co-ops. Again, they said a lot about family.
This time, the testimony that stuck with me most was from a resident of Rad-ish Collective, a co-op whose floor once harbored me during a visit before I moved to town. The speaker first clarified their gender pronoun as "they" after the mayor referred to them as "she," then proceeded to call for triage. Referring to the numerous stories we'd heard of co-ops as places of refuge for those who could afford nothing else, as pockets of economic, ethnic, sexual, and gender diversity, they suggested the council members think of themselves for the moment as doctors. Which case takes precedence—the papercut or the trauma, the property values or the displacement?
Some speakers later, around eleven-thirty that night, my turn to step forward came, which is worth mentioning only because it gave me the chance to see the council members up close. I don't think it was solely my remarks on the self-regulating capacities of the cooperative model that left them rubbing their faces, out of fatigue, into such frightening contortions that they reappeared to me when I finally got into bed later that night.
The decision finally came through, 7–2, at one o'clock in the morning. The co-op ordinance passed, mainly in the form that the Boulder Community Housing Association had been calling for. The compromises necessary for passage still resulted in a list of provisions long and specific enough to risk making impossible the very formations they were supposed to enable. Just barely, they supported the kinds of co-ops that already existed underground in Boulder, while leaving little room for much-needed innovation. But there was some flexibility—two hundred square feet per person, plus the option for rental, nonprofit, and equity co-ops. The cooperators' victory was complete enough that they might be tempted to think they'd dodged Niwot's Curse, at least for the moment, and vanquished a demon of affluent-liberal hypocrisy. For their opponents, however, this outcome was the curse's meaning precisely. Despite its cooperative guise, this was disruption.
#
# Gold Rush
## _Money_
The octogenarian artist Mary Frank traces her earliest debts to the prehistoric images in books that her mother kept around the house. Their shadows have reappeared throughout her sculptures, paintings, and photographs. But she knows none of their creators' names; there is no address where she can send a royalty check. The best repayment she can offer is the work of her own hands, and so she works.
Those of us who came of age in the millennial period have learned to think about debt and money quite otherwise. Debt does not motivate so much as it inhibits and stigmatizes. We accumulate it in order to have an education, to make a home, to pay for medical necessities. Servicing debts can prevent us from doing work we believe in, compelling us into better-paying livelihoods that might compromise our values. Our lenders' identities seem as obscure as those of ancient artists, as they trade our debts on veiled secondary markets, but the sums we owe are as precise as they are daunting. The collection agencies won't let us forget them. These debts haunt lives.
The creditors that Frank can name are those who have motivated and influenced her. She talks about studying dance under the legendary, demanding choreographer Martha Graham, about El Greco and Marcel Proust and Gerard Manley Hopkins, about a pair of Guggenheim fellowships, about the writer Peter Matthiessen, her departed friend, and about music. When she was broke, she'd trade pictures for things she needed. ("Dentists, you know, have great art collections.") As time went on, her debts grew larger and even harder to quantify. She lost her two children; all the world's children came to feel like hers. The first thing she always wants to show me are her brochures promoting low-cost solar cookers in regions where women would otherwise have to cook over flames fueled by scarce wood or poisonous garbage. "I feel a debt to the sun," she says.
That's very different from the debt arrangements many people depend on, which determine who can have access to what and how. Nonwhite communities in the United States, to which banks had in the past refused to extend credit, became targets for predatory lending before the 2008 crash; new financial "products" and government bailouts ensured that the banks won regardless of what happened to the lives of borrowers. Debt also maintains the international pecking order—subtler than armies, though no less vicious. From Athens to Bangkok, globe-spanning lending agencies dangle new loans (needed to pay old ones) as rewards for slashing public services and lowering trade barriers that might protect local economies. Whether through dollar bills or the International Monetary Fund, rule by debt is as omnipresent as sunlight.
It now seems quaint to refer to the time when premodern Christian, Jewish, and Muslim civilizations were united in their prohibitions of usury—the definition of which could range from merely the charging of any interest at all to the most abusive lending. We might ridicule the medieval metaphysicians' trepidation about money begetting money through interest, or the Islamic banks that devise techniques to avoid interest-charging today. But as more people break the silence and shame of their financial indebtedness, perhaps we're forced to recognize that those forebears had a point. Those religious traditions—built on notions of sin, fealty, and mercy—regarded debt as a precious and sacred thing to be handled with care. They insisted on clarifying the difference between the debts worth having and those that are not. They regarded debt not just as a transaction but as a relationship.
Consider, for instance, Salish Sea Cooperative Finance. It began with a series of intergenerational meetings in Washington state, where the Gen Xers present began to grasp just how much student debt was crippling recent college graduates. The respective groups got over their mutual resentments—the jadedness of the young, the affluence of their elders—and designed a cooperative that would refinance the graduates' debts under less burdensome terms. After the refinancing, rather than leaving the borrowers to fend for themselves, the model calls on the lenders to be mentors and help the borrowers find the sources of income they'll need.
The benefits go both ways. "My partner and I were never burdened with student debt, and so we feel obligated to help those who are," says Rose Hughes, who is both an architect of Salish Sea Cooperative Finance and an investor-member in it. "We also get to network with younger people who are doing fascinating things to help our society."
In the process, says borrower-member Erika Lundahl (accumulated student debt: more than $16,000), "the people with capital are taking some systematic responsibility for student debt and the effect it has on society as a whole." When organized like this, financial institutions can resemble the loans that happen among friends and family. They can incline us toward trusting each other more, rather than giving up on trust and entrusting our economic lives to markets alone.
Hughes's involvement in alternative finance brought her into the twilight zone of trying to develop community-oriented institutions around existing financial regulations. "All the rules are written assuming a profit motive is what drives everything." And there's consistently a bias, she says, "for the benefit of the lender, not the borrower."
The cooperative tradition has tried to play by different rules, to preserve democracy by making sure lenders remain lenders, rather than becoming bosses. "Our model has been to rent capital from the outside and give it no control," says Rink Dickinson, a founder of the fair-trade worker cooperative Equal Exchange. His company generates returns for investors that back it, but the more than one hundred workers don't give up governing power. When Loomio raised nearly half a million dollars in 2016, it did the same thing. It sold redeemable preference shares, which entitled investors to a return based on revenue, but no voting rights. For co-op savvy lenders, this is a smart investment; the people who are in control of the business, the member-owners, have a direct stake in seeing it succeed.
Entire systems of finance can be, and have been, built on this approach. Credit unions and other cooperative banks hold money and provide loans, but they do so on behalf of the same people doing the depositing and the borrowing. Here, debt is a relationship among members of a community, rather than one between a bank's customers and its investor-owners. Typically, credit union members are individuals, and there are about 114 million total memberships in nearly six thousand credit unions in the United States. But some cooperative banks are themselves made up of the cooperative businesses that use them. One such institution is CoBank, headquartered on the southern end of Denver, whose assets total more than $100 billion. It is an outgrowth of the national Farm Credit System, designed over the course of the past century to serve the critical agricultural co-op sector. As co-ops flourish, they need their own kind of finance, and they design it in their own image.
The debt worth having, cooperativism holds, is the kind that allows us to be more fully ourselves, that we use with our freedom rather than our servitude. It resembles Frank's anonymous, ancient artists—who live on not by collecting royalties and enforcing constraints, but through the flourishing of their debtors.
Money itself is a kind of debt. It appears from nothing through bank loans, according to rules that governments set. People who have lived among multiple currencies, or collapsing currencies, know from experience that money is no stable thing, that its value can vanish overnight. That's why, when it comes to monetary policy, average Argentinians and Ecuadorians today can talk circles around average North Americans, who have lived through decades of well-behaved dollars. Here, we mistake money for a constant, for something real and stable, rather than a complex of fickle debt relations. But that can change. The old populist farmers demanded more democratic means of money creation, and now tempestuous digital currencies have come to represent billions of dollars in value. People tired of banknotes, or simply seeking to keep their money under their control, are setting up alternatives to state-issued tender.
From the Brixton Pound, in an immigrant neighborhood of London, to Ithaca Hours and BerkShares in the northeastern United States, local currency schemes are turning up even in currency monocultures. Some peg the unit of value to the dollar or the pound, whereas others work as equalizing time-banks, pegging value to an hour of a person's life. The point is that the community of users can decide how it works, a capacity that distant central banks don't allow. Money itself could become cooperative, if meaningful democracy held sway over its issuance and nature. New technologies are helping such schemes proliferate, thanks to tools with such inviting names as Common Good (a payment system) and Main St. Market (a cooperative market app co-owned by local currencies).
The most effectual developments, however, have been in service of more ambivalent purposes. In times of flux like this, it's easy to lose sight of the basics—those nagging questions of ownership and governance that the cooperative tradition continually insists on posing.
The Bitcoin Center NYC, the self-described "center of the Bitcoin revolution," used to inhabit a retail storefront on Manhattan's Broad Street, a block from the New York Stock Exchange. The staff of an Asian-infused kosher steak house next door shooed loitering Bitcoiners from the sidewalk, indifferent to the revolution allegedly underway. Inside the Bitcoin Center, two small tables off to one side housed a menagerie of internet-age extraction equipment: Bitcoin mining machines. They resembled boxy desktop computers, only larger and without screens or keyboards attached. During a visit I paid to the center in November 2014, only one of them, the CoinTerra TerraMiner IV, was in use, emitting a purr of white noise. But the thing was still pretty much dead weight.
The TerraMiner IV rested on the table horizontally, encased in black metal, with rack-mounts and two stainless steel grates on either end that looked like the eyeholes of a deep-sea diver. The grates covered fans that cooled its array of application-specific integrated circuits, or ASICs—advanced chips that do little else but churn through the complex cryptographic math. In return for their calculations, miners earn payouts of new bitcoins from the network, plus transaction fees from users. (Capitalized _Bitcoin_ is the system; _bitcoin_ is the unit of currency.) Like mining precious metals, mining cryptocurrencies can be lucrative. But this TerraMiner IV had little hope of reward.
At just about a year old, the miner represented a particularly rapid and fateful instance of the obsolescence that awaits every gizmo that alights on the cutting edge. Because of competition from faster, sleeker models already on the network, it could no longer mine enough bitcoins to pay for the electricity it burned. CoinTerra, the TerraMiner IV's maker, filed for bankruptcy in early 2015. Like a used-up gold mine, the machine lent even the Bitcoin Center's busiest evenings the sensation of a ghost town.
Bitcoin was supposed to usher in a new global economy—gold for the internet age—and mining it was supposed to be an act of democracy. On February 11, 2009, Bitcoin's pseudonymous creator, Satoshi Nakamoto, announced his invention in an online forum by explaining, "The root problem with conventional currency is all the trust that's required to make it work." This was just as the financial giants were breaching the world's trust. At the time, only a month after Bitcoin's initial "genesis block" went online, users could mine with an ordinary computer, though doing so was technically difficult and barely lucrative. But the citizen-miners could also choose which version of the software to run, a kind of voting power over the future of the network.
This was unquestionably a breakthrough. For the first time, the technology underlying Bitcoin made possible a secure, decentralized, open-source financial network. Users wouldn't have to trust any bank or government, just the software. Boosters announced that financial freedom would soon be at the fingertips of the previously under-banked, and people anywhere in the world could send money over the internet with negligible overhead. Nakamoto prophesied in that 2009 forum post, "It takes advantage of the nature of information being easy to spread but hard to stifle."
In essence, Bitcoin is a list, held in common among its users—a list of transactions, a record of which account holds what. The list is called a blockchain. The list's value lies in its security and reliability. Enthusiasts like to emphasize the impressive math involved in keeping the system secure, but what holds the whole thing together just as much is game theory—the assumption that users are rational actors and won't blow up their own virtual wealth. As much as Bitcoin is a feat of cryptography, it's also an experiment in anthropology. And to a remarkable degree it works. Despite countless hacks and crashes and human foibles that have befallen the infrastructure around it, the core hasn't cracked.
The first converts were tech-savvy utopians, whose bitcoins went from being worth just cents to hundreds of dollars; many believed that the old financial industry's days were numbered. Traffickers looking for a discreet way to transact for drugs, weapons, and the like came soon after. An industry of magazines and websites appeared to simultaneously report on and promote the new currency. A Bitcoin-based charity in Florida bought a nine-acre forest as a sanctuary for the homeless; _Wired_ deemed Bitcoin "the great equalizer" for its potential to put financial services in the hands of the poor. It also attracted the interest of such innovation-hungry investors as the Winklevoss twins, Mark Zuckerberg's old nemeses. Bill Gates called it "better than currency." But soon the Bitcoin revolution began to look more and more like the system it was intended to replace—except perhaps more centralized, less egalitarian, and similarly clogged with unseemly interests.
As the value of bitcoins swelled against the dollar over the course of 2013, a mining arms race began. People realized that their computers' graphics chips were better suited to Bitcoin's mining algorithms than standard CPUs, so they built specialized machines overloaded with graphics processors, which increased their chances of reaping a reward. Starting in the first months of that year, ASICs arrived. Before long, the lone miner with a regular computer was a lost cause, unable to compete with the new mining syndicates, or "pools." Multimillion-dollar data centers appeared in places around the world with the most profitable combination of cold weather and cheap electricity—forty-five thousand miners in a Swedish helicopter hangar, for instance, or twenty million watts in the Republic of Georgia. Together, Bitcoin's miners amount to many times more computing power than the combined output of the world's top five hundred supercomputers. Processing and protecting the billions of dollars' worth of bitcoins in circulation requires hundreds of millions of dollars in electricity each year, plus the carbon emissions to match.
The prospects for democracy in the system grew dimmer still. By the middle of 2014, the largest mining pools came within reach of a 50 percent market share—making it possible for them to endanger the whole system by falsifying transactions. What prevented them from actually doing so, apparently, was that it would reduce confidence in the value of the bitcoins they invest so much to mine. They also started preventing changes to the Bitcoin software that would lessen their dominance. In pursuit of trustless money, a distributed network of users had to trust a mysterious oligarchy of capital-intensive miners.
_The value of a bitcoin in US dollars._
A certain style of evangelistic piety prevails in the Bitcoin "space," as participants in the burgeoning industry tend to call it. (From the "wallet" software used to manage accounts to the "coins" in virtual circulation, cryptocurrency jargon relies on the most physical of metaphors.) Optimism is the dominant idiom among enthusiasts, but at times it has seemed to rest less on any genuine belief than on an anxiety not to see their bitcoins further depreciate.
"Some of the New York Bitcoin Center guys are pretty religious," said Tim Swanson, an early analyst who had written two self-published e-books on cryptocurrencies. Before that, while living in China, he built his own graphics-chip miners. But Swanson grew increasingly skeptical that Bitcoin would unsettle the existing finance megaliths. "You have centralization without the benefits of centralization," he told me. He calculated that the cost of bringing Bitcoin services to the developing world would wipe away the savings from the system's low transaction costs. By the time I met the TerraMiner IV, Bitcoin wealth was distributed far more unequally than in the conventional economy. Users were probably more than 90 percent male.
Entrusting money to algorithms, it turns out, was no guarantee of a better result than managing it with institutions and people. Nakamoto's longing for money free from trust simply shifted the location of that trust. The blockchain technology at work in Bitcoin is flexible; it can be rearranged for cooperation rather than competition, for reputation tracking rather than anonymity, for democracy rather than oligarchy. Some early experiments along these lines, among the hundreds of "altcoins," did away with intensive mining altogether. But unlike Bitcoin, they were short on financing and evangelists. A lot of the people I knew who had been around for the early days of cryptocurrency—software hackers who became overnight whizzes in monetary theory—were soon building Bitcoin-like systems for the very banks they thought they would utterly disrupt. Other imperatives took over.
I remember this shift in priorities becoming especially evident one evening at the Bitcoin Center. In a cluttered corner of the room, the notorious hacker-troll Weev, recently released from prison and veering into full-on neo-Nazism, was tinkering on a laptop; "Living off my bitcoins," he told me when I asked what he was up to. Attendees drifted around him eating pizza and sipping rum-and-Cokes. As the evening began winding down, a middle-aged woman with a pearl necklace visible beneath her trench coat approached a shaggy-haired staffer standing next to the miners. She was from Harlem; the only name she cared to give was "Ms. E."
"What is this Bitcoin?" she asked the staffer, who embarked on a long explanation of Bitcoin as a "layer" on the internet for finance, a valuable contribution to the work taking place in the towers around them. He was far from done when Ms. E started to look like she was ready to leave.
"I thought I would come in here and find someone who was gonna replace these banks," she said, gesturing out the window to Broad Street. "We need to distribute the wealth, you know what I'm saying? I thought this was something for the small people."
I first heard about Bitcoin in 2012, but I wasn't interested. I don't tend to get excited about money for its own sake—to a fault. (A dollar of the stuff then would be worth hundreds of dollars now.) I didn't start paying attention until a visit to San Francisco in January 2014, when Joel Dietz and Anthony D'Onofrio cornered me at a downtown pop-up cafe run by war veterans and explained to me that this new kind of money was about a lot more than money.
Dietz was an old friend; I'd seen his brooding genius pass through phases as a theologian, a linguist, a coder, and a tea aficionado. D'Onofrio was new to me; he turned out to be a serial visionary, too, who at the time was in the cannabis-edibles business. His partner, pregnant, sat quietly nearby while we talked.
Just a few weeks earlier, a nineteen-year-old Russian Canadian named Vitalik Buterin had published a proposal for what he called Ethereum. What Bitcoin was for money, Ethereum would be for everything else. It turns out that the basic idea of an ironclad list with no single caretaker—the blockchain—has an enormous range of potential applications. Rather than listing transactions, for instance, it can list contracts and enforce them computationally, resulting in an autonomous legal system without courts or cops. A blockchain of websites could be the basis of a more secure kind of internet.
"It's an operating system for society," D'Onofrio said.
Before long, coders were sketching out prototypes for what they called decentralized autonomous organizations, or DAOs—entities made up of Ethereum "smart contracts." One might code a constitution for a nongeographic country that people can choose to join, pay taxes to, receive benefits from, and cast votes in—and whose rules they would then have to obey. One could design a transnational microlending program or a new kind of credit score. In an online video, Dietz and a friend demonstrated how to code a simple marriage contract. The world's next social contracts, the successors to the Declaration of the Rights of Man and the US Constitution, could be written on Ethereum's protocol. The cooperatives of the future, too, might be built with smart contracts, inscribing co-ownership and co-governance for vast networks with a freer hand than local laws allow. Or, as Buterin sometimes joked at the time, it could be used to create Skynet, the armed robot network in the _Terminator_ movies determined to exterminate its human creators. Ethereum could go either way.
During those early months of trying to follow the hackers rallying around Buterin's idea, including run-ins with the savant himself, the word _blockchain_ would repeat in my head at night, like a divine incantation. The universal ledger, that arbiter of value—the sensation of seeing into a future of all-seeing lists, revealing and yet hiding. Everything is a transaction, in every corner of our lives.
In a Reddit discussion about an early article I wrote on Ethereum, Buterin explained:
Lately I have become much more comfortable with the idea of computer-controlled systems for one simple reason: our world is already computer controlled. The computer in question is the universe with its laws of physics and humans provide the inputs to this great multisig by manipulating their body parts.
In midsummer 2014, back in the Bay Area, I rode a friend's rickety bike to Hacker Dojo, a member-run hackerspace not far from the Googleplex in Mountain View. An office-park storefront opens into an expanding series of rooms with clusters of people, mostly white and Asian young men, staring into their individual screens, but at least breathing the same air. At the door, you're met not by a receptionist, but by a computer asking for your email address. When you give it, you're told the rules. Among their distinctions: everywhere and everything is "100 Percent Communal," but it is "Not a Public Facility." Naps are okay, but sleeping is not.
Hacker Dojo was host to an event that night in which one could find some features of the new order being worked out, one of the first gatherings of the area's Ethereum Meetup group. Steve Randy Waldman, a coder and economics blogger, spoke to a room of about twenty enthusiasts. He talked about the cooperative and fraternal organizations that, a century ago, provided insurance and other benefits to millions of Americans. Many of these mutual-support networks have fallen away in an age of mobility and frayed communities, but he believed blockchains could bring them back.
Waldman said he hoped to see DAOs that are "designed as strategic actors." By collecting dues and holding members responsible to contracts, a DAO could be a means of organizing new kinds of labor unions or fostering disciplined consumer activism, which had failed to appear in online social media so far. What if, rather than just indicating on Facebook that you plan to participate in a protest, you joined a group of people contractually bound to do so? Could smart contracts bring back solidarity?
It was a statement of digital possibilities but also, intentionally or not, a testament to what the digital world had lost. Waldman cited such pre-internet curiosities as in-person meetings, distinctive clothing, even religious belief—"a powerful engineering tool, and we should take it seriously." He talked about orders such as the Freemasons and Elks in the past tense, as sources of inspiration for the DAOs to come. But three-fourths of the way through his talk, one of the engineers present—middle-aged, with a thick beard and large glasses—raised his hand and declared himself a real-life Freemason.
"We're still around!" he insisted. He later interrupted the discussions on technical feasibility and implementation with stories of real-life good deeds done through his lodge, offline.
Ethereum went live in 2015. Its underlying currency, ether, soon became second only to bitcoin on the crypto-markets, with a total value in the billions of dollars. Walmart is using Ethereum to manage supply chains, and J. P. Morgan is writing smart contracts to automate transactions. A coalition of US credit unions is building a "CU Ledger" to manage member identities. Some people are trying to craft the perfect co-ops or other sorts of egalitarian DAOs, but they're not making money like the ones concocting blockchain ledgers for big, old banks.
A year into Ethereum's life, the system hit trouble. A glitch in the code enabled a hacker to siphon millions of dollars' worth of ether from a flagship DAO known simply as "the DAO." Thus, a basic dilemma for a world built of code: must the code be honored, glitches and hackers and all, or do the intentions behind the code matter? By and large, the "community" chose the latter—it chose human intention and opted to wipe away the hack. At least for the moment, the system was young and flexible enough for there to be a choice. It was an improvisation but also the harbinger of a whole new kind of governance.
That was only the start. People are building companies with this stuff now, funding themselves with made-up crypto-tokens that they sell to contributors and users, who hope to cash out in a windfall of speculative magic. These initial coin offerings, or ICOs, have re-created a little-regulated free-for-all like the pre–Great Depression stock markets, before government oversight ruined the dangerous fun. They have democratic potential but mostly anarcho-capitalist adoption. Blockchains will become what we use them for, and we will become creatures of those uses.
One of those nights visiting Silicon Valley, I stopped by Joel Dietz's house for the meeting of a group that called itself the Cryptocommons. The house itself had a name, the Love Nest, having become home to a shifting cast of residents who shared Joel's interests in blockchains, art, and "exponential" relationships. Dietz wore a black T-shirt bearing the white circle that represented his current project, Swarm, a prototype for crypto-crowdfunding, still so new as to be of ambiguous legality; it would later be resurrected as a "cooperative ownership platform for real assets." Vitalik Buterin's cousin Anastasia arrived late. The speaker that evening was Eric Smalls, a Stanford undergrad, on leave from school to work on his drone startup. He talked about Leland Stanford's interest in co-ops and Dunbar's Number and the burning of the Library of Alexandria as "a single point of failure." He quoted Angela Davis and proposed abolishing prisons and replacing them with blockchain-based reputation systems. Then autopoesis and systems theory. Everything.
I never did catch the name of the guy there who remarked, "I'm interested in freedom as a product to be built."
When I'm among groups like this, I get an irrepressible impulse to start drafting rules and social systems of my own in code. Code is precise, needing no interpretation except how the computer reads it. No corruptible judges or juries; perfect transparency. Here is a routine in the Python programming language, for instance, for adding a new member to a virtual community:
def addMember(person, votes):
if len(MEMBERS) == votes:
MEMBERS.append(person)
These lines define a function, addMember, that, upon being fed the name of a person and a number of votes, adds that name to the membership list when the number of votes equals the number of names already on the list. Simple, but pure.
Industrial cooperation first arose among those with the gall to tinker with the habitual social algorithms of their time. They found value where others couldn't see it. They were system-makers, but the systems would only work when they accounted for the human beings involved—the selfish urges, the bonds of trust, the capacity to choose. Now that kind of stumbling, iterative tinkering is happening again, remaking society from lines of code.
Being underground is not a condition Enric Duran always takes literally, but one late-January night in 2015, I followed him from one basement to another. At a hackerspace under a tiny library just south of Paris, he met a group of activists from across France and then journeyed with them by bus and Métro to another meeting place, in an old palace on the north end of the city. The main floor looked like an art gallery, with white walls and sensitive acoustics, but the basement below was like a cave, full of costumes and scientific instruments and exposed masonry. There, Duran arranged chairs in a circle for the dozen or so people who had come. As they were settling in and discussing which language they'd speak, a woman from upstairs, attending an event about open licenses for scientific research, peeked in through the doorway. She pointed Duran out to her friend—trying, barely, to contain herself. After the meeting was over, she came right up to him and said, "You're the bank robber!"
Although little known in the United States, Duran's name, or at least his reputation, is easy to come by among the activist and hacktivist sets in Western Europe. I'd been hearing about him for years. I'd been told that if I wanted to see a real, living model of the ideas others were just talking about, I should find him. Other people said that his latest scheme would probably go nowhere. Mutual friends connected us over encrypted email, and I followed him around Paris, day and night, for the better part of a week.
In that basement, Duran held court. The thirty-eight-year-old, nearly two-year fugitive had a space between his two front teeth, grizzly hair, and a matching beard—black except for stray grays mixed in throughout. He wore a white sweatshirt. His presence was discreet and stilted, yet it carried authority in the room. While others made small talk he looked off elsewhere, but his attention became total as soon as the conversation turned to the matter on his mind and the opportunity to collaborate.
He had gathered the group to describe his latest undertaking, FairCoop, which gradually revealed itself to be no less than a whole new kind of global financial system. With it, he said, cooperatives around the world would be able to trade, fund one another's growth, redistribute wealth, and make collective decisions. They would hack currency markets to fund themselves while replacing competitive capitalism with cooperation. He proceeded to reel off the names of its sprawling component parts: FairMarket, FairCredit, Fairtoearth, the Global South Fund, and so on. "We will be able to make exchanges with no government controls," he promised in broken English. To get the project going, he had hijacked a Bitcoin-like cryptocurrency called FairCoin.
The French activists indulged him with questions based on whatever hazy grasp of it they could manage—some political, some technical. How does FairCoin relate to FairCredit? What can you buy in the FairMarket? How many faircoins go into each fund, and what are they for? Most of these came from the men, all more or less young, who stroked their chins as they listened. Most of the women left before it was over. Duran's voice was never other than monotone, but his responses nonetheless sang a kind of rhapsody. The answers to a lot of the various what-if questions were some variation of "We can decide."
The only reason the group would even consider this bewildering set of possibilities was that Duran was, in fact, the bank robber. He rejects that term for himself, but he doesn't deny that he expropriated several hundred thousand euros from Spanish banks during the lead-up to the 2008 financial crisis. He then used the momentum from his heist to organize the Catalan Integral Cooperative—or CIC, pronounced "seek"—a network of cooperatives functioning throughout the separatist region of Catalonia, in northeast Spain, which the activists in Paris were attempting to replicate across France. Even if it meant years of living underground, in hiding from the law, his undertakings tended to work. Perhaps even this one.
_Enric Duran at work in Paris._
Long before messing with banks, Enric Duran connected people. As a teenager he was a professional table-tennis player and helped restructure the Catalan competition circuit. He turned his attention to larger injustices in his early twenties, when he read Erich Fromm's diagnosis of materialist society and Henry David Thoreau's call to disobedience. This was the late 1990s, high times for what is alternately called the global-justice or anti-globalization movement. The Zapatistas had set up autonomous zones in southern Mexico, and just weeks before Y2K, activists with limbs locked together and faces in masks shut down the World Trade Organization meeting in Seattle. According to Northeastern University anthropologist Jeffrey Juris, in Barcelona "Enric was at the center of organizing everything." People called him _el hombre conectado_.
Duran helped organize the Catalan contingent for protests at the 2000 World Bank and International Monetary Fund meetings in Prague; a cop there whacked him on the head in the streets. He called for ending reliance on oil and for canceling the debts of poor countries. He was then living on a small allowance from his father, a pharmacist, until using the remainder of it to help set up a cooperative infoshop in Barcelona called Infospai in 2003. He'd hoped to support himself with Infospai, but it was soon plagued with money problems, like the projects of so many activist groups around him. They needed streams of revenue that capitalism was unlikely to provide.
Duran had been studying the nature of money, which he came to see as an instrument of global debt servitude on behalf of financial elites, carrying the stain of their usurious dealings wherever it went. He became convinced that big banks were the chief causes of injustice in the world. But, he thought, maybe they could be a solution, too.
An entrepreneur friend of his first suggested the idea of borrowing money from banks and not giving it back. At first they talked about organizing a mass action, involving many borrowers, or else just making a fictional film about it. But after the friend died in a car accident, Duran decided to act by himself. In the fall of 2005, he began setting up companies on paper and applying for loans. Soon he had a mortgage from Caixa Terrassa worth €201,000, nearly $310,000 at the time. It was the first of sixty-eight acts of borrowing, from car loans to credit cards, involving thirty-nine banks. The loans, he says, totaled around €492,000—€360,000, not including interest and fees along the way. That was more than $500,000.
For almost three years, Duran proceeded. "My strategy was completely systematic," he wrote in his testimony, _Abolish the Banks_ , "as if my actions were part of an assembly line in a Fordist production system." He'd carry a briefcase to meetings with bankers, though he couldn't bring himself to wear a tie. For a single item—say, a video camera—he'd get the same loan from multiple banks. As he acquired more cash, he funded groups around him that he knew and trusted. He backed the Degrowth March, a mass bicycle ride around Catalonia organized in opposition to the logic of economic growth, and equipped Infospai with a TV studio.
The beginning of the end came in the summer of 2007. Duran says he noticed signs of the mortgage crisis forming in the United States and decided that it was time to prepare for going public. For the next year, he assembled a collective to produce a newspaper detailing the evils of banks and what he had done to trick them. The people who helped organize the Degrowth March provided a ready-made distribution network throughout Catalonia. He selected a date: September 17, 2008.
The timing was pretty amazing. On September 15, Lehman Brothers filed for bankruptcy, marking beyond doubt the arrival of a global chain reaction. That morning Duran flew from Barcelona to Lisbon, Portugal, and then the next day from Lisbon to São Paulo, Brazil, where his friend Lirca was living. On the seventeenth, volunteers across Catalonia handed out two hundred thousand copies of Duran's newspaper, _Crisis_. Until then, most of them had no idea what news they'd be spreading. The international media picked up the story, and Duran became known as the Robin Hood of the banks.
He came to refer to this as his "public action." All along he'd planned it that way—a spectacle, but one that would create networks for other projects. "This is not the story of one action," he said. "It is a process of building an alternative economic system."
In Brazil, Duran set up a website for supporters to discuss the next move. At first, the plan was to mount a mass debt strike. People around the world started organizing to renege on their loans, but the scale of participation necessary to hurt the banks seemed overwhelming, and the plan was scuttled. In the last months of 2008, Duran, Lirca, and their friends pivoted toward another proposal—the Integral Cooperative and, eventually, the Integral Revolution.
Like the bank action, the idea was both political and practical. Infospai, despite its money troubles, taught him that there were certain benefits to organizing as a cooperative. The Spanish government normally exacted a hefty self-employment tax for independent workers—on the order of about $315 per month, plus a percentage of income—but if one could claim one's work as taking place within a cooperative, the tax didn't apply. Amid the crisis, people were losing their jobs, and the tax made it hard for them to pick up gigs on the side to get by—unless they were willing to join together as a cooperative. Duran wasn't planning a traditional cooperative business, owned and operated by its workers or by those who use its services. Instead, he wanted to create a co-op umbrella under which people could live and work on their own terms, in all sorts of ways. The idea was to help people out and radicalize them at the same time. The rich use tax loopholes to their advantage; he realized that cooperators could do the same.
Duran looked around for more parts to connect to his system. He knew about a group of alternative currencies that had started forming in Catalan towns called _ecoxarxes_ , or eco-networks; the first, by coincidence, began the day after Bitcoin went online in 2009. These currencies reflected shared interests and values, but they lacked a unifying structure. Duran proposed to connect them through this new cooperative, and their users became another gateway into what he was hatching.
He and his friends adopted the word _integral_ , which is used for "whole wheat" in Spanish and Catalan, to connote the totality, synthesis, and variety of the project. It emboldened Duran, and he began making promises of his return to Catalonia. He devoted much of the remaining money from his loans to a second newspaper, _We Can!_ Whereas _Crisis_ had focused on the problems of the banking system, _We Can!_ would be about solutions. The front page declared, "We can live without capitalism. We can be the change that we want!" It outlined the vision Duran and his friends had been developing for the Integral Cooperative. On March 17, 2009, exactly six months after _Crisis_ , 350,000 copies of _We Can!_ appeared throughout Spain. The same day, Duran surfaced on the campus of the University of Barcelona, and he was promptly arrested. Several banks had filed complaints against him. The Spanish prosecutor called for an eight-year prison sentence.
Duran was thrown into jail, but he went free two months later after a donor posted his bail. Thus began almost four years of freedom and organizing with his friends. They made sure to set up the cooperative legal structure at the outset, so that the tax benefits could draw people into the system. Then the priority was to arrange for necessities: food from farmers, housing in squats and communes, health care by natural and affordable means. By early 2010, the Catalan Integral Cooperative was real, with commissions and monthly assemblies. The following year, when protesters occupied city squares across Spain to rail against austerity and corruption, participants entered the co-op's ranks. Replica organizations began to emerge in other regions of Spain and in France, and then Greece. None of the money from Duran's loans actually went to forming the CIC, but it grew with his notoriety, his networks, and his fervid activity.
After months among the Bitcoiners, my time in hiding with Duran came as a relief and a release. A lot of it was due to the fact that, although he shared their complaints about the money system and their hope for decentralized ledgers, he had cooperativism. He had that basic concern for accountable ownership and governance, even though what he was building looked little like any cooperative before it. Rather than setting out to turn more and more parts of life into trustless transactions, he wanted more trust. The CIC reminded me of those cutout diagrams of the Earth's geology. The hard, crusty outer layers offered newcomers specific services they could join and benefit from, requiring little knowledge of what was happening beneath for their use. The newcomers could stay there. But that could also be a step closer to the center, where members found more services and more trust—a molten, liquid, shared commons where formal transactions are less necessary. It's far from the rock-solid, transactional paradise at the heart of planet Bitcoin. Start with usefulness, lead toward community.
One rainy night in Paris, I was in the middle of articulating some long-winded question about "the commons," trying to ascertain where Duran stood in some theoretical debate or other, when he interrupted me. "I don't want to build commons for people who talk about the commons," he said. "I want to build commons for commoners."
That stuck with me. It humbled me, for one thing. And it was also a lesson and warning about cooperativism in general: none of it is worth much of anything unless it is of use.
A few blocks from Antoni Gaudí's ever-unfinished basilica, the Sagrada Família, I found Aurea Social, a three-story former health spa that since 2012 has served as the Barcelona headquarters of the CIC. Past the sliding glass doors and the reception desk was a hallway where products made by members were on display—soaps, children's clothes, wooden toys and bird feeders, a solar-powered reflective cooker. There were brochures for Espai de l'Harmonia, a hostel and wellness center, where one could receive Reiki treatments or take aikido lessons. Beyond, there was a small library, a Bitcoin ATM, and offices used by some of the seventy-five people who received stipends for the work they did to keep the CIC running. On certain days, Aurea Social hosted a market with produce fresh from the Catalan Supply Center—the co-op's distribution warehouse in a town an hour or so to the south, which provided markets throughout the region with thousands of pounds of goods each month, most of which came from CIC farmers and producers.
_Weighing out products at the Catalan Supply Center._
Joel Mòrist, a member of the CIC's public-facing Communication Commission, greeted me when I arrived. He loves Jack Kerouac but more resembles Walt Whitman and Slavoj Žižek—almost a dead ringer for the latter, with similar spasms of gesticulation and cleverness. His left eye is lazy, though no less wild. He's a filmmaker. He displayed reverence toward little but Enric, speaking of him in a running joke as an absent god, perhaps soon to return. And he went on to tell me the history of the CIC, starting with the first inklings of civilization—the first bosses, the first priests, the first armies, the first money, and the first debt. He sketched on small scraps of paper an explanation of usury-based money and the need for another way.
Each of the enterprises advertised at Aurea Social operates more or less independently while being, to varying degrees, linked to the CIC. When I visited in 2015, the CIC consisted of 674 different projects spread across Catalonia, with 954 people working on them. The CIC provided these projects with a legal umbrella, as far as taxes and incorporation were concerned. Their members traded with one another in ecos, the unit of alternative currency from among the Catalan eco-networks. They shared health workers, legal experts, software developers, scientists, and babysitters. They financed one another with the CIC's half-million-dollar annual budget, a crowdfunding platform, and an interest-free investment bank called Casx. (In Catalan, _x_ makes a "sh" sound.) To be part of the CIC, projects needed to be managed by consensus and to follow certain basic principles such as transparency and sustainability. Once the assembly admitted a new project, its income could run through the CIC accounting office, where a portion went toward funding the shared infrastructure. Any participant could benefit from the services and help decide how the common pool would be used.
Affiliates might choose to live in an affiliated block of apartments in Barcelona, or at Lung Ta, a farming commune with tepees and yurts and stone circles and horses, where residents organized themselves into "families" according to their alignments with respect to Mayan astrology. Others moved to Calafou, a "postcapitalist ecoindustrial colony" in the ruins of a century-old factory town, which Duran and a few others purchased after he found it for sale on the internet. (Further details about my visit to Calafou cannot appear here because this book isn't published under an open license, a requirement the colony's assembly had for press wishing to cover it.) Not far from there, a group of anarchists operated a bar and screen-printing studio in a building that once belonged to the CNT, the anarcho-syndicalist union that ran collectivized factories and militias during the civil war of the 1930s, orchestrating what was almost assuredly the modern world's largest experiment in functional anarchy. Like the CNT, the CIC was making a new world in the shell of the old—so the utopian mantra goes—and, to a degree that is not at all utopian, creating livelihoods for themselves in a place where livelihoods were not at all easy to come by.
For years Spain had been sunk in a perpetual downturn, with an unemployment rate exceeding 20 percent for the general population and hovering around 50 percent for those under twenty-five. The exasperation gave rise to Podemos, a new populist political party that opposed austerity policies and, when I visited, was poised to displace the establishment. But the less-noticed sides of this uprising were movements like the CIC, working closer to the ground and reshaping the structure of everyday life. These cooperators were done seeking steady, full-time jobs along the lines of Mondragon. More industrial bureaucracy churning out consumer goods en masse was not the point. I asked once if they had taken lessons from those famous cooperatives in a nearby, also-separatist region of Spain; the reply I got was a glance to the effect of "Why would we bother?" They wanted a fuller kind of freedom than that.
The office of the CIC's five-member Economic Commission, on the first floor of Aurea Social, didn't look like the usual accounting office. A flock of paper birds hanging from the ceiling flew toward the whiteboard, which covered one wall and read, "All you need is love." The opposite wall was covered with art made by children. The staff members' computers ran an open-source Linux operating system and the custom software that the IT Commission developed for them, which they used to process the incomes of the CIC's cooperative projects, handle the payment of dues, and disperse the remainder to project members upon request.
If the taxman ever came to CIC members, there was a script: they would say that they're volunteers for a cooperative, and then point him in the direction of the Economic Commission, which could provide the proper documentation. Officially, there was no such thing as the CIC; it operated through a series of legal entities established for various purposes in the organization. Insiders referred to their system, and the tax benefits that went with it, as "fiscal disobedience," or "juridical forms," or simply "the tool."
Accounting took place both in euros and in ecos, which had become the CIC's native currency. Ecos don't require high-tech software like Bitcoin, just a simple mutual-credit ledger. Whereas Bitcoin is supposed to bypass central authorities and flawed human beings, ecos depend on a community of people who trust one another. Anybody with one of the several thousand accounts can log in to the web interface of the Community Exchange System, a package of open-source software first developed in South Africa. There, users can see everyone else's balances and transfer ecos from one account to another. The measure of wealth, too, is upside down. It's not frowned upon to have a low balance or to be a bit in debt; rather, it's troublesome when someone's balance ventures too far from zero in either direction and stays there. Because interest is nonexistent, having lots of ecos sitting around won't do any good. Creditworthiness in the system comes not from accumulation but from use, from achieving a balance between contribution and consumption.
The CIC's answer to the Federal Reserve is the Social Currency Monitoring Commission, whose job it is to contact members not making many transactions and to help them figure out how they can meet more of their needs within the system. If someone wants pants, say, and she can't buy any in ecos nearby, she can try to persuade a tailor to accept them. But the tailor, in turn, will accept ecos only to the extent that he, too, can get something he needs with ecos. This forces people to work together across urban-rural divides, connecting punks with hippies, farmers with hackers, bakers with scientists. It's a process of assembling an economy like a puzzle. The currency is not just a medium of exchange; it's a measure of the CIC's independence from usurious finance.
A word I often heard around the CIC was _autogestió_. People used it with an affection similar to the way Americans talk about "self-sufficiency," but without the screw-everyone-else individualism. They translated it as "self-management," though what they meant was more community than self. This ethic was more cherished in the CIC than any particular legal loophole; the tax benefits merely drew people in. The more they could self-manage how they eat, sleep, learn, and work, the closer the Integral Revolution had come.
About an hour's drive east toward the coast, one of the CIC's punks lived in a tiny medieval town with a death-metal name, Ultramort. Raquel Benedicto wore a black _Clockwork Orange_ hoodie and had dyed-red hair. There were rings all over her ears. Her nose was pierced at the bridge and septum. She said she had to avoid street protests, because when cops attack her she fights back, and she couldn't risk that now that she was a mother.
_Raquel Benedicto and Joel Mòrist on the roof of Aurea Social._
With her brother, who returned after years of food service and surfing in the British Isles, she started the town's only restaurant, Restaurant Terra, at the end of 2014. It was a CIC project through and through: meals could be paid for in ecos, and it regularly played host to regional assemblies. Members of the local forestry cooperative, which used a donkey to help carry away logs, came to her to collect their pay. In the back, Benedicto started a nursery school for local kids, including her son, Roc.
Benedicto met Duran during the 15M movement's occupation in 2011. She was already pissed off, but he showed her something to do with it—"something real," she said. She began working with the CIC in the Welcome Commission, learning the Integral logic by teaching others, and by talking as much as she could with Duran. Soon, she was on the Coordination Commission, the group that orchestrates the assemblies and helps the other commissions collaborate better. But her new focus was running the restaurant. "I'm starting to do what I want, finally," she told me.
Duran and Benedicto were often in touch, but she had to be careful. The police once took her phone, and they'd interrogated her friends about his whereabouts. Now she put her phone in another room when she talked about him and encrypted her email. Benedicto was also one of the people who kept the CIC running in Duran's absence, who ensured that it no longer needed him.
I got to witness the CIC's annual weekend-long assembly, devoted to planning the coming year's budget. Sixty or so people sat in a circle in Aurea Social's large back room, with spreadsheets projected above them. A woman breast-fed in the back, while semi-supervised older children had the run of the rest of the building. Benedicto took notes on her Linux-loaded laptop as debates came and went about how to reorganize the commissions more effectively, about who would get paid and how. That weekend they also decided to end EcoBasic, a cautious hybrid currency backed by euros that the CIC had been using—a decision that brought them one step away from fiat money and closer to pure social currency. In the fatigue and frustration of it all, one could be forgiven for failing to appreciate the miracle that this many people, in an organization this size, were making detailed and consequential decisions by consensus.
_Assembly at Aurea Social._
Over the minutiae, too, hung the looming prospect that whatever local decisions they made were part of a model for something bigger. During an argument about whether Zapatista coffee constituted a basic need, I noticed that a web developer in the assembly was quietly writing an encrypted email to Duran about changes to the FairCoin website, the public face of the CIC's new, global stepchild. Most people there at least knew about it, but only a few were ready at this point to let it distract them from their particular projects.
"Enric thinks about something and everybody starts to tremble," Benedicto told me during a break. "No, no—we've got a lot of stuff to do, and now you want to do that, really?"
In France, I found that Duran was filling his days and nights with as much activity on behalf of Integralism as his underground condition allowed. He was out and about, passing police officers on the street without a flinch, changing where he lived and worked from time to time in order not to be found too easily. He shared his whereabouts on a need-to-know basis. Perhaps the strangest thing about his daily existence was its steadiness, and the lack of apparent anxiety or self-doubt about the scale of his ambition.
"I feel that I have these capacities," he told me plainly.
One overcast day in Paris, following an afternoon meeting with a developer working on the FairMarket website, Duran set off to one of the hackerspaces he frequents, one whose WiFi configuration he knew would let him send email over a VPN, which can obscure one's location. He was sending an update to the more than ten thousand people on his mailing list. After that was done, he went to meet with a French credit-union executive at the office of a think tank. Her skepticism about FairCoop didn't faze him in the least. Although the discussion seemed to go nowhere, his only thought afterward was about how best to put her networks to use. At around midnight, he introduced FairCoop to the heads of OuiShare in the back of their co-working space. In order to continue the conversation later, he showed them how to use a secure chat program.
Following the cryptography lesson, we went back to the Airbnb apartment that we were sharing, and he sat down with his computer. There he worked until 4:30 in the morning—eating the occasional cookie, smiling every now and then at whatever email or forum thread had his attention, and typing back by hunt-and-peck. All day and all night, a second laptop in the room emitted a glow as the FairCoin wallet program ran on it, helping to keep the currency's decentralized network secure. He slept four or five hours, usually. No cigarettes, no coffee, rarely any beer. He's not a cook. He makes one want to care for him like a mother.
Duran was attempting his third great hack. The first was the "public action"—hacking the financial system to benefit activists. The second was the CIC and its "fiscal disobedience"—hacking the legal system to invent a new kind of cooperative. The third was FairCoop—hacking a currency to fund a global financial system. Being on the run from the law made this task no easier.
Duran's trial was slated to begin in February 2013. But by that time, it didn't seem like it would be much of a trial at all. None of the defense's proposed witnesses had been approved to testify; the authorities didn't want the courtroom to become a stage for political theater. A few days before the first proceedings, Duran went underground again. (The English word he uses for his condition is _clandestinity_.) At first he shut himself away in a house in Catalonia, but when that became too restrictive, he left for France, where he'd be farther from the Spanish police and less recognizable in public.
With not much else to do, he began learning all he could about cryptocurrencies. Friends of his had already been building Bitcoin-related software. Calafou had been a center for Bitcoin development; Vitalik Buterin spent time there while developing the ideas behind Ethereum. But Duran noticed the market-adulating speculation that tended to pervade the cryptocurrency scene and wondered whether the technology could be used for better ends. "I was thinking about how to hack something like this to fund the Integral Revolution," he recalled.
Among the hundreds of Bitcoin clones out there, each with its particular tweaks to the code, Duran found FairCoin. A pseudonymous developer had announced it in March 2014 and gave coins to whomever wanted them. Duran liked the name. Part of what supposedly made FairCoin fair was that it didn't rely on Bitcoin's proof-of-work algorithm, which rewards the miners who have warehouses full of machines that do nothing but guzzle electricity and churn out math. Instead, faircoins were distributed with what seemed like a spirit of fairness. But the whole thing looked like a scam; the currency went through a quick boom-and-bust cycle, after which the developer disappeared, apparently quite a bit wealthier.
The total value of faircoins peaked in mid-April that year at more than $1 million. Halfway through the subsequent free fall, on April 21, Duran made an announcement on the FairCoin forum thread and on Reddit: he had begun buying faircoins. "Building the success of FairCoin should be something collective," he wrote. "FairCoin should become the coin of fair-trade." Between April and September, Duran used the stash of bitcoins he'd been surviving on to buy around ten million faircoins—20 percent of the entire supply. For most of that time, the coin was close to worthless, abandoned by its community. He then teamed up with Thomas König, an especially earnest web developer in Austria, who tweaked FairCoin's code, fixing security problems. They began experimenting with ways to replace the competitive mechanisms FairCoin had inherited from Bitcoin with more cooperative ones designed to fit into the FairCoop structure. By the end of September, CIC members started to invest in faircoins, and the value shot up again to fifteen times what it had been while Duran was buying them in the summer.
Just as the CIC was more than its patchwork of local currencies, FairCoop was much more than FairCoin. Duran intended FairCoop to be a financial network, governed by its member cooperatives. They could sell their products in the FairMarket, trade with one another using FairCredit, and finance their growth with FairFunding. They could buy in at GetFairCoin.net and cash out with Fairtoearth.com. It was meant to be for the whole world what the CIC was in Catalonia. He had laid out the beginnings of a structure, in the shape of a tree—councils and commissions, markets and exchanges, each seeded with faircoins. One fund's job was to build software for the ecosystem, and another's was to redistribute wealth to the Global South. Bolstered by a $13,800 grant from the cosmetics maker Lush (thanks to a friend from his global-justice days), Duran was spending every waking hour enlisting everyone he knew to help make FairCoop something useful for postcapitalists everywhere.
The trick to making this hack work was as much a matter of organizing as it was of tech. The more that local cooperatives became part of the network and used its tools, the more faircoins would be worth in cryptocurrency markets, where wide adoption helps make a coin valuable. To build the community, therefore, was simultaneously to finance it. If the price of faircoins reached the price of bitcoins now, for instance, Duran's initial investment would be worth billions.
The plan has since far out-earned his bank loans. At the end of our time together, Duran sent me some faircoin to cover his share of the apartment we stayed in; during the cryptocurrency boom of 2017, with shady ICOs and crypto-millionaires blowing up everywhere, that reimbursement multiplied to one hundred times its original value. New collaborators were flocking to FairCoop to be part of at least one corner of this inflationary universe that was engineering something that wasn't ruthlessly speculative. Organizations around the world were starting to accept faircoin for purchases and donations. By then, the FairCoin team had implemented a new algorithm to help stabilize the system; as opposed to Bitcoin's proof-of-work mechanism, they called it proof-of-cooperation.
This remains a risky game. The value of a cryptocurrency can be gone as quickly as it appears. But Duran didn't see the currency as the kind of salvific software that tech culture trains us to expect, one that will correct human imperfection if we hand ourselves over to its algorithms. He wanted to use it to create trust among people, not to replace trust with a superior technology. "If you are not creating new cultural relations," he told me, "you're not changing anything." Just as CIC members tried to make their cooperative stronger than any one legal structure, he hoped to see FairCoop become strong enough to be able to outgrow FairCoin altogether.
For all the plan's manic complexity, it was also a plain and simple extension of the logic of Duran's previous endeavors: cheat capitalism to fund the movement, take what already exists and recombine it. But even this unlikely track record was no guarantee. In the hackerspace basement-cave in Paris, while attempting to on-board the French Integralists for his new project, Duran added, as if it were no problem at all, "We don't know if this is going to work."
He needed to find partners, to arrange meetings, to carry out the various tasks a new enterprise demands, and doing so in the confines of clandestinity put daily constraints on an undertaking that would be difficult enough on its own. Jail would be worse, of course, but he was tired of hiding. The bank robber was ready to be a banker.
#
# Slow Computing
## _Platforms_
Well-meaning people have, for a good many years now, been forming a "consciousness" about where their food comes from, who produces it, and how. This gets tedious. But it's also sensible, given how important food is in our lives. Perhaps computers deserve similar conscientiousness. They are constant companions; they shape our experience. Many of us entrust to them our private lives, our lives' work, and much of the time we spend carrying those out. Perhaps we owe our computer-lives some extra tedium, too.
Several winters ago, after a decade of MacBooks, I put myself at the mercy of this supposition. I bought a newly obsolete laptop PC. I cleared the hard drive, replacing the obligatory Windows with Ubuntu, a free, open-source operating system managed by a UK-based company (founded by a South African) and a large network of volunteers. It's one of the more user-friendly variants of GNU/Linux, which emerged after 1991, when Linus Torvalds, a student at the University of Helsinki, wrote his own version of Unix, a then-popular operating system that AT&T invented in the 1970s. He released it under the GNU General Public License, which made it legally available for the world to use and modify. Linux now runs many of the internet's servers, most supercomputers, and Google's Android mobile operating system. Despite its scale, the original amateurism of Linux is alive and well; once, when a student was helping me set up my computer for a lecture at his college, he told me that he'd helped design the icons on my desktop.
I couldn't afford for my new consciousness to become a huge time-suck. I had work to do, and collaborators who wouldn't put up with weird .odt and .ogg file-types. I had to install some extra utilities on the command-line to get the touchpad and my printer to work properly. There were moments when I feared that with a single click or an _rm -f_ command I would break everything. But it never happened. Within hours, in fact, Ubuntu was working about as smoothly as Mac OS ever had—which is to say, with occasional hiccups, both unexpected and chronic. For years, the same vague "system program problem detected" error message recurred every time I turned on the computer, until a system update replaced it with another glitch; some programs have an erratic relationship with my printer. The free-and-open software for complex tasks, like vector graphics and video editing, is still catching up with features the commercial versions had years ago. But it's surprising how little all this bothers me.
More than reducing the literal tempo, the slow-food movement has sought values-oriented economies and thicker communities. Similarly, though my computer is for the most part very speedy and able, slow computing means slowing down enough to compute in community. This turns annoyances into pleasures, just as one learns to appreciate unhygienic soil, disorderly farmers' markets, and inconvenient seasons. The software I use now lacks the veneer of flawlessness that Apple products provide; it is quite clearly a work in progress, forever under construction by programmers who notice a need and share their fixes with everyone. But early on, I found that the glitches felt different than they used to. What would have driven me crazy on a MacBook didn't upset me anymore. No longer could I curse some abstract corporation somewhere. With community-made software, there's no one to blame but us. We're not perfect, but we're working on it.
I do most of my writing in Emacs, a program in active development since the mid-1970s that runs on a text-only terminal screen. (Try it: in Mac OS X, open the Terminal app and type "emacs," and then Enter.) Like produce grown the old-fashioned way, Emacs invites one into connection and continuity with the past. It requires knowledge of ancient keystrokes involving ctrl-x and alt-x. There are no fonts or wizards. But it displays multiple files side by side and plays Tetris. To get the formatting I need, I write in Markdown, a simple set of human-readable tricks. *This* gives me italics, for instance, and I can use this to indicate a link. With a few lines of code borrowed from the internet, I taught my ever-extendable Emacs to convert its text files to the .docx files that my editors expect. Anthropologist Christopher M. Kelty, in his study of the free-software movement, describes creating these sorts of Emacs scripts as "one of the joys of my avocational life."
My cloud resides in a co-location center in the Chelsea neighborhood of Manhattan, on a server managed by May First/People Link, a "democratic membership organization"—a cooperative, essentially—to which I belong. May First is based in the United States and Mexico; governance is bilingual. When I was first deciding whether to join, I went to visit May First's founders, Jamie McClelland and Alfredo Lopez, at their office in Sunset Park, Brooklyn, where we spent a few hours discussing our technological preferences and life stories. I learned that they pay a premium to keep the servers in the city, rather than in some far-off data center. It's important for them to have physical access in case something goes haywire. They like to keep our data close.
I joined May First about a year after Edward Snowden's leaks, when it became clearer how the National Security Agency had deputized corporate cloud services for blanket surveillance. I'm not sure if I do anything especially worth spying on, but I figured I'd try to opt out. The May First team has a record of resistance to snooping law-enforcement agencies; McClelland more recently told me about the security system they'd built around the servers, which relays its data outside US borders. After that, we chatted about our travel plans for the coming months, in case they'd overlap. Try doing that with the folks who run your Gmail.
Now my calendars, contacts, and backup files all sync with an open-source program called NextCloud, which McClelland maintains on the May First servers. None of that information about me churns through Google anymore. NextCloud is like an adolescent lovechild of Dropbox, Google Drive, Google Calendar, and Google Contacts—plus whatever other apps people create as plug-ins. A hobby of mine is trolling programmers on Twitter to get them to make more.
My new cloud mostly works. For a while the sync client on my laptop was hanging and had to be restarted sometimes; I posted a bug report on the developers' forums, and before long an update put a stop to it. Then syncing contacts began to crash Thunderbird, my open-source email program; eventually I found a thread in another online forum that helped me fix it. One way or another, someone in the vast and geeky community figures out a solution. We always do.
Such faith, however, should not be mistaken for a cure-all. Like sipping fair-trade coffee and tending a community-garden plot, my commitments to Emacs and May First produce limited macroeconomic effect. "Goldman Sachs doesn't care if you're raising chickens," political theorist Jodi Dean once remarked. Google doesn't care if I'm using Emacs. But I care, and I like it. More important, there's an economy at work in this noodling. Economies can spread.
Tech companies expect us to participate in their networks without really knowing how they work. We're transparent about every detail of our lives with them, while they're private about what they do with it. Community-based software operates on a different logic. Because nobody owns it, it's harder to become fabulously wealthy from keeping secrets. Transparency is the default. People make these programs because they need them, not because they think they can manipulate someone to want them. Instead of relying on rich kids in a Googleplex somewhere, slow computing works best when we're employing people like Jamie McClelland to adapt open tools to local needs. He's my farmer; May First is my community-supported agriculture, my CSA.
Still, to those interested in some consciousness-raising about the machines with which we spend so much of our lives, there's a need for more than my acts of piety—there's a need for better business models, models accountable to users more than the whims of capital markets, that reward contributions to the commons more than tricks that make data of public import artificially scarce and the data of our private lives surreptitiously profitable. Business models matter all the more as the internet graduates from being a mere toy, trick, or convenience to a basic substrate of the economy.
The conventional wisdom of twentieth-century industrialism offered little reason to expect that volunteerism and information-sharing would help form the basis of the next economic infrastructure. Yet they have. The products of free, open-source software—that is, an economy of pure sharing and collaborating—serve as the less-visible skeleton beneath the corporate-controlled, user-facing internet. Linux and Unix servers host more than half of all websites. Commercial search engines, including Google, rely on the unpaid contributions of self-governing Wikipedia editors, and e-commerce is possible thanks to the open encryption protocol Secure Sockets Layer. These work precisely because their inner workings are public, for all to see.
The story began with a hack. In order to protect the code-sharing habits of early hacker culture, and to protect them from the proprietary urges of corporations and universities, a geek at MIT named Richard Stallman inaugurated the free-software movement with the GNU General Public License. This and other "copyleft" licenses turned the law against itself; they employed an author's copyright privileges in order to preserve the code as a commons, free for anyone else to use, adapt, and improve. Subsequently, legal scholar Lawrence Lessig translated this same hack to non-software cultural production through the array of Creative Commons licenses. Now, thanks to Creative Commons, a descendant of Stallman's hack is a built-in option when you upload a video on YouTube.
Alongside such legal hacks have been clusters of social ones. Theodore Roszak, best known for coining the term _counterculture_ in the late 1960s, published a book in 1986 on what he called the "cult of information." By the early 1970s, those whom Roszak dubbed "guerrilla hackers" had begun to appear at the intersection of the West Coast's tech industry and radical subculture. They had their own publication, the _People's Computer Company Newsletter_ , and a mostly theoretical network (with only one actual node, in a Berkeley record store) called Community Memory. Their propaganda described the computer as a "radical social artifact" that would usher in a "direct democracy of information"—"actively free ('open') information," of course.
This was the culture out of which arose such icons as Steve Wozniak, inventor of the Apple computer, and the _Whole Earth Catalog_ , which hyped the digital revolution with all that newsprint and mail-order could muster. Like the unMonastery, these guerrilla hackers blended the old with the new, the ancient with the postindustrial. Although their projects often relied on state or corporate subsidies, they envisioned their efforts as apolitical, wrapped in the "safe neutrality" of information, as Roszak put it. With the power of information, they imagined, old-fashioned political and economic power wouldn't be needed anymore. Meanwhile, Wozniak's "homebrew" gadget grew into Steve Jobs's Wall Street behemoth, which now holds more cash reserves than the US Treasury.
Alongside its proprietary tendencies, the Bay Area tech culture still provides leaven for experiments in social organization. Pop-up [freespace] sites have turned unused downtown storefronts into drop-in hackathons—before the founders moved the model to refugee camps in Greece and Africa. In the gentrifying Mission District, there is the famous (and notorious) hackerspace Noisebridge, together with the original location of its feminist rejoinder, Double Union. On the Oakland side of the border with Berkeley, a cavernous nightclub-turned-community-center called the Omni Commons is home to Sudo Room, a hackerspace with an anarchist bent, and Counter Culture Labs, where civilian scientists tinker with donated instruments and synthesize new forms of vegan cheese. And of course there is Burning Man, the Bay Area's annual sojourn into the barren Nevada desert that manages to be both free and expensive, open and exclusive, all at once.
_Sign at a 2014 [freespace] storefront on Market Street in San Francisco._
Hacker experiments turn into systems and workflows, then ways of life, then corporations. Git, for instance, is a program Linus Torvalds designed to manage the deluge of code contributions for Linux from all over the world; now it's the basis of GitHub, a corporate social network and project manager that determines the pecking order of coders. The more than a thousand developers who work on Debian, an important version of Linux, govern themselves through procedures and elected positions outlined in their Debian Constitution. They have created a republic for code, and my computer runs on it.
Inspired by such communities, tech-industry consultants promote new management philosophies with such names as Holacracy, Agile, and Teal. These feats of dynamic, distributed workflow seem to outstrip the democracy of most big, established cooperatives nowadays, which tend to have carbon-copied their hierarchies from industrial-age bureaucracies. Techie capitalism can appear to be out-cooperating the co-ops.
For instance, Holacracy: borrowing a name from Arthur Koestler's concept of the holon—"a whole that is part of a larger whole"—it proposes to replace the top-down hierarchy of the industrial corporation with the free flow of an open-source project. There is some hierarchy in Holacracy—officially capitalized, a registered trademark of the company HolacracyOne—but, rather than the metaphor of a pyramid, the system relies on nested "circles." Rather than a single job description, each worker can hold any number of carefully specified "roles," within which the worker has authority to make relevant decisions, whether the CEO likes them or not. For bosses used to command-and-control, Holacracy means giving up the power to micromanage. Meetings are short and highly regimented. Rather than mouthing off at will, the people formerly called managers have to trust the process and the code-like rules that define it. The system has been implemented partly or fully in various corners of the tech industry—for instance, at Zappos and Medium—though in investor-oriented settings like these, it has a tendency to implode.
Maybe the contradictions become too easily apparent. Although Holacracy grants even the lowliest employees autonomy in their domain, that autonomy must always accord with the rules of the game, with the overriding purpose of the company. The purpose is everything in Holacracy. And, for most sizable tech companies, that purpose is to furnish wealth for investors. Self-determination gets dangled before people but then yanked away as soon as it might really matter.
Despite tech culture's clever hacks of intellectual-property law and organizational charts, it has left the basic accountability of the firm mostly unscathed—in particular, its ownership structure and its profits. Companies have exhibited some cooperative tendencies in their use of employee stock options to lure talent to early startups, and this has meant windfalls for some, but investor control takes over before long. This system benefits mostly a fairly small set of insiders, leaving little for the commoners.
As elements of Stallman's free-software movement went mainstream under the moniker "open source" in the late 1990s, advocates such as Eric Raymond and Tim O'Reilly rebranded code-sharing as friendly to corporate value-capture. Large open-source projects operated under the guidance of foundations controlled and funded by representatives of corporations that benefit from the community-developed code. The effects can be quite congenial. Thanks to Creative Commons, a vast archive of user-generated photos is available for public use through Flickr, which was acquired by Yahoo in 2005; the power of Git wasn't fully apparent until GitHub put it on a proprietary cloud with a friendly interface. But this same pattern of adaptation is what allows Google to redeploy the Linux kernel as Android, the world's most popular mobile operating system and perhaps the most successful corporate surveillance tool ever invented.
Free and open-source software communities have also remained troublingly homogeneous. A 2017 GitHub study found that only 3 percent of open-source contributors identified as female and 16 percent as ethnic minorities where they lived. Theories for why this is the case vary, because open-source cultures often self-identify as meritocratic and open to anyone. Yet in order to contribute, a person must either be paid to do so or have surplus leisure hours—a surplus some are less likely to have than others. Slow computing takes time.
Thus, the marvelous digital commons may actually amplify inequalities in the surrounding society, while funneling the profits to corporations. This doesn't seem to disturb many rank-and-file coders, who participate precisely because they already reap benefits from the corporate system. But if commoners cannot obtain the means of survival through the commons, that commons is actually an enclosure.
By the mid-1980s, Roszak was already speaking of "hopeful democratic spirits like the guerrilla hackers" in the past tense. "Such minimal and marginal uses of the computer," he wrote, "are simply dwarfed into insignificance by its predominant applications, many of which seriously endanger our freedom and survival." Even then he recognized the digitalization of education as a privatization scheme, and the near absence of worker organizing in the tech sector, and the unchecked information-gathering capacities of the National Security Agency. He stressed that the response was not merely a parade of better apps, or nobler ideals, but fairer and stronger forms of association.
"Making the democratic most of the Information Age," Roszak wrote, "is a matter not only of technology but also of the social organization of that technology."
The modes of social organization have been shifting. Industries that once built, distributed, and sold things are giving way to a new breed of business models, which go by the allegedly neutral, blank-slate name _platforms_. These platforms are multi-sided markets that connect people—to rent spare rooms, to share news, to do jobs—reaping fees from our transactions and artificial intelligence from the data of our use. They are finding their way into ever more areas of our lives. In 2016, as many as 24 percent of US adults reported earning income over online platforms. The ever-shuffling list of the most valuable companies in the world now is consistently top-heavy with platforms, from Apple and Google's Alphabet in the United States to Alibaba and Tencent in China. Co-ops, which once specialized in the art of connection, are facing disruption by platforms, too. And as platforms coalesce into the new regime, it matters more than ever how these things are owned and governed.
When Jean-François Millet unveiled his painting _The Gleaners_ in 1857, a critic of the time expressed repulsion at the three women in the foreground for their "gigantic and pretentious ugliness." Each is bent toward the ground to a different degree, each gathering the stray wheat left by the landowner's appointed army of harvesters, who are working under the eyes of a foreman on a horse in the background. The women don't have much. They're in a shadow, compared to the light on the official operation behind them. It's not evident whether they'll find enough of the leftover grain to make a decent loaf of bread.
Before we were farmers, we were gatherers. Gathering became gleaning when agriculture gave rise to landowning, leaving out the non-owners. Gleaning was the original welfare. This principle was a basic feature of the medieval European economy, when a small minority owned the land and most people had to live by what they could glean and gather. It remains the motive force in the underground economies that support billions of people on this planet, those who survive on cash and knock-offs rather than stock markets and brand names. The platform business models taking over the internet are making more of us gleaners again.
We share the stories of our lives, the data of our relationships, and the news that interests us. Maybe this is a practice that we enter willingly. It can even be a joy; we see a real friend's face, we reconnect after years, we spot opportunities that would otherwise go missed. We can find paying work online without the day-to-day drudgery of a job. These platforms have given us so much. They seem to make anything possible. Like the great cathedrals and castles once were, they are our world's cosmic glue. Increasingly, such sharing is requisite for maintaining relationships and obtaining employment. But this means we have less and less choice. Although the interfaces are organized to help us feel in charge and in control, the reality is like that of Millet's women picking at the edges of the field. We see only tiny scraps of the information about ourselves and our "friends" that is available to the lords of the platforms. We think we are getting something for free while we give away our valuable data. We think we are in some sense members of a digital commons while we relinquish our ownership rights. At least Millet's gleaners knew that's what they were.
Ubiquitous platforms like Facebook and Google gather reams of data about users and offer it for sale to advertisers and others. We know this, to an extent. But our data is also the business of the ride-sharing apps, the office productivity apps, and the apps that use us to train the intelligence of other apps, along with data brokers whose names we'll never know but who trade in the stuff of our lives. Users supply a growing surveillance economy based on targeted advertising and pricing, which, intentionally or not, can bleed into discrimination of vulnerable populations. The prospect that one's online activity can affect a credit rating, or find its way into the database of a spy agency, has already dampened the free speech that the internet otherwise might enable. We users might feel like customers, but to these companies' investor-owners, we are both workers and product. ("My consumers are they not my producers?" mused James Joyce, prefiguratively.) Although Facebook, for instance, may insist that users retain ownership of their data, immense and unintelligible service agreements grant the platform such sweeping rights over that data as to render user ownership close to meaningless. Because of this—because of us—such platform companies can be among the most valuable in the world with only tens of thousands of formal employees, rather than the hundreds of thousands that a major car manufacturer commands, or Walmart's millions.
In between the aristocratic employees and the gleaning peasant users, platforms hire legions of online freelancers for piecework tasks. These people are the leading edge of a growing workforce that is permanently part-time, gig-to-gig—part empowered freelancer, part exile from the rights and benefits that once accompanied employment. Their offline lives, too, can start to feel like a kind of piecework. Rochelle LaPlante, once a social worker, began a second career on Amazon's Mechanical Turk platform in 2012, doing tasks to help support her family, such as moderating offensive images and taking academic surveys. With this came new habits of mind. She told me, "You go to the grocery store and see a candy bar, and you think, _Is that worth two surveys?_ " The piecework mentality is spreading, with little legal restraint, from Amazon's newer Flex delivery platform to countless other contenders beckoning an underemployed workforce into ephemeral gigs.
These are the sounds of a social contract shifting. New rules are taking hold, even if it is happening in ways and places that many of us don't see. The implicit rules that can be gotten away with on platforms now could stick around for generations.
The active ingredient that has brought the platform economy to life is venture-capital financing. Most people can be forgiven for not knowing much about it, because it's not for them. It's a trick almost exclusively available to privileged subcultures in a small number of highly networked urban tech hubs, unknown to virtually everyone else who might want to get a business going.
_The availability and lack of venture capital in the United States._
When a startup is still just an idea or a minimal prototype, venture capitalists can inject large sums of money for a chunk of ownership. The VCs do that for a lot of startups, most of which don't pan out. But for those that do, the VCs expect profits to make up for not only that investment but also the ones that fail. Such payouts don't come from sustainable, linear growth. They come from the "unicorns"—companies that can swallow entire industries. As markets, not just products, platforms are well suited to this. Their game is often winner-takes-all. And as they win, VCs steer their platforms toward a hallowed "exit" event—either an acquisition by a bigger company or an initial public offering on public markets. In the exit, we the users are part of what is being sold.
I've started to hear a story on repeat from apparently successful founders of tech companies: Their startup had a great idea, and users thought it was great, too, so it became worth something. Investors offered fast money in exchange for stock. The founders liked a lot of the investors as people and valued their advice. Some became real-life friends. But before long, the founders discovered that their companies were no longer built around that original idea, or even around the users it could serve. The whole point had become to extract gigantic returns for shareholders—and to disguise that fact from users. The great idea, together with the users it attracted, became a commodity.
Young people with clever ideas, but not a lot of business experience, get drawn in. Their mentors and accelerators groom them to be what investors want to see. For some, it works. But most good ideas are not that rare, monopoly-scale unicorn that disrupts the world and delivers the huge returns investors need to keep lavishing the next new startups with easy money. It's not enough for a platform to be merely useful or profitable; investment funds need commodities, not communities.
Consider Paul Allen—not the billionaire who co-founded Microsoft, but the one who brought the world Ancestry.com, the genealogy platform. Allen and his co-founder started with CD-ROMs in 1990 and then started making websites later that decade. They owned nearly the whole company and were soon turning a profit. They raised millions of dollars from investors, moved the headquarters from Utah to San Francisco, and by Y2K, they were edging toward being one of the top ten web properties in the world.
Then there was an aborted public offering and a sequence of deals—deals that Allen now admits he didn't fully understand. The slice of shares he owned grew smaller, and he finally left the company and its board in 2002, watching as Ancestry endured the vicissitudes of various private-equity buyers and sellers. He's still proud of what the platform he helped build offers its users, but he has grown philosophical as he watches the current investor-owners squeeze the company for whatever they can get—even eliminating troves of users' family memories in the process.
"If you ask me what modern invention has led to the most inequality in modern civilization," Allen told me, "the answer I'd give is the modern corporation."
The seven cooperative principles actually overlap in places with the social contracts of the online economy. "Voluntary and open membership" is a default practice among platforms, which typically enable anyone (with access to requisite technology) to create an account; "autonomy and independence" are values that platform owners assert when skirting local regulations, even while proclaiming a well-meaning "concern for community." There is much "cooperation" among platform companies, such as through API protocols and standards-setting organizations such as the World Wide Web Consortium. Practices of "education, training, and information" happen around platforms, too—whether in online forums and in-person meetups—resembling the kind of mutual education that cooperatives might encourage among members.
The resonance, however, only goes so far. Cooperative principles two and three—democratic governance and ownership, crucially—are absent from the dominant platforms. Online user-experience design seeks to divert users' attention from matters of governance and ownership, such as by rendering opaque how apparently free services squeeze out revenue. Consultation with users on changes to features or policies is superficial, when it happens at all.
In place of meaningful self-governance, the internet has hackers. They're the Jedi knights, the mysterious rogues who supposedly keep the system both honest and a little dangerous—a check on the powerful, a symbol that ordinary people can still have control. To hack is to manipulate a system as an outsider, to be unconfined by law or decorum, to find whatever back doors might lead the way to a break-in or a fix. Some hackers end up in jail for years, while others get big paychecks from companies and governments. This fringe identity has become an aspired-to corporate norm. The address of Facebook's headquarters is 1 Hacker Way.
I wonder if my generation, the first generation of "digital natives," is a generation of hackers. Many of us have never had the feeling that our supposed democracies are listening to us; we glean sporadic work from organizations that gobble up the value we produce for those at the top. We have to hack to get by. Maybe we can at least hack better than whoever is in charge—though they have hackers of their own now. We become so used to hacking into the back doors that we forget there could be any other way.
Who wants to hack forever? What would it mean to open up the front door—to an online economy where _democracy_ actually means democracy and technology does its part to help, where we can spend less time hacking and hustling and more time getting better at being human? Tech won't do it for us, because it can't, because the forms that it takes depend on how we organize ourselves.
By her early twenties, Brianna Wettlaufer was an executive at iStock, a fast-growing platform for stock photos and multimedia. But at meeting after meeting, Wettlaufer began to feel conflicted. She was caught in the middle. The imperatives coming from the company's investor-owners compelled managers like her to keep cutting what they paid the independent artists whom the company claimed to represent. She's a photographer herself; this mattered to her. The same restless frustration with lousy systems that powered Wettlaufer's climb up the corporate ladder finally compelled her to leave iStock and, with others, start her own company. They were able to pool a bit over $1 million, thanks to a windfall from iStock's sale to Getty Images, and they lent it to the project. Wettlaufer moved from Los Angeles back home to Victoria, Canada. Stocksy United went online in 2013, incorporated as a cooperative.
The result was a different kind of platform business. Rather than seeking growth at all costs, like at Wettlaufer's old job, Stocksy United managers have to ask the photographers and videographers when they're ready to add new members. Fair pay and excellent work are the top priorities. That's why Stocksy has been able to retain some of the world's best stock artists, in dozens of countries, and attract lucrative clients in a competitive market. Wettlaufer and the other early lenders have long since been paid back; the company doubled its revenue in 2015 to $7.9 million, and hit $10.7 million the following year. Now, as CEO, Wettlaufer has little difficulty championing artistic quality and fair treatment for artists at company meetings: the artists are her bosses.
_Margaret Vincent, senior counsel of Stocksy United, and CEO Brianna Wettlaufer._
Wettlaufer is her own boss, too. Stocksy United, like many of its aspiring peers, is a multi-stakeholder cooperative. The company's bylaws balance the interests of three classes: artists, employees, and advisers like Wettlaufer, who retain unique powers. Once, over lunch, Wettlaufer and her co-worker Nuno Silva allowed me a glimpse at the members' internal website, where they debate company decisions in forums and vote on major decisions. Silva scrolled through an annual report—the long version, the version meant for members' eyes only. It was a work of elegance and care and attention to detail. Wettlaufer's accountability to her members is not only economic, it is aesthetic.
Stocksy United was a pioneer in bringing a cooperative model into the new platform economy. Wettlaufer and her team did it in isolation; cooperation helped solve a problem they had. But they were not alone.
The Spanish collective Las Indias distinguished platforms as one category of cooperative in a 2011 blog post. In 2012, the Italian federation Legacoop promulgated a manifesto for "Cooperative Commons," stressing the need for cooperative business models to manage the growing stores of data that users feed to online platforms. That year, too, a soft-spoken German entrepreneur named Felix Weth founded a fair-trade, online marketplace called Fairmondo, cooperatively owned by its buyers, sellers, and workers alike. By October 2014, Janelle Orsi of the Sustainable Economies Law Center, in Oakland, promulgated a cartoon video online that called for "the next sharing economy"—a sharing of cooperative ownership. Orsi was also helping to design the bylaws for Loconomics Cooperative, a gig platform owned by gig workers. Small web-development shops were finding worker-ownership a congenial means of attracting talent and distinguishing themselves in a crowded industry.
Three people I met in Paris at OuiShareFest that summer were gesturing in the same directions during the months afterward. Venture capitalist Lisa Gansky had been nudging sharing-economy startups to understand and imitate cooperative tradition. Neal Gorenflo of the online newsletter _Shareable_ commissioned me to write an article about a handful of entrepreneurs already trying to share more than just stuff—to share ownership of companies themselves. Media scholar Trebor Scholz was organizing the latest of his conferences on digital labor at The New School in New York City that November. There, the talk among platform workers, labor activists, and scholars mostly dwelled on the dismal standards that had come to prevail for online labor, illustrated through international research studies and the stories of workers. But from time to time, a pointed question would come up among the workers present: What if _we_ owned the platforms? How would _we_ set the rules?
It was one of those moments of simultaneity that happen when the conditions are ripe, when lots of people land on a particular set of ideas at about the same time. The following month, December 2014, I published my article for _Shareable_ , and Scholz posted an essay online whose title posed a choice: "Platform Cooperativism vs. the Sharing Economy." Thus he gave a name to the idea that lots of people around us had been more or less thinking—a many-syllabled name, but it worked, and it stuck. This was platform cooperativism, this was #platformcoop.
Scholz and I teamed up. We started meeting with groups at the front lines of the platform economy, including the National Domestic Workers Alliance, whose cleaning and service workers were seeing their conditions decline with new apps, and another, the Freelancers Union. I called upon the lessons I'd learned from Enric Duran, from the unMonastery, from Kenya. The following November, we put on another conference at The New School. We brought in a cast of investors, CEOs, organizers, critics, and platform workers. Entrepreneurs showcased their actually existing platform co-ops—many encountering each other for the first time. More than one thousand people came to take part. Others began organizing events in Barcelona, Melbourne, Mexico City, London, Brussels, and beyond. The idea was becoming a movement.
Platform cooperativism was an invitation to a broad range of possibilities, to bringing online the art of what business ethicist Marjorie Kelly calls "ownership design." We welcomed developments like when Managed by Q, an investor-backed gig platform for office cleaning, opted to share 5 percent of the company with its workers. But when we called something a platform co-op, outright, we meant _co-op_ , in the same way the International Cooperative Alliance and the global sector means it, seven principles and all— _co-op_ the way Mondragon means it, the way the Rochdale Pioneers meant it. But rather than sharing ownership among neighbors or co-workers, these were sharing it over the internet.
Early on, lots of people came into this effort craving an instant co-op Uber replica—the same world-disrupting unicorn, except a nice, cooperative version. But we had to realize that Uber came out of a particular kind of ecosystem in Silicon Valley, of accelerators and investors and Burning Man camps and tech schools. To do things cooperatively, we'd need to undertake the patient work of building another kind of ecosystem. Scholz began forming a Platform Cooperativism Consortium to wrangle the various organizations involved, while I took to mapping the network in an online directory, the Internet of Ownership. I noticed that the ownership designs appearing among the baby platform co-ops weren't just copying what was out there already. They challenged some of the basic business models of the internet, as well as some long-held habits in the global co-op movement so far.
My slow computing runs into a lot of dead ends. I can control my operating system, the programs on my machines, even the cloud tools I use to manage my personal data. But once I run into public platforms, once I need to connect with others and do things together, it's over. I'm stuck. This is where my personal piety doesn't help. If I want to do slow computing over networks, sensitive to the communities and value chains I'm interacting with, I need platform cooperativism. I need platform co-ops.
There are too few of them. Most that do exist are still getting their start. Except for a few cases here and there, in a few parts of the world, life in the platform co-op stack remains mostly a feat of imagination, a possible future based on projects of the present that may or may not succeed. As some do, it will be easier for more to as well. For now, we're building on each other.
As I write, some of the time at least, I'm listening to music I've never heard of on Resonate. So far, the beta-version player mostly works, and the music keeps being better than I expect. It's a streaming-music co-op, co-owned by its listeners, musicians, developers, and more. Each time I listen to something, a tiny bit of money goes to the musicians who created it. The more I listen, the more I pay, until my ninth stream of a song, when it's mine for good. I wish I had such decent fair-trade options for more of the stuff I might want to buy. I wish more of the networks I spend hours on each day were designed so well to serve the people they connect.
There may be networked cooperators around you already. The car-sharing nonprofit in my town, for instance, benefits from the software that the Canadian cooperative Modo developed to help its members schedule their reservations. Modo was founded back in 1997. And also well before there was any talk of platform co-ops, in 2008, the High Plains Food Cooperative began making grocery deliveries to Colorado's Front Range from farms as far away as Kansas, coordinating its long-distance orders online. But these pose little threat to the giants.
I can keep my calendars, contacts, and email with May First, but a lot of a day's work for me still involves feeding data into Facebook Groups, Google Docs, and Slack channels, all for the sake of collaborating. There needs to be another way. This is a kind of holy grail for today's guerrilla hackers—an antidote to the surveillance addiction that plagues so much of our online lives. Tim Berners-Lee, who invented the World Wide Web, is working on this problem with researchers at MIT, as are countless blockchain startups. But cooperatives could be especially well suited to offering data a trustworthy home, one free from acquisitive investor-owners—a collaborative cloud that is truly ours.
In 2013, a collective of artists developed the prototype website commodify.us, inviting people to download their data from Facebook, re-upload it to their site, and allow it to be sold, on the users' own terms, through third-party data markets. (From the FAQ: " _Is this for real?_ Yes.") That's something like the idea behind TheGoodData, a London-based co-op that obtains members' data through a browser plug-in, then sells it off in transparent ways and reinvests the proceeds in microloan programs abroad. Farmers are doing something similar. The vast reams of data that modern farm machines churn out are of growing interest to investor-backed companies. The Growers Agricultural Data Cooperative builds on the long cooperative legacy of US farmers, using a platform called AgXchange to protect their data, process it, and return it to them in forms that can help them do their jobs better. And then there's MIDATA, a project of Swiss scientists. It offers member-owners a safe place to store their personal, valuable medical data, enabling them to choose who can have access to what information. The co-op covers its costs by allowing members' data—with members' permission—to be used for medical-research studies, though it doesn't allow members to earn income directly, for fear of creating perverse incentives. Opting out of a surveillance economy need not require commodifying ourselves.
At a meeting on an old aircraft carrier floating in the San Francisco Bay, I learned that a group of community colleges was planning to introduce their students to gig work on platforms as an employment opportunity. This was troubling not only because many online labor brokerages ignore such protections as minimum wage, sick days, and basic insurance; it struck me as a poor pedagogical choice. On platforms, workers see only the user-facing side, and they don't really learn, as in a good internship, how the business works. In the end, mercifully, none of the corporate platforms would adopt the federal Americans with Disabilities Act standards that the colleges required. But we found them a platform that would: Loconomics.
Loconomics Cooperative is the creation, principally, of Joshua Danielson, a San Francisco entrepreneur with an MBA and some coding chops. Its member-owners are independent professionals—personal trainers, dog walkers, housekeepers, and the like—whose clients can schedule and pay for appointments through a website or mobile app. The members help determine how the platform works, the standards it sets, and what it does with surpluses. Without conventional financing, it was having trouble reaching critical mass. An influx of community-college students has begun to change that.
Higher education is becoming a fruitful breeding ground for platform co-ops, just as it helped build older co-ops like the Online Computer Library Center, or OCLC, which grew out of Ohio universities in the 1960s. Researchers at Stanford have been building Daemo, a platform for worker-governed crowdsourcing, and a group of my students at the University of Colorado designed a student-run gig co-op. Through cooperation, universities can do business, education, and public service all at once.
Platform co-ops have found other patrons as well. The labor union SEIU-United Healthcare Workers West attempted to develop a platform for home-care nurses, and in New York the Robin Hood Foundation supported Up & Go, a platform for home-cleaning worker cooperatives, built by a tech co-op in collaboration with the home cleaners who use it. The Cooperative Management Group, a development consultancy, helped organize the Golf Ball Divers Alliance, a co-op of independent divers who recover balls from golf-course lakes and resell them online.
And more. LibreTaxi and Arcade City are trying to replace closed apps like Uber and Lyft with open protocols that would be well-suited for driver co-ops. Fairbnb, with founders spread across Europe, plans to challenge Airbnb by offering benefits to local organizations. Savvy Cooperative is a platform co-owned by patients who earn income by providing insights to researchers and companies on their own terms. Word Jammers is a cooperative of copywriters who grew frustrated with the existing crowdsourcing platforms they were using and decided to strike out on their own. The founders of both Savvy and Word Jammers live with chronic conditions, and their concern for the standards of platform work stem from experiences of being differently abled. They know, better than most, that the dominant online economy wasn't designed with them in mind.
Some platform users are already serving as trainers for their robot replacements. Uber drivers feed their data to the future self-driving cars, and Google's algorithms learn every time a website asks us to identify the street signs in a reCAPTCHA quiz. Artificial intelligence should be a wonderful thing, but so far the bulk of it is being owned and controlled by a few big-data giants. That's why a group of researchers in the United States and India has proposed "cooperative models for training artificial intelligence"—enabling trainers to receive benefits through shared ownership. Yet these are still only models, and they're competing against up-and-running juggernauts. For now, platform cooperativism can claim little more than a set of modest experiments in slow computing. They hold prospects, but not much strength. They're not challenging the internet monopolies or their owners yet, and they won't without the means available to let them thrive.
What would it take so that a can-do group of pioneers—people with a need to meet or an idea to share with the world—might conclude that the best, easiest way to build their business is by practicing democracy?
This is not an abstraction for me. It's a question I return to several times a week in the exchanges I have with entrepreneurs building or contemplating platform co-ops. We're the blind leading the blind. Consider, for instance, the founder of one very promising startup, with extensive personal and professional knowledge of her target market, plus the do-or-die attitude that's nearly prerequisite for bringing something new and excellent into the world. Nothing should be able to stop her, but starting a co-op might.
At first, on the phone, I want to apologize. We're not there yet. It would probably be easier for her company to get going with a big chunk of venture capital, which she could get if she wanted. There have been offers. She's going after a sector massively vulnerable to disruption. But she doesn't want that. She already thinks of her future users like family, like community, and going co-op is the only thing that makes sense to her. It's the only way she thinks the business will be its best self. The offers haven't changed her mind, thank goodness; this is the way equitable pioneers are.
Still, the founder needs financing. What can I say? Platform co-ops can't easily absorb the free-flowing capital in Silicon Valley or Silicon Alley; VCs want ownership and control. Knowing co-op history, though, makes me confident. Financing gets figured out. When farmers formed cooperative processing plants and national brands, they set up cooperative banks to finance bigger, better ones. As urban workers formed cooperative stores and workshops to help them survive the industrial system, they created credit unions and mutual insurance companies. Co-ops have financed skyscrapers and nuclear power plants. Mondragon's Father Arizmendi insisted that co-ops have a responsibility to capitalize: "A cooperativism without the structural ability to attract and assimilate capital at the level of the demands of industrial productivity is a transitory solution, an obsolete formula."
We're starting to figure out how to do this for platform co-ops. Even the VCs are starting to notice the limits of their existing models. The New York firm Union Square Ventures, for instance, has been an unlikely friend of platform cooperativism. USV partner Brad Burnham spoke at the first New School conference; he envisions a new generation of less risky "skinny platforms" that are less centralized and share their benefits more widely. "We can generate a return participating in that," he said in 2015, "and we think that's what we should be doing." Still, he can't imagine investing directly in co-ops.
There need to be other ways. Co-ops were the original crowdfunding. They were how people got together and financed a business to do things nobody else would do for them. Online crowdfunding borrows this idea, but platforms such as Kickstarter and GoFundMe subtract the co-ownership and mutual accountability of their cooperative predecessors. Platform co-ops are trying to bring this back. One of the earliest platform co-ops of all, Snowdrift.coop, is honing a model for helping its co-owners crowdfund free-and-open projects for the commons that nobody will own. Seedbloom, based in Berlin, enables backers of a new project to become its co-owners—a kind of "equity crowdfunding." It ran the initial membership drive for Resonate, which uses blockchain tech as well, and which later raised $1 million in tokens through a cooperative blockchain project called RChain. The total value of RChain's Ethereum-based crowd-sale tokens has reached over $800 million; while proposing to develop a sophisticated, next-generation protocol, founder Greg Meredith modeled RChain's co-op structure on old-fashioned REI.
A healthy financing buffet needs more than crowdfunding. Purpose Ventures is a new venture fund designed to enable companies to remain "steward-owned" and purpose-oriented—rather than forever seeking an exit that turns the company into a commodity. In order to do that, its young founders have created a model much like an old cooperative bank, a network of mutually supporting enterprises. On a local scale, such financing networks are forming through co-ops such as Uptima Business Bootcamp, a group of member-owned accelerators starting in the Bay Area, and Work Hard PGH in Pittsburgh.
We even have robots. Robin Hood Cooperative, incorporated in Finland, is a kind of hedge fund that earns revenue by investing in stock markets on the advice of the Parasite, a piece of software that mimics the behavior of successful investors; in addition to delivering returns to members, a portion of the co-op's profits go toward supporting commons-oriented projects.
A growing part of the platform co-op surge comes from the older, bigger co-ops themselves. National co-op associations, up to the International Cooperative Alliance, have started speaking up about the need to take on the challenge of platforms. But mobilizing the sector's strength won't be easy. Credit unions and mutual insurers have their own venture capital funds, but they're mostly just doing speculative deals, not seeding new co-ops. They're creating websites and mobile apps for what were once offline services, but they're not generating meaningful alternatives in the connective economy of platforms. Rarely do they take advantage of open-source software or the worker-owned software companies that are becoming widespread. They prefer to play catch-up with the overcapitalized competition. Managers contend their conservatism is in their members' interests, and perhaps it is. It's also a consequence of regulation. After Internet Archive founder Brewster Kahle attempted to start an Internet Archive Federal Credit Union in 2011—an ambitious attempt to scale up credit unionism for the internet age—the effort finally foundered on the rocks of the hefty regulations that credit unions now face. But I think most of the problem is a lack of imagination.
This I would like to change. I want to bridge the gap between the existing, hiding commonwealth of co-ops and the glittery tech startups that get all the fanfare now.
What if startups could aim for an exit to co-op—selling the company to its users or employees, rather than to more investors? What would an incubator or accelerator designed just for co-ops look like? The worry that haunts me is that the founders I work with can't afford to wait for the answers.
A verdant platform co-op ecosystem, meanwhile, will need more than financing. It will need forms of education that train owners, not just workers. Some of these might be versions of the unaccredited tech boot camps that promise to produce coders in a matter of weeks, like the Enspiral Dev Academy that I visited in New Zealand. Some might look like the degree-granting institution that Leland Stanford envisioned for the university that became the corporate training-ground for Silicon Valley. But education also happens through culture. Cooperative tech will need festivals more inclusive than Burning Man, journalism less gaga for startup bros than _Wired_ , and a geography that doesn't concentrate the gains into unaffordable places like Mountain View and Palo Alto. A group of women founders has called for a new culture of "zebra" startups, as opposed to the unicorns that VCs covet. Zebras are real, they say, whereas unicorns are imaginary; zebras run in herds and care for each other, but unicorns always seem to be alone.
We're sorting out that culture as we go. In our platform co-op email and social-media groups, we push each other to be more inclusive, more transparent. With the start of each new platform co-op project comes the discussion of which collaboration tools to use. Loomio is a common place to begin, as it's made by a co-op, and it's good for making early decisions in small groups, but the need for more synchronous chatter blows open the debate about whether to use Slack or one of its open-source copycats, such as Mattermost and Rocket.Chat. Should we track our contributions on a spreadsheet, or should we set up our own crypto-token in Ethereum? How many stakeholder classes can we fathom to include, and how do we balance their relative power? Do we incorporate as a co-op now, or run the thing informally through someone's PayPal account for a while? The passion for process among these cooperators, many of whom never meet in person, can turn fatal. I've seen it doom promising projects. But some get far enough to see the process start to work.
Such agonies may soon subside. Tools are beginning to appear that fit platform co-ops' particular needs. Drutopia is a web-hosting co-op for building websites with the open-source Drupal codebase. A company friendly to the movement, Open Collective, lets co-ops get started without the trouble of formal incorporation. It displays members' contributions and shared expenses so openly that the public front end is the same as the administrators' back end. Starting up is getting easier. And platform co-ops need not be breathlessly radical at every turn; even if they mostly work the way other tech companies do, if their ownership and accountability point to participants more than to capital, that's radical in itself.
Platform cooperativism's early advocates have tended to be partisans of the free, open-source software movement. Some platform founders have held to free-software licenses as an article of faith, but others have opted for the user-friendliness of more proprietary platforms for the sake of their user-members. Still others have found options in between. In his 2010 _Telekommunist Manifesto_ , for instance, Dmytri Kleiner outlined a proposal for a Peer Production License, which altered the Creative Commons Attribution-NonCommercial-ShareAlike license by adding a clause that permits commercial use by worker-owned enterprises that distribute surpluses solely to the value-producers.
Say Linux were licensed this way; Google couldn't use it for free anymore, but a worker-owned company developing mobile devices could. Lost is the mainstreaming effect of corporate adoption, but the value conjured by peer-producers would be not so easily grabbed away. Such licenses could help keep the lords' hands out of the commons. Startups wanting to use the code would have an incentive to go co-op. A few projects, such as the interpreters' co-op Guerrilla Translation and CoopCycle, a platform for bike courier co-ops, have adopted this license as a general policy, though it remains largely untested in practice.
Code-sharing, meanwhile, has already begun to take hold as a growth strategy for co-ops. When people in the United Kingdom expressed interest in opening the Fairmondo marketplace for their country, the German company didn't simply expand across borders to achieve scale as an end in itself, like an investor-owned corporation would; instead the Germans and the British are building two separate co-ops that both use and contribute to the same open-source codebase. As more local Fairmondos form, the more collaborators they'll have for improving the software, scaling their product by replication rather than just conglomeration. In such ways, platform cooperativism could add a fairer, more explicit economic layer to open-source culture. It's an antidote to being dependent, even parasitic, on an investor-oriented economy. It's also a way to freshen the old cooperative tradition with the verve of open-source.
There are no fixed rules to this. We're learning. But our slow computing can't go too slowly, because the disruptions keep coming, and the stakes for those being disrupted are too high. We need all the allies we can get.
For years now, well-meaning politicians have found themselves in the position of trying to say no to the onrush of digital disruptions, in various and generally futile ways, as they attempt to retain appropriate say over transportation systems and labor relations, and to keep local wealth under local control. Now policymakers can say yes to platform cooperativism.
New York City council member Maria del Carmen Arroyo had already helped secure funding for worker co-ops when she agreed to take part in the 2015 platform co-op conference. In a statement beforehand, she wrote that platform cooperativism "can put the public in greater control of the internet, which can often feel like an abyss we are powerless over." Another city council member, Brad Lander, showed up at the last minute to share his plans for open data. Municipal and national politicians have come to Scholz and me, among others, in search of policies to consider and evidence they will work. The city of Barcelona has taken steps to enshrine platform cooperativism into its economic strategies. After Austin, Texas, required Uber and Lyft drivers to perform standard safety screenings, the companies pulled their services from the city in May 2015, and the city council aided in the formation of a new co-op taxi company and a nonprofit ride-sharing app; the replacements worked so well that Uber and Lyft paid millions of dollars in lobbying to force their way back before Austin became an example. Meanwhile, UK Labour Party leader Jeremy Corbyn issued a "Digital Democracy Manifesto" that included "platform cooperatives" among its eight planks.
The challenge of such digital democracy goes beyond local tweaks. So must co-ops. When a platform serves the role of organizing and enabling the transactions throughout an entire sector of the economy, it should be regarded as a public service. Just as the monopolies of connective railroads inspired the US antitrust laws of a century ago, a recognition is growing that we need new laws and new will for enforcement to regulate the emerging online utilities. Enabling transitions to more democratic ownership designs may be a way to help these companies better self-regulate, rather than inviting more stifling regulatory regimes.
It's also necessary to look beyond the virtual platforms to their material substrates. This means considering the human conditions surrounding the mineral extraction and assembly of the hardware on which platforms depend. Notably, Britain's Phone Co-op promotes the Fairphone, a Dutch smartphone built with decent working conditions and conflict-free minerals, and the Indonesian co-op KDIM is building its own locally produced smartphone. In the United States, where the large internet-service providers are among the country's most hated companies, cooperative and city-owned ISPs have already shown that there's a faster, cheaper, accountable alternative. Some neighbors built their own internet co-op in the mountains west of me, where the big companies wouldn't invest, and to the east the city of Longmont offers service that blows away my corporate connection speeds. These options are so good that in many states, industry lobbyists have preemptively banned them.
A democratic internet will require more than clever startups and impressive founders. It needs not just platforms but infrastructure. And it needs not just a future but a history.
On November 7, 1918, newspapers across the United States put out extra editions announcing that the Great War was over. Germany had finally backed down. Trading stopped at the New York Stock Exchange; church bells rang. The only trouble: it was four days early.
This feat of unity in falsehood was the doing of the E. W. Scripps Company's United Press wire service, which the offending papers relied on for news they couldn't gather on their own. Along with William Randolph Hearst's International News Service, it was a challenger to the older, more exclusive wire service, Associated Press. The urge to compete lured UP and INS to sensational, even truth-bending habits.
Newspaper-editor-turned-historian Victor Rosewater, writing in 1930, deemed this a systemic problem. He charged the two upstart wire services with preferring salacious headlines to dispassionate reportage, which the Associated Press excelled in providing. "No obstructive neutral policy stood in the way," he observed. And thus the 1918 incident: "Overzeal gave the United Press the unrelished role of sponsoring and disseminating that greatest of false news items, the spurious premature report of World War truce."
The difference between the upstarts and AP was not merely in their age or their relationships with the New York news establishment. They had different ownership structures. Whereas UP and INS were the creations of towering newspaper magnates, AP was a cooperative—jointly owned (to various degrees, depending on the era) by the newspapers it served. And even today, in the freshly polarized, sensationalized media environment the internet has nourished, AP has continued to excel in what it does best: boring, reliable, factual news.
AP's origins lie in unrecorded conspiracies among New York City newspapermen between 1846 and 1848. Their papers were fierce competitors, but they were stuck. If they all used the new telegraph lines separately, there wouldn't be enough lines. So the competitors had no choice but to cooperate—to import news from Europe via undersea cables, to co-sponsor horse-borne dispatches from the Mexican front, to circulate one another's reporting. The New York papers shared ownership and control of the enterprise, and they sold their dispatches to other organizations beyond the docks of the Hudson.
The temptations to hoard this news-gathering resource were immense, and their defeat came only gradually, over the course of a century. Early on, Upton Sinclair called AP "the most powerful and most sinister monopoly in America." After a scandal resulted in its relocation to Chicago in 1897, the Illinois Supreme Court ruled against AP's restrictions on membership as anti-competitive, and in 1900, the company came back to New York, which had more permissive laws for cooperative associations. But it would take a wartime Justice Department investigation, and a 1945 Supreme Court ruling, to turn AP from an exclusive guild into a true, open-membership co-op. (Its British sister, the Press Association, had operated under this stipulation all along.)
Despite its rocky history and plentiful shortcomings, AP has been an irreplaceable fixture of the US media system. More than half of the world's population sees its reports every day, the company says. And it owes its uniqueness and stature in no small part to its cooperative advantages.
AP allows its members to reduce the cost of reportage, giving them access to reports from more than 250 teams around the world. The wide range of political outlooks that its members hold ensure something as close to neutrality as journalism can hope for; it's an overlapping consensus that inclines toward facts. The company's business model depends not on virality and click-bait, unlike most customer-facing publications, but on trustworthiness. It does what many news organizations claim to do but can't quite accomplish—insulating news-gathering from news-selling.
We have new media fixtures now. When I was starting out as a reporter, tweets were my AP. They were how I got the latest news from places where I couldn't afford to travel, raw and apparently immediate. I fell for Twitter first during Cairo's Tahrir Square uprising in 2011, before the likes of Anderson Cooper got there. Like AP, too, it has become the means by which media outlets today speak with each other and share news. Twitter CEO Jack Dorsey has called it the "people's news network"—but it's not. It's a creature of Wall Street, a commodity for the highest bidder.
This became especially clear in the fall of 2016, when headlines announced that Twitter might be up for sale. Prospective buyers as various as Verizon, Google, Salesforce, Microsoft, and Disney circled overhead. By the measure of Wall Street, the company wasn't doing well. The user-base wasn't growing quickly enough. The $14 billion-or-so valuation wasn't enough to satisfy investors' monopolistic expectations, especially not those who'd bought in when the valuation was closer to $40 billion.
Tell that to the users, though. From Black Lives Matter activists to Donald Trump, Twitter has become a vital public square, truly a network of its people (and its many bots). It's also a network of networks; TV news anchors show their Twitter handles next to their names on-screen. The company has even been on-and-off profitable—pretty good by internet standards. So, in an article for the _Guardian_ , I proposed an option that wasn't being talked about: What if Twitter were sold to the users who rely on it? The article conjured the image of the Green Bay Packers, a top football team that has stayed in a smallish city, kept ads in its stadium to a minimum, and maintained moderate ticket prices—thanks to its nonprofit, fan-owned structure, dating to the 1920s. While a Packers game was on in a Northwoods Wisconsin bar, I once asked a woman there why she liked the team; once she got over the idiocy of my question, she talked about her various family members who were co-owners.
Usually when I publish such off-kilter suggestions as the _Guardian_ article, little comes of it. Not so this time. Twitter users responded by fantasizing about what they would do if they were to #BuyTwitter—step up the spam and abuse policies, re-open the API data, charge reasonable fees for use. Albert Wenger, a partner at Union Square Ventures, tweeted, "I would contribute to this idea by @ntnsndr in a heartbeat." (USV was an early Twitter investor.) Hundreds of people joined Loomio and Slack groups to discuss the idea; many had already been involved in platform co-op networks. They shared online petitions that attracted thousands more. Soon #BuyTwitter was being discussed in _Wired_ , _Der Spiegel_ , the _Financial Times_ , _Vanity Fair_ , and dozens of other outlets. Participants' strategies diverged; some wanted to focus on starting co-op competitors for Twitter and others wanted to take on Twitter directly. Both proceeded. An investment club formed to take on the former challenge, and those interested in the latter began looking, among the petition signers, for holders of TWTR stock.
That December, together with willing shareholders, several of us drafted a proposal for the next Twitter annual meeting. It was modest; it merely asked that the company commission "a report on the nature and feasibility of selling the platform to its users via a cooperative or similar structure with broad-based ownership and accountability mechanisms"—a report, that's all. We tried to make the case that the company and its shareholders would be best served by such a transition. We referred to AP. We did so as a way of insisting that this kind of buyout wouldn't be an act of giving up or cutting losses. A people's network can be more fully itself if it's owned like one.
Twitter's lawyers filed an objection, trying to get the proposal barred, alleging vagueness and purposeful misleading. On March 10, 2017, the Securities and Exchange Commission dismissed the claim. When Twitter's official proxy statement came out in advance of the May 22 shareholder meeting, it included our proposal—together with a letter of opposition from the company.
A young Bay Area co-op veteran with a campaign-strategy consultancy, Danny Spitzberg, stepped up to lead the effort, coordinating volunteers to build websites and friendly organizations to persuade shareholders, all along plastering Twitter with chick-in-a-half-shell emojis. He took on the trolls. Lots of us considered the campaign more stunt than serious, but Spitzberg was serious, and his seriousness rubbed off. Major co-op organizations stepped in to vouch for the idea, including the International Cooperative Alliance, the National Cooperative Business Association, and Co-operatives UK. The way this kind of corporate ballot is stacked with proxy votes and institutional investors, winning a full majority hardly seemed feasible; influential shareholders feared that even commissioning a study would spook the markets. We aimed to reach even just 3 percent—itself, not an easy reach—which would be enough to resubmit a proposal in the future.
The day of the shareholder meeting at the Twitter headquarters in San Francisco, Spitzberg was there, along with our main shareholder activist, Jim McRitchie. McRitchie, a straight-talking corporate governance expert, read the proposal through his gray goatee, which inspired a subsequent sheriff meme. Jack Dorsey and other senior executives were there in the room listening. We won nearly 5 percent of the vote.
That day another subgroup of #BuyTwitter, instigated by Vermont cooperator Matthew Cropp, announced the existence of Social.coop. It hosted a server for Mastodon, a new open-source, "fediverse" alternative to Twitter. Social.coop, as the domain suggested, was a cooperative managed by its users. Rather than being controlled by any one company, a federated social network like Mastodon is made up of interconnected nodes; users choose which node to trust with their data, and through the network they can interact with users on other nodes without everyone consigning everything they post to a central hub. Like sending email from gmail.com to someone at yahoo.com, users can communicate with the full network regardless of their host. The technology for doing this has been around for a while. I'd used one example of it, GNU Social, through my May First membership. But these hadn't taken off. Companies looking to profit from surveillance and monopoly don't see enough value in a technology made for privacy and distributed ownership. Social.coop was our small attempt to change that. Social.coop members were soon making decisions on Loomio and managing money on Open Collective. The fledgling platform co-op ecosystem made this small, simple startup easy. Backed by cooperation, the federated technology now had an economy to make it work.
One night in New York City, at the late-2016 platform co-op conference, one of the speakers introduced me to his friend, a man with a warm smile and long, blond hair parted in the middle. He explained this was Blaine Cook, Twitter's first engineer; the reply functionality, and the word "tweet"—that was him. He'd heard about #BuyTwitter, and he loved the idea. He said, actually, that early on he'd written code to make Twitter an open, federated network. But his prototype didn't stick.
"I suspect it was avoided out of a generalized fear of the unknown," Cook told me, "a concern about how it might make the business model even more complex and difficult, at a time when _any_ business model was still imaginary." The company clung to a more familiar strategy in tech, which was what most investors expected: a well-fenced enclosure and the chance of seizing an entire new market.
One fan of the federation idea, at least, was Fred Wilson, another partner at Union Square Ventures—a longtime VC who has since written that, more than people tend to realize, "business model innovation is more disruptive than technological innovation." And in this case he was right. The technology wasn't what kept Twitter from being the open utility it could have been from the start; the trouble was the business model. Federation seemed at odds with the usual habits of investor ownership. Cooperatives, on the other hand, have been federating for ages. It's in their nature. A spree of modest-sized, trustworthy co-op nodes, sharing open-source code, could build another kind of social network. It wouldn't be just a co-op version of the same thing. It could work with forms of connection and value that investor-owned companies won't allow themselves to notice.
There is a hidden internet, a kind of dark web, that lurks among stray tools, habits, and unmet needs that could be marshaled into economies of cooperation. There is no special browser plug-in that allows us to see it, but ingesting the patterns of co-op history can help. Those of us who have come to be involved believe, or at least hope, that a more cooperative internet would be a better one—fairer, more just, more free. We can't know what would happen there, but we would have more of a say in making it. Our internet would be more fully ours to lurk and troll, to contribute and debug, to explore and share.
#
# Free the Land
## _Power_
Candidate Donald Trump made a campaign stop in February 2016 hosted by South Carolina's Broad River Electric Cooperative. After taking the auditorium stage, observing that "it's a lot of people" and joining the audience in a chant of his surname, Trump began by asking, "Do we love electricity, by the way, all you electricity people?" He went on, "How about life without electricity? Not so good, right, not so good." Then he changed the subject.
His remarks suggest that Trump had just been briefed on the US electric co-ops' cherished origin story. It goes something like this: By the onset of the Great Depression, as little as 10 percent of people in the rural United States had electricity at home. The companies that had lit up the cities simply didn't see enough profit in serving far-flung farmers. But gradually some of those farmers started forming electric cooperatives—utility companies owned and governed by their rate-payers—and strung up their own lines. Many bought cheap power from dams on federal land. Their ingenuity inspired a New Deal program, which Franklin Roosevelt initiated in 1935 and Congress funded the following year. The Department of Agriculture began dispensing low-interest-rate loans across the country. The farmers used them to organize co-ops, even as corporate competitors tried to undermine them, building stray "spite lines" through their prospective territories. But the cooperators prevailed. Together with the policy nudge from Washington, they brought electricity to most of the unserved areas within a decade. They switched on the lights.
Cooperators tend not to like counting on politics from on high. They like their co-ops to be really theirs to build and shape. Co-ops are autonomous, the International Cooperative Alliance insists. Governments have tried to control them in various times and places, such as in the Soviet bloc and Peronist Argentina; it rarely does much good. Yet, like any other kind of business, co-ops depend on the laws and benefits that governments do or don't set out. They have to confront the political perks that investor-owned competitors are already getting. To level the field, they have to enter the same untidy business.
The right and capacity to cooperate have come through amassing political power—as have the contradictions that come with holding it. That's certainly the story of rural electric power in the United States.
People who are used to paying their utility bills in cities tend not to know that 75 percent of the US landmass gets its electricity from cooperatives. That adds up to about 42 million member-owners, 11 percent of the total electricity sold, and $164 billion in assets, amounting to a vehicle for wealth creation in 93 percent of persistent-poverty counties in the country. Local co-ops band together in larger co-ops of co-ops—power suppliers that run power plants, shared mining operations, co-op banks, and co-owned tech firms. Population growth and sprawl have brought wealthy suburbs to many of their once-rural territories. It's a scale of cooperative enterprise unheard-of for those who associate _co-op_ with grocery stores or apartment buildings. It's also a neglected democracy—neglected by member-owners of the co-ops, who often don't know that they're anything more than customers, and by a society that forgets how much the combination of government power and cooperative enterprise once enabled it to achieve. We neglect what we might achieve next.
Republican Presidents Eisenhower and Nixon regarded electric cooperatives as creeping communism, whereas Democratic presidents tended to benefit from the sector's support in elections; Lyndon Johnson helped set up the co-op that served his ranch, and Jimmy Carter's father had been on the board of theirs. But the progressive base retreated to urban centers, and Bill Clinton singled out the co-ops for cuts. More recently, between 2010 and 2016, the political giving of the National Rural Electric Cooperative Association, or NRECA, flipped from 50-50 between the parties to 72 percent Republican. Vice President Mike Pence has had long-standing ties with Indiana electric co-ops. And the co-ops, this remnant of rural progressivism, helped deliver the Electoral College and Congress to him and President Trump.
Among those celebrating after the 2016 election was Jim Matheson, a former Democratic congressman from Utah who had come to serve as CEO of the NRECA. "Rural America's voice was heard in this election and it will be a powerful voice moving forward," he was quoted in a press release as having said. A spike in rural, right-leaning voter turnout coincided with his organization's Co-ops Vote campaign, which mobilized member-owners in a subset of the country's 838 local electric cooperatives. What's more, the next president would be the candidate who had promised to scrap his predecessor's Clean Power Plan, which the NRECA under Matheson regarded as too onerous for its membership. Subsequent press releases praised Trump's climate-denialist, regulation-smashing cabinet appointees.
The administration's initial "America First" budget draft proposed slashing a batch of rural programs, however, including the Department of Agriculture's Rural Cooperative Development Grants. When the draft came out in March of 2017, Matheson attempted to reassure his members. "This is only the first step in the budget process," he said in a statement. Days later, Matheson had the opportunity to celebrate an executive order meant to doom the Clean Power Plan.
Electric cooperatives have become conservative institutions, carrying out the business of reliability while balancing their members' interests with formidable inertia. But they're also poised to lead a shift to a more renewable, distributed energy grid. They can harbor long-entrenched establishments, but they're also bastions of bottom-up, local self-governance. They tend to be far less regulated by states than investor-owned utilities, on the rationale that their member-owners do their own regulation. This is a chunk of the US energy system that depends not just on the whims of investors, or on the promises of a president, but on the readiness of the people who use it to organize.
Some local co-ops have been bucking the inertia. One of them is Delta-Montrose Electric Association, on the western end of Colorado. Jim Heneghan, DMEA's renewable energy engineer, drove me around DMEA's territory in the fall of 2016. We checked out a company pickup from DMEA's headquarters, a complex that includes one of the cooperative's two ten-kilowatt solar farms. From there, we drove to the hydroelectric plants by which DMEA draws power from the South Canal, a narrow waterway that winds through dusty hills and sagebrush out from the Gunnison Tunnel, which President William Howard Taft inaugurated in 1909.
_Jim Heneghan at the controls of a DMEA hydro plant._
Heneghan was project manager for the construction of the first two plants. They opened in 2013 and operate mostly without human intervention, but he tends to them when he can. "I like to start the plant manually," he told me in one of the control rooms. His talk was as precise as the shape of his mustache. A small man of terrific posture, he made his way among the towering, whirring machines like a librarian among shelves of rare books.
The first two plants proved the business model. Soon, other developers wanted to build plants along South Canal and sell the power to the local co-op. By 2015, the model was the subject of a federal regulatory dispute.
Like most electric "distribution" co-ops, DMEA is a member-owner of a larger "generation and transmission" co-op, or G&T. The contract DMEA has with its G&T, Tri-State, specifies that Tri-State must provide at least 95 percent of the energy DMEA sells. This has long been a sensible arrangement; distribution co-ops don't have the resources to run big power plants, and a near-monopoly helps the G&T, and thus its forty-three member co-ops, obtain affordable financing from the government, the cooperative banks, and private markets. Federal policy dating to the 1970s required that much of this investment went into coal plants, which account for 71 percent of all G&T power production, compared to 33 percent for the national grid. But DMEA was finding opportunities to generate more of its power locally—from ever-cheaper solar panels and hydro plants to the methane leaking from the area's retired mines. The member-elected board liked these opportunities, for reasons of cost, conservation, and development.
"Part of the culture here in this area is the desire to keep things local," says Virginia Harman, manager of member relations and human resources. DMEA is also one of the co-ops across the country that has begun bringing fiber-borne, affordable, broadband internet to its underserved rural membership—a development that parallels the circumstances that gave rise to electric co-ops in the first place.
When DMEA hired Jasen Bronec as CEO from a Montana co-op in 2014, he brought with him a new strategy; half a smile sneaks into his all-business demeanor when he talks about it. The co-op filed a request with the Federal Energy Regulatory Commission, inquiring about whether a Carter-era law enabled DMEA to exceed the allowance for local power in the Tri-State contract if a more affordable, renewable option were to appear. In June 2015, FERC ruled that DMEA was in fact required to do so. Tri-State objected, but the ruling held.
Heneghan lives on a farm so out of the way that it's off even the DMEA grid. He produces his own power there. "I'm confident that we won't keep the central generation model," he said as we drove on the narrow dirt roads between plants. "There are so many things that point to a structural change in the electrical industry." He compared the change to what cellular did to telephones. He daydreamed about testing one of the new Tesla Powerwall batteries and reveled in the ongoing convergence of moral, environmental, technological, and economic imperatives—if only we give up the self-imposed constraints to embracing them.
Heneghan believes co-ops are uniquely poised to benefit. Their lean, local, customer-centered kind of business has already made them pioneers in providing new members with easy financing for energy-efficiency improvements and renewables. Like city-owned power companies, they're accountable to a more flexible bottom-line than investor profits. In 2016, about one-fourth of the power delivered to Tri-State's members came from renewables, and the G&T announced the closure of two coal stations that were no longer economical. According to the NRECA, the co-op sector's solar capacity more than doubled over the course of 2017. Co-ops without G&T contracts have been especially ambitious in switching to renewables. DMEA's southern neighbor, Kit Carson Electric Cooperative, ended its Tri-State contract altogether and now aims to meet its entire daytime demand with solar by 2022. Hawaii's Kauai Island Utility Cooperative, formed in a 2002 resident buyout of the island's electric monopoly, is on track to reach 50 percent renewable by 2023. It generates so much solar that it encourages consumers to install storage batteries in their homes.
"We are experiencing a phenomenally exciting technological revolution," says Christopher McLean, who oversees electric programs at the Department of Agriculture's Rural Utilities Service, the federal agency that still provides low-interest loans to co-ops—today, a nearly $4 billion, revenue-positive fund. "Used to be the electric program was kind of like the boring program, but now we get all the exciting stuff."
McLean's enthusiasm obscures the fact that electric co-ops lag behind the national average in their use of renewables. The local co-ops are bound to their decades-long G&T contracts, and the G&Ts can't afford to walk away from their past investments in coal anytime soon. They owe it to their members, the co-ops say. On the record and off, executives talk a lot about their commitment to the seven principles that hang on their boardroom walls, and Heneghan was careful to justify every project in terms of a cost-benefit calculus for members. But this democracy is in some respects nominal—a right on paper, though by no means a guarantee in practice. Other forces govern their behavior, too. After the FERC ruling, for instance, Tri-State and fellow G&Ts started encouraging member co-ops to submit waivers, ensuring their boards won't follow in DMEA's footsteps. Economic constraints that date back decades are still constraining the pace of change.
"There are some cracks in the chains," says John Farrell, who directs the program on energy democracy at the Institute for Local Self-Reliance, a careful observer of electric co-ops. If so, it has been a long time coming. By the late 1970s, the author of a study on electric co-ops, _Lines Across the Land_ , described a situation that is precisely the case today: "Rural electric interests have turned their political muscle to undoing environmental laws rather than leading the fight for their compliance." Yet even then it seemed clear that "rural electric cooperatives are in a unique position to pursue a range of localized energy alternatives." Then, as now, the co-ops' future depended on whether members bothered to raise their voices louder than market forces and the old inertia.
As I concluded my visit to DMEA's headquarters, I met a woman on the way out the door who had come to pay her bill. Photos of board members hung on the wall next to us. I asked if she liked being a member of the co-op, and she looked at me like I was speaking the wrong language. I asked the question again but said "customer" instead. She smiled and said she'd been getting power from DMEA for twenty years and loved it—great service, super reliable. She'd grown up in Hawaii with no electricity, so she appreciated being able to turn the lights on when she came home.
In the early years of the federal co-op program, the Rural Electrification Administration (now the Rural Utilities Service) produced booklets to explain co-op principles and practice to future member-owners. The bureaucrats also saw the need to explain electricity itself. Throughout, they included artful prints depicting the uses of electrical power ("There are over 200 of them") and enticements to exploit its full potential ("The more you use electricity the cheaper it gets").
Those were years when the US government backed co-ops not just with loan funds but with propaganda. Films depicted the democratic promise of an interlocking cooperative economy, enjoining citizens to sign up as co-op members; membership would become the next extension of citizenship. In a preface to one of the electric co-op booklets, Secretary of Agriculture Henry A. Wallace wrote, "Do not let anyone tell you that your cooperative will fail. Or that the Government will have to take it over in a short time and will be forced to sell it to the nearest private utility for a song. Such a disaster can happen only if you and your fellow cooperators fall asleep on the job."
_Pages from the 1939 edition of_ A Guide for Members of REA Cooperatives _._
Five times during the fall of 2016, Della Brown-Davis and her twelve-year-old daughter made the five-hour round-trip drive from their home in Tylertown, Mississippi, to Jackson and back. Their purpose was to learn about electric cooperatives. Brown-Davis was a schoolteacher and therapist, as well as a member-owner of Magnolia Electric Power Association, one of the nine co-ops that fell under a new campaign orchestrated by One Voice, a mobilization affiliate of the state's NAACP.
In the sessions One Voice held in Jackson, Brown-Davis and her daughter became acquainted with the lofty cooperative principles shared by co-ops around the world. They learned how to read the tax forms that the electric co-ops' nonprofit status requires they make public. And they saw evidence that fellow African American co-op members across Mississippi were not getting their due—exorbitant bills, all-white boards in black-majority districts, opaque governance procedures that prevent participation. Brown-Davis noticed a picture of white high-school students representing her co-op on a trip to Washington, DC. On the drives home, she and her daughter would discuss what they learned.
"It's disappointing to find that, in this day and age so many things are occurring the way it did back in the fifties and the sixties," Brown-Davis told me.
In 2014, Benita Wells, One Voice's chief financial officer, helped out on a review of co-ops by the state Public Service Commission. It was her first exposure to the distinct mechanics of cooperative accounting, but she knew enough to notice incongruities. Executives were getting inflated salaries, together with board members who had been on the payroll for decades. Co-ops weren't returning millions of dollars in accumulated equity to members, to the point of risking their privileges as nonprofits. "None of the numbers added up," she says. Making her task harder, co-ops have few disclosure requirements, and they frequently resist sharing financials even with members.
One Voice invited down researchers from MIT and Cornell to better understand the problem. They conducted listening tours, scrutinized utility bills across the state's Black Belt, and used what they learned to help develop the Electric Cooperative Leadership Institute—with Brown-Davis and her daughter in the first cohort, along with other co-op ratepayers ready to organize their neighbors. But the first day, many weren't yet aware of their status as co-owners with voting power over their co-ops' boards.
Mississippi is unusually dense with electric cooperatives. Nearly half of residents get their power from one. And although 37 percent of Mississippians are African American, One Voice found at the outset of its effort that they held only 6.6 percent of co-op board seats. Women held only 4 percent. In the largely poor districts the campaign identified, residents might spend upward of 40 percent or more of their incomes on electricity.
Basic co-op education was the first step of a larger plan. According to Derrick Johnson, president of both the state NAACP and One Voice, "Our ultimate goal is to help them understand how to develop a strategy to maximize member participation." Then, he also hoped, "they can begin to think about renewable energy differently."
There does appear to be some correlation between member participation and energy innovation. Roanoke Electric Cooperative in North Carolina, for instance, underwent a black-led member-organizing campaign in the 1960s; that set a process in motion that is still at work today. Its current CEO, Curtis Wynn, is vice president of the NRECA board and the board's sole African American member. Roanoke has meanwhile become the first co-op in the state to adopt financing for members to make energy-efficiency improvements. It also allows members to buy in on a community solar array and is developing a broadband internet program.
"When the make-up of your management staff or your board of directors isn't fully reflecting the make-up of your communities," Wynn told me, "there could easily be a disconnect between what the constituents want and need, and what decisions the board and the management team will make." Without member pressure, for instance, managers may default to simply trying to sell more power, rather than helping members reduce their consumption, their costs, and their carbon footprints.
The successful organizing at Roanoke was more an exception than the rule. During the 1980s and 1990s, the Southern Regional Council mounted the Co-op Democracy and Development Project, a series of campaigns in co-op districts across the South, including some of the same ones that One Voice has been targeting more recently. The campaigns won only a single Louisiana board seat. It was too easy for incumbent boards to adjust the bylaws and election procedures to protect themselves. In some cases, these co-ops were carrying on habits that went back to their origins in the 1930s and 1940s, when white residents could expect to see power lines earlier than their black neighbors and to pay less for them. But One Voice may fare better than its predecessors. Before the first set of trainings was over, Johnson told me, at least two Mississippi co-ops appointed their first African American directors.
The co-op associations tend to remain aloof to the kind of organizing efforts One Voice has undertaken. A spokesman for the state association, Electric Cooperatives of Mississippi, told me he'd never heard of the campaign. His counterpart at NRECA merely alluded to the organization's general support for fair elections. Nor have concerns about racial justice unsettled the Rural Utilities Service, whose lending comes with a requirement of nondiscrimination. "We have a very low level of complaint to the Office of Civil Rights on issues like this," says Christopher McLean. Even so, the concerns motivating co-op members like Della Brown-Davis are limited to neither Mississippi nor African Americans. They're symptoms of more widespread neglect.
Jim Cooper, a Democratic congressman from the Tennessee district that includes Nashville, was raised by a father who helped start an electric co-op where they lived. When Cooper later visited co-ops as a politician, he'd make a point of browsing their tax forms, and he noticed some of the same things that Benita Wells did. "I'd congratulate them for being so wealthy, and they'd look at me like I was crazy," Cooper told me. This led him into an investigation into what he calls "a massive, nationwide cover-up." He published his findings in a scathing 2008 essay for the _Harvard Journal on Legislation_. In particular, he pointed out the billions of dollars in "capital credits" that co-ops collectively hold—surplus revenues technically owned by members, but which often go unclaimed, serving as a pool of interest-free financing. Policies vary, but some co-ops even prevent members or their families from recouping equity. This can go on for generations. "Local co-ops are primarily owned by dead people," Cooper says.
Cooper's article proposed a series of reforms, including mergers to unlock efficiencies and more mandatory disclosures to members and the public. He suggested that unless co-ops take on a new New Deal of economic development and environmental conservation, they should not be entitled to never-ending federal support. His essay entered the congressional record the year it was published, but the co-op lobby fought back hard, and his proposals didn't get any further than that. "When I talk with my colleagues about this, they shut their eyes and close their ears," he says. "The NRECA pretty much gets what it wants."
The see-no-evil stance of the associations has helped inspire a new wave of agitation, of which One Voice is only part. We Own It, for instance, is a network started by young but seasoned cooperators determined to support organizing among co-op members—rather than the executives and directors who steer the associations. They're connecting activist members at electric co-ops around the country, helping them learn from one another about policies to seek and strategies for winning them. In an online forum, they pass around news about co-op corruption alongside tricks for financing solar power and efficiency improvements. "Our goal is to build a social movement," says founder Jake Schlachter.
A movement will take some doing. According to a study by the Institute for Local Self-Reliance, nearly three-fourths of co-ops see voter turnout of less than 10 percent in board elections. When I attended a board-candidate forum for an electric co-op near where I live, there were more candidates and staff present than anyone else. Only one of the four seats on the ballot was contested. (Hundreds of members nevertheless come to the annual meetings, where the final vote is held, which include door prizes, a hearty dinner, live entertainment, and Tri-State's robot mascot.) By way of explanation, a staff member repeated what I've been told by leaders of other big co-ops: low turnout means members are satisfied.
The movement-makers don't accept that. "The most important lesson I've learned over the years is that the cooperative system is really dependent on member involvement," says Mark Hackett, a We Own It participant who was part of a successful organizing effort after a corruption debacle at his co-op in Georgia, Cobb EMC. "If the members are not involved in any significant way, the directors become very insular, and they can basically do with the co-op as they please."
The conditions of managerial capture are not so arbitrary. The best and worst co-op managers alike carry on their books and in their habits the weight of decades-long contracts, of old loan conditions, of billion-dollar coal plants. There have been astonishing cases of self-dealing by boards and staff. But co-ops can still serve as vehicles of participatory economics at vast scale, just as when farmers suspicious of banks and abandoned by capitalists built utilities for themselves—so well that Washington saw fit to give them almost bank-rate loans. The Colorado Rural Electric Association still holds summer camps where kids learn to organize and run a co-op of their own. These co-ops came from a rare bit of development policy designed to actually, directly empower the intended recipients.
Murray Lincoln, who later led the Cooperative League and Nationwide Mutual Insurance Company, was an early architect of the electric co-op system in Ohio. He recalls in his memoir the nature of the enterprise. "Farmers were just itching to have electricity, and to have it from their own cooperative was a dream come true," he wrote. "We rushed into the business half-blind, not knowing what it was going to cost us, but knowing that it was something that ought to be done and something that we ought to be doing for ourselves." That was the spirit these co-ops were born in, and their vitality depends on it somehow recurring.
Congressman Cooper raised another uncomfortable question about the electric co-ops: What if they're not really co-ops? "Part government agency, part agricultural cooperative, and part not-for-profit company," he wrote in the 2008 article, "this curious hybrid was named for the most innocent-sounding of its three components." The first International Cooperative Alliance principle, "voluntary and open membership," doesn't fare well when the co-op has a monopoly over an essential service in its state-designated territory. The electric co-ops like to talk about the "open" part, but "voluntary" is a problem. In a sector dependent on government loans, the principle of autonomy suffers as well.
The US Department of Agriculture uses _cooperative_ as a technical term for determining program eligibility, and it has concocted its own set of cooperative principles in which the matter of voluntarism is conveniently absent:
1. _User-Owner Principle:_ Those who own and finance the cooperative are those who use the cooperative.
2. _User-Control Principle:_ Those who control the cooperative are those who use the cooperative.
3. _User-Benefits Principle:_ The cooperative's sole purpose is to provide and distribute benefits to its users on the basis of their use.
It's not a bad list. But when a set of cooperative principles hangs in the office of an electric co-op, it's typically not the concise formulation of the US Department of Agriculture; it's the lovelier International Cooperative Alliance principles, whose very first word these co-ops seem to systematically violate. Scratch any co-op, really, and there are likely to be vices against the principles. There will be compromises with and for power.
At the time of Roosevelt's Rural Electrification Act, the national Cooperative League's founder and president, James Peter Warbasse, was ambivalent. Once a member of the anarchist-leaning Industrial Workers of the World, Warbasse professed "constructive radicalism," a version of revolution that required no barricades, no general strikes, no dictatorship of the proletariat. But the transformation he envisioned was no less radical.
"In the cooperative movement," Warbasse contended, "the ultimate tendency is toward the creation of a social structure capable of supplanting both profit-making industry and the compulsory political state." Corporations and governments would recede before the co-op tide, in other words, withering away until they finally disappear. Corporate profits wouldn't be able to withstand the onrush of cooperative savings, and government coercion would crumble in the face of cooperative free association. Gone with them would be courts and jails, replaced by co-op arbitration committees. The cooperatives' endemic educational activities would replace state schools. Rather than being citizens of a single government, people would hold membership in some overlapping combination of co-ops; certain functions of a federal government would become the purview of the federations and associations—organizations like the one Warbasse founded.
His belief that co-ops' self-reproducing acid would dissolve the state—along with investor-owned corporations—has not weathered evidence well. The insurance industry that began with cooperative-like mutuals tended to reorganize, by the second half of the twentieth century, under government control in Europe and corporate control in the United States. From Benjamin Franklin's cooperative fire station and library came additional expectations of government; from grocery co-ops came Whole Foods Market. Socialist regimes, from Yugoslavia to Venezuela, have used state-controlled co-ops as a vehicle of economic policy. In a manner only somewhat more subtle, US electric co-ops have held on to their cooperation partly thanks to a privileged relationship with the Department of Agriculture.
This relationship was the result of a deliberate political strategy, combined with institutional inventiveness. And as political deadlocks and private shortsightedness stymie necessary infrastructure, we might turn to this strategy again. We might, as Warbasse hoped, govern through cooperation. In the 1930s, farmers who needed electricity bypassed corporate providers to do it for themselves; today, the health-care impasse might require similar treatment.
When Aleta Kazadi took to the streets of Denver to collect petition signatures throughout the summer of 2015, the most common response she got was, "I'm okay." This normally meaningless idiom seemed more telling than usual under the circumstances. She was, after all, asking people whether they'd like to support a state ballot initiative for universal health care. Maybe they were okay, but what about the more than three hundred thousand Coloradans without medical coverage?
"The concept that we are our brother's keeper obviously never entered their minds," Kazadi told me. "If we don't see our neighbor in need, what kind of society are we living in?" She was okay herself, as a retired teacher with insurance for life. But a decade living in the Democratic Republic of the Congo taught the Illinois native and grandmother something about neighbors in need. She remembered her whole village waking up to the wailing of families who had lost a child to malaria.
Kazadi figured that she could claim at least seven hundred signatures of the 158,831 collected by more than five hundred fellow volunteers, along with paid help, between April and October that year. Bernie Sanders rallies at the beginning and end of the process provided especially sympathetic crowds, as did Pride and Juneteenth. The campaign needed 98,492 signatures to get the issue on the ballot; the secretary of state's office deemed 109,134 valid in the end. Thanks to people like Kazadi, medical coverage for all was a choice before Colorado voters in November 2016. And it would take the form of a cooperative—one with an ambiguous relationship to government.
ColoradoCare would opt the state out of the Affordable Care Act and provide comprehensive coverage for every resident. This would be paid for by a 3.33 percent income tax and a 6.67 percent payroll tax for employers—or up to 10 percent for the self-employed. These were steep hikes, but for most Coloradans it would mean paying less than they previously paid for insurance premiums. (Penalizing contract workers, however, was no way to win friends among the state's many young and entrepreneurial newcomers.) Supporters believed the system would cost a total of $6 billion less than the status quo in a given year.
ColoradoCare's original name was the Colorado Health Care Cooperative, until co-op people complained that membership wouldn't be voluntary, because Coloradans couldn't opt out of the tax. But the quasi-cooperative design was a necessary trick. It was an attempt to bypass a constitutional provision that prevents the state legislature from levying new taxes. The legislature wouldn't be able to touch ColoradoCare's revenues; they would go straight to a fund overseen by trustees whom residents would elect directly. It was a half-socialist, half-libertarian experiment in co-ownership and co-governance on the scale of more than five million people.
_Colorado state senator Irene Aguilar, a physician and the architect of ColoradoCare._
ColoradoCare was the design of state senator Irene Aguilar, a family doctor who entered politics several years earlier to fix a system that she'd watched harm her underinsured patients for decades. She made a few earnest attempts to pass health care reform in the state capitol, but to no avail. Eventually, Aguilar and a core band of allies—disproportionately psychologists, as it happens—decided to go for a ballot initiative, putting tens of thousands of their own dollars into the effort.
Using this same referendum process in 2012, Colorado voters made their state, along with Washington, the first to legalize recreational marijuana. Other states followed. ColoradoCare's backers hoped to set off a similar chain reaction in health care. Bernie Sanders said the state could "lead the nation" if it passed ColoradoCare, and he stumped for the proposal before the final vote.
It would be hard to cast a better antagonist for this undertaking than Jonathan Lockwood—executive director of Advancing Colorado, an outfit formed in 2014 to serve, says Lockwood, "as a voice for free-market believers and advocates." He was a slick dresser and a fast talker, slight in build and vociferous with opinions. A veteran of the Koch brothers' millennial-outreach operation, Generation Opportunity, he also looked young enough that, he told me, people sometimes wouldn't believe that he was his own boss. On the morning of October 23, Lockwood counted among the handful of those who came to witness the delivery of petitions to the back entrance of the Colorado secretary of state's office. He stuck close to a young woman from America Rising PAC—"a new generation of Republican research and rapid response"—who was recording the proceedings with a camcorder.
The petitions arrived, for effect, on a gurney in a rented ambulance. (The driver confessed to me, "I've done crazier things before for enough money.") Aguilar, in her white lab coat, helped guide the gurney toward a service entrance. Afterward, she and several dozen supporters gathered at the Greek Theater, an outdoor colonnade in Denver's political district, for a press conference. Discerning that I was one of the few reporters present, Lockwood introduced himself and suggested that I interview him. I knew him by reputation already; together with the Kochs' Americans for Prosperity, Advancing Colorado was so far one of the few public opponents that had bothered to confront ColoradoCare head on.
Lockwood made several attempts to convince me of ColoradoCare's follies, each based on an inaccurate claim about the contents of the proposal. But there was an especially radical, factual feature of it that he didn't bring up, one which I never saw discussed during the campaign: ColoradoCare would cast a model for politics detached from the budget and decision-making for the rest of the state. Many jurisdictions already have issue-specific elections for school boards and other seats, but this would go further. Beyond medical coverage, ColoradoCare could lead a shift of other ill-managed services from government or corporations to cooperative mechanisms.
The campaigners tried to appeal to the state's go-it-alone political culture. "This is not government health care," Aguilar said from the steps of the Greek Theater. "I've been in government, and we can't get health care done."
ColoradoCare followed in the footsteps of Michael Shadid, an immigrant from what is now Lebanon. Starting in 1929, he formed the first patient-owned cooperative hospital in Elk City, Oklahoma, an arrangement that the doctors of the American Medical Association set out to suppress as a threat to their guild's authority, rendering the model illegal in states across the country. Something similar happened to the more recent CO-OPs, or "consumer operated and oriented plans," that the Affordable Care Act enabled, which soon suffered crippling restrictions and a two-thirds cut in their promised loan budget from Congress while still in their startup phase. ColoradoCare threatened even more constituencies, and they stopped it before it began. Opposed by prominent Democrats and Republicans alike, and with a daunting reference to the tax hike at the start of the ballot text, the proposal won just over 20 percent of the vote.
During the campaign, Aguilar liked to recite the Margaret Mead line about "a small group of thoughtful, committed citizens" changing the world. But not this time. The state missed a chance for universal coverage; the cooperative commonwealth missed a chance to spread again, and to meet an essential need for millions of people with a political coup.
In fits of sense at various times and places, politicians have adopted policies that support the development of cooperative enterprise. They have seen value, for instance, in the capacity of co-ops to keep profits recirculating in their communities—which is to say, their tax base—and to compensate for the failures of markets to meet the needs of vulnerable constituents. These policies have included, for instance:
• _Financing aids_ , such as low-interest loans, loan guarantees, and tax exemptions, enabling co-ops to compete with the low costs of capital for investor-owned firms
• _Development assistance_ , by funding organizations that offer advice and advocacy for the local cooperative economy
• _Mandates_ , requiring sensitive sectors of the economy to operate through cooperative models, or requiring that government purchasing agents give preference to co-ops
• _Enablers_ , including appropriate incorporation statutes and incentives for co-ops to cooperate with each other
Italy has some of the world's most developed co-op laws. The national constitution itself has a provision, Article 45, that enshrines free, cooperative enterprise as a right—much needed in the wake of Benito Mussolini, who regarded independent co-ops as a threat to his regime. He dissolved both the socialist and Catholic federations, attempting to replace them with a federation of his own, but after his demise they promptly reorganized and gained the political might to write their own rules. Cooperators from around the world now come to Italy to study these arrangements.
A law dating to the early 1970s, for instance, lets co-ops hold tax-free "indivisible reserves," making it easier to raise capital from members. The following decade, co-ops gained the ability to own and manage noncooperative subsidiary firms. A 1991 law created a corporate container and tax benefits for social cooperatives, which serve as an extension of the public welfare system. A law passed the following year requires co-ops to contribute 3 percent of their surpluses—profits, in capitalist-speak—to their federations, for the sake of financing new co-ops and the growth of existing ones. The result has been an ever more self-perpetuating sector, a network of cooperating co-ops that aid each other's flourishing.
Until recently, the United States has mostly forgone co-op policymaking and has relied on the remnants of pre–World War II laws. But that is changing, especially among cities looking to spur worker-owned business, led by entrepreneurs who have learned firsthand how fully the economy is organized in favor of investor ownership. The law can be a mighty lever. Policies like these have been borrowed and adapted, forgotten, and then revived. But there is no single formula.
Policies don't stand in isolation from the habits and history that precede them, that inform what they might mean for those carrying them out. Policies are politics. And for those who need equitable policies most, politics means struggle.
On February 21, 2014, forty-nine years to the day after Malcolm X's earthly form fell to assassins' bullets in Harlem, Chokwe Lumumba, the mayor of Jackson, Mississippi, came home to find the power out. The outage affected only his house, not any others on the block. He phoned friends for help, including an electrician, an electrical engineer, and his longtime bodyguard—each in some way associated with his administration. They couldn't figure out the problem at first. They called the power company, and waited, and as they did they talked about the strange notions that had been circulating. At the grand opening of Jackson's first Whole Foods a few weeks earlier, for instance, a white woman said she'd been told at her neighborhood-association meeting that the mayor was dead. He'd been coughing more than he should have, and his blood pressure was running high, but he was very much alive. That day at the grocery store, he made a speech.
Lumumba's friends found it hard not to be on edge. He had come to office in a Southern capital on a platform of black power and human rights. He built a nationwide network of supporters and a local political base after decades as one of the most outspoken lawyers in the black nationalist movement. At the time, Black Lives Matter was still nascent, more a hashtag than an on-the-ground movement. DeRay Mckesson was still working for the Minneapolis Public Schools between sending off tweets. But those paying attention were coming to see Jackson as a model, the capital of a new African American politics and economics, a form of resistance more durable than protest.
Earlier that February, Lumumba gave a video interview to progressive journalist Laura Flanders. Flanders pressed him on his goals on camera, and the mayor was more forthcoming than he'd been since taking office the previous July. He discussed the principle of cooperative economics in Kwanzaa, _ujamaa_ , which guided his plans for upending how the city awarded its lucrative infrastructure contracts; he wanted to redirect that money from outside firms toward creating local worker-owned co-ops. He also spoke about something called the Kush District, starting with eighteen contiguous counties with large black populations, which he and his closest allies wanted to establish as a safe homeland for African American self-determination. Jackson was to be its capital. Implied in this kind of talk was a very tangible transfer of power from the white suburbs to the region's black majority.
Four days after the outage at Lumumba's home, he phoned his thirty-year-old son, Chokwe Antar Lumumba. He felt tightness in his chest. Chokwe Antar, an attorney like his father, was in court, but he rushed over to the house, eased his father into the car, and drove him over Jackson's cracked and cratered roads to St. Dominic Hospital. There were tests, and then they waited. Nurses brought Lumumba into a room for a transfusion around four o'clock that afternoon. They weighed him. After they finished, he leaned back on the bed, cried out about his heart, shook, trembled, and lost consciousness. Less than eight months after he had taken office, Lumumba was dead.
As word of what had happened began to spread through city hall, Kali Akuno made calls. Akuno had been one of the mayor's top deputies. He set in motion the local and national security protocol of the Malcolm X Grassroots Movement, the organization to which he, Lumumba, and many of the others in the administration belonged. He saw clerks rummaging through the mayor's office, and downstairs, the city council was already jockeying to fill the power vacuum. The administration, together with Akuno's job, was already all but over.
That evening, Akuno himself started feeling something strange in his chest. He'd been having heart problems, too, a clotting issue. He checked himself into St. Dominic at about ten o'clock and was taken near where the mayor's body lay. As Akuno waited to be seen for whatever was happening to him, he heard voices down the hall.
"I'm glad he's dead," Akuno remembers hearing. "I don't know what the hell he thought he was doing. He was trying to turn this place into Cuba."
There is a way of doing things in Mississippi, and Lumumba had his own way. There are lines you don't cross, and he had crossed some. One county supervisor wondered aloud on TV what a lot of black people in Jackson were thinking: "Who killed the mayor?"
Louis Farrakhan helped pay for an autopsy by Michael Baden, who had also examined the exhumed remains of Jackson's most famous civil-rights martyr, Medgar Evers, and who performed an autopsy on Ferguson martyr Michael Brown. Baden judged the cause of death to be an aortic aneurysm, likely enough a consequence of the mayor's tendencies for overwork and undernourishment. He had been trying harder than was healthy to make the most of the opportunity, to do as much as he could with the time he had left.
As Akuno, off camera, watched Lumumba give his interview with Flanders that February, he felt that his boss was finally ready to stop playing nice with the establishment, as he had been so far. The honeymoon was over; the gloves were coming off.
"Mayors typically don't do the things we're trying to do," Lumumba said. "On the other hand, revolutionaries don't typically find themselves as mayor."
At the center of Jackson's civic district, Mississippi's former capitol building looms over Capitol Street, which has been subject to a variably successful renovation effort seeking to replicate the urban revival sweeping hollowed-out cities across the country. Intersecting Capitol Street to the north, the segregation-era black business district, Farish Street stands nearly empty. Historical signs are more plentiful than pedestrians. The Old Capitol Museum presents slavery and Indian removal—the city was named after President Andrew Jackson, in gratitude for his role in the latter—as quandaries to be pondered rather than obvious moral disasters. After all, these were law; there were treaties and contracts. The same could also be said of the predatory mortgages that, in the Great Recession, wiped away what gains civil rights had brought to African American wealth, especially in places like Jackson.
Capitol Street changes abruptly after crossing the railroad tracks on the west end of downtown as it heads toward the city zoo. Lots are empty and overgrown, right in the shadow of the refurbished King Edward Hotel. Poverty lurks; opportunity for renewal beckons. And right there, at the gateway of this boarded-up frontier, is a one-story former day-care building painted red, green, and black: the Chokwe Lumumba Center for Economic Democracy and Development. Standing guard against the gentrification en route, this became the most visible remnant of the late mayor's four-decade legacy in the city.
Lumumba first arrived in Mississippi when he was twenty-three years old, in 1971. He had been born Edwin Finley Taliaferro in Detroit, but like many who entered black nationalist movements in the 1960s, he relinquished his European names and took African ones—each, in his case, with connotations of anticolonial resistance. While at Kalamazoo College, in southwest Michigan, he joined an organization called the Republic of New Afrika, or RNA. Its purpose was not to achieve mere integration or voting rights, but to establish a new nation in the heartland of US slavery, one where black people could rule themselves, mounting their own secession from both Northern and Southern styles of racism. This quest was, to its adherents, a natural extension of the independence movements then spreading across Africa.
The authorities in Jackson did not prove welcoming. That August, police officers and FBI agents, armed with heavy weapons and a small tank, raided a house RNA members were living in; the resulting confrontation left an officer dead. Lumumba wasn't there that day, but the fallout kept him in Jackson a few years longer. A 1973 RNA document in the archives of the Mississippi Sovereignty Commission—the state's segregationist Gestapo—records him as the RNA's minister of justice. The document calls for reparations, in cooperative form: "We are urging Congress to provide 200 million dollars to blacks in Mississippi for a pilot co-op project to make New Communities, jobs, training, fine free housing, and adequate food and health for thousands."
Lumumba soon returned to Detroit, where he graduated from law school at Wayne State University in 1975. Malcolm X wished he could become a lawyer; Lumumba's aspiration, he'd later tell his son, was to be the kind of lawyer Malcolm would have been. He defended Black Panthers and prison rioters. He unsuccessfully argued that Mutulu Shakur—who was facing charges of bank robbery, murder, and aiding the jailbreak of Assata Shakur—deserved the protections of the 1949 Geneva Convention as a captured freedom fighter. (He would later also defend Mutulu's stepson, the rapper Tupac Shakur.) He became renowned to some and notorious to others. A federal court in New York held him in contempt for referring to the judge as "a racist dog." Then, in 1988, he persuaded his wife, Nubia, a flight attendant, to move with their two children back to Mississippi. He wanted to continue what he and the RNA had started years before.
The change that came over Jackson after the early 1970s was a cataclysmic but also entirely familiar story of American urban life. ("As far as I am concerned, Mississippi is anywhere south of the Canadian border," Malcolm X once said.) The end of segregation inclined most of the city's white residents to flee for the suburbs, while maintaining their hold on political power and the economic benefits of city contracts. They regarded the city's subsequent decline as a case in point. To Hollis Watkins, a local civil rights hero, the story of the city's transformation after white flight was simple: "intentional sabotage."
Lumumba helped found the New Afrikan People's Organization in 1984, and the Malcolm X Grassroots Movement formed as an offshoot by 1990. MXGM, whose first chapter was in Jackson, set out to bring black nationalism to a new generation of activists. Adults organized and strategized; kids joined the New Afrikan Scouts and attended their own summer camp.
Safiya Omari, Lumumba's future chief of staff, came to Jackson in 1989. At rallies, they chanted the old RNA slogan, "Free the land!"—three times, in quick triplets with call-and-response—followed by, in dead-serious unison, its Malcolmian addendum, "By any means necessary." Their names and message were foreign to local black folks, and scary to many whites, but with time they became part of the landscape.
Holding court at his makeshift desk in the Lumumba Center's multipurpose room, Kali Akuno described his world to me as a confluence of "forces." For a generation whose radicals tend toward impossible demands and reactive rage, he is the rare strategist. He thinks in bullet points, enumerating and analyzing past mistakes as readily as future plans, stroking the goatee under his chin as his wide and wandering eyes look out for forces swirling around him. After Lumumba's passing, Akuno became the spokesman for what remained of their movement.
Akuno came of age in California—Watts of the 1970s and 1980s—immersed in the culture of black pride and power, descended from followers of Marcus Garvey and New Afrikans. His use of _Akuno_ came later in life, but his first name was Kali from birth. People he grew up around talked about cooperative economics, about Mondragon, about businesses controlled democratically by the people they serve. In college at UC–Davis and after, Akuno drifted among experiments in cooperative living and organizing. After Lumumba and his comrades founded MXGM, Akuno gravitated to its Oakland chapter. He would become one of the organization's guiding theorists.
Hurricane Katrina brought him south. When it became evident how the storm had devastated black neighborhoods of New Orleans, and the government response only made matters worse, MXGM mobilized. Lumumba's daughter Rukia, then in law school at Howard University, began flying down every chance she could to organize volunteers. Akuno moved from Oakland and took a position with the People's Hurricane Relief Fund.
"We were trying to push a people's reconstruction platform," said Akuno, "a Marshall Plan for the Gulf Coast, where the resources would be democratically distributed." But mostly they had to watch as the reconstruction became an excuse for tearing down public housing and dismembering the public schools. It was not rebuilding; it seemed more like expulsion.
"Katrina taught us a lot of lessons," Rukia Lumumba said. The group started to think about the need to control the seats of government, and to control land. "Without land, you really don't have freedom."
Akuno and MXGM's theorists around the country got to work. What they developed would become public in 2012 as _The Jackson-Kush Plan: The Struggle for Black Self-Determination and Economic Democracy_ , a full-color, twenty-four-page pamphlet Akuno authored, with maps, charts, photographs, and extended quotations from black nationalist heroes. It calls for "a critical break with capitalism and the dismantling of the American settler colonial project," starting in Jackson and Mississippi's Black Belt, by way of three concurrent strategies: assemblies to elevate ordinary people's voices, an independent political party accountable to the assemblies, and publicly financed economic development through local cooperatives. Each would inform and reinforce the others.
By 2008, the scheming led to talk of running a candidate. MXGM had been organizing in Jackson for almost two decades, and it had a robust base there. Akuno suggested that MXGM should run the elder Lumumba and begin training Chokwe Antar—who was then finishing law school in Texas—to run for office in the future. The Jackson-Kush revolution would start with mere elections.
In 2009, Lumumba ran for a city council seat in Jackson; with the help of MXGM's cadres and his name recognition as an attorney of the people, he won. On the council he cast votes to protect funding for public transit and expand police accountability. But in Jackson, the real power—in particular, power over infrastructure contracts—lay with the mayor's office. Those contracts were still going largely to suburban, white-owned firms. Black people had long been the majority of Jackson's population, but MXGM's strategists held that the city's land wasn't really free until the majority benefited economically.
Few among Jackson's small, collegial elite bothered to notice the Jackson-Kush Plan when Lumumba announced his run for mayor in 2013. He was just one in a crowded pool of candidates. And the plan was still little more than a set of ideas. The co-ops didn't exist; the assemblies, when they actually took place, were small and populated mostly by true believers. Yet Lumumba understood his role as an expression of the popular will, which the co-ops and assemblies would someday articulate. At important junctures he would say, "The people must decide."
The mayoral campaign was a testament to what Lumumba had built in Jackson and the support MXGM members nationally could muster. He soundly defeated the incumbent in the primary, together with Jonathan Lee, a young black businessman who was little known in town, except to his friends on the state chamber of commerce. The $334,560 that Lee raised in 2013 was much more than the $68,753 Lumumba's campaign raised the same year. But MXGM's organizing efforts, combined with Lumumba's reputation, resulted in a landslide. On May 21, he won 86 percent of the Democratic primary vote, guaranteeing him the mayoralty. The Lumumba campaign's slogan, "One city, one aim, one destiny"—an homage to an old Garveyite saying—seemed to be coming true.
Not everyone was on board, however. "I remember getting all these calls when he was elected mayor from white business owners—they were terrified," City Councilman Melvin Priester Jr. told me. "They were afraid that he was going to treat them like they had treated a lot of black people, like a Rhodesia situation."
For Lumumba and his new administration—full of MXGM partisans—the first order of business was damage control. The city's roads and pipes had been allowed to deteriorate to the point of dysfunction. A federal Environmental Protection Agency consent decree required action on the crumbling wastewater system. Funds needed to be raised for repairs; perhaps afterward, the money could be used to seed cooperative businesses for doing the necessary work. Lumumba used the political capital he'd won in the election to pass, by referendum, a 1 percent sales tax increase. He raised water rates. Practical exigencies won the day.
"We didn't win power in Jackson," Akuno later said. "We won an election. It's two different things."
To pass the 1 percent tax, Lumumba had to accept oversight for the funds from a commission partly controlled by the state legislature—a concession that not even his more conservative predecessor would accept. He hoped that, later on, he could mobilize people in Jackson to demand full control over their own tax revenues, but the city was in an emergency, so for the moment the commission would have to do.
From his new position as director of special projects and external funding, Akuno tried to keep the Jackson-Kush Plan on track. However long the administration would last, he wanted to set up structures that would outlive it. He drew up plans for a $15 million development fund for cooperatives, using money from the city, credit unions, and outside donors. He wanted to create worker-owned co-ops corresponding to the city's major expenses—for collecting garbage, for growing the food served at schools, for taking on the plentiful infrastructure challenges. The city would put co-op education in schools, provide co-op training, and help co-ops obtain financing and real estate. And there were plans to roll out a participatory budgeting process, based on models in Brazil and New York, through which Jacksonians could decide how to allocate public funds. Lumumba, meanwhile, moved more cautiously.
Jackson's troubles, by 2013, were more than black and white. An investment firm in Santa Monica had bought up more than half of the private buildings downtown. Investors from Israel and China were getting in on the action, too. Far from the RNA's old secessionist strategy of the 1970s, Lumumba was forming coalitions where he could, with whomever would work with him. Co-ops and assemblies took a backseat to balancing the budget, at least as far as official business went.
Ben Allen, president of the city's development corporation, started getting to know the new mayor, and he was pleasantly surprised. When he invited Lumumba to a garden party at his country club, the mayor made an appearance. "Our fears were gone," remembered Allen, who is white. "He wanted to work with us."
Two miles from downtown along Capitol Street, just blocks from the entrance to the zoo, another germ of the cooperative vision was beginning to sprout. In early 2013, MXGM members Nia and Takuma Umoja moved with their children from Fort Worth, Texas, into a small wooden house next to a local dumping ground. As they befriended their new neighbors, they started clearing the garbage away and replacing it with raised soil beds. Their neighbors, many of whom grew up as sharecroppers, formed a construction crew and started growing food. Together, they designated an eight-block district the Cooperative Community of New West Jackson and began buying lots there, intending to transfer them to a community land trust. The construction crew renovated abandoned houses and painted them with bright colors. The Umojas and their neighbors were making on-the-ground progress while Akuno remained focused on fund-raising and elections.
It was all part of the struggle. But every success still felt tenuous. Back in Fort Worth, the Umojas' community center had fallen victim to the threat of eminent domain. The danger was just as real in Jackson. According to Ben Allen's email signature at the time, "downtown redevelopment is like war."
The forces that kept #BlackLivesMatter trending after the hashtag first appeared in 2013 were not exactly what one might expect from the headlines of black men killed by police. In reality, it was frequently a queer- and women-led uprising. The leaders were not afraid to use the word _capitalism_ , and they did so derisively. (The "Black Lives Matter" slogan originated with Alicia Garza, a labor organizer with the National Domestic Workers Alliance.) They believed that black lives will not matter without a different system for determining what and who matters, and cooperative economics figured prominently in the movement's policy proposals. Yet, as in so many social movements of the past, only a tiny sliver of its variform lifeblood got into the news.
The civil rights struggle of the 1960s was no exception, for it was never about civil rights alone. Malcolm X preferred to speak of "human rights," and it was in those terms that he wanted to bring a case against the United States before the United Nations. Martin Luther King Jr. marched for "justice and jobs"; he died supporting sanitation workers. "Black power," "black liberation," "black lives"—these betray demands more comprehensive than either headlines or mythic hindsight allow. And they always had to do with economics.
In the mid 1960s, _black power_ entered the movement lexicon while Stokely Carmichael was living among landowning co-op members in Lowndes County, Alabama. Wendell Paris, a civil rights activist and cooperative developer at the time, explained this to me when I visited his office at a Jackson-area church. "The black power concept came into being," he said, "because of those farmers who were independent in and of themselves and understood the value of collective organizing and collective ownership." In cities, black power would conjure images of the Black Panthers' rifle-toting demonstrations, but it was also at work in their less-visible programs for providing food, housing, and health care.
For years, Paris traveled around the South helping black farmers hold on to their land and build wealth cooperatively. It was a strategy for survival as well as resistance. Black farmers in Louisiana weren't getting paid fairly for their sweet potatoes, so they started a sweet potato cooperative and found their own markets—in many cases way up in the North. In Alabama, farmers who were getting a raw deal on local fertilizer formed a co-op to buy it in bulk elsewhere. Paris assisted in the formation of the Federation of Southern Cooperatives in 1967. Black activists during that period visited co-ops in Africa and Israel. Martin Luther King Jr. tried to set up credit unions during the Montgomery Bus Boycott and at his church in Atlanta—efforts that faced resistance from federal regulators. After years of agitating for voting rights, Fannie Lou Hamer organized the Freedom Farm, a cooperative meant to secure the gains of civil rights with food sovereignty. When Student Nonviolent Coordinating Committee members agitated for voting rights in Jackson, they also helped create cooperatives; later, black churches kept up the work by building bulwark institutions such as the Hope Credit Union. Cooperation has bound survival and resistance together.
The generation of farmers that organized under the Federation of Southern Cooperatives in the 1960s and 1970s is aging out of existence, and the next generation of black-led cooperation is still just beginning to emerge. Individual co-ops are getting started in many cities, and the new Southern Reparations Loan Fund has been making its first loans. The story continues. But this story of black cooperatives, as much as it is one of tenacity and enterprise, is a story of loss. The loss once came in the form of Governor George Wallace's Alabama state troopers pulling over a truck full of cucumbers and keeping it there until the crop turned to mush in the summer sun, then it was a police raid with a tank, then an aortic aneurysm.
When Chokwe Antar first looked upon his father's body in the hospital room, he made the decision to finish what had been begun. He didn't say anything at first; there still had to be discussions in MXGM about the next move. His wife was pregnant. Some felt he wasn't experienced enough. But eventually the movement's decision echoed his own, and he ran for mayor in the special election to succeed his father. Throughout the country, MXGM members mobilized again. But by the time of Lumumba's death, the Jackson-Kush Plan was secret no more, and the city's business class was better prepared to oppose it.
Socrates Garrett is Jackson's most prominent black entrepreneur. He went into business for himself in 1980, selling cleaning products to the government; now, he and about one hundred employees specialize in heavy-duty environmental services. The story of his success is one of breaking through Mississippi's white old-boy network, and to do that his politics have become mainly reducible to his business interests. He is a former chairman of the chamber of commerce and serves on the boards of charities. He is a self-described progressive who supported the Republican governor Haley Barbour. He became a political operator—one with less ideological freight than the partisans of MXGM.
"I had to have relationships with politicians," Garrett told me. "If you're not doing business with the government, you're not in mainstream America."
Garrett became a Lumumba supporter only when it became clear who was going to win the election, and he grew disillusioned quickly. The MXGM-led administration didn't play his kind of politics. "They started putting people in from different walks of life," he recalled. "They had a lot of funny names, like Muslim names." Garrett was informed that he should not expect special treatment. Safiya Omari, Lumumba's chief of staff, insisted that he was being treated like any other contractor, but Garrett perceived it as a snub—right when the militant black mayor seemed to be bending over backward to assuage the white establishment. Garrett couldn't wrap his head around how cooperatives were going to take on big-city contracts, with all the financing and hardware such work requires. Mississippi law doesn't even have a provision for worker or consumer cooperatives; those that do exist must incorporate out of state.
"Here you are, a black man—you start from scratch and work your way up, thirty years out here struggling—and there's something wrong with my business model?" Garrett said. "In my opinion, it was going to produce chaos."
Garrett set about looking for a new mayor to raise up and before long came upon Tony Yarber, a young, bow-tied city council member and pastor from a poor neighborhood. What he lacked in age and experience was more than made up for in his willingness to collaborate. Garrett and Yarber quietly set out to organize a run against Lumumba in 2017, but when the mayor died, their chance came sooner than expected. The establishment that had tolerated and even come to like Mayor Lumumba wasn't ready to risk his little-known son. _Jackson Jambalaya_ , a straight-talking conservative blog, ridiculed him as "Octavian." Chokwe Antar's posters, between plentiful exclamation points, made promises of "continuing the vision"; Yarber, for his part, told the _Jackson Free Press_ , "I don't make promises to people other than to provide good government." Garrett was his top individual donor.
The result was a reversal from the election a year earlier. Jackson's population is 80 percent black, and Chokwe Antar won a solid majority of the vote in black neighborhoods. But the white minority turned out in droves, urged by last-minute canvassing in more-affluent areas, which voted 90 percent for Yarber. Narrowly, on April 22, Yarber won.
Yarber removed almost all the members of the previous administration. Even Wendell Paris, who'd been working part-time to develop community gardens on city land since before Lumumba took office, was dismissed. When I visited city hall a year later, Yarber's sister, a police officer, was sitting by the metal detector at the entrance, pecking on the same iPhone that was once issued to Lumumba.
"The whole sense that we were going to do something great sort of dissipated," Safiya Omari told me.
Sitting on his front porch, wearing a faded T-shirt from the first mayoral campaign and a black cap with Che Guevara inside a small red star, Akuno tried to explain to me the experience as he slathered his two small children in natural bug repellent. With the 1 percent tax and the water-rate hikes, they'd alienated part of their base. But capitalism didn't leave them a choice. He was following the news of Syriza, the leftist party in Greece, as it tangoed with the Troika. "I feel like I know exactly the conversations they are having behind the scenes," he said. "I've been there."
_Chokwe Antar Lumumba in his law office in 2015, behind a photograph of himself as a child with his father._
Across town, Garrett was feeling blessed. Mayor Yarber put things back to what he was used to. "Every time, God sends an answer," he told me. "But I can assure you that that movement is alive and well. And I can assure you that unless Yarber is razor sharp, they'll be back."
So they were. In May 2014, just months after Lumumba's death, hundreds of people came to Jackson State University from around the country and the world for a conference called "Jackson Rising." They heard the history of black-led cooperatives from Jessica Gordon Nembhard, who had just published her book on the subject, and they took stock of what might have been in Jackson—and what might be. Lumumba's image appeared on the cover of the program, and on the first page, he spoke from the grave with a signed-and-sealed resolution from the mayor's desk. "Our city is enthused about the Jackson Rising Conference and the prospects of cooperative development," it said, as if nothing had changed.
MXGM was meanwhile hatching a new organization, Cooperation Jackson, to carry on the work that had been started. Akuno enumerated a four-part agenda: a co-op incubator, an education center, a financial institution, and an association of cooperatives. Plans were soon underway to seed, first, three interlocking co-ops: an urban farm; a catering company named in honor of Lumumba's wife, Nubia, who died in 2003; and a composting company to recycle the caterers' waste back into the farm. Akuno raised money from foundations, entertainers, and small donors, and the Southern Reparations Loan Fund pitched in as well. Cooperation Jackson started buying up land for its own community land trust. Its members restored and painted what would become the Lumumba Center.
Jackson's summer heat felt especially apocalyptic in 2015. In South Carolina, Dylann Roof murdered nine African American worshipers in a Charleston church; day after day, there was news of black churches across the South burning. Calls were mounting to take down the Confederate battle flag flying over the South Carolina capitol, but comparatively few were talking about the stars-and-bars that still covered a substantial portion of the Mississippi state flag everywhere it appears. The Supreme Court declared same-sex marriage the law of the land, overturning the Mississippi constitution's marriage amendment, and the preachers who heavily populate the radio spectrum in Jackson declared the United States of America now, at last, definitively captive to the devil's grip.
In the Lumumba Center's backyard, Cooperation Jackson's Freedom Farm consisted of a few rows of tilled earth, and in the kitchen, Nubia's Place Cafe and Catering Co-op was having its first test run. Akuno and others were planning a trip to Paris for the UN climate summit. Down the road at the Cooperative Community of New West Jackson, Nia Umoja and her neighbors had bought fifty-six properties for their land trust. "We've taken almost all the abandoned property off the speculative market," Umoja said.
In the wake of Roof's shooting spree, Chokwe Antar helped organize a rally at the state capitol to demand changing Mississippi's flag, alongside local politicians, personalities, and hopefuls. The actress Aunjanue Ellis, flanked on either side by guards in black MXGM T-shirts, called for "rebranding our state" and "a different way of doing business." Chokwe Antar led a chant: "Stand up, take it down!" "Free the land!" followed. Then, of course, "By any means necessary."
Chokwe Antar's name was in the national news a week later. In Clarke County, a police officer stopped Jonathan Sanders, a black man on a horse-drawn buggy, who wound up dead after the officer put him in a chokehold. Chokwe Antar took the case. The incident became a potential flash point for the Black Lives Matter movement's roving attention, but the story didn't long hold the national gaze, and the following January, a grand jury declined to indict the officer. The rebel flag still flies over Mississippi.
Chokwe Antar told me a few days before the flag rally that he'd decided to run for the mayor's office again. As the 2017 Democratic primary approached, in the wake of Donald Trump's election, he ran with support from emboldened progressives across the country. He didn't disavow the Jackson-Kush Plan, nor did he advertise it. But he did talk about shared ownership—about the Green Bay Packers and Land O'Lakes and Ace Hardware. "My vision is that the city use its bully pulpit to encourage the development of cooperative businesses," he told a reporter. Yarber had succumbed to a series of scandals and mishaps; Garrett withdrew support. Chokwe Antar won by a landslide. But winning an election was still just winning an election.
Back in late June of 2015, the flag campaign was the subject of conversation while cooking vegetables and chicken for dinner in the Lumumba Center's backyard. Akuno, pacing back and forth over the grill, led the discussion. "I think with some of this Confederate stuff—that's a distraction," he said. "Is that really our agenda? Did we define it, or did the media define it, saying that this is within the limits?" He'd been saying as much to Chokwe Antar. Akuno wanted to keep the focus on the co-ops and assemblies and elections—real counterpower, backed by self-sufficiency.
"Nothing don't change, whether the flag comes down or not," said New Orleans housing activist Stephanie Mingo, from the other side of a picnic table. "There's still going to be red, white, and blue."
"I'm not a fan of the Black Lives Matter thing—because, to be honest with you, they don't," Akuno went on. "Your life did matter, when you were valuable property. You were very valuable at one point in time. We're not valuable property anymore." His pacing took him and his gaze back to the grill, where he flipped over a piece of chicken.
"My argument is to tell other black folk, let's start with the reality."
It can be hard to sort out reality sometimes, especially in the midst of brave, big dreams. Cooperation Jackson's enterprises, when I visited, paled in comparison to how Akuno could talk about them. I've lived among great cooperative achievements and barely noticed; others I've heard much about but never seen. I confess: I've never made the pilgrimage to see mighty Mondragon for myself.
I don't know if a cooperative commonwealth can really take power and hold it, if it can dissolve the state and the corporations as Warbasse imagined, if its democracy can be durable enough to last beyond the founding generation. But flashes of the commonwealth keep appearing, if you know where to look—each time a new evolution for the old cooperative movement, the next equitable pioneers expanding the territory of democracy.
I can think of one place, at least, where Warbasse's stateless commonwealth might be closest to happening. Ever since I first learned about Rojava—at a fund-raiser in a New York City anarchist storefront, carefully skirting laws on financing foreign militants—I've been trying to understand what is real there. People I know have gone to visit, including a nemesis, a freelance diplomat, and a magazine editor, but there is a certain untrustworthy self-selection in who ships out to join a revolution. Pablo Prieto, a friendly biologist who showed me around the Catalan Integral Cooperative's Calafou colony, made his way to Rojava with the Bitcoin hacker Amir Taaki. We corresponded for months by encrypted email, but he could never quite arrange the interviews with local leaders I asked for. It was a war zone, after all.
Rojava is an idea shared across three Kurdish-majority regions in northern Syria, along the Turkish border. These regions furnished the Kurdish fighters, including women and foreign recruits, that US forces came to rely on in the fight against ISIS. (This was a troubling arrangement for Turkey, whose rulers have spent decades suppressing Kurdish insurgencies inside their borders.) The Kurds, at last out of Damascus's reach, declared their new regime in 2012, among the ruins left from the ISIS occupation and subsequent liberation. They professed a doctrine of "democratic confederalism," derived from the ideas of US philosopher Murray Bookchin, as synthesized by Kurdish leader Abdullah Öcalan from his jail cell in Turkey. It's a system meant to render the nation-state obsolete through overlapping networks of local "communes." Gender equality, environmentalism, and ethnic pluralism are celebrated, and the police—while perhaps necessary for a time as the war goes on—are designed for eventual abolition.
The confederalist economy is made of co-ops. First, after the 2012 liberation, this started with agricultural co-ops; land that the Syrian government had owned was parceled out to locals, especially the families of fighters. But soon there were co-ops for bread baking, for textiles, for producing cleaning materials. Networks of co-ops formed—including ones for creating and supporting co-ops of women. But the co-ops were designed to resist outside control. They were to be accountable to local communes, the basic unit of the confederalist system. A person's commune, for instance, could revoke her co-op membership.
The global powers attempting to steer the Syrian conflict have mostly ignored the revolution at hand or wished it didn't exist, even while benefiting from the resolve of its fighters. It's an economy inscrutable to those not willing to cooperate. An analyst from The Washington Institute, a DC-based think tank tied to the hawkish Israel lobby, once complained of Rojava that "attracting investors into such an anti-capitalist system would be difficult. Entrepreneurship is encouraged in Rojava, but only within the framework of cooperatives." It was a rare bit of outside confirmation that the commonwealth so celebrated in anarchist infoshops around the world was really happening.
In October 2015, Prieto invited me to come join him. I wish I could have—I think. He wrote, "It's just like the Spanish revolution all over. There are so many similarities." He was referring to the period when anarchist collectives controlled much of Barcelona and the countryside, a passing utopia in the vacuum of war. "We have access to as much land as we want, and lots of resources. The possibilities here are endless, but we need people to come. We are going to build our open-source city here. It will be like an anarchist village, sort of like Calafou, but much bigger and better."
He wrote in another message, "This is THE goddamn real revolution! Or at least the closest we can get."
#
# Phase Transition
## _Commonwealth_
The first time I saw it, I took the metaphor literally. "We will all meet in Quito for a 'crater-like summit,'" the website said. "We will ascend the sides of the volcano together in order to go down to the crater and work." Alongside those words was a picture of Quilotoa, a caldera in the Ecuadorian Andes where a blue-green lake has accumulated in the hole left by a cataclysmic eruption seven hundred years ago, enclosed by the volcano's two-mile-wide rim.
What the website beckoned visitors to was something less geologically spectacular than Quilotoa, but possibly earth-shaking in its own right. The government of Ecuador had sponsored a project to develop policies for a new kind of economy, one based on concepts more familiar in hackerspaces and startups than in legislatures. The project was called FLOK Society— _f_ ree, _l_ ibre, _o_ pen _k_ nowledge. Its climactic event, which took place in May 2014, was called a summit, but the nod to Quilotoa's crater was a way of saying this wasn't the usual top-down policy meeting. Nor were the people behind it the usual policymakers.
Michel Bauwens, the fifty-six-year-old leader of the FLOK Society research team, held no PhD, nor experience in government, nor steady job, nor health insurance. A native of Belgium, he lived in Chiang Mai, Thailand, with his wife and their two children, except when he left on long speaking tours. He dressed simply—a T-shirt to the first day of the summit, then a striped tie the day of his big address. His graying hair was cropped close around his bald crown like a monk's. He spoke softly; people around him tended to listen closely. The Spanish hacktivists and Ecuadorian bureaucrats who dreamed up FLOK chose for their policy adviser an unemployed commoner.
If Ecuador was to leapfrog ahead of the global hegemons, it would need a subversive strategy. "It's precisely because the rest of the world is tending toward greater restrictions around knowledge that we have to figure out ways of producing that don't fall within the confines of these predominant models," Ecuador's minister of education, science, technology, and innovation, René Ramírez, told me. He and other government officials were talking about dispensing with such strictures as copyright, patents, and corporate hierarchies. "We are essentially pioneers in this endeavor. We're breaking new ground."
At first this was a subversion mutually beneficial to guests and hosts alike. Several months before the summit, Bauwens said that FLOK was a "sideways hack"—of the country, maybe even of the global economy. "It's taking advantage of a historic opportunity to do something innovative and transformative in Ecuador." He saw a chance to set the conditions for a commonwealth.
FLOK bore the style and contradictions of Ecuador's brand at the time. The president, Rafael Correa, sometimes spoke in favor of open-source software; WikiLeaks founder Julian Assange had been living in Ecuador's London embassy since 2012. Even while exploiting rain-forest oil resources and silencing dissenters, Correa's administration called for changing the country's "productive matrix" from reliance on finite resources in the ground to the infinite possibilities of unfettered information. Yet most of the North Americans I met in Quito were out of a job because Correa had recently outlawed foreign organizations, likely for circulating inconvenient information about human rights.
_Michel Bauwens at the convention center in Quito._
As the summit approached, local politicians seemed to evade Bauwens and the team of researchers he'd brought there. Team members weren't paid on time. Two dozen workshops about open knowledge took place across the country, with mixed response. By the time I met Bauwens in the gaudy apartment he was renting in Quito, a few days before the summit began, he looked exhausted from infighting with the Spaniards and wresting his staff's salaries from the government. "It's going to be a much harder fight than I anticipated," he said.
Bauwens had a knack for seeking out potent knowledge. He grew up in Belgium as the only child of two orphan parents. His curiosities drifted from Marxism as a teenager to, as an adult, various Californian spiritualities, which led him to Asian ones, then esoteric sects like Rosicrucianism and Freemasonry. Meanwhile, Bauwens put his cravings to work in business. He worked as an analyst for British Petroleum and then, in the early 1990s, started a magazine that helped introduce Flemish readers to the promise of the internet. As an executive at Belgacom, Belgium's largest telecommunications company, he guided its entry into the online world by acquiring startups. And then, in 2002, he'd had enough. He quit, then moved with his second wife to her family's home in Chiang Mai.
"Capitalism is a paradoxical system, where even the ruling class has a crappy life," he says. He started to believe his unhappiness had cataclysmic causes.
For two years in Thailand, Bauwens read history. He studied the fall of Rome and the rise of feudalism—a "phase transition," as he puts it. It was an age when the previous civilization was in crisis, and he concluded that what led the way forward was a shift in the primary modes of production. The Roman slave system collapsed, and then networks of monasteries spread innovations across Europe, helping to sow the seeds of the new order. What emerged was an interplay of craft guilds organizing free cities, warlords ruling from behind castle walls, and peasants living off common land. As the feudal system grew top-heavy, networks of merchants prepared the way for the commercial, industrial reordering that followed.
With the internet's networks, he came to believe that industrial civilization faced a crisis of comparable import, as well as the germ of what could come next. He zeroed in on the notion of commons-based peer production—the modes by which online networks enable people to create and share horizontally, not as bosses and employees but as equals. It was a new rendition of the old medieval commons, but poised to become the dominant paradigm, not just a means of survival at the peripheries. He set out to find examples of where this world-transformation was already taking place. By seeking, he found.
The bulk of Bauwens' oeuvre lives on the collaborative wiki that long served as the website of his Foundation for Peer-to-Peer Alternatives—the P2P Foundation, for short. Its more than thirty thousand pages, which he has compiled with more than two thousand online coauthors, include material on topics from crowdsourcing to distributed energy to virtual currencies. His life's work takes the form of a commons.
Bauwens tends to talk about his vision in the communal "we," speaking not just for himself but for a movement in formation. He borrows a lot of the terms he relies on from others, then slyly fits them into a grander scheme than the originators envisioned. Put another way: "I steal from everyone." Nevertheless, one is hard-pressed to locate any enemies; rather than denouncing others, he tends to figure out a place for them somewhere in his system.
It was in and for Ecuador, together with his team, that Bauwens mapped out the next world-historical phase transition for the first time. He believes that cooperatives are the event horizon. They're bubbles of peer-to-peer potential that can persist within capitalism, and they can help the coming transition proceed. They can decentralize production through local makerspaces while continually improving a common stock of open-source designs. They can practice open-book accounting to harmonize their supply chains and reduce carbon emissions. Open intellectual-property licenses can help them share their resources for mutual benefit. As these networks grow, so will the commons they build, which will take over roles now played by government and private markets. Soon all the free-flowing information, combined with co-op businesses, will turn the economy into a great big Wikipedia or Linux—by anyone, for anyone. The industrial firm, whether capitalist or cooperative, will dissolve into collaborations among peers. Bauwens calls this process "cooperative accumulation."
Co-ops are not an end in themselves. They're not the destination. But they're the passageway to a peer-to-peer commons. "We see it as _the_ strategic sector," he told me. New cooperative experiments were spreading from Mississippi to Syria, and here was a chance to show how they could grow to the scale of an entire country.
The Quito convention center is a two-story complex with stately white columns and hallways enclosed in walls of glass. Visible just a few blocks away is the National Congress building, the supposed destination of FLOK Society's proposals. Volcanoes stand in the distance behind it, the city rising up as high on their slopes as it can manage. During the four days of the "Good Knowledge Summit," as the event was called, bureaucrats in business casual worked alongside hackers in T-shirts to develop and distill the discussions into policy.
The opening night included bold pronouncements. "This is not just an abstract dream," said Guillaume Long, Ecuador's minister of knowledge and human talent. "Many of the things we talk about these days will become a reality." Rather than tax havens, added the subsecretary of science, technology, and innovation, Rina Pazos, "we need to establish havens of open and common knowledge."
Bauwens spent most of his time in the sessions on policies for cooperatives. In Ecuador, as in many places, it is harder to start a co-op than a private company. The Canadian co-op expert John Restakis, a member of Bauwens's research team, called on Ecuadorian officials to loosen the regulations and reporting requirements on co-ops, and to enable more flexible, multi-stakeholder structures. The officials pushed back; the regulations were there for a reason, after waves of co-op failures and abuses. Restakis and Bauwens pressed on. They wanted Ecuador's government to serve as what they called a "partner state," nurturing commons-oriented activities without seeking to direct or control them.
By the summit's end, the working groups had amassed a set of proposals, some more developed than others: wiki textbooks and free software in schools, open government data, new licenses for indigenous knowledge, community seed banks, a decentralized university. Mario Andino, the newly elected governor of Sigchos, one of Ecuador's poorer regions, wanted to develop open-source farm tools for difficult hillside terrain. Before the summit, Bauwens visited Sigchos and received a standing ovation for his presentation. "We could be a model community," Andino said. But there were no promises.
Over the course of his life, Plato made several journeys from Athens to Syracuse, in Sicily, with the hope of making it a model of the kind of society he described in his _Republic_. The rulers there, however, fell far short of being the philosopher-kings he needed; he returned home to retire and compose a more cynical kind of political theory. If not quite so discouraged, Bauwens seemed adrift after the summit ended. The work of FLOK Society was now in the hands of the Ecuadorians, and by that time, there was little indication the government would take more from the whole effort than a publicity stunt. Bauwens was already starting to look toward the next iteration; thanks in part to the process in Ecuador, there were signs of interest from people in Spain, Greece, Brazil, Italy, and Seattle. The same month as the summit, Cooperation Jackson held its Jackson Rising conference.
"Recognition by a nation-state brings the whole idea of the commons to a new level," Bauwens said. "We have to abandon the idea, though, that we can hack a country. A country and its people are not an executable program."
The fourteenth-century Tunisian polymath Ibn Khaldun described world history as an interplay between two groups of people: the sedentary and the nomadic. There are those attached to a place, who build power through buildings and property and civilization, and then there are those who swirl at their world's edges. Ibn Khaldun was a dedicated skeptic, and he would be the first to point out that no single distinction explains everything. But today his distinction strikes me as especially useful again. It helps describe the "phase transition" that so concerned Bauwens. It's a distinction about how we own and what we need.
In Ibn Khaldun's time, sedentary civilization was ascendant, as feudalism began consolidating into mercantilism. Today, nomadism appears to be on the rise. When I was a toddler my son's age, I'd lived in two homes that my parents owned; they owned two cars between them. My father was a partner in a small, busy real-estate brokerage. He poured his energy into shepherding families through the process of purchasing their home, usually their most important asset. My son, in contrast, was born into a rental apartment with rental furniture; his parents have between them one car and a car-sharing membership. We partake in a generational trend, partly thanks to the concurrent rise in education debt and real-estate prices, together with a post-recession job slowdown. But it's also a choice and an investment. My wife and I see value in owning less so we can move around more easily, following opportunities as they appear. We don't have a backyard, but we have a community garden plot and our choice of common, public parks. We know there are benefits to staying as nomadic as we can manage.
This is a sort-of-chosen kind of nomadism. Others come by their nomadism less voluntarily. Following the 2008 financial crisis, giant holding companies started buying homes once owned by resident families, turning more residents into tenants. We live in a time, meanwhile, of mass migrations due to the linked causes of war, climate change, and famine. Stateless insurgents sow terror through spectacle. Spells of automation and other disruptions keep workers on the run, changing occupations more during their lifetimes than in times past. We're living through a shift of population from rural areas to cities, a shift far more drastic and sudden than anything in Ibn Khaldun's historical data set. But our cities are different; they're not so sedentary. Transnational corporations have turned disparate cities into franchisees. Business travelers can jet around the world, stay in the same hotel chains everywhere they go, and buy citizenship wherever it's most convenient. Hovering over all this are the clouds—the physical, technological, and metaphorical objects that offer the allure of constancy. Wherever you go, Google's cloud is there to collect your search data in exchange for whatever information you could possibly want. Uber and Airbnb will introduce you to useful locals without the trouble of cultural competency or haggling over a price.
Surely Bauwens is right that something world-historical is going on here. But the outcome may not be an egalitarian commons of borderless, permissionless, peer-to-peer productivity. Alongside the new nomads, there remains an enormous sedentary class—those of us not swept up in either jet-setting or sudden migration, whose fortunes have been constant or declining. On the whole, in the United States, geographic mobility is on the decline; the new nomadism is too expensive. The sedentary peoples denounce both the involuntary migrants and the privileged "globalists." This mass of us is voting for firmer borders, for ethnic retrenchment, for brakes on democracy until the world stops changing so quickly. The postindustrial identity crisis for some is built from the trauma of an industrial revolution happening all over again for billions more.
Part of the sedentary peoples' complaint is that ownership has become nomadic, too. In the old feudalism, the lord was lord of a place; power had to do with land. Now wealth roams freely around the world, more freely than people, like the far-flung ownership of buildings in downtown Jackson or the California apps squeezing Denver's taxi drivers. From crisis zones to absentee investments to tax shelters, capital alights for a while where it can accumulate, then flits elsewhere to accumulate more. The domains of the new lords are virtual, and through the virtual clouds they own and control, their reach is far beyond what feudalisms of the past could have imagined. Their kind of nomadism is everywhere and nowhere at once, or at least it's meant to be perceived that way. At bottom, as with lords past, these lords depend on everyone else's respect for their ownership claims—over warehouses full of whirring servers, over proprietary algorithms, over rights backed by the force of governments and treaties.
The tech industry has long sought to claim otherwise. John Perry Barlow's 1996 "Declaration of the Independence of Cyberspace" asserted on behalf of the internet that the industrial world's notions of property and control no longer apply. "They are all based on matter," he wrote, "and there is no matter here." The Silicon Valley culture for which Barlow served as a prophet enacts this claim in the user experiences its companies design. There's no need to own a car; Uber can find someone willing to drive you. Don't bother managing the data of your life; share it with your friends on Facebook. Replace old-fashioned institutions and bureaucracies with free-form projects among freely associating commoners. Such invitations even seem to edge us closer to that old universal destination of goods, by which all things are truly common. The ownership-oriented cooperative tradition that has been the subject of this book might be verging on obsolescence.
Part of me wishes we could dispense with the freight of property as easily as Barlow imagines. The early anarchists were onto something when they declared that property is theft. But as commoners relinquish ownership today, the lords of the cloud do not. They keep on claiming their ownership rights. If there is to be a new era of sharing, they want it to be on their terms, by their rules, for their benefit.
Lawyers talk about ownership as a bundle of rights. The bundle can be untied, picked apart, and rearranged. This is what has happened on the clouds, where users allegedly own their data even after, knowingly or not, they've granted the cloud-owners nearly limitless rights to hoard and profit from it. But this is also how coders hack copyright law to create free, open-source software and how Guatemalan weavers secure collective ownership of traditional patterns against corporate copycats. They know they can't afford to skip straight to some perfect, ready-made commons; they're holding their ground on the terrain of property, building their values into how they own. A historic unbundling and rebundling is happening again, and how it turns out will depend on how we organize ownership.
The transitions apparently underway come with a choice. Will lordship emerge as the more dominant principle, or will the commons? Clean air, free time, private data—these could each end up as luxuries for a few or as common goods. Together, we are writing the next social contracts as we go, deciding what goes in and what we ignore. Yet the questions that the cooperative movement persisted in raising for generations have too often been neglected: Who owns the engines of the economy, and how are they governed?
In early 2017, Facebook CEO (and Ibn Khaldun enthusiast) Mark Zuckerberg posted a nearly 6,000-word letter called "Building Global Community." The name _Trump_ doesn't appear in it, but it's hard not to read as a postmortem on the election several months before, in whose aftermath Facebook came under scrutiny for enabling foreign interventions to spread. "Democracy is receding in many countries," Zuckerberg observed, "and there is a large opportunity across the world to encourage civic participation." The last third of the letter outlines how Facebook can "explore examples of how community governance might work at scale."
_The inverse relationship between organization membership and inequality in the United States._
His proposal amounts to a cascading series of online experiments in which users may or may not know they are taking part. Artificial intelligence would cull and interpret user inputs, fine-tuning Facebook's discursive habitats to suit various world cultures while also encouraging healthy, cross-cluster integration. By "community governance," he seems to mean a never-ending focus group.
It may well be true that online platforms are the best hope for democracy in a time of reactionary politics. There are more Facebook users in the world than citizens of any country, or even adherents of any religion. But meaningful democracy begins with meaningful control. In a corporation like Facebook, even while users wishfully treat it as a commons, control begins with ownership.
A century ago in the North Atlantic countries, as heavy industry matured from disruption to normalcy, the social contract was up for grabs in this same way. We're still living the consequences of how that struggle played out. The modern corporation was born, streamlined for competition in capital markets. Even so, in certain sectors, more democratic structures took hold. What if US farmers had been left to rely on big-city firms to decide where electricity would come and when? What if northern Italy's food industry were the purview of conglomerates rather than artisanal producers linked by co-ops? What if credit unions weren't able to lend in areas where big banks fear to tread?
Maybe Enric Duran's FairCoop really will become a credit union on the scale of a transnational bank, powering local co-ops. New sorts of passports or medical insurance might span borders with agreements among co-ops, undermining the walls that states erect as they try to shore up their power. Networks of unMonasteries might become the next capillaries of innovation, sharing their inventions under licenses that favor fellow co-ops. Neighbors might replace the old electric grid with small solar panels, windmills, and batteries that they control, like the members of Delta-Montrose Electric Association; next, they could drop the monopoly internet-service providers and set up their own broadband service as well. And so on, in every part of life—with local nodes federating every turn, reaching upward to economies of scale with accountability to the roots.
If the social contracts to come are to be democratic ones, democratic experiments need to take hold in how we produce, trade, and consume. We need the lessons of the cooperative tradition in generations past—as well as the learnings of its latest equitable pioneers. Without them, less-democratic urges will offer to lead us through the maelstrom of change instead. These are times when what seems like far-off sci-fi turns into reality before we know it.
Singularity University inhabits a small cluster of buildings in the NASA Research Park between downtown Mountain View and the San Francisco Bay. Around it are the crumbling remains of government-backed adventurism—the steel skeleton of a gigantic hangar designed to house airships, the rusting fuselages of airplanes, the dull barracks. They're reminders of the public investment that long ago dug the foundations of Silicon Valley's business empires, but it's a memory easy to forget in the thrall of private venture capital. Not far away, across a string of high-voltage wires, a bike path, and a trailer park, one finds a sprawl of parking lots and office parks, all with signs for the same familiar company, spread out around their mothership, the Googleplex. Singularity University doesn't grant degrees in the normal sense; it is a kind of secular seminary devoted to the faith that technology is the harbinger of human progress, until it outwits us altogether. Students pay for the experience with an ownership stake in the startups they create there. "Be exponential," Singularity's slogan reminds them.
In June 2014, the institution's co-founder and chairman, Peter Diamandis, a space-tourism entrepreneur, convened a gathering of fellow tech luminaries to discuss the conundrum of automation-caused unemployment. "Tell me something that you think robots cannot do, and I will tell you a time frame in which they can actually do it," claims Federico Pistono, a young Italian who spoke there. Among other accomplishments, Pistono had written a book called _Robots Will Steal Your Job, but That's OK_. At the Singularity meeting, he was the chief proponent of universal basic income, an idea that at the time still seemed novel. He cited recent basic-income experiments in India that showed promise for combating poverty among people the tech economy has left behind. Diamandis later reported having been "amazed" by the potential.
That year, also, celebrity investor Marc Andreessen told _New York_ magazine that he considered basic income "a very interesting idea," and Sam Altman of the elite startup accelerator Y Combinator called its implementation an "obvious conclusion." Those were just the early salvos.
What people generally mean by universal basic income is the idea of giving everyone enough money to provide for the necessities of life. Imagine, say, a $20,000 check every year for every US citizen. The idea appeals to hopeful longings for a humane, egalitarian sort of commonwealth—a recognition that people, including those who are currently poor, will know better than any top-down welfare program what to spend the money on. It also appeals to Silicon Valley's preference for simple, elegant algorithms that can solve big problems once and for all. Supporters list the possible outcomes: It could end poverty and reduce inequality with hardly any bureaucracy. Recipients with more time and resources at hand would dream up startups and attend to their families. Some, as critics complain, would surf. But perhaps most attractively for the executive class, the payouts would ensure that even an underemployed population could maintain the consumer demand that the robot companies would need to function.
As if Silicon Valley hasn't given us enough already, it may have to start giving us all money. Less clear, however, are the answers to those old cooperative questions: Who owns what, and who governs?
Karl Widerquist, a professor of political philosophy at Georgetown University's School of Foreign Service in Qatar, has been preaching basic income since he was in high school in the early 1980s. He says that we are now in the third wave of US basic-income activism. The first was during the economic crises between the world wars. The second was in the 1960s and 1970s, when libertarian heroes such as Milton Friedman were advocating a negative income tax, when ensuring a minimum income for the poor was just about the only thing Martin Luther King Jr., and President Richard Nixon could agree on. (Nixon's Family Assistance Plan, which bore some resemblance to basic income, passed the House but died in the Senate.) The present wave seems to have picked up in late 2013, as the news went viral about a mounting campaign in Switzerland to put basic income to a vote. Widerquist is glad to see the renewed interest, but he's cautious about what the techies have in mind.
One of the attendees at the Singularity University meeting was Marshall Brain, the founder of HowStuffWorks.com, who outlined his vision for basic income in a novella published on his website. It's called _Manna_. The book tells the story of a man who loses his fast-food job to robots, only to find salvation in a basic-income colony carved out of the Australian Outback by a visionary entrepreneur named Eric. (The fate of whatever Aboriginal peoples might live there already is unclear.) The colony is a kind of cooperative, held by its citizens on a one-person, one-share basis. They pass the time by innovating. They become a venture capitalist's ideal subjects, a vast supply of flexible entrepreneurs with the time and privilege to pursue worthy projects. Yet the colony's guiding principles declare, "Nothing is owned"—and, "Obey the rules," which are Eric's to make. It's innovation on his terms, like the paternalism of Robert Owen's textile factory. Eric's commonwealth in the Outback conspicuously lacks the human friction of politics.
Chris Hawkins, an investor in his thirties who made his money building software that automates office work, credits _Manna_ as an influence. To him, the appeal of basic income lies in its bureaucracy-killing potential. "Shut down government programs as you fund redistribution," he told me—mothball public housing, food assistance, Medicaid, and the rest—and replace them with a single check. Do away, also, with debates and decisions about common priorities; let the market of cash-equipped consumers vote among competing corporations with their purchases.
This kind of reasoning soon started to find a constituency in Washington. The Cato Institute, Charles Koch's libertarian think tank, published a series of essays in 2014 debating the pros and cons of basic income. That same week, an article appeared in the _Atlantic_ making a "conservative case for a guaranteed basic income" on the basis of devolving federal powers. This is one of those rare notions that is sneaking into plausibility from both the political left and right, more quickly than many proponents expected.
The idea gets less utopian by the moment. Barack Obama mentioned basic income approvingly in the waning days of his presidency. Governments from Finland to Hawaii are exploring policy options, and Y Combinator's nonprofit arm is funding a private experiment of its own in Oakland. For years, the journalist and entrepreneur Peter Barnes has been calling for a universal dividend funded through the use of common goods, particularly a tax on carbon emissions; now, governments in places from California and Oregon to the District of Columbia have considered plans to implement such a system. One of Barnes's champions is digital organizer Natalie Foster, who teamed up with Facebook co-founder Chris Hughes to mobilize executives, unions, and thought leaders of many stripes to unite behind payouts for all.
Some basic income schemes bypass regular money altogether. Cryptocurrencies derived from Bitcoin or Ethereum have been designed to come into being as basic income, and to gain value through their universality. These attempt to form an entire monetary system in which basic income is the starting point. Under the present regime, new money appears when banks lend it out. What if money began its life, instead, as an apparition in equal quantities to everyone?
With a guaranteed income to count on, in whatever form, the liberations could pile on top of each other. Feminist scholar Kathi Weeks envisions a world of expanding time, where women wouldn't be so caught between housework and job work. Some labor organizers hope that workers, not forced to take whatever job they can get, would regain leverage lost in the decline of unions. And more—for in the liberated time a basic income might afford, that unpredictable democracy-to-come would have new ground in which to germinate. But feudalisms might find roots there, too.
There are signs of such a situation on hand already. One way to think about the economic arrangement most users have with, say, their Gmail or Facebook account is that it amounts to a small stream of income—the value of whatever price they might otherwise pay for the service. The more universal these services become, the more we depend on them, just as people of the future might depend on their basic income check. The recipients could end up with no more say in where their income comes from than Facebook users have in how the company monetizes their data. We could wind up with a basic income generated by churning the data of our online habits or by polluting the air we breathe, without levers of ownership or governance to stop it. As algorithms take charge of important decisions, the lines of accountability would become harder to draw. We'd be bought in and bought off.
Giving people free money could surely help vanquish poverty, lessen inequality, and liberate time. But under what terms would the lords of the platforms deliver it? Those left out of economies past have learned that shared prosperity only really comes with shared power.
Ed Whitfield doesn't get the same starry-eyed look at the thought of basic income proposals as the techies do. He co-directs the Fund for Democratic Communities and its offshoot, the Southern Reparations Loan Fund. A big man with round, dark glasses who likes to play exotic musical instruments, Whitfield talks about the future with stories about the past. Once, in a conversation with Kali Akuno and Jessica Gordon Nembhard, I heard him point out that when their ancestors shed off slavery and demanded forty acres and a mule, they wanted the means of _production_ , not the means of _consumption_. They wanted a hand in shaping the economy, not just a portion of its output. To keep their freedom from getting snatched away again, they knew they had to be owners.
The evidence, anyway, doesn't fully agree that the wonders of automation are doing away with jobs on their own. Productivity growth has been sluggish by historical standards in the United States, and a decade after the 2008 crash, job numbers are back up. The trouble is, those jobs are less secure or reliable than before, and the owners are taking more of the spoils. More than machines replacing humans, the new jobs seem to expect humans to act like machines. Perhaps the real visionaries of the future of work are not the app makers but those organizing co-ops in the fast-growing care sectors, ensuring that the most difficult work remains accountable to flesh and blood and heart. If the cooperative legacy did not exist, their task might seem insurmountable. But it's really no worse than hard.
As the stories I've told in this book declare, cooperation is no drop-in solution-for-everything. It's a process that happens a million ways at once, a diversified democracy. The troubles are as endemic as the promise. It starts with the capacities we already have, recombined to solve common problems. The commonwealth doesn't defer its business until after the world passes through some revolutionary event. It doesn't wait for things to get worse so they can get better. It doesn't appear from nowhere and disrupt everything. Instead, it grows through what Grace Lee Boggs called "critical connections"—bridging generations, forging bonds too strong for profiteers to break. It requires people who know their own strengths.
A lot of those who have been drawn into the co-op movement in recent years hope it can be something like universal basic income—a drastic, radical fix that changes everything. They try to create co-ops for the hardest of problems, using the most untested of means, building their dreams out of policy proposals and foundation grants and panels at conferences. I watch the news of these developments closely. But some of the most remarkable things are happening more quietly, making use of latent resources already in our midst.
When I first took a phone call from Felipe Witchger, the young executive director of the Community Purchasing Alliance in Washington DC, I'd never heard of him or his organization. I'd never come across it on the newsletters and feeds I follow. And when I attended CPA's 2017 annual meeting, I realized what a lapse this was.
Seated around me were representatives of the 160 DC-area organizations—mainly churches and charter schools, largely people of color—that used CPA for purchasing such unglamorous things as electricity, security, sanitation, and landscaping. After three years in existence, CPA had saved them and the people they serve nearly $3 million. (A woman seated next to me, a part-time church staffer, said she'd cut out $17,000 on copier contracts alone.) The co-op had helped many of them switch to renewable energy, and their purchase of 580 solar panels, so far, had already brought down the price of solar for everyone in the region. On one end of the room were employees of a black-owned security company whose size more than doubled because of CPA contracts. Witchger was talking with some of CPA's contractors about converting their businesses to worker co-ops.
This kind of stepwise, ground-up cooperation has enjoyed less fanfare since the Great Recession than the pursuit of theoretical tropes that seem fresh and radical. Some, for instance, regard the precise locus of production as so important that they would reserve governance rights in a worker-owned co-op solely to "producer" workers, who physically make a given widget, over the "enablers," who answer phones, sweep floors, craft contracts, and the like. This kind of doctrinal fixation doesn't do much to anticipate automated or offshore production, rising demand for service work, and the disguised labor of online platforms. It also inclines us to neglect how pockets of commonwealth might emerge from zones of economic life other than factory floors—from schools, from churches, from taking out the trash. Hints from the cooperative past, and latent opportunities in the present, might be better suited to survive among profiteers with a multibillion-dollar head start.
Rusty old farmer co-ops could show urban contract workers how to organize joint bargaining and insurance. A buttoned-up mutual fund like Vanguard might be the model for a basic income grounded in genuine shared ownership.
Whether or not the Silicon Valley prognosticators are right to expect an economy less dependent on human labor, cooperators need to build on a diverse foundation, one that recognizes the diverse ways people interact with their economies—not only as certain kinds of workers but as consumers, users, contributors, small-business owners, and crowdfunders. We can learn to revive the democratic spirits dormant in so many credit unions, electric co-ops, insurance mutuals, and employee stock-ownership plans. There is no single, gleaming, out-of-the-box model. Commonwealths spread through variety.
The largest worker co-op in my town is Namasté Solar, a solar-panel installation company with more than one hundred member-owners. Since converting to a co-op in 2011, it has been a thriving business—and a certified B Corp whose members get six paid weeks off every year. It has no trouble finding investors willing to finance growth without demanding control. But its greatest systemic effect has happened outside the worker-ownership structure. First, Namasté spawned a spin-off, Amicus Solar, a purchasing cooperative that helps small solar companies across North America stay competitive against large corporations. That, in turn, spun off another co-op that pools maintenance services. Now the Namasté team is helping to create the Clean Energy Federal Credit Union, designed to provide loans for homeowners nationwide switching to renewables. One thing led to another, and out came a sizable chunk of commonwealth. Our newly legalized housing co-ops did much the same thing; cooperative grocery stores have never done well in Boulder, as the market for good food is already crowded, but when the co-op houses put their purchasing power together, they created a business that sells local and organic food for a fraction of the retail price. They realized their latent power and put it to use.
When we know the diversity and dexterity of past models, we'll be better at finding the combinations we need for the present. The trouble is, longings for a perfect order can tempt us more than the unfinished commonwealths of the past, whose salvation remains incomplete and locked in procedural dullness. Unlike capitalism's penchant for perpetual disruption, cooperation works best when it can work with what is already at hand.
The eminent scholars of the Italian co-op sector are Vera and Stefano Zamagni—historian and economist, wife and husband. Vera once served as the equivalent of lieutenant governor for the Emilia-Romagna region; Stefano was an architect of Pope Benedict XVI's economic statements, which baffled Cold War–minded readers with critiques of capitalism and socialism alike. Both teach at the University of Bologna, Europe's oldest university; it began in 1088 as a kind of cooperative among students who hired professors to teach them. When the Zamagnis talk about the origins of what modern Italian cooperation has accomplished, they start not with Rochdale or Italy's 1948 constitution, or with the earliest Italian co-ops a century before. They go back to the Middle Ages.
_Vera Zamagni lecturing in front of notes written earlier by Stefano Zamagni._
Since then, says Vera Zamagni, "Italy has tried to substitute economies of scale with economies of network." The northern Italian districts where cooperation now flourishes tended to be republican city-states, even in the age of emperors and princes and monasteries. From these came some basic features of the modern market economy—double-entry accounting, insurance, municipal regulation, professional guilds. The Zamagnis distinguish this region's "civil economy" from the capitalism that would emerge elsewhere in Europe to fund colonial expansion and exploitation.
Like Prime Produce and the unMonks, they see utility in old patterns. The system of interlinked, human-scaled co-ops in northern Italy, the Zamagnis believe, is a remnant of habits learned long ago; the comparative lack of co-ops in the southern part of the country reflects the monarchic rule that long prevailed there. When political scientist Robert Putnam studied variations among Italian regional governments starting in the 1970s, he also noticed this correlation. "Mirroring almost precisely that area where the communal republics had longest endured five centuries earlier," he wrote, "the medieval traditions of collaboration persisted, even among poor peasants."
According to the International Cooperative Alliance, "Cooperatives are businesses owned and run by and for their members." This is part of the basic definition, recognized around the world, including in Italy. But in Italy one hears executives and boards also insisting that their co-ops are _not_ for their members—they're for future generations. They're for the community. One hears this from both the big-time manufacturing executives and back-to-the-land farmers. The members are stewards, like a family with an apartment in what was once a regal palazzo, like the people who sweep the tourists' trash at a Roman ruin. This sense of history has helped make Italy's co-ops among the world's strongest. But history also tolerates their contradictions, their tendencies to drift into oligarchic control or capitalist conformity.
I want to take members from small, radical, and allegedly pure grocery co-ops in the United States on a field trip to visit an Ipercoop in Italy. They will find a dilemma. Ipercoop is the largest kind of store in the Coop Italia system, the country's largest grocery chain, resulting from decades of mergers among local consumer cooperatives throughout the country. It is not pure. Picture, on one end of a sprawling strip mall, a gigantic superstore with globalization's full variety of cheap, imported household goods beneath fluorescent suns overhead. Employees, many of them part-time, aren't especially well-paid or empowered in their workplace. Only twenty thousand of nearly nine million consumer-members take part in meetings. But the in-house brands have no genetically modified organisms or palm oil, and suppliers—many of which are themselves Italian co-ops—must conform to certain codes of ethics in their labor practices. Things could be worse. But this is unapologetic consumerism, for a competitive price.
Would the visiting cooperators want this for their co-ops? Most of them probably wouldn't. If it's our company, we might like it to be pure. But purity means accepting the fact that in addition to shopping at our co-op, we are probably also stopping by Target or Walmart for bulk necessities, or condescending toward our neighbors who do so. Ipercoop stands for the impure claim that if people are going to do gross consumerism anyway, they can at least not funnel the profits to investor-owners somewhere; they can add the leftovers to their savings. They can manage their own compromises.
Florescent superstores are only the start of the contradictions in Italy's cooperative commonwealth. At the headquarters of SACMI, an international manufacturing conglomerate near Bologna, one finds a prosperous machinery factory behind a pristine office building with a museum on the ground floor. SACMI is a worker co-op in which only about one-third of the more than one thousand eligible Italian workers are actually members; among the company's dozens of international subsidiaries, the Italian worker-owners don't bother promulgating cooperative values or possibilities in any way. ("We do not intend to do it," confirms one executive.) And this is one of the real co-ops—a dues-paying, upstanding Legacoop member. There are also tens of thousands of "false" co-ops in the country, firms that permit no oversight from the big associations and whose sole purpose may be to enable erstwhile employers to bypass workers' collective-bargaining rights. Even the storied social co-ops can play this kind of role; as critics feared, their rise has coincided with a long process of privatizing public services, enabling local governments to deliver services without paying government-level wages.
"Cooperatives have transformed into institutional loopholes," contends Lisa Dorigatti, a young researcher at the University of Milan who has studied co-op labor markets. Even Pope Francis, a frequent co-op advocate, has noticed the problem. "Counter the false cooperatives," he told a 2015 Confcooperative meeting, "because cooperatives must promote an economy of honesty."
Today, the pioneering types of people who built Italy's cooperative movement a century ago are not necessarily flooding into co-ops. They're not attending Coop Italia's annual meetings or holding out hope of becoming a SACMI member. If they're organizing co-ops, they're often treating the required board structures as a legal formality and governing themselves more like an open-source software project—whether they're writing code or growing vegetables. They're forgoing co-op language altogether, speaking instead about "political consumerism" and "solidarity purchasing." Yet according to University of Bergamo sociologist Francesca Forno, "I think we are going back to the roots of cooperativism." They want something more cooperative than Ipercoop.
Insiders and outsiders alike frequently mistake cooperative enterprise for a utopian project. But it never has been, or it never remains one for long. Constructing a commonwealth means insisting on principles while tolerating compromise.
"I rebuke them every day," Stefano Zamagni says of the big co-ops. But he's patient. With time, even partial manifestations of the commonwealth help the ideals spread.
The canon of international co-op values and principles that I began this book with can be deceptive; it seems to claim that there's a formula. Shared principles really just string together the cooperative habits that diverse peoples have carried with them, and that they bring to the common challenges of twenty-first-century survival. Economy is a form of culture. This is why a Kenyan woman I know who works at Vancity credit union in Canada could start a lending circle with fellow Kenyans, though the idea baffles her native-born Canadian friends—even ones at the credit union where she works. They didn't grow up watching their mothers going to lending-circle meetings.
Cooperators today neglect the local, diverse, compromised legacies at their peril—the aging cooperative grain elevators across the rural United States, or the gleaming aisles of an Italian Ipercoop. These are achievements that can lend the commonwealth of the future a leg up, and that can help it cross lines of political party and social class. Small, pioneering experiments help new generations hone their ambitions. But we also need to build on what we already have, where we already are.
If advocates for a cooperative commonwealth in the United States were to encourage not just worker co-ops but agricultural, utility, purchasing and credit co-ops as well, they might see their political support become drastically wider—not just Bernie Sanders, a longtime champion of worker ownership in Vermont, but Mike Pence, whose base has included electric co-ops and credit unions. That kind of bridge-crossing can seem unpleasant in hyperpartisan times, but it's possible. If Italy's Catholics and communists could unite around the practical work of building a commonwealth, perhaps Democrats and Republicans can, too.
Now, co-ops in Italy have to reach across an even wider gulf than political divisions. Migrants from Africa and the Middle East have upended the demographics of the country in less than a generation, and social co-ops have made a point of employing and integrating the newcomers. These people can't claim the same medieval inheritances that the native-born Catholics and communists had in common. Yet migrants are creating co-ops of their own now in Italy, bringing their cultures and cooperative habits with them. Just as for my own family's immigrant story, this kind of business opens doors that would otherwise be shut. People seeking an inclusive, responsive economy must continually relearn the lessons of commonwealths past—to work with what they have, to seek out the fullness of what they might share with one another.
There is a trap built into that International Cooperative Alliance formula about how co-ops are "businesses owned and run by and for their members." When all a business does is serve its existing members, and those members' perceptions of their worlds, it can fall stagnant, and stagnation in a changing world is no help to members. Investor-owned businesses attract investor-owners on the premise that they'll forever exceed expectations; it is both a virtue and a peril that co-ops tend to find their members under the humbler premise of meeting known, day-to-day needs.
A generation gap divides the cooperative movement today. The wealth and know-how and power is in older co-ops, which first arose to serve a sedentary economy no longer with us. Their directors are used to being maintainers; they're rarely equipped to mentor founders. Meanwhile, the new cooperators, confronting more nomadic forces, act as if they have to build the commonwealth they need all on their own, starting from zero. They can't find financing to support their startups, even if there's a massive cooperative bank just down the road (as there is from me); if they study business in school and they're taught to furnish investor profits, even though businesses all around them quietly practice cooperation. Today's equitable pioneers have invented new cooperative forms and pushed the commonwealth into untried territories, often because they didn't know any better and didn't have a choice.
A commonwealth must evolve—its technology, of course, but also its cultures and its structures. Somehow, despite the co-ops' laudable risk aversion, they need to find means of taking the risks necessary to support new ventures. Democracy has always been a risk; the inheritors of a co-op deserve the chance to take risks just as the founders did.
The future need not be a province reserved for profiteers. More or less democratic institutions have put people on the moon. They sponsored much of the technology that Silicon Valley investors now act as if they invented. And cooperatives have been taking care of people in ways that the reigning economy found otherwise impossible. The future may yet be, more than the present, a commonwealth.
I was still little when my Colorado grandfather died, but I remember the silver belt buckle he'd wear as if he were here right now. There was a brand name on it: _TRUSTWORTHY_ , with the _T_ s in _TRUST_ reaching down into _WORTHY_ below. Long before I knew that word's significance to him, I could tell it signified something important. He seemed to wear that buckle like he meant it.
I think I know a bit more now about why. Trustworthy was a brand that his company, Liberty Distributors, offered the stores it served. They could use it if they wanted to, or they could stick with their own. The brand was a claim to authenticity and reality against an ever-more big-box hardware industry, a claim that Liberty Distributors backed up with its cooperative ownership design and its bulk purchasing for local stores. It was a claim my grandfather wore on his belt even after he retired from the business.
_Two of my grandfather's buttons._
The equitable pioneers I meet lately don't much resemble my grandfather. They turn to cooperation for different reasons and in different ways. The achievements of commonwealths past have receded to an unremembered memory, a door on which they don't know how to knock. But it doesn't have to be that way. When the pioneers start to find each other, they also start piecing together what patches of commonwealth they've individually found. They become less alone. What they'd thought was pioneering becomes more like continuing, like pressing on.
While writing this book, I helped put together a group we call the Colorado Co-ops Study Circle. First it was just me and a friend in Denver who was struggling to start up her own co-op development consultancy. We tried to make it easy on ourselves—simple gatherings, announced online, on topics we were interested in, with a few snacks.
It wasn't long before twenty or thirty or forty people were coming to meetings. They were grilling a co-op lawyer we'd invited with questions, or learning esoteric secrets from a real-live Grange member, or tussling with divides of race and class. The people who came were working with partial knowledge, and partial experience, and eagerness to do more—to be, together, the makings of a new Colorado commonwealth. As we started, it could seem like we were starting from nothing. We weren't. On our simple website, I spent some late nights assembling a directory of co-ops in Colorado, thinking it would be an easy exercise, until night after night the list worked its way up to nearly four hundred entries. We were surrounded. We had shoulders on which to stand. We would soon begin an effort to try linking that commonwealth together through joint marketing and purchasing, in partnership with one of the country's biggest co-ops, and we formed an investment club of diverse, largely first-time investors to put our own money into the cooperatives to come.
When the Association of Cooperative Educators met in Denver during the Study Circle's first year, we decided it was time for a party. We'd been talking about a party for months, but finally we did it. The residents of Queen City Cooperative welcomed us to their house for supper with a full spread of home-cooked dishes. One Queen City member held court behind the bar out back, with a tap from a friendly brewery and a mojito punchbowl. An elder neighbor wanted to teach us a levitation trick. Most of us who had been at the conference found our way there late, but we came—co-op business consultants, a researcher studying how co-ops document themselves, a recent college graduate who'd just joined Denver's Community Language Cooperative as an interpreter. The farmers, young and old, mostly stayed home that night. I sat on the porch for a while with one of the political operatives from Boulder's housing co-ops; he updated me about the new house he was trying to fill and his new worker co-op, which was making software to analyze incriminating data about fossil-fuel power plants. He had the co-op symbol of the twin pines tattooed on one arm. But the champions of the evening were the Puerto Rican cooperators, their ages spanning four decades or more, who had already blown the mainlanders away with a presentation about their youth programs. They had swimming lessons and art contests and Olympic athletes as spokespeople. That night, as promised, they blew us away on the dance floor.
I'd been to Queen City on a few occasions before, but this was the first time I noticed the sign just inside the front door, to the left—one of those enclosed boxes with movable white plastic letters on black felt. It had come from a chiropractor's office; near the bottom it still said, "Ask us about our gift certificates." Above that were the first names of the members and "est. 2015." But the central item was a quotation, duly attributed to "MLK." It was the one that goes, "We may have come here on different ships, but we're in the same boat now."
# Acknowledgments
Throughout the preceding, I remix material—sometimes verbatim, often not—from previously published articles of mine, listed below. I am grateful for the collaboration of the editors, fact-checkers, copyeditors, transcribers, patrons, and readers who helped me hone the reporting that serves as the backbone of this book.
**Chapter 1**
"Commies for Christ," _New Inquiry_ (December 13, 2013).
"'Truly, Much Can Be Done!': Cooperative Economics from the Book of Acts to Pope Francis," in _Laudato Si': Ethical, Legal, and Political Implications_ , ed. Frank Pasquale (Cambridge University Press, forthcoming).
"Can Monasteries Be a Model for Reclaiming Tech Culture for Good?" _Nation_ (November 27, 2014).
**Chapter 2**
"10 Lessons from Kenya's Remarkable Cooperatives," _Shareable_ (May 4, 2015).
"Interviewed: The Leaders of Kenya's College for Cooperatives," _Shareable_ (April 24, 2015).
"'Truly, Much Can Be Done!': Cooperative Economics from the Book of Acts to Pope Francis," in _Laudato Si': Ethical, Legal, and Political Implications_ , ed. Frank Pasquale (Cambridge University Press, forthcoming).
"How Communists and Catholics Built a Commonwealth," _America_ (September 7, 2017).
"A New Way to Work," _America_ (August 15–22, 2016).
"Curricular Cop-Out on Co-ops," _Chronicle of Higher Education_ (October 9, 2016).
**Chapter 3**
"Detroit at Work," _America_ (October 24, 2014).
"Denver Taxi Drivers Are Turning Uber's Disruption on Its Head," _Nation_ (September 7, 2016).
"Sharing Isn't Always Caring," _Al Jazeera America_ (May 18, 2014).
"Owning Is the New Sharing," _Shareable_ (December 21, 2014).
"Figuring Out the Freelance Economy," _Vice_ (September 2016).
"Living, Breathing Platforms," _Enspiral Tales_ (June 23, 2016).
"Why One City Is Backing a Different Kind of Family Values: Housing Co-ops," _America_ (January 4, 2017).
**Chapter 4**
"For These Borrowers and Lenders, Debt Is a Relationship Based on Love," _YES! Magazine_ (September 21, 2015).
"After the Bitcoin Gold Rush," _New Republic_ (February 24, 2015).
"Code Your Own Utopia," _Al Jazeera America_ (April 7, 2014).
"Are You Ready to Trust a Decentralized Autonomous Organization?" _Shareable_ (July 14, 2014).
"A Techy Management Fad Gives Workers More Power—Up to a Point," _YES! Magazine_ (September 30, 2015).
"Be the Bank You Want to See in the World," _Vice_ (April 2015).
**Chapter 5**
"The Joy of Slow Computing," _New Republic_ (May 29, 2015).
"A Techy Management Fad Gives Workers More Power—Up to a Point," _YES! Magazine_ (September 30, 2015).
"Can Monasteries Be a Model for Reclaiming Tech Culture for Good?" _Nation_ (November 27, 2014).
"An Internet of Ownership: Democratic Design for the Online Economy," _Sociological Review_ 66, no. 2 (March 2018).
"How the Digital Economy Is Making Us Gleaners Again," _America_ (October 17, 2015).
"Intellectual Piecework," _Chronicle of Higher Education_ (February 16, 2015).
"Users Should Be Able to Own the Businesses They Love Instead of Investors," _Quartz_ (March 27, 2017).
"Our Generation of Hackers," _Vice_ (November 11, 2014).
"The Rise of a Cooperatively Owned Internet," _Nation_ (October 13, 2016).
"The Associated Press Is a Joint Media Venture. Maybe Twitter Should Be Too," _America_ (April 21, 2017).
**Chapter 6**
"Economic Democracy and the Billion-Dollar Co-op," _Nation_ (May 8, 2017).
"How Colorado Voters Could Usher in the Future of Healthcare in America," _Vice_ (December 14, 2015).
"Colorado's Universal Health Care Proposal Is Also a Seismic Expansion of Democracy," _America_ (June 30, 2016).
"How Communists and Catholics Built a Commonwealth," _America_ (September 7, 2017).
"Free the Land," _Vice_ (April 2016).
**Chapter 7**
"Why We Hack," in _Wisdom Hackers_ (The Pigeonhole, 2014).
"Why the Tech Elite Is Getting Behind Universal Basic Income," _Vice_ (January 2015).
"Dear Mark Zuckerberg: Democracy Is Not a Facebook Focus Group," _America_ (February 21, 2017).
"How Communists and Catholics Built a Commonwealth," _America_ (September 7, 2017).
I also stand in debt to the teams at Nation Books, Hachette, and Stuart Krichevsky Literary Agency for their aid in reassembling and reimagining that reporting here, particularly my agent David Patterson and my editor Katy O'Donnell. Barbara Croissant and Doug O'Brien provided generous feedback on drafts. My colleagues at the University of Colorado Boulder, especially through the leadership of Nabil Echchaibi, have shown me the solidarity of an ancient guild. And I've learned constantly from the cooperativism of my wife, Claire Kelley, in the business of our growing family and beyond.
This book would not be possible, finally, without those who allowed me to experience their stories and share them, the new equitable pioneers. In addition to people profiled herein, these guides include (but are not limited to) Nicole Alix, Martijn Arets, Ahmed Attia, Devin Balkind, Kaeleigh Barker Van Valkenburgh, Harriet Barlow, Paul Bindel, Joseph Blasi, David Bollier, Becks Boone, Jennifer Briggs, Greg Brodsky, Howard Brodsky, Alexa Clay, Nithin Coca, Matt Cropp, Brendan Denovan, Avery Edenfield, Hanan El Youssef, Laura Flanders, Natalie Foster, Karen Gargamelli, Shamika Goddard, Marina Gorbis, Jonathan Gordon-Farleigh, Jessica Gordon Nembhard, Neal Gorenflo, Stephanie Guico, Yessica Holguin, Jen Horonjeff, Sara Horowitz, Brent Hueth, Alanna Irving, Camille Kerr, Ben Knight, Corey Kohn, Marcia Lee, Rhys Lindmark, Pia Mancini, Annie McShiras, Micky Metts, Melina Morrison, Doug O'Brien, Janelle Orsi, Linda Phillips, Ludovica Rogers, Douglas Rushkoff, Caroline Savery, Trebor Scholz, Adam Schwartz, Zane Selvans, Palak Shah, Nuno Silva, Danny Spitzberg, Armin Steuernagel, Bill Stevenson, Michelle Sturm, Keith Taylor, Stacco Troncoso, Sandeep Vaheesan, Margaret Vincent, Halisi Vinson, Tom Webb, Jason Wiener, Elandria Williams, Felipe Witchger, and Erik Olin Wright. May what I've gleaned from you be of use.
#
**Nathan Schneider** is a professor of media studies at the University of Colorado Boulder. He is the author, most recently, of _Thank You, Anarchy: Notes from the Occupy Apocalypse_ and coeditor of _Ours to Hack and to Own: The Rise of Platform Cooperativism, a New Vision for the Future of Work and a Fairer Internet_.
# Illustration Credits
All photographs were taken by me in the course of reporting. For charts, maps, and other graphics, I draw from the following sources, with permission from relevant organizations.
Here Liberty Distributors, _Policies and Procedures_ (December 1978).
Here James Peter Warbasse, _Cooperative Democracy Through Voluntary Association of the People as Consumers_ , 3rd ed. (Harper and Brothers, 1936).
Here University of Wisconsin Center for Cooperatives.
Here Southeastern Michigan Council of Governments and Courtney Flynn, Wayne State University Center for Urban Studies.
Here Lawrence Mishel, "The Wedges Between Productivity and Median Compensation Growth," Economic Policy Institute, Issue Brief no. 330 (April 26, 2012).
Here Blockchain Luxembourg SA, api.blockchain.info/charts/preview /market-price.png?timespan=all&lang=en.
Here Richard Florida and Karen M. King, "Spiky Venture Capital: The Geography of Venture Capital Investment by Metro and Zip Code," Martin Prosperity Institute (February 22, 2016).
Here Rural Electrification Administration, _A Guide for Members of REA Cooperatives_ (US Department of Agriculture, 1939), 20–21.
Here Concept from Peter Turchin, "The Strange Disappearance of Cooperation in America," _Cliodynamica_ (blog) (June 21, 2013), peterturchin.com/cliodynamica/strange-disappearance. Data from Robert D. Putnam, _Bowling Alone: The Collapse and Revival of American Community_ (Simon & Schuster, 2000), 54, and Facundo Alvaredo, Anthony B. Atkinson, Thomas Piketty, and Emmanuel Saez, "The Top 1 Percent in International and Historical Perspective," _Journal of Economic Perspectives_ 27, no. 3 (Summer 2013): 3–20.
# Notes
Introduction: Equitable Pioneers
1. LeRoy Croissant, _Ancestors and Descendants of Fred Henry Croissant (1791–2001)_ , private family history (2001); the cassette tapes were made as part of Croissant's research for the book, recorded January 14 and 15, 1989.
2. Liberty Distributors, _Policies and Procedures_ (December 1978). The manual, found by my aunt Janet Finley in her basement, includes documents with various dates. The financial data comes from 1980, when the company's estimated sales volume was $660 million. I also spoke about the company with Chuck Short of Amarillo Hardware, one of Liberty's member-owners. Liberty dates back to 1935, and according to Short, it was not legally a cooperative but operated as one. In 1991, through a merger, what had been Liberty Distributors became part of another co-op, Distribution America.
3. Croissant, _Ancestors and Descendants_ ; according to Western Sugar Cooperative, "History," westernsugar.com/who-we-are/history, the company became a co-op in 2002.
4. Repeated throughout Peter Maurin, _Easy Essays_ (Wipf and Stock, 2010).
5. John Curl, _For All the People: Uncovering the Hidden History of Cooperation, Cooperative Movements, and Communalism in America_ , 2nd ed. (PM Press, 2012), 190–191; for analysis of earlier repression of US co-ops, see Marc Schneiberg, "Movements as Political Conditions for Diffusion: Anti-Corporate Movements and the Spread of Cooperative Forms in American Capitalism," _Organization Studies_ 34, no. 5–6 (2013).
6. The term _cooperative commonwealth_ first took hold with Laurence Gronlund, _The Co-operative Commonwealth in Its Outlines: An Exposition of Modern Socialism_ (Lee and Shepard, 1884), which translated Karl Marx into a more gradualist, explicitly Darwinist evolution into cooperative arrangements, while retaining Marx's all-encompassing state; Norman Thomas, _The Choice Before Us: Mankind at the Crossroads_ (AMS Press, 1934); on Du Bois and the commonwealth, see Olabode Ibironke, "W.E.B. Du Bois and the Ideology or Anthropological Discourse of Modernity: The African Union Reconsidered," _Social Identities_ 18, no. 1 (2012), and Jessica Gordon Nembhard, _Building a Cooperative Solidarity Commonwealth_ (The Next System Project, 2016); see also Edward K. Spann, _Brotherly Tomorrows: Movements for a Cooperative Society in America, 1820–1920_ (Columbia University Press, 1989), and Alex Gourevitch, _From Slavery to the Cooperative Commonwealth: Labor and Republican Liberty in the Nineteenth Century_ (Cambridge University Press, 2014).
7. Although the 1912 speech is frequently used as its source text, the phrase predated that occasion, as it had already inspired a poem by James Oppenheim in 1911. Minerva K. Brooks, "Votes for Women: Rose Schneiderman in Ohio," _Life and Labor_ (September 1912), 288; Margaret Dreier Robins, "Self-Government in the Workshop," _Life and Labor_ (April 1912), 108–110; for an account of US struggles over working hours, see Benjamin Kline Hunnicutt, _Free Time: The Forgotten American Dream_ (Temple University Press, 2013).
8. The laws in question are the Joint Stock Companies Act of 1856 and the Industrial and Provident Societies Partnership Act of 1852; Henry Hansmann, "All Firms Are Cooperatives—and So Are Governments," _Journal of Entrepreneurial and Organizational Diversity_ 2, no. 2 (2013).
9. _State of the Global Workplace_ (Gallup, 2017); Francesca Gino, "How to Make Employees Feel Like They Own Their Work," _Harvard Business Review_ (December 7, 2015); Jocko Willink and Leif Babin, _Extreme Ownership: How U.S. Navy SEALs Lead and Win_ (St. Martin's Press, 2015); see also widespread examples such as Micah Solomon, "The Secret of a Successful Company Culture: Spread a Sense of Ownership," _Forbes_ (July 7, 2014), and Joel Basgall, "Build a Culture of Ownership at Your Company," _Entrepreneur_ (October 1, 2014); on diverse forms of employee ownership, see Joseph R. Blasi, Richard B. Freeman, and Douglas L. Kruse, _The Citizen's Share: Reducing Inequality in the 21st Century_ (Yale University Press, 2012).
10. "ESOPs by the Numbers," National Center for Employee Ownership, nceo.org/articles/esops-by-the-numbers; however, only about two million workers experience an ESOP with significant scale or governance rights, according to Thomas Dudley, "How Big Is America's Employee-Owned Economy?" _Fifty by Fifty,_ on Medium (June 22, 2017).
11. The alliance uses " _Co-operative_ " in its name, but I omit the hyphen (which is standard British usage) for consistency, as with other deviations from US usage; I will continue to use "cooperative" in the main text but retain hyphens in these notes for bibliographic correctness. Dave Grace and Associates, _Measuring the Size and Scope of the Cooperative Economy: Results of the 2014 Global Census on Co-operatives_ (United Nations Secretariat Department of Economic and Social Affairs Division for Social Policy and Development, 2014); Hyungsik Eum, _Cooperatives and Employment: Second Global Report_ (CICOPA, 2017); International Cooperative Alliance, "Facts and Figures," ica.coop/en/facts-and-figures.
12. Liminality, "Cooperative Awareness Survey" (April 2017), commissioned by Cooperatives for a Better World.
13. Brent Hueth, "Missing Markets and the Cooperative Firm," Toulouse School of Economics, Conference on Producer Organizations (September 5–6, 2014).
14. Roberto Stefan Foa and Yascha Mounk, "The Danger of Deconsolidation: The Democratic Disconnect," _Journal of Democracy_ 27, no. 3 (July 2016).
15. President George W. Bush sought to promote both democratic politics abroad and an "ownership society" at home; this ownership society, however, was based on schemes that would replace shared, public ownership of health-care and education with individual purchasing of private-sector services. His British counterpart, Tony Blair, envisioned an ownership society with somewhat more cooperative components.
16. On Apple, see Lori Emerson, _Reading Writing Interfaces: From the Digital to the Bookbound_ (University of Minnesota Press, 2014), 77 and 81; Naisbitt quoted in Theodore Roszak, _The Cult of Information: The Folklore of Computers and the True Art of Thinking_ (Pantheon, 1986), 161.
17. International Cooperative Alliance, "Cooperative Identity, Values, and Principles," ica.coop/en/whats-co-op/co-operative-identity-values-principles; see also _Guidance Notes to the Cooperative Principles_ (International Cooperative Alliance, 2015). There are other sets of principles as well. The US government has its own set, focused on agricultural co-ops, discussed in Bruce J. Reynolds, _Comparing Cooperative Principles of the US Department of Agriculture and the International Cooperative Alliance_ (US Department of Agriculture, June 2014); worker co-ops in particular articulate distinct sets, largely overlapping with those of the ICA, in International Organisation of Industrial and Service Cooperatives, _World Declaration on Worker Cooperatives_ , approved by the ICA General Assembly in Cartagena, Colombia (September 23, 2005); Mondragon Corporation, "Our Principles," mondragon-corporation.com/en/co-operative-experience/our-principles.
18. Jonathan Stempel, "Arconic Is Sued in US over Fatal London Tower Fire," _Reuters_ (July 13, 2017); Geoffrey Supran and Naomi Oreskes, "What Exxon Mobil Didn't Say About Climate Change," _New York Times_ (August 22, 2017).
19. On union-cooperative alliances, see 1worker1vote.org and cincinnatiunioncoop.org; on Pope Francis, see my article "How Pope Francis Is Reviving Radical Catholic Economics," _Nation_ (September 9, 2015); on the Movement for Black Lives platform, see policy.m4bl.org/economic-justice; on the Labour Party, see Anca Voinea, "Corbyn's Digital Democracy Manifesto Promotes Co-operative Ownership of Digital Platforms," _Co-operative News_ (August 30, 2016); Bernie Sanders's original campaign website included "creating worker co-ops" as the last of its twelve policy proposals, but he rarely spoke of this publicly, and the idea was soon demoted to a lesser bullet point in his platform (see web.archive.org/web/20150430045208/berniesanders.com/issues); for a general discussion on the relationship between social movements and cooperation, see Schneiberg, "Movements as Political Conditions for Diffusion."
20. George Lakey, _Viking Economics: How the Scandinavians Got It Right—and How We Can, Too_ (Melville House, 2016); Jessica Gordon Nembhard, _Collective Courage: A History of African American Cooperative Economic Thought and Practice_ (University of Pennsylvania Press, 2014); M. K. Gandhi, _Constructive Programme: Its Meaning and Place_ , 2nd ed. (Navajivan, 1945).
21. This is AnyShare, an online platform designed through FairShares, a UK-based framework for developing multi-stakeholder co-ops; Josef Davies-Coates, "Open Co-ops—An Idea Whose Time Has Come?" Open Co-op blog (January 7, 2014); Michel Bauwens, "Open Cooperativism for the P2P Age," P2P Foundation blog (June 16, 2014); Pat Conaty and David Bollier, _Toward an Open Co-operativism: A New Social Economy Based on Open Platforms, Co-operative Models and the Commons_ (Commons Strategies Group, 2014), commonsstrategies.org/towards-an-open-co-operativism.
22. A useful critical discussion, for instance, is Matthew D. Dinan, "Keeping the Old Name: Derrida and the Deconstructive Foundations of Democracy," _European Journal of Political Theory_ 13, no. 1 (2014).
Chapter 1: All Things in Common
1. John Coney (dir.), _Space Is the Place_ (1974), 32:00.
2. Jean Leclercq, _The Love of Learning and the Desire for God_ (Fordham University Press, 1961), 175.
3. E.g., Lynn Margulis, _Symbiotic Planet: A New Look at Evolution_ (Basic Books, 1998); Martin A. Nowak and Roger Highfield, _Super-Cooperators: Altruism, Evolution, and Why We Need Each Other to Succeed_ (Free Press, 2012).
4. Margaret Mead, ed., _Cooperation and Competition Among Primitive Peoples_ (McGraw-Hill, 1937), 16; Alexa Clay, "Neo-Tribes: The Future Is Tribal," keynote at re:publica in Berlin, Germany (May 4, 2016).
5. Adapted, not verbatim, from Elinor Ostrom, _Governing the Commons: The Evolution of Institutions for Collective Action_ (Cambridge University Press, 1990), 90; for applications of Ostrom's framework to historical commons, see "Collective Action Institutions in a Long-Term Perspective," a special issue of the _International Journal of the Commons_ 10, no. 2 (2016); an excellent primer on the commons is David Bollier, _Think Like a Commoner: A Short Introduction to the Life of the Commons_ (New Society Publishers, 2014).
6. Ed Mayo, _A Short History of Co-operation and Mutuality_ (Co-operatives UK, 2017).
7. Acts 2:43–45. This and all subsequent biblical quotations are from the New American Bible.
8. Acts 4:32 and 5:12.
9. Acts 6:1–6.
10. Augustine of Hippo, _The Rule of St. Augustine_ , trans. Robert Russell (Brothers of the Order of Hermits of Saint Augustine, 1976); Benedict of Nursia, _RB 1980: The Rule of St. Benedict in English_ , trans. Timothy Fry (Liturgical Press, 1981), chap. 3; the relevance of the Benedictine rule to modern cooperativism is the subject of Greg MacLeod, "The Monastic System as a Model for the Corporate Global System," Work as Key to the Social Question conference, Vatican City (September 12–15, 2001).
11. Chap. 4 of the Rule of St. Clare, in _Francis and Clare: The Complete Works_ , trans. R. J. Armstrong (Paulist Press, 1988), 215–216. The words "among us" are in brackets in the original.
12. For an extended discussion of this debate, see Giorgio Agamben, _The Highest Poverty: Monastic Rules and Form-of-Life_ , trans. Adam Kotsko (Stanford University Press, 2013).
13. Robert Harry Inglis Palgrave, ed., _Dictionary of Political Economy_ , vol. 1 (Macmillan, 1915), 212; I've changed "all men" to "everyone," which is also the translation used in Agamben, _The Highest Poverty_ , 112. _Catechism of the Catholic Church_ , 2nd ed. (Liberia Editrice Vaticana, 1993), pt. 3, sec. 2, chap. 2, art. 7.I.
14. Benedict of Nursia, _RB 1980_ , chap. 33.
15. Steven A. Epstein, _Wage Labor and Guilds in Medieval Europe_ (University of North Carolina Press, 1995), 40–41.
16. Thomas Müntzer, _Sermon to the Princes_ (Verso, 2010), 96–97.
17. A more Protestant-oriented version of the history of Christian cooperation can be found in Andrew McLeod, _Holy Cooperation! Building Graceful Economies_ (Cascade Books, 2009).
18. See Peter Linebaugh, _The Magna Carta Manifesto: Liberties and Commons for All_ (University of California Press, 2009); Karl Polanyi, _The Great Transformation: The Political and Economic Origins of Our Time_ (Beacon Press, 2001 [1944]); Silvia Federici, _Caliban and the Witch: Women, the Body and Primitive Accumulation_ (Autonomedia, 2014 [2004]).
19. "The True Levellers Standard Advanced," in Gerrard Winstanley, _A Common Treasury_ (Verso, 2011), 17.
Chapter 2: The Lovely Principle
1. James Peter Warbasse, _Cooperative Democracy Through Voluntary Association of the People as Consumers_ , 3rd ed. (Harper and Brothers, 1936), 61–62. Originally called the Cooperative League of America, its name first changed in 1922. The organization was partly an outgrowth of the Jewish Cooperative League, founded in 1909 on New York's Lower East Side.
2. Murray D. Lincoln, _Vice President in Charge of Revolution_ (McGraw-Hill, 1960), 108.
3. Warbasse, _Cooperative Democracy_ , 270.
4. Here, and for much of the early history of US cooperation, I draw from John Curl, _For All the People: Uncovering the Hidden History of Cooperation, Cooperative Movements, and Communalism in America_ , 2nd ed. (PM Press, 2012); Jessica Gordon Nembhard, _Collective Courage: A History of African American Cooperative Economic Thought and Practice_ (University of Pennsylvania Press, 2014); Joseph G. Knapp, _The Rise of American Cooperative Enterprise: 1620–1920_ (Interstate, 1969); and Edward K. Spann, _Brotherly Tomorrows: Movements for a Cooperative Society in America, 1820–1920_ (Columbia University Press, 1989). The cod-fishery story is recounted in the introduction to Joseph R. Blasi, Richard B. Freeman, and Douglas L. Kruse, _The Citizen's Share: Reducing Inequality in the 21st Century_ (Yale University Press, 2012).
5. Quoted in Gordon Nembhard, _Collective Courage_ , 36.
6. Abraham Lincoln, "Address Before the Wisconsin State Agricultural Society, Milwaukee, Wisconsin," in _Collected Works of Abraham Lincoln_ , vol. 3 (University of Michigan Digital Library Production Services, 2001).
7. For the longer philosophical tradition, David Ellerman, "On the Renting of Persons," _Economic Thought_ 4, no. 1 (2015); the account of Lowell is from Bruce Laurie, _Artisans into Workers: Labor in Nineteenth-Century America_ (University of Illinois Press, 1997), 87; the lyric was a parody of a popular song, "I Won't Be a Nun."
8. George Jacob Holyoake, _The History of Cooperation_ , rev. ed. (T. Fisher Unwin, 1908 [1875]), 11 and 13. Another prominent, parallel chronicle of the period is Beatrice Potter Webb, _The Co-operative Movement in Great Britain_ (Allen and Unwin, 1899).
9. Holyoake, _The History of Cooperation_ , 34.
10. Holyoake, 40.
11. There are suggestions that the significance of Rochdale has been overblown by the influence of Holyoake, for instance, in Brett Fairbairn, _The Meaning of Rochdale: The Rochdale Pioneers and the Co-operative Principles_ (Centre for the Study of Co-operatives, University of Saskatchewan, 1994), and John F. Wilson, Anthony Webster, and Rachael Vorberg-Rugh, _Building Co-operation: A Business History of The Co-operative Group, 1863–2013_ (Oxford University Press, 2013); a map of pre-Rochdale cooperatives in England can be found in Ed Mayo, _A Short History of Co-operation and Mutuality_ (Co-operatives UK, 2017); but given the role of Rochdale in the establishment of Britain's dominant cooperative organizations, such revisionist histories don't fully contradict Holyoake's boosterism.
12. Holyoake, _The History of Cooperation_ , 280–281; Webb, _The Co-operative Movement in Great Britain_ , emphasizes the comparison in approaches to private property.
13. George Jacob Holyoake, _The History of the Rochdale Pioneers_ , 10th ed. (George Allen and Unwin, 1893), 21; Holyoake, _The History of Cooperation_ , 287–288.
14. The definitive source for this history is Wilson, _Building Co-operation_.
15. Missing markets: Brent Hueth, "Missing Markets and the Cooperative Firm," Toulouse School of Economics, Conference on Producer Organizations (September 5–6, 2014); Kazuhiko Mikami, _Enterprise Forms and Economic Efficiency: Capitalist, Cooperative and Government Firms_ (Routledge, 2013); E. G. Nourse, "The Economic Philosophy of Co-operation," _American Economic Review_ 12, no. 4 (December 1922). Startup costs: Hueth, "Missing Markets." Productivity benefits: Peter Bogetoft, "An Information Economic Rationale for Cooperatives," _European Review of Agricultural Economics_ 32 (2005); Peter Molk, "The Puzzling Lack of Cooperatives," _Tulane Law Review_ 88 (2014); Virginie Pérotin, _What Do We Really Know About Worker Cooperatives?_ (Co-operatives UK, 2016). Protection: Henry Hansmann, _The Ownership of Enterprise_ (Harvard University Press, 2000); Pérotin, _What Do We Really Know_. Information sharing: Bogetoft, "An Information Economic Rationale"; Timothy W. Guinnane, "Cooperatives as Information Machines: German Rural Credit Cooperatives, 1883–1914," _Journal of Economic History_ 61, no. 2 (2001); Mikami, _Enterprise Forms_. Chance of failure: John W. Mellor, _Measuring Cooperative Success: New Challenges and Opportunities in Low- and Middle-Income Countries_ (United States Overseas Cooperative Development Council and United States Agency for International Development, 2009); Molk, "The Puzzling Lack"; Erik K. Olsen, "The Relative Survival of Worker Cooperatives and Barriers to Their Creation," in _Sharing Ownership, Profits, and Decision-Making in the 21st Century_ , ed. Douglas Kruse (Emerald Group Publishing, 2013); Pérotin, _What Do We Really Know_. Resilience: Johnston Birchall, _Resilience in a Downturn: The Power of Financial Cooperatives_ (International Labour Organization, 2013); Clifford Rosenthal, _Credit Unions, Community Development Finance, and the Great Recession_ (Federal Reserve Bank of San Francisco, 2012); Guillermo Alves, Gabriel Burdín, and Andrés Dean, "Workplace Democracy and Job Flows," _Journal of Comparative Economics_ 44, no. 2 (May 2016). Cost savings: Hansmann, _The Ownership of Enterprise_ ; Hueth, "Missing Markets"; Pérotin, _What Do We Really Know_.
16. Quoted from an epigraph in Holyoake, _The History of Cooperation_ , 312 and 355–356; Curl, _For All the People_ , pt. I, chap. 3, epub; Victor Rosewater, _History of Cooperative News-Gathering in the United States_ (D. Appleton, 1930).
17. Poster for the Union Co-operative Association No. 1 of Philadelphia, quoted in Steve Leikin, _The Practical Utopians: American Workers and the Cooperative Movement in the Gilded Age_ (Wayne State University Press, 2005), 1; _Iron Molders' International Journal_ (May 1868), quoted in Leikin, 28.
18. David T. Beito, _From Mutual Aid to the Welfare State: Fraternal Societies and Social Services, 1890–1967_ (University of North Carolina Press, 2000); Blasi, Freeman, and Kruse, _The Citizen's Share_ , 141–142.
19. Curl, _For All the People_ , pt. I, chaps. 5–6, epub; Lawrence Goodwyn, _The Populist Moment: A Short History of the Agrarian Revolt in America_ (Oxford University Press, 1978); Knapp, _The Rise of American Cooperative Enterprise;_ Leikin, _The Practical Utopians_.
20. W. E. Burghardt Du Bois, ed., _Economic Co-operation Among Negro Americans_ (Atlanta University Press, 1907), 4. See also Gordon Nembhard, _Collective Courage_.
21. Gordon Nembhard, _Collective Courage_ , 85.
22. Charles Caryl, _New Era: Presenting the Plans for the New Era Union_ [...] (1897); Silvia Pettem, _Only in Boulder: The County's Colorful Characters_ (History Press, 2010); Bradford Peck, _The World a Department Store: A Story of Life Under a Coöperative System_ (1900); Spann, _Brotherly Tomorrows_ , 216–219. The works of both Caryl and Peck resemble the style of Edward Bellamy's hugely popular _Looking Backward_ , published in 1888.
23. See especially Knapp, _The Rise of American Cooperative Enterprise_ ; on antitrust, see John Hanna, "Antitrust Immunities of Cooperative Associations," _Law and Contemporary Problems_ 13 (Summer 1948), and Christine A. Varney, "The Capper-Volstead Act, Agricultural Cooperatives, and Antitrust Immunity," _Antitrust Source_ (December 2012).
24. Cooperative League of the USA, _The Co-ops Are Comin'_ (1941), archive.org/details/the-co-ops-are-comin-1941. In the film, "study groups" is italicized.
25. Andrea Gagliarducci, "The Man Who Put _Laudato Si_ into Practice in Ecuador—Forty Years Ago," _Catholic News Agency_ (July 8, 2015).
26. J. Carroll Moody and Gilbert C. Fite, _The Credit Union Movement: Origins and Development, 1850-1980_ (Kendall/Hunt, 1984); Susan MacVittie, "Credit Unions: The Farmers' Bank," _Watershed Sentinel_ (January 16, 2018); William Foote Whyte and Kathleen King Whyte, _Making Mondragón: The Growth and Dynamics of the Worker Cooperative Complex_ , 2nd ed. (ILR Press, 1991).
27. On Judaism, see Noémi Giszpenc, "Cooperatives: The (Jewish) World's Best-Kept Secret," _Jewish Currents_ (Autumn 2012); on Protestantism, see Andrew McLeod, _Holy Cooperation! Building Graceful Economies_ (Cascade Books, 2009); cooperatives are widespread in many Muslim- and Buddhist-majority regions, as well as among their diasporic communities elsewhere, and cooperators reinterpret the model through the local religious vernacular.
28. Leo XIII, _Rerum Novarum_ , sec. 46.
29. The ideological foundations of Catholic cooperativism make for a checkered pedigree. Pope Pius XI, who echoed Leo XIII in more explicitly cooperative form, became caught up in prewar entanglements with Benito Mussolini, and Belloc and Chesterton harbored fascist, racist sympathies alongside their distributist longings. These tendencies were less common among the actual practitioners of Catholic cooperation.
30. José María Arizmendiarrieta, _Reflections_ (Otalora, 2013), sec. 213; see also Race Mathews, _Jobs of Our Own: Building a Stakeholder Society; Alternatives to the Market and the State_ , 2nd ed. (Distributist Review Press, 2009), and _Of Labour and Liberty: Distributism in Victoria 1891–1966_ (Monash University Publishing, 2017); another important account of the Mondragon system is Whyte and Whyte, _Making Mondragón_. As one Basque biographer put it in the opening lines of his book, "Arizmendiarrieta did not start—historically or systematically—from the philosophical analysis of a theory of history or production; his primary source of inspiration, rather, is in a concrete philosophical conception of the person" (Joxe Azurmendi, _El Hombre Cooperativo: Pensamiento de Arizmendiarrieta_ [Lan Kide Aurrezkia, 1984], via a draft translation by Steve Herrick of the Interpreters' Cooperative of Madison).
31. "Father Albert McKnight," Cooperative Hall of Fame, heroes.coop/archive/father-albert-mcknight; Albert J. McKnight, _Whistling in the Wind: The Autobiography of The Rev. Albert J. McKnight, C. S. Sp._ (Southern Development Foundation, 2011), epub; Mary Anne Rivera, "Jubilee: A Magazine of the Church and Her People: Toward a Vatican II Ecclesiology," _Logos: A Journal of Catholic Thought and Culture_ 10, no. 4 (Fall 2007); see Catholic Relief Services, "Agency Strategy," crs.org/about/agency-strategy; "Interfaith Partners," Equal Exchange, equalexchange.coop/our-partners/interfaith-partners; for more on Catholic tradition, Pope Francis, and cooperation, see my chapter "'Truly, Much Can Be Done!': Cooperative Economics from the Book of Acts to Pope Francis," in _Laudato Si': Ethical, Legal, and Political Implications_ , ed. Frank Pasquale (Cambridge University Press, forthcoming).
32. L. Cannari and G. D'Alessio, "La Distribuzione del Reddito e della Ricchezza nelle Regioni Italiane," Banca d'Italia, _Temi di Discussione del Servizio Studi_ no. 482 (June 2003); Flavio Delbono, "The Sources of GDP in [the] Emilia Romagna Region and the Role of Co-operation," Emilia Romagna Cooperative Study Tour lecture at the University of Bologna (June 8, 2017); Delbono, a prominent economist and former mayor of Bologna, argued both in that lecture and in subsequent correspondence for a causal relationship that the co-ops have on the region's economic indicators. I draw here considerably from the experience of the study tour, co-organized by the Co-operative Management Education program at Saint Mary's University and the Department of Economics at the University of Bologna.
33. Spelled "Co-operative Bank," following British usage.
34. For overviews of the Kenyan cooperative economy and its history, see Ndwakhulu Tshishonga and Andrew Emmanuel Okem, "A Review of the Kenyan Cooperative Movement," in _Theoretical and Empirical Studies on Cooperatives_ , ed. Andrew Emmanuel Okem (Springer, 2016); Fredrick O. Wanyama, "The Qualitative and Quantitative Growth of the Cooperative Movement in Kenya," in _Cooperating Out of Poverty: The Renaissance of the African Cooperative Movement_ , ed. Patrick Develtere, Ignace Pollet, and Fredrick Wanyama (International Labour Organization, 2008).
35. E. N. Gicheru, "Engaging Co-operatives in Addressing Local and Global Challenges: The Role of Co-operatives in Generating Sustainable Livelihood," presented at a United Nations meeting on cooperatives in Addis Ababa, Ethiopia (September 4–6, 2012); CoopAfrica, "Kenya," International Labour Organization, ilo.org/public/english/employment/ent/coop/africa/countries/eastafrica/kenya.htm.
36. Roderick Hill, "The Case of the Missing Organizations: Co-operatives and the Textbooks," _Journal of Economic Education_ (Summer 2000); see also Panu Kalmi, "The Disappearance of Cooperatives from Economics Textbooks," _Cambridge Journal of Economics_ 31, no. 4 (2007).
37. Quoted in Lee Altenberg, "An End to Capitalism: Leland Stanford's Forgotten Vision," _Sandstone and Tile_ 14, no. 1 (Winter 1990).
38. Joss Winn, "Democratically Controlled, Co-operative Higher Education." _openDemocracy_ (April 23, 2015); The Schools Co-operative Society, co-operativeschools.coop.
39. Altenberg, "An End to Capitalism."
Chapter 3: The Clock of the World
1. See the final summary of her thinking, Grace Lee Boggs with Scott Kurashige, _The Next American Revolution: Sustainable Activism for the Twenty-First Century_ , 2nd ed. (University of California Press, 2012).
2. See Kathi Weeks, _The Problem with Work: Feminism, Marxism, Antiwork Politics, and Postwork Imaginaries_ (Duke University Press, 2011).
3. Jared Bernstein coined the term based on 2011 Bureau of Labor Statistics data comparing productivity to private-sector employment: Bernstein, "The Challenge of Long Term Job Growth: Two Big Hints," _On the Economy_ (blog) (June 5, 2011), jaredbernsteinblog.com/the-challenge-of-long-term-job-growth-two-big-hints; Andrew McAfee, "Productivity and Employment (and Technology): In the Jaws of the Snake" (March 22, 2012), andrewmcafee.org/2012/03/mcafee-bernstein-productivity-employment-technology-jaws-snake. See also Lawrence Mishel, "The Wedges Between Productivity and Median Compensation Growth," Economic Policy Institute, Issue Brief no. 330 (April 26, 2012).
4. Jim Tankersley, "Meet the 26-Year-Old Who's Taking on Thomas Piketty's Ominous Warnings About Inequality," _Washington Post_ (March 19, 2015).
5. Joseph L. Bower and Clayton M. Christensen, "Disruptive Technologies: Catching the Wave," _Harvard Business Review_ (January–February 1995); Clayton M. Christensen, _The Innovator's Solution: Creating and Sustaining Successful Growth_ (Harvard Business Press, 2003). Between the former and the latter, he adjusted the term from "disruptive technology" to "disruptive innovation."
6. James Manyika et al., _Jobs Lost, Jobs Gained: Workforce Transitions in a Time of Automation_ (McKinsey Global Institute, 2017).
7. See Thomas I. Palley, _Financialization: The Economics of Finance Capital Domination_ (Palgrave Macmillan, 2013).
8. Johnston Birchall, _Resilience in a Downturn: The Power of Financial Cooperatives_ (International Labour Organization, 2013); Clifford Rosenthal, _Credit Unions, Community Development Finance, and the Great Recession_ (Federal Reserve Bank of San Francisco, 2012).
9. For seminal accounts of these and other major examples from the recent cooperative movement, see John Restakis, _Humanizing the Economy: Co-operatives in the Age of Capital_ (New Society Publishers, 2010), J. Tom Webb, _From Corporate Globalization to Global Co-operation: We Owe It to Our Grandchildren_ (Fernwood Publishing, 2016); Jonathan Michie, Joseph R. Blasi, and Carlo Borzaga, eds., _The Oxford Handbook of Mutual, Co-operative, and Co-owned Business_ (Oxford University Press, 2017). For more examples of worker co-governance, which doesn't necessarily involve cooperative ownership, see Immanuel Ness and Dario Azzellini, eds., _Ours to Master and to Own: Workers' Control from the Commune to the Present_ (Haymarket, 2011); Catherine P. Mulder, _Transcending Capitalism Through Cooperative Practices_ (Palgrave Macmillan, 2015); Daniel Zwerdling, _Workplace Democracy: A Guide to Workplace Ownership, Participation and Self-Management Experiments in the United States and Europe_ (Harper Colophon, 1980). On ESOPs, "ESOPs by the Numbers," National Center for Employee Ownership, nceo.org/articles/esops-by-the-numbers; the initiative Fifty by Fifty (fiftybyfifty.org) seeks to reach fifty million employee owners by 2050. Visa has since demutualized; Dee Hock described this fate to me in an email as "organizationally inevitable, economically greedy, socially unjust, creatively barren, philosophically foolish, and a disappointment to its founder." I also can't mention the Park Slope Food Co-op without confessing to having broken its rules by not becoming a member myself while sharing a household with my wife, a member and a far better cooperator than I am.
10. Oscar Perry Abello, "NYC Set to Triple Number of Worker Cooperatives," _Next City_ (January 11, 2016); Marielle Mondon, "Co-Op Success in Cleveland Is Catching On," _Next City_ , (March 17, 2015); for more on the "Cleveland model," see community-wealth.org, produced by the Democracy Collaborative, and a critique at Atlee McFellin, "The Untold Story of the Evergreen Cooperatives," _Grassroots Economic Organizing_ (November 7, 2016); Ajowa Nzinga Ifateyo, "$5 Million for Co-op Development in Madison," _Grassroots Economic Organizing_ (January 26, 2015); Malcolm Burnley, "Oakland Is Claiming Its Worker Cooperative Capital Title," _Next City_ (September 22, 2015); "Legislative Package Introduced to Encourage Employee-Owned Companies," Senator Bernie Sanders press release (May 11, 2017); Mary Hoyer, "Labor Unions and Worker Co-ops: The Power of Collaboration," _Grassroots Economic Organizing_ (July 9, 2015).
11. Kari Lydersen, _Revolt on Goose Island: The Chicago Factory Takeover and What It Says About the Economic Crisis_ (Melville House, 2009); Astra Taylor, "Hope and Ka-ching," _The Baffler_ 25 (2014); the Working World's loans to New Era appear at theworkingworld.org/us/loans/loans/1344.
12. For more on Airbnb's special relationship with Paris, see Jeff Sharlet, "Cult of Hospitality," _Travel + Leisure_ (April 21, 2016).
13. Trebor Scholz, notably, challenged Botsman's enthusiasm for online labor markets: "This is a total affront to what the labor movement has struggled for for centuries"; find his argument, in book form, in _Uberworked and Underpaid: How Workers Are Disrupting the Digital Economy_ (Polity, 2017). For a broader account of debates over the sharing economy, see Juliet Schor, "Debating the Sharing Economy," Great Transition Initiative (October 2014).
14. For an overview of similar responses to precarious work, see Pat Conaty, Alex Bird, and Cilla Ross, _Working Together: Trade Union and Co-operative Innovations for Precarious Workers_ (Co-operatives UK, 2018).
15. The organization's internal documentation is public at handbook.enspiral.com.
16. Alex Burness, "At Long Last, Boulder Approves New Co-op Housing Ordinance," _Daily Camera_ (January 4, 2017).
17. James Howard Kunstler, "The Ghastly Tragedy of the Suburbs," TED talk (May 2007).
Chapter 4: Gold Rush
1. See John T. Noonan Jr., _The Scholastic Analysis of Usury_ (Harvard University Press, 1957); Jacques Le Goff, _Your Money or Your Life: Economy and Religion in the Middle Ages_ (Zone Books, 1988).
2. See Nathan Schneider, "How a Worker-Owned Tech Startup Found Investors—and Kept Its Values," _YES! Magazine_ (April 26, 2016).
3. Credit Union National Association, "Credit Union Data and Statistics," cuna.org/Research-And-Strategy/Credit-Union-Data-And-Statistics; CoBank, "About CoBank," cobank.com/About-CoBank.aspx.
4. Satoshi Nakamoto, "Bitcoin Open Source Implementation of P2P Currency," P2P Foundation Ning forum (February 11, 2009), p2pfoundation.ning.com/forum/topics/bitcoin-open-source; see also the original Bitcoin white paper at bitcoin.org/bitcoin.pdf; for a fuller account of the rise of Bitcoin, see Nathaniel Popper, _Digital Gold: Bitcoin and the Inside Story of the Misfits and Millionaires Trying to Reinvent Money_ (Harper, 2015).
5. Daniela Hernandez, "Homeless, Unemployed, and Surviving on Bitcoins," _Wired_ (September 13, 2013); Kim Lachance Shandrow, "Bill Gates: Bitcoin Is 'Better Than Currency,'" _Entrepreneur_ (October 3, 2014); for an eloquent critique of bitcoin, see Brett Scott's "Visions of a Techno-Leviathan: The Politics of the Bitcoin Blockchain," _E-International Relations_ (June 1, 2014) and "How Can Cryptocurrency and Blockchain Technology Play a Role in Building Social and Solidarity Finance?" working paper for the United Nations Research Institute for Social Development (February 2016).
6. Because many people who were writing about Bitcoin early on were also holders of bitcoins, reliable analysts were few and far between; Swanson's work was a welcome exception. See his books at ofnum bers.com. Although Bitcoin's open ledger is a statistician's dream, it's not easy to associate accounts to actual human beings. For demographic data, see Lui Smyth, "Bitcoin Community Survey 2014" (February 1, 2014), http://simulacrum.cc/2014/02/01/bitcoin-community-survey-2014; Neil Sardesai, "Who Owns All the Bitcoins—An Infographic of Wealth Distribution," _CryptoCoinsNews_ (March 31, 2014); CoinDesk, _Who Really Uses Bitcoin?_ (June 10, 2015), coindesk.com/research/who-really-uses-bitcoin; Olga Kharif, "The Bitcoin Whales: 1,000 People Who Own 40 Percent of the Market," _Bloomberg Businessweek_ (December 8, 2017); Coin Dance, "Bitcoin Community Engagement by Gender Summary," coin.dance/stats/gender (94.73 percent male in March 2018).
7. Buterin's original white paper can be found at github.com/ethereum/wiki/wiki/White-Paper.
8. Perhaps the first scholarly presentation to take Ethereum seriously was Primavera De Filippi, "Ethereum: Freenet or Skynet?" luncheon at Berkman Klein Center for Internet and Society at Harvard University (April 15, 2014), cyber.harvard.edu/events/luncheon/2014/04/difilippi; see also the widely circulated video "Vitalik Buterin Reveals Ethereum at Bitcoin Miami 2014," youtube.com/watch?v=l9dpjN3Mwps; a compelling early analysis of Buterin's worldview is Sam Frank, "Come With Us If You Want to Live," _Harper's Magazine_ (January 2015); for a technical perspective, see Ethereum Foundation, "How to Build a Democracy on the Blockchain," ethereum.org/dao.
9. Vitalik Buterin, comment on Reddit thread (April 6, 2014), reddit.com/r/ethereum/comments/22av9m/code_your_own_utopia.
10. Follow the ongoing contest of currencies at coinmarketcap.com; for CU Ledger, see culedger.com.
11. Joon Ian Wong and Ian Kar, "Everything You Need to Know About the Ethereum 'Hard Fork,'" _Quartz_ (July 18, 2016).
12. Duran served as a significant informant, referred to as "Pau," in Jeffrey S. Juris, _Networking Futures: The Movements Against Corporate Globalization_ (Duke University Press, 2008).
13. Enric Duran, _Abolim la Banca_ (Ara Llibres, 2009).
14. For a more recent overview of the CIC, as well as more details on its organizational structure, see George Dafermos, _The Catalan Integral Cooperative: An Organizational Study of a Post-Capitalist Cooperative_ (P2P Foundation and Robin Hood Coop, 2017).
15. The mysterious first chapter of FairCoin's life remains archived in a popular cryptocurrency forum: bitcointalk.org/index.php?topic=487212.0.
Chapter 5: Slow Computing
1. Christopher M. Kelty, _Two Bits: The Cultural Significance of Free Software_ (Duke University Press, 2008).
2. Jodi Dean, "The Communist Horizon," lecture at No-Space in Brooklyn, New York (July 28, 2011), vimeo.com/27327373.
3. W3Techs, "Usage of Operating Systems for Websites," w3techs.com/technologies/overview/operating_system/all.
4. E. Gabriella Coleman, _Coding Freedom: The Ethics and Aesthetics of Hacking_ (Princeton University Press, 2012); Christopher M. Kelty, _Two Bits_ ; David Bollier, "Inventing the Creative Commons," in _Viral Spiral: How the Commoners Built a Digital Republic of Their Own_ (New Press, 2008).
5. Theodore Roszak, _The Cult of Information: The Folklore of Computers and the True Art of Thinking_ (Pantheon, 1986), 138–141; see also Fred Turner, _From Counterculture to Cyberculture: Stewart Brand, the Whole Earth Network, and the Rise of Digital Utopianism_ (University of Chicago Press, 2006), and Judy Malloy, ed., _Social Media Archeology and Poetics_ (MIT Press, 2016).
6. Coleman, _Coding Freedom_ ; Brian J. Robertson, _Holacracy: The New Management System for a Rapidly Changing World_ (Henry Holt, 2015); Frederic Laloux, _Reinventing Organizations: A Guide to Creating Organizations Inspired by the Next Stage of Human Consciousness_ (Nelson Parker, 2014). Perhaps it's worth noting that I used Git to manage version-control for this book.
7. Jennifer Reingold, "How a Radical Shift Left Zappos Reeling," _Fortune_ (March 4, 2016).
8. Evgeny Morozov, "The Meme Hustler," _Baffler_ 22 (2013).
9. GitHub, "Open Source Survey," opensourcesurvey.org/2017; Coraline Ada Ehmke, "The Dehumanizing Myth of the Meritocracy," _Model View Culture_ 21 (May 19, 2015); Ashe Dryden, "The Ethics of Unpaid Labor and the OSS Community," (November 13, 2013), ashedryden.com/blog/the-ethics-of-unpaid-labor-and-the-oss-community.
10. Roszak, _The Cult of Information_ , 175.
11. Aaron Smith, "Gig Work, Online Selling and Home Sharing," Pew Research Center (November 17, 2016); on the platform economy in general, see Martin Kenney and John Zysman, "The Rise of the Platform Economy," _Issues in Science and Technology_ 32, no. 3 (Spring 2016), and Geoffrey G. Parker, Marshall W. Van Alstyne, and Sangeet Paul Choudary, _Platform Revolution: How Networked Markets Are Transforming the Economy and How to Make Them Work for You_ (W. W. Norton, 2016); for a critique of the "platform" concept, see Tarleton Gillespie, "The Platform Metaphor, Revisited," Social Media Collective research blog (August 24, 2017); valuation statistics based on _Forbes_ magazine data via statista.com/statistics/263264.
12. Julia Cartwright, _Jean François Millet: His Life and Letters_ (Swan Sonnenschein, 1902), 177; for an exploration of the economic significance of gleaning in Jewish tradition, see Joseph William Singer, _The Edges of the Field: Lessons on the Obligations of Ownership_ (Beacon Press, 2000).
13. See Anna Bernasek and D. T. Mongan, _All You Can Pay: How Companies Use Our Data to Empty Our Wallets_ (Nation Books, 2015); Nick Couldry, "The Price of Connection: 'Surveillance Capitalism,'" _Conversation_ (September 22, 2016); Virginia Eubanks, _Automating Inequality: How High-Tech Tools Profile, Police, and Punish the Poor_ (St. Martin's Press, 2018); Frank Pasquale, _The Black Box Society: The Secret Algorithms That Control Money and Information_ (Harvard University Press, 2015); Astra Taylor, _The People's Platform: Taking Back Power and Culture in the Digital Age_ (Metropolitan Books, 2014); Joseph Turow et al., _The Tradeoff Fallacy: How Marketers Are Misrepresenting American Consumers and Opening Them Up to Exploitation_ , report from the Annenberg School for Communication at the University of Pennsylvania (June 2015); James Joyce quoted from _Finnegans Wake_ in Marshall McLuhan, _The Gutenberg Galaxy: The Making of Typographic Man_ (University of Toronto Press, 1962), 278.
14. Greetje F. Corporaal and Vili Lehdonvirta, _Platform Sourcing: How Fortune 500 Firms Are Adopting Online Freelancing Platforms_ (Oxford Internet Institute, 2017); Lawrence F. Katz and Alan B. Krueger, "The Rise and Nature of Alternative Work Arrangements in the United States, 1995–2015," National Bureau of Economic Research working paper no. 22667 (September 2016).
15. David de Ugarte, "Tipologías de las Cooperativas de Trabajo," _El Jardín Indiano_ (September 18, 2011); Sebastiano Maffettone et al., "Manifesto" (2012), www.cooperativecommons.coop/index.php/en/manifesto; Janelle Orsi, "The Next Sharing Economy" (October 17, 2014), youtube.com/watch?v=xpg4PjGtbu0; her call was echoed in Brian Van Slyke and David Morgan, "The 'Sharing Economy' Is the Problem," _Grassroots Economic Organizing_ (July 3, 2015); see a directory of North American tech worker co-ops at techworker.coop and coops.tech for the UK; for accounts of the rationale for tech co-ops, see Brian Van Slyke, "The Argument for Worker-Owned Tech Collectives," _Fast Company_ (November 20, 2013), and Gabrielle Anctil, "Can Coops Revolutionize the Tech Industry?" _Model View Culture_ 34 (March 16, 2016).
16. Nathan Schneider, "Owning Is the New Sharing," _Shareable_ (December 21, 2014); Trebor Scholz, "Platform Cooperativism vs. the Sharing Economy" (December 5, 2014), medium.com/@trebors/platform-cooperativism-vs-the-sharing-economy-2ea737f1b5ad. See also Scholz's subsequent, fuller account of the concept in his pamphlet _Platform Cooperativism: Challenging the Corporate Sharing Economy_ (Rosa Luxemburg Stiftung, 2016), as well as the collective manifesto he and I coedited, _Ours to Hack and to Own: The Rise of Platform Cooperativism, a New Vision for the Future of Work and a Fairer Internet_ (OR Books, 2016). Scholz also writes at length about platform cooperativism in _Uberworked and Underpaid: How Workers Are Disrupting the Digital Economy_ (Polity, 2017). Douglas Rushkoff, the concluding speaker at the 2015 Platform Cooperativism conference, advocates the model in _Throwing Rocks at the Google Bus: How Growth Became the Enemy of Prosperity_ (Portfolio, 2016).
17. Highly recommended: Marjorie Kelly, _Owning Our Future: The Emerging Ownership Revolution_ (Berrett-Koehler Publishers, 2012); Managed by Q, "Managed by Q Stock Option Program Press Conference," (March 18, 2016), vimeo.com/159580593.
18. See platform.coop for the conferences and the consortium, and ioo.coop for the directory. For my use of "ecosystem," apologies to Adam Curtis (dir.), _All Watched Over by Machines of Loving Grace_ , BBC (2011).
19. E.g., selfhosted.libhunt.com and ioo.coop/clouds.
20. Anand Sriraman, Jonathan Bragg, and Anand Kulkarni, "Worker-Owned Cooperative Models for Training Artificial Intelligence," _CSCW '17 Companion_ (February 25–March 1, 2017).
21. José María Arizmendiarrieta, _Reflections_ (Otalora, 2013), sec. 486.
22. John Geraci, "Interviewed: Venture Capitalist Brad Burnham on Skinny Platforms," _Shareable_ (June 22, 2015).
23. On November 17, 2017, the ICA General Assembly in Malaysia unanimously passed a resolution in support of platform co-ops, sponsored by Co-operatives UK and the US National Cooperative Business Association; Brewster Kahle, "Difficult Times at Our Credit Union," _Internet Archive Blogs_ (November 24, 2015).
24. Dmytri Kleiner, _The Telekommunist Manifesto_ (Institute of Network Cultures, 2010); Stacco Troncoso, "Think Global, Print Local and Licensing for the Commons," P2P Foundation blog (May 10, 2016).
25. Devin Balkind, founder of coopData.org and a collaborator of mine in building the Internet of Ownership, offers a critique of data practices in the co-op sector in "When Platform Coops Are Seen, What Goes Unseen?" The Internet of Ownership blog (February 10, 2017).
26. See platform.coop/2015/participants/maria-del-carmen-arroyo; on Austin and the aftermath, Jeff Kirk, "The Austin Ride-Hail Chronicles: Game Over for RideAustin?" _Austin Startups_ (June 15, 2017); Anca Voinea, "Corbyn's Digital Democracy Manifesto Promotes Co-operative Ownership of Digital Platforms," _Co-operative News_ (August 30, 2016).
27. Lina Khan, "Amazon's Antitrust Paradox," _Yale Law Journal_ 126, no. 3 (January 2017); Jonathan Taplin, "Is It Time to Break Up Google?" _New York Times_ (April 22, 2017); Ryan Grim, "Steve Bannon Wants Facebook and Google Regulated Like Utilities," _Intercept_ (July 27, 2017).
28. David Talbot, Kira Hessekiel, and Danielle Kehl, _Community-Owned Fiber Networks: Value Leaders in America_ (Berkman Klein Center for Internet and Society, 2018); for resources on co-op and municipal broadband programs, see muninetworks.org, a project of the Institute for Local Self-Reliance.
29. Victor Rosewater, _History of Cooperative News-Gathering in the United States_ (D. Appleton, 1930), 351; William Bryk, "A False Armistice," _New York Sun_ (November 10, 2004).
30. Walter R. Mears, "A Brief History of AP," in Reporters of the Associated Press, _Breaking News: How the Associated Press Has Covered War, Peace, and Everything Else_ (Princeton University Press, 2007); Rosewater, _History of Cooperative News-Gathering_ ; Jonathan Silberstein-Loeb, _The International Distribution of News: The Associated Press, Press Association, and Reuters, 1848–1947_ (Cambridge University Press, 2014).
31. Liana B. Baker, "Twitter CEO Calls Company 'People's News Network,'" _Reuters_ (October 10, 2016).
32. Nathan Schneider, "Here's My Plan to Save Twitter: Let's Buy It," _Guardian_ (September 29, 2016).
33. Twitter, Inc., _Proxy Statement: Notice of 2017 Annual Meeting of Stockholders_ (April 7, 2017); the SEC ruling can be found at sec.gov/divisions/corpfin/cf-noaction/14a-8/2017/mcritchiesauerteig031017-14a8.pdf; for a comprehensive account, see also Danny Spitzberg, "#GoCoop: How the #BuyTwitter Campaign Could Signal a New Co-op Economy," _Cooperative Business Journal_ (Summer 2017); a relevant precedent to the Twitter proposal is the "consumer stock ownership plan" model proposed by Louis Kelso (who also first proposed the widespread employee stock ownership plan), see Louis O. Kelso and Patricia Hetter Kelso, _Democracy and Economic Power: Extending the ESOP Revolution Through Binary Economics_ (Ballinger, 1986).
34. Fred Wilson, "The Golden Age of Open Protocols," _AVC_ (July 31, 2016). There is a typo in the original, which reads "more disruptive that."
Chapter 6: Free the Land
1. "Full Speech: Donald Trump Event in Gaffney, SC (2-18-16)," Right Side Broadcasting Network (February 18, 2016), youtube.com/watch?v=pq4wA_jQ8-k.
2. Data from various National Rural Electric Cooperative Association publications; see maps at cooperative.com/public/maps.
3. For the political history of electric co-ops, see Jack Doyle, _Lines Across the Land: Rural Electric Cooperatives: The Changing Politics of Energy in Rural America_ (Environmental Policy Institute, 1979), and Ted Case, _Power Plays: The U.S. Presidency, Electric Cooperatives, and the Transformation of Rural America_ (self-published, 2013); contribution data from the Center for Responsive Politics, opensecrets.org; Steven Johnson, "Mike Pence Familiar to Indiana Co-ops," National Rural Electric Cooperative Association press release (July 25, 2016); Abby Spinak, "Infrastructure and Agency: Rural Electric Cooperatives and the Fight for Economic Democracy in the United States" (PhD diss., Massachusetts Institute of Technology, 2014).
4. Cathy Cash, "'Co-ops Vote' Called a Success," National Rural Electric Cooperative Association press release (November 14, 2016).
5. "NRECA Statement on Budget Proposal," National Rural Electric Cooperative Association press release (March 16, 2017); Rebecca Harvey, "Trump's Budget Blueprint Sees Cuts for Co-ops and Credit Unions," _Co-operative News_ (March 17, 2017); Cathy Cash, "Trump Orders Clean Power Plan Review," National Rural Electric Cooperative Association press release (March 28, 2017).
6. G&T numbers courtesy of the National Rural Electric Cooperative Association; "What Is U.S. Electricity Generation by Energy Source?" US Energy Information Administration (April 1, 2016), eia.gov/tools/faqs/faq.php?id=427&t=3.
7. "Cooperative Solar Skyrockets," National Rural Electric Cooperative Association press release (March 9, 2017).
8. Doyle, _Lines Across the Land_ , 141 and 300. I'm grateful for the guidance of longtime electric co-op consultant and expert Adam Schwartz.
9. Rural Electrification Administration, _A Guide for Members of REA Cooperatives_ (US Department of Agriculture, 1939); for examples of government films, see Rural Electrification Administration, _Power and the Land_ (1951 [1940]), and United States Information Service, _The Rural Co-op_ (c. 1950).
10. For explanations of this and other financial abuses among electric co-ops, see Jim Cooper, "Electric Co-operatives: From New Deal to Bad Deal?" _Harvard Journal on Legislation_ 45, no. 2 (Summer 2008).
11. For an account of the Co-op Democracy Project, see a special issue on the subject, _Southern Changes_ 18, no. 3–4 (1996).
12. "Subpoenaed Witnesses Evade House Oversight Committee," Congressman Jim Cooper press release (June 26, 2008).
13. John Farrell, _Re-Member-ing the Electric Cooperative_ (Institute for Local Self-Reliance, 2016).
14. Murray D. Lincoln, _Vice President in Charge of Revolution_ (McGraw-Hill, 1960), 133.
15. Cooper, "Electric Co-operatives," 346.
16. For an extended comparison of the USDA and ICA principles, see Bruce J. Reynolds, _Comparing Cooperative Principles of the US Department of Agriculture and the International Cooperative Alliance_ (US Department of Agriculture, June 2014).
17. James Peter Warbasse, _Cooperative Democracy Through Voluntary Association of the People as Consumers_ , 3rd ed. (Harper and Brothers, 1936), 25, 266, and 7.
18. Corey Hutchins, "Bernie Sanders: Colorado Could 'Lead the Nation' with Its Universal Healthcare Ballot Measure," _Colorado Independent_ (October 26, 2015).
19. Michael A. Shadid, _A Doctor for the People: The Autobiography of the Founder of America's First Co-operative Hospital_ (Vanguard Press, 1939); Paul Starr, _The Social Transformation of American Medicine: The Rise of a Sovereign Profession and the Making of a Vast Industry_ (Basic Books, 1984), 302–306; Sabrina Corlette, Kevin Lucia, Justin Giovannelli, and Sean Miskell, "The Affordable Care Act CO-OP Program: Facing Both Barriers and Opportunities for More Competitive Health Insurance Markets," _To the Point_ , published by the Commonwealth Fund (March 12, 2015).
20. Financing: Camile Kerr, _Local Government Support for Cooperatives_ (Democracy at Work Institute, 2015); Peter Molk, "The Puzzling Lack of Cooperatives," _Tulane Law Review_ 88 (2014); Laura Hanson Schlachter, "MCDC Milestone Reflections: City of Madison Grant Writing Process" (University of Wisconsin–Madison Center for Cooperatives, August 2016); USDA Rural Development, _Income Tax Treatment of Cooperatives_ (US Department of Agriculture, June 2013). Development: Oscar Perry Abello, "NYC Set to Triple Number of Worker Cooperatives," _Next City_ (January 11, 2016); Kerr, _Local Government Support for Cooperatives_ ; Lauren McCauley, "'An Idea Whose Time Has Come': Lawmakers Roll Out Plan to Expand Worker Ownership," _Common Dreams_ (May 11, 2017); Schlachter, "MCDC Milestone Reflections." Mandates: Kerr, _Local Government Support for Cooperatives_ ; Molk, "The Puzzling Lack of Cooperatives." Enablers: Antonio Fici, "Cooperation Among Cooperatives in Italian and Comparative Law," _Journal of Entrepreneurial and Organizational Diversity_ 4, no. 2 (2015); Sustainable Economies Law Center, "Worker Coop City Policies," theselc.org/worker_coop_city_policies.
21. Antonio Fici, "Italy," in _International Handbook of Cooperative Law_ , ed. Dante Cracogna et al. (Springer-Verlag, 2013); Tito Menzani and Vera Zamagni, "Co-operative Networks in the Italian Economy," _Enterprise and Society_ (2009).
22. Laura Flanders, "Remembering Chokwe Lumumba," _YES! Magazine_ (February 26, 2014); see also Flanders's excellent profile of Lumumba, "After Death of Radical Mayor, Mississippi's Capital Wrestles with His Economic Vision," _YES! Magazine_ (April 1, 2014).
23. See the results of a 2014–2016 Freedom of Information Act request, archived on muckrock.com at perma.cc/H6T3-GPYM; Donna Ladd, "Jackson Tragedy: The RNA, Revisited," _Jackson Free Press_ (March 5, 2014).
24. National Conference of Black Lawyers, "Chokwe Lumumba: A Legal Biography" (March 3, 2014); R. L. Nave, "A 'New Justice Frontier,'" _Jackson Free Press_ (April 3, 2014).
25. The slogan comes from an event in 1971, when hundreds of revelers broke a vigilante and law-enforcement blockade that attempted to prevent them from celebrating the purchase of land in Mississippi by the Provisional Government of the Republic of New Afrika; the story is retold in Rukia Lumumba, "All Roads Lead to Jackson," in _Jackson Rising: The Struggle for Economic Democracy, Socialism and Black Self-Determination in Jackson, Mississippi_ , ed. Kali Akuno and Ajamu Nangwaya (Daraja Press, 2017).
26. See Kali Akuno, _Casting Shadows: Chokwe Lumumba and the Struggle for Racial Justice and Economic Democracy in Jackson, Mississippi_ (Rosa Luxemburg Siftung, 2015); for extensive reporting on the Lumumba candidacy and mayoral administration, see the archives of the _Jackson Free Press_ , a local paper, which also posted the campaign-finance documents on its website.
27. Details can be found in Ajamu Nangwaya, "Seek Ye First the Worker Self-management Kingdom: Toward the Solidarity Economy in Jackson, MS," in _Jackson Rising_.
28. Allen was convicted of embezzlement in 2017 but continues to hold his post at the downtown development corporation.
29. Overviews of this history appear in Jessica Gordon Nembhard, _Collective Courage: A History of African American Cooperative Economic Thought and Practice_ (University of Pennsylvania Press, 2014), and Michael Miles, "Black Cooperatives," _New Republic_ (September 21, 1968); Matt Cropp, "Martin Luther King, Jr., Credit Unionist," _Credit Union History_ (blog) (January 20, 2014); the role of Student Nonviolent Coordinating Committee comes to me from the testimony of SNCC organizer Mary Elizabeth King.
30. R. L. Nave, "Candidate Profile: Tony Yarber," _Jackson Free Press_ (April 2, 2014); see also _Jackson Jambalaya_ archives at kingfish1935.blogspot.com.
31. Donna Ladd, "Making of a Landslide: Chokwe A. Lumumba and a Changing Jackson," _Jackson Free Press_ (May 10, 2017); D. D. Guttenplan, "Is This the Most Radical Mayor in America?" _Nation_ (December 4–11, 2017).
32. Prieto is mentioned in Andy Greenberg's profile of Taaki, "How an Anarchist Bitcoin Coder Found Himself Fighting ISIS in Syria," _Wired_ (March 29, 2017).
33. "The Social Economy," in Michael Knapp, Anja Flach, and Ercan Ayboga, _Revolution in Rojava: Democratic Autonomy and Women's Liberation in the Syrian Kurdistan_ , trans. Janet Biehl (Pluto Press, 2016); Strangers in a Tangled Wilderness, eds., _A Small Key Can Open a Large Door: The Rojava Revolution_ (AK Press, 2015). The Institute for Solidarity Economics and Corporate Watch maintain a useful blog on "Co-operative Economy in Rojava and Bakur" at cooperativeeconomy.info.
34. Fabrice Balanche, "The Kurdish Path to Socialism in Syria," The Washington Institute (May 16, 2017).
Chapter 7: Phase Transition
1. An archive of the original website is at web.archive.org/web/20131210152950/http://floksociety.org:80/cuando-va-a-suceder.
2. The wiki is now at p2pfoundation.net/Main_Page; more accessible presentations of the foundation's work, built on the basis of the FLOK research, are available at commonstransition.org.
3. For more on such open accounting, see Michel Bauwens and Vasilis Niaros, _Value in the Commons Economy: Developments in Open and Contributory Value Accounting_ (Heinrich-Böll-Foundation and P2P Foundation, 2017); this is tied, also, with the vision of "open cooperativism": Michel Bauwens, "Open Cooperativism for the P2P Age," P2P Foundation blog (June 16, 2014).
4. See Vasilis Kostakis and Michel Bauwens, _Network Society and Future Scenarios for a Collaborative Economy_ (Palgrave Macmillan, 2014); Michel Bauwens, "Blueprint for P2P Society: The Partner State and Ethical Economy," _Shareable_ (April 7, 2012); John Restakis, _Cooperative Commonwealth and the Partner State_ (The Next System Project, 2017).
5. Ibn Khaldun, _The Muqaddimah: An Introduction to History_ , trans. Franz Rosenthal (Princeton University Press, 2015).
6. An early statement of the trend is Derek Thompson and Jordan Weissmann, "The Cheapest Generation," _Atlantic_ (September 2012); for a statistical critique of the "myth of the 'don't own' economy," see _The Millennial Study_ (Accel and Qualtrics, 2017); for a critique of this "investment" see Malcolm Harris, _Kids These Days: Human Capital and the Making of Millennials_ (Little, Brown, 2017).
7. On housing, see Laura Gottesdiener, "The Empire Strikes Back," _TomDispatch_ (November 26, 2013); on employment, see Guy Standing, _The Precariat: The New Dangerous Class_ (Bloomsbury Academic, 2011); on citizenship, see Atossa Araxia Abrahamian, _The Cosmopolites: The Coming of the Global Citizen_ (Columbia Global Reports, 2015); on clouds, see John Durham Peters, _The Marvelous Clouds: Toward a Philosophy of Elemental Media_ (University of Chicago Press, 2015).
8. Richard Florida, _Who's Your City? How the Creative Economy Is Making Where to Live the Most Important Decision of Your Life_ (Basic Books, 2008), argued for a tripartite distinction among the "mobile," the "stuck," and the "rooted"; for a more recent policy analysis, see David Schleicher, "Stuck! The Law and Economics of Residential Stability," _Yale Law Journal_ 127 (2017).
9. Jeff Abbott, "Indigenous Weavers Organize for Collective Intellectual Property Rights," _Waging Nonviolence_ (July 17, 2017).
10. Richard Feloni, "Why Mark Zuckerberg Wants Everyone to Read the Fourteenth-Century Islamic Book _The Muqaddimah_ ," _Business Insider_ (June 2, 2015); Mark Zuckerberg, "Building Global Community" (February 16, 2017), facebook.com/notes/mark-zuckerberg/building-global-community/10154544292806634.
11. I have been a guest speaker at Singularity University's Global Solutions Program.
12. Peter Diamandis, "I Am Peter Diamandis, from XPRIZE, Singularity University, Planetary Resources, Human Longevity Inc., and More. Ask Me Anything," Reddit AMA discussion (July 11, 2014), reddit.com/r/Futurology/comments/2afiw5/i_am_peter_diamandis_from_xprize_singularity/ciulffv.
13. Kevin Roose, "In Conversation: Marc Andreessen," _New York_ (October 19, 2014); Sam Altman, "Technology and Wealth Inequality" (January 28, 2014), blog.samaltman.com/technology-and-wealth-inequality.
14. Recent overviews of universal basic income include Philippe Van Parijs and Yannick Vanderborght, _Basic Income: A Radical Proposal for a Free Society and a Sane Economy_ (Harvard University Press, 2017), and Rutger Bregman, _Utopia for Realists: How We Can Build the Ideal World_ (Little, Brown, 2017).
15. Marshall Brain, _Manna: Two Views of Humanity's Future_ (2012), marshallbrain.com/manna1.htm; for another perspective on parallels between basic income and venture capital, see Steve Randy Waldman, "VC for the People" (April 16, 2014), interfluidity.com/v2/5066.html.
16. Matt Zwolinski, Michael Huemer, Jim Manzi, and Robert H. Frank, "Basic Income and the Welfare State," _Cato Unbound_ (August 2014); Noah Gordon, "The Conservative Case for a Guaranteed Basic Income," _Atlantic_ (August 6, 2014).
17. In Scott Dadich, "Barack Obama, Neural Nets, Self-Driving Cars, and the Future of the World," _Wired_ (November 2016), Obama said, "Whether a universal income is the right model—is it gonna be accepted by a broad base of people?—that's a debate that we'll be having over the next ten or twenty years." On universal dividends funded through common goods, see, for example, Peter Barnes, _With Liberty and Dividends for All: How to Save Our Middle Class When Jobs Don't Pay Enough_ (Berrett-Koehler Publishers, 2014); for the Oregon case, see Nathan Schneider, "Soon, Oregon Polluters May Have to Pay Residents for Changing the Climate," _YES! Magazine_ (December 9, 2015); Foster's and Hughes's organization is called the Economic Security Project, and more about its approach can be found in Chris Hughes, _Fair Shot: Rethinking Inequality and How We Earn_ (St. Martin's Press, 2018).
18. Cryptocurrency basic-income projects go by such names as Circles, Grantcoin, Group Currency, and Resilience; they interact at reddit.com/r/CryptoUBI.
19. Kathi Weeks, _The Problem with Work: Feminism, Marxism, Antiwork Politics, and Postwork Imaginaries_ (Duke University Press, 2011); Andy Stern and Lee Kravitz, _Raising the Floor: How a Universal Basic Income Can Renew Our Economy and Rebuild the American Dream_ (PublicAffairs, 2016).
20. "Black Cooperatives and the Fight for Economic Democracy," session at the Left Forum at the John Jay College of Criminal Justice (May 31, 2015); see also Marina Gorbis's calls for "universal basic assets" rather than merely income.
21. On technological unemployment, see a summary in James Surowiecki, "Robopocalypse Not," _Wired_ (September 2017); on employment and inequality, see (among many other studies) Michael Förster and Horacio Levy, _United States: Tackling High Inequalities, Creating Opportunities for All_ (OECD, 2014); on workplace surveillance, see Esther Kaplan, "The Spy Who Fired Me," _Harper's_ (March 2015); on human computerization, see Brett M. Frischmann, "Human-Focused Turing Tests: A Framework for Judging Nudging and Techno-Social Engineering of Human Beings," Cardozo Legal Studies Research Paper no. 441 (2014).
22. Community Purchasing Alliance, _2016 Annual Report_ (February 2017). I delivered the keynote address at that meeting and was compensated for doing so.
23. E.g., Richard D. Wolff, _Democracy at Work: A Cure for Capitalism_ (Haymarket, 2012); for an application of Wolff's framework, see Catherine P. Mulder, _Transcending Capitalism Through Cooperative Practices_ (Palgrave Macmillan, 2015).
24. Robert D. Putnam, _Making Democracy Work: Civic Traditions in Modern Italy_ (Princeton University Press, 1993), 142; appendix F of the same volume identifies statistical correlations between the presence of cooperatives and other forms of civic involvement. Among the Zamagnis' many writings, see especially Stefano Zamagni and Vera Zamagni, _Cooperative Enterprise: Facing the Challenge of Globalization_ (Edward Elgar, 2010).
25. Lisa Dorigatti, "Workers' Cooperatives and the Transformation of Value Chains: Exploiting Institutional Loopholes and Reducing Labour Costs," presentation at Cooperative Pathways Meeting, University of Padua (June 8, 2017); see more about the overall project, Erik Olin Wright's Pathways to a Cooperative Market Economy, at ssc.wisc.edu/~wright/Cooperative-pathways.htm; "Pope Francis Encourages Cooperatives to Build Solidarity," _Vatican Radio_ (May 5, 2015); for more on Francis, see my chapter "'Truly, Much Can Be Done!': Cooperative Economics from the Book of Acts to Pope Francis," in _Laudato Si': Ethical, Legal, and Political Implications_ , ed. Frank Pasquale (Cambridge University Press, forthcoming).
26. Comment during Francesca Forno and Paolo Graziano, "Reconnecting the Social: How Political Consumerism Enacts Collective Action," presentation at Cooperative Pathways Meeting, University of Padua (June 9, 2017).
27. The directory is at coloradocoops.info/directory; I received decisive help from the Rocky Mountain Farmers Union, which had developed a list based on state incorporation data.
# Index
Ace Hardware,
Affordable Care Act,
Africa, socialism in,
Afridi, Saks, 36 (photo)
agricultural brands, 56–57
Aguilar, Irene, 185 (photo), 186–188
AgXchange,
Airbnb app, 89–91,
Akuno, Kali, 191–192, 194–195, 202–203,
co-op focus of,
Jackson-Kush Plan on track by, 197–198
_All Things in Common_ (Bishop),
Allen, Ben, ,
Allen, Paul, 146–147
alternative currencies,
Altman, Sam,
American Federation of Labor,
Amicus Solar,
Ananias,
Ancestry.com, 146–147
Andino, Mario,
Andreessen, Marc,
anti-globalization movement,
AP. _See_ Associated Press
Apple, ,
application-specific integrated circuits (ASIC),
Arizmendiarrieta, José María, ,
Arroyo, Maria del Carmen,
artificial intelligence, ,
ASIC. _See_ application-specific integrated circuits
Assange, Julian,
Associated Press (AP), 163–164
Association of Cooperative Educators, 235–236
Augustine of Hippo,
Aurea Social, 122–123, 127–128, 128 (photo)
auto industry,
_autogestió_ (self-management),
automation,
autonomy (cooperative principle), , , , , ,
Baden, Michael,
Barbour, Haley,
Barlow, John Perry,
Barnes, Peter,
Bauwens, Michel, 209–213, 211 (photo),
Belayneh, Kidist,
Belloc, Hilaire,
Benedict of Nursia, 22–23, ,
Benedicto, Raquel, 126 (photo),
Bergmann, Frithjof, , ,
Berners-Lee, Tim,
Bezos, Jeff,
Bishop, Clare Hutchet,
Bitcoin Center NYC, 105–106, 109–110
Bitcoin, 106–110
blockchain of,
democracy in world of, 108–109
unequal distribution of,
United States dollar value of, 108 (fig.)
Black Lives Matter, , , , , 205–206
black power, 194–195,
blockchain, , , 111–114, ,
Bluestone Farm,
Boggs, Grace Lee, 74–75, ,
Boggs, Jimmy, ,
Book of Acts, 21–22
Bookchin, Murray,
Botsman, Rachel,
Boulder Community Housing Association, ,
Boulder Neighborhood Alliance,
Bradford, Mark,
Brain, Marshall, 222–223
Britain, co-op legislation in, ,
British Cooperative Wholesale Society, 42–43
Bronec, Jasen,
Brown, Michael,
Brown-Davis, Della, ,
"Building Global Community" (Zuckerberg),
Buni, Abdi, 85–86,
Buterin, Vitalik, 111–112, ,
#BuyTwitter, 165–167
Byck, Maria Juliana,
Caesar, Julius,
Calafou,
Calvinists,
capital credits,
_Capital in the Twenty-First Century_ (Piketty),
capitalism, 14–15, , ,
co-op businesses compared to, 14–15
as feudal lord, 46–47
feudalism and,
Capra, Robert,
Carmichael, Stokely,
Carter, Jimmy,
Cartier-Bresson, Henri,
Catalan Integral Cooperative (CIC), , 121–127,
Aurea Social assembly of, 127–128, 128 (photo)
Economic Commission of, 124–125
projects and budget of,
Catalan Supply Center, 122 (photo),
Catholicism, , 59–65,
Chaplin, Charlie,
Charter of the Forest,
Chartism,
Chavez, Chris, 32–34
Chesterton, G. K.,
Chokwe Lumumba Center for Economic Democracy and Development,
Christensen, Clayton,
Christian early church, 21–22
CIC. _See_ Catalan Integral Cooperative
civil economy,
Clare of Assisi,
Clean Energy Federal Credit Union,
Clinton, Bill,
cloud services, 135–136, 152–153, 216–218
CLUSA. _See_ Cooperative League of the United States of America
CoinTerra,
Colorado Co-Ops Study Circle,
Colorado Rural Electric Association,
ColoradoCare, 185–187
coming together ( _harambee_ ),
commodify.us,
common-pool resources,
Communism, , , , ,
community land trust,
Community Exchange System,
Community Language Cooperative,
Community Purchasing Alliance (CPA),
computers, 10–11, 114–115, 143–144, ,
Confcooperative, ,
Constantine,
constructive radicalism,
Continental Congress,
Cook, Blaine,
Co-op Democracy and Development Project,
CoopCycle,
Cooper, Jim, ,
_Cooperation and Competition Among Primitive Peoples_ (Mead),
Cooperation Jackson, , ,
cooperative accumulation,
Cooperative Association of America,
Cooperative Bank,
cooperative commonwealth, , , , , 230–231,
_Cooperative Democracy_ (Warbasse), 41–42, 42 (fig.),
Cooperative Home Care Associates,
Cooperative League of the United States of America (CLUSA),
Cooperative Union of America,
Cooperative University of Kenya, 65 (photo),
Cooperative Wholesale Society (CWS),
cooperatives (co-ops)
agricultural brands in, 56–57
AP benefiting as, 163–164
businesses, 3–5, , 14–15
capitalism and, 14–15
cooperation among,
co-owners of,
crowdfunding and,
department stores, 57–58
disruptive innovation and,
economy with, ,
electricity from, 170–171
fair-trade movements from, 49–50,
farming, , , 69–70,
federation of, , , , , ,
housing, 98–100
as institutional loopholes,
Italian laws of, 188–189, 232–233
Italian social,
in Italy, 62–63, 229–230
in Kenya, 64–68
MBA programs dismissive of,
missing markets causing, ,
one member one vote in,
open-source software shared by,
participation and control of, 12–13
principles of, 12–13, , 68–69, 182–183
social reformers and, ,
tax benefits for, 120–121
taxi, ,
throughout the United States, 57 (fig.)
universal health care as, 184–185
university systems as, 70–71
voter turnout for,
wealth created by,
worker, 82–83, 226–227
cooperativism, , 121–122, 150–152, ,
_The Co-ops Are Comin'_ (film),
copyright law,
Corbyn, Jeremy, ,
Correa, Rafael,
Cottica, Alberto, ,
CPA. _See_ Community Purchasing Alliance
Creative Commons licenses, ,
Credit Union Act,
credit unions, 13–14, , 57–59,
_Crisis_ (newspaper),
Cropp, Matthew,
crowdfunding,
Cryptocommons,
cryptocurrencies, ,
universal basic income used with, 223–224
_See also_ Bitcoin; blockchain
currencies, , , , . _See also_ cryptocurrencies
CWS. _See_ Cooperative Wholesale Society
Daemo,
Danielson, Joshua,
DAOs. _See_ decentralized autonomous organizations
data, 143–144,
data justice,
Davies, Bembo, , 30–31
Davis, Joseph,
Debian software,
debt, 101–102
alternative finance and, 103–104
money as, 104–105
strike,
student,
decentralized autonomous organizations (DAOs), 111–112
"Declaration of the Independence of Cyberspace" (Barlow),
_Decretum_ (Gratian),
Degrowth March, 118–119
Delta-Montrose Electric Association (DMEA), 172–174, 172 (photo),
democracy, , , 98–99, , 138–139, , , ,
in Bitcoin, , 108–109
co-ops as, , , 41–42, 58–60,
diversified,
in electricity co-ops, ,
entrepreneurs practicing, 155–156
United States, decline of, ,
dental chairs, 63 (photo)
department stores, 57–58
Derrida, Jacques,
design principles, 20–21
Desjardins, Alphonse,
Detroit, MI, 72–73, 74 (fig.)
Diamandis, Peter,
Dickens, Charles,
Dickinson, Rink,
Dietz, Joel, ,
the Diggers, 39–40
Digital Democracy Manifesto,
disruption, , 78–80, , , ,
diversity, 36–37
Divine Office,
DMEA. _See_ Delta-Montrose Electric Association
D'Onofrio, Anthony, 110–111
Dorigatti, Lisa,
Dorsey, Jack, ,
Douglass, Frederick,
Drutopia,
Du Bois, W. E. B., , 55–56
Duran, Enric, 115–117,
borrowing without repaying of, 118–119
FairCoin fair-trade and, 130–131
FairCoop work of, 131–132
hacking of,
Infospai set up by,
Integralism work of, 128–129
underground activities of,
"Economic Cooperation Among Negro Americans" (conference),
ecos (CIC native currency),
Ecuador, 209–215
Edgeryders, 25–26, 29–31
education, , , , 158–159
Electric Cooperative Leadership Institute,
electric co-ops, , 169–170
community not represented by officials of,
customer-centered business of,
farmers using, 4–5, 181–182,
federal regulatory disputes of,
government backed, 176–177
renewable energy use of,
self-governance of, 171–172
Ellis, Aunjaune,
Emacs software, 135–136
Emilia-Romagna, Italy, 62–63
employee ownership, , , , , , , ,
employee stock-ownership plans (ESOPs), , , ,
Enspiral, 93–96
Enspiral Dev Academy, 95–96,
entrepreneurs, , , 155–156
Epstein, Steven A., 34–35
Espai de l'Harmonia,
Ethereum, 111–113, , ,
European Capital of Culture, ,
Evans, Blair,
Evers, Medgar,
Facebook, , 143–144, , 218–219
Fairbnb,
FairCoin, , , 130–131
FairCoop, , , 131–132,
Fairmondo, ,
Fairphone,
fair-trade movement, , 49–50,
Farm Bureau insurance system, 56–57
Farm Credit System,
farmers
African American, ,
co-op systems used by,
co-ops helping independent, 69–70
co-ops of, ,
data sold by,
electric co-ops used by, 4–5, 181–182,
Farmers' Alliance,
Farrakhan, Louis,
Farrell, John,
federation, , , , , ,
Federation of Southern Cooperatives,
fediverse, 167–168
feedback loops,
feudalism, , , ,
Filene, Edward, ,
finance, , 77–78, 103–104, ,
fiscal disobedience,
Flanders, Laura, ,
FLOK Society, 209–210,
Forno, Francesca,
Foster, Natalie,
Francis of Assisi,
Franciscan communities,
Franco, Francisco,
Frank, Mary,
Franklin, Benjamin, ,
free labor,
Freedom Farm, ,
freelancers,
free-market advocates,
free-software movement, , , 140–141
freespace] storefront, , [139 (photo)
Friedman, Milton,
Fromm, Erich,
game theory,
Gandhi, Mohandas K.,
Garrett, Socrates, 201–203
Garza, Alicia,
Gates, Bill,
Generation Opportunity,
geographic mobility,
Getty Images,
Gibson, Mel,
Gicheru, Esther, , 67 (photo)
gig work,
Gino, Francesca,
Git software,
GitHub, , ,
_The Gleaners_ (painting),
gleaning, 142–143
God's creation, in Digger cosmology, 39–40
Golf Ball Divers Alliance,
"Good Knowledge Summit,"
Google, , , 136–137, , , , , , , ,
Googleplex, , ,
Gorenflo, Neal,
Graham, Martha,
Gratian,
Greeley, Horace, ,
Green Bay Packers, ,
Green Taxi Cooperative, 84–89, 87 (photo)
grocery stores, 80–81
gross domestic product,
Growers Agricultural Data Cooperative,
_Guardian_ article, author's,
Guerrilla Translation,
_A Guide for Members of REA Cooperatives_ (booklet), 176 (fig.)
guilds, 34–36, ,
Hacker Dojo,
hackers
of copyright law,
Creative Commons licenses and,
on Internet, 147–148
hackerspace, , , , 138–139
Hackett, Mark,
Hamer, Fannie Lou,
_harambee_ (coming together),
Harman, Virginia,
Hausel, Katalin,
Hawkins, Chris,
Haymarket riot,
Hearst, William Randolph,
Hell's Kitchen,
Heneghan, Jim, 172 (photo), 173–175
Hicks, Charity,
High Plains Food Cooperative, 152–153
higher education, , 68–71,
_History of Cooperation_ (Holyoake),
Hock, Dee,
Holacracy, 139–140
HolacracyOne,
Holyoake, George Jacob, , 48–49,
Hoover, Melissa,
housing co-ops, 98–100
Hsu, Jerone, , , 36 (photo)
Hueth, Brent, , 69–70
Huffington, Ariana,
Hughes, Chris,
Hughes, Rose,
human rights, , ,
Hurricane Sandy, 81–82
Ibn Khaldun, 215–216,
Industrial and Provident Societies Act (1852),
Industrial Revolution, , , ,
inequality, 218 (fig.)
Infospai, 118–119
Innocent IV (pope),
Institute for Cooperative Development,
Institute for Local Self-Reliance,
Institute for the Formation of Character,
insurance industry, , , , , , 54–56, ,
Integral Cooperative, ,
integral human development,
Integral Revolution, ,
Integralism, 128–129
International Cooperative Alliance, 8–9, 11–12, ,
International Ladies' Garment Workers' Union,
International Summit of Cooperatives, ,
Internet, 147–148, ,
investors, , ,
Ipercoop store,
iStock,
Italy
co-op laws in, 188–189, 232–233
co-ops in, 62–63, 229–230
Emilia-Romagna region, 62–63
Matera, 24–25, ,
social co-ops in,
Jackson, Andrew,
_Jackson Jambalaya_ (blog),
"Jackson Rising" (conference), 203–204,
Jackson-Kush Plan, , 196–198,
_Jackson-Kush Plan: The Struggle for Black Self-Determination and Economic Democracy_ (pamphlet),
Jay Z,
Jefferson, Thomas,
Jesus Christ,
jobs
as ideology,
technology and vulnerability of, ,
Jobs, Steve,
_Jobs of Our Own_ (Mathews),
Johnson, Derrick,
Johnson, Lyndon,
Johnstown, CO,
Joint Stock Companies Act (1856),
Joyce, James,
Juris, Jeffrey,
Jurowicz, Julek,
Kahle, Brewster,
Kauai Island Utility Cooperative,
Kazadi, Aleta,
Kelly, Marjorie,
Kelty, Christopher M.,
Kenya, 65–67
King, Martin Luther, Jr., 199–200,
Kit Carson Electric Cooperative,
Kleiner, Dmytri,
Knights of Labor, 54–56, 61–62
Knuth, Donald,
Koch, Charles,
Koestler, Arthur,
König, Thomas,
Krause, Alanna, 95–96
Kunstler, James Howard,
Kurds,
Kush District,
labor unions, 6–7, , , , 53–54, , , 83–84, , , , ,
Lander, Brad,
LaPlante, Rochelle,
Las Indias, 149–150
Laurini, Gianluca,
law school,
learning, lifetime of,
Lee, Jonathan,
Lee, Marcia, ,
Legacoop, , ,
Lehman Brothers,
Leo XIII (pope),
Leroux, Monique,
Lessig, Lawrence,
Liberty Distributors, , 3 (fig.), , 234–235
Lieder, Sheila, ,
Lim, Leng,
Lincoln, Abraham, 44–45
Lincoln, Murray, , ,
_Lines Across the Land_ ,
Linux software, 133–134
Lockwood, Jonathan, 186–187
Loconomics Cooperative, ,
_The Lone Ranger_ (radio dramas),
Long, Guillaume,
Loomio, 93–95, , ,
Lopez, Alfredo,
Lumumba, Chokwe, 189–192, 197–198
mayoral campaign of, 196–197
Mississippi arrival of, 192–193
New Afrikan People's Organization founded by,
Lumumba, Chokwe Antar, , 200–201, 203 (photo)
mayoral election of,
Mississippi's flag changed and, 204–205
Lumumba, Rukia,
Lundahl, Erika,
Lung Ta (farming commune), 123–124
Luther, Martin,
Magnolia Electric Power Association,
Malcolm X, , , , ,
Malcolm X Grassroots Movement, ,
_Manna_ (Brain), 222–223
manufacturing cooperative, 63 (photo)
Martin, Brendan, ,
Marx, Karl, ,
Matera, Italy, 24–25, ,
Matheson, Jim,
Mathews, Race, 60–61
Maurin, Peter,
May First/People Link organization, 135–136
MBA programs,
McClelland, Jamie, 135–136
Mckesson, DeRay,
McKnight, Albert J.,
McLean, Christopher, 174–175, 179–180
McRitchie, Jim,
Mead, Margaret, ,
Mechanical Turk, , ,
medieval guilds, 33–37, ,
_Megatrends_ (Naisbitt),
mendicant movement,
mercantilism,
Meredith, Greg,
migration,
Millet, Jean-François,
Mingo, Stephanie,
missing markets, ,
Mississippi Sovereignty Commission,
Mississippi's flag, 204–205
Modo cooperative,
monasteries, 22–23, 25–26,
Mondragon Corporation, 59–62, , , , ,
money, as debt, 104–105
Moraa, Nyong'a Hyrine, 67–68
Mòrist, Joel, , 126 (photo)
mortgage crisis,
movements, , , , 49–50
anti-globalization,
communal, 212–213
for co-ops, , 43–44, 225–226,
cryptocurrencies and,
free-software, , , 140–141
Malcolm X Grassroots, ,
Mubarak, Hosni,
Müntzer, Thomas, 37–39
Musk, Elon,
Mussolini, Benito,
Mutual Broadcasting System,
MXGM organization, 194–197, 200–201,
Naisbitt, John,
Najm, Qinza, 36 (photo)
Nakamoto, Satoshi, 106–107
Namasté Solar,
National Cooperative Business Association (NCBA),
National Domestic Workers Alliance,
National Grange of the Order of Patrons of Husbandry,
National Rural Electric Cooperative Association (NRECA),
National Security Agency, 135–136
National Trades Union,
NCBA. _See_ National Cooperative Business Association
Negro Cooperative Guild,
Nembhard, Jessica Gordon, , ,
neo-tribes,
network economy, 91–92
New Afrikan People's Organization, 194–195
New Deal programs, , 169–170
New Economy Coalition,
New Era Windows Cooperative, 83 (photo),
New Harmony,
New Work Field Street Collective,
New Work New Culture,
New York City Network of Worker Cooperatives (NYC NOWC),
New Zealand,
NextCloud,
Niwot's Curse, 96–97,
Nixon, Richard,
nomadism, 215–217
NRECA. _See_ National Rural Electric Cooperative Association
NYC NOWC. _See_ New York City Network of Worker Cooperatives
Obama, Barack, ,
Öcalan, Abdullah,
Occupy Sandy, 81–82
Ogilvie, Sheilagh,
Omari, Safiya, , 201–202
one member one vote,
One Voice sessions, 177–180
Open Collective, ,
open cooperativism,
Open Energy Monitor,
open-source life, 31–32
open-source software, , , , ,
O'Reilly, Tim,
organization membership, 218 (fig.)
Orlando, Rita, 31–32
Orsi, Janelle,
Ostrom, Elinor, 20–21,
OuiShare Fest, 90–92,
Owen, Robert, 47–49,
ownership
employee, , , , , , , ,
Green Taxi Cooperative and,
job for wages compared to,
psychological,
rights, 217–218
P2P Foundation,
Paris, Wendell, 199–200,
Pasolini, Paolo,
patient-owned cooperative hospital,
patronage dividend,
Paul, Ron,
Pavlik, elf, , 30–31, 30 (photo)
Pazos, Rina,
Peck, Bradford,
Pence, Mike, ,
_People's Computer Company Newsletter_ ,
Perseverance Benevolent and Mutual Aid Association,
Petty, Tawana,
phase transitions, 212–213,
piecework tasks,
Piketty, Thomas,
Pistono, Federico,
platform cooperativism, 151–162
Platform Cooperativism Consortium,
platforms, 142–147
gig work on,
venture capitalists steering,
Plato,
Podemos (populist political party),
Poudre Valley Rural Electric Association,
Powderly, Terence,
Prak, Maarten, 35–36
Priester, Melvin, Jr.,
Prieto, Pablo, ,
Prime Produce, 33–37, 36 (photo)
Project Equity,
psychological ownership,
Puritans,
Purpose Ventures,
Putnam, Robert,
Python programming language, 114–115
Queen City Cooperative,
Quito,
radical Reformation, 38–39
radio dramas,
Raymond, Eric,
renewable energy, , 174–175, , ,
_Republic_ (Plato),
Republic of New Afrika (RNA),
Republic Windows and Doors, 83–84
_Rerum Novarum_ ( _Rights and Duties of Capital and Labor_ ), 60–61
Resonate, ,
Restakis, John,
Restaurant Terra,
Rifkin, Jeremy, 15–16
_Rights and Duties of Capital and Labor_ ( _Rerum Novarum_ ), 60–61
RNA. _See_ Republic of New Afrika
Roanoke Electric Cooperative, 178–179
Robin Hood Cooperative,
Robles, Armando, 83 (photo),
_Robots Will Steal Your Job, but That's OK_ (Pistono),
Rochdale, 48–52, , ,
Rochdale Society of Equitable Pioneers, , , 49–50,
Rognlie, Matthew,
Rojava, 206–207
Roof, Dylann,
Roosevelt, Franklin, ,
Rosewater, Victor,
Roszak, Theodore, , 141–142
Rule of St. Benedict, 22–23, ,
Rural Electrification Act, ,
SACCO. _See_ savings and credit cooperative
SACMI, 230–231
Salazar, Marcos,
Salinas de Guaranda, , 59 (photo)
Salish Sea Cooperative Finance,
Sanders, Bernie, , , , ,
Sanders, Jonathan,
Sapphira,
Sassi,
savings and credit cooperative (SACCO), 64–65,
Savvy Cooperative,
Schlachter, Jake,
Schneiderman, Rose, ,
Scholz, Trebor, 150–151
Schumpeter, Joseph,
Scripps, E. W.,
Seedbloom,
self-employment tax, 119–120
Shadid, Michael,
_The Shadow_ (radio drama),
Shakur, Assata,
Shakur, Mutulu,
sharing economy, 90–92, ,
Silva, Nuno,
Simmons, Sandra,
Sinclair, Upton,
Singularity University, 220–221,
slavery, , , ,
slow computing, 133–136, ,
Smalls, Eric,
SMart. _See_ Société Mutuelle pour Artistes
smart contracts, 111–112
Smith, Adam,
Snowden, Edward,
Snowdrift.coop,
Social Cohesion Research and Early Warning Division,
social contracts, , , , , , , ,
social cooperatives, ,
Social Currency Monitoring Commission, 125–126
social networks, , , 167–168
social reformers, ,
Social.coop,
socialism,
Société Mutuelle pour Artistes (SMart), 92–93
solidarity economy,
Southern Reparations Loan Fund,
_Space Is the Place_ (film),
Spitzberg, Danny,
St. Mary's Bank, 58–59
Stallman, Richard, ,
Stanford, Leland, ,
Stocksy United, 148–149
student debt,
Sun Ra,
Swanson, Tim,
Swartz, Aaron,
Syria,
Taaki, Amir,
Taeyoung, Dan, ,
Taft, William Howard,
Taliaferro, Edwin Finley. _See_ Lumumba, Chokwe
taxi co-ops, , , 85–89,
Taylor, Keith,
technology, 25–26
currency schemes and,
jobs vulnerable to,
machinery's rise and, 46–47
social interactions through,
_Terminator_ (movie),
TerraMiner IV, ,
textile industry, , ,
TheGoodData,
Thomas, Norman,
3D printers, 75–76
Tocqueville, Alexis de,
Torvalds, Linus, , ,
True Levellers. _See_ the Diggers
Trump, Donald, , ,
Trustworthy, 234 (photo)
Truth, Sojourner,
Twitter, 164–167
Uber, ,
Ubuntu software, 133–134
Umoja, Nia, ,
Umoja, Takuma,
unicorns, 145–146,
Unipol,
United States
co-op businesses in,
co-op policymaking in, 56–57, 169–172, 176–177, , ,
cooperative commonwealth in, , , , ,
co-ops throughout, 57 (fig.)
democracy declining in, ,
first credit union in, 58–59
organization membership and inequality in, 218 (fig.)
venture capital in, 145 (fig.)
worker productivity in, 76–77
universal basic income, , 223–224
universal destination of goods, , ,
universal health care, 184–185
University of Wisconsin–Madison's Center for Cooperatives,
unMonastery, 24–32, 27 (photo), 30 (photo)
Up & Go,
Uptima Business Bootcamp,
urban-rural divides, 125–126
user data, 143–144
venture capital (VC), 144–145, 145 (fig.), 156–157
Vial, Joshua, 94–95
Vickers, Ben, ,
Vincent, Margaret, 149 (photo)
voter turnout, for co-ops,
_Wage Labor and Guilds in Medieval Europe_ (Epstein),
wages, 76–77
Waldman, Steve Randy, 112–113
Wales, Jimmy,
Wallace, George,
Wallace, Henry A.,
Warbasse, James Peter, 41–43, 42 (fig.), ,
Watkins, Hollis,
Wayne State University, 73–75
_We Can!_ (newspaper),
We Own It, 180–181
Weeks, Kathi, ,
Weev (hacker-troll),
Wells, Benita,
Wenger, Albert,
Western Sugar Cooperative,
Weth, Felix,
Wettlaufer, Brianna, , 149 (photo)
Whitfield, Ed,
_Whole Earth Catalog_ ,
Whole Foods,
Widerquist, Karl,
Wiener, Jason,
Wilson, Fred,
Wind, Dominik, 89–90
Winstanley, Gerrard,
wire services,
Witchger, Felipe,
women's suffrage,
Women's Trade Union League,
WORCs. _See_ Worker-Owned Rockaway Cooperatives
Word Jammers,
Worker-Owned Rockaway Cooperatives (WORCs),
workers
businesses owned by, 83–86,
cooperation and organizing of,
co-ops, 82–83, 226–227
ownership and dispossessed,
piecework tasks of,
strikes by,
_See also_ employee ownership
Working World, the,
_The World a Department Store_ (Peck),
World Wide Web Consortium, ,
Wozniak, Steve,
Wynn, Curtis, 178–179
Yarber, Tony,
Zamagni, Stefano, 228–229,
Zamagni, Vera, 228–229, 228 (photo)
Zebra startups,
Žižek, Slavoj,
Zuckerberg, Mark, , 218–219
| {
"redpajama_set_name": "RedPajamaBook"
} | 9,195 |
Étoile des neiges is een Frans lied uit 1949 dat sindsdien in Franstalige landen is uitgegroeid tot een evergreen. De tekst is geschreven door Jacques Plante, de muziek door Jacques Hélian. Het lied is talloze keren gecoverd en uitgegroeid tot een publiekslieveling.
Populariteit
In november 1949 introduceerde de Franse orkestleider Jacques Hélian het lied "Étoile des neiges" (De sneeuwster) op grammofoonplaat. Het plaatje werd opgemerkt door de bekende zangeres Line Renaud, die het lied populair heeft gemaakt in 1950. Het werd een van de bekendere chansons van de chansonniere. Het lied is sindsdien talloze keren gecoverd. Bekende coverversies van "Étoile des neiges" zijn onder andere van Tino Rossi, Patrice et Mario en Les Petits Chanteurs de Sainte-Croix de Neuilly. De uitvoering van Simon et les Modanais werd in 1988 een grote hit in de Franse hitlijsten. Mede door een variant van het lied in de populaire Franse cultfilm "Les Bronzés font du ski" kent het lied vandaag nog altijd een grote populariteit en groeide in de Franstalige landen uit tot een evergreen.
Herkomst
Het lied vertelt een verhaal van een arme Savoyaardse schoorsteenveger uit de 19e eeuw of 20e eeuw, die verliefd is op een herderin, maar verplicht moet vertrekken uit zijn bescheiden bergdorpje om 's winters de kost te verdienen als gastarbeider in welvarende gebieden. Het vuile werk als schoorsteenveger was niet geheel ongevaarlijk, het kwam voor dat men bij ongevallen kwam te overlijden. De schoorsteenveger moet gedwongen afscheid nemen van zijn geliefde, maar ondanks de zware vooruitzichten, belooft hij in het voorjaar terug te keren met voldoende geld om te kunnen trouwen. Als het voorjaar eenmaal aangebroken is, wacht de herderin op haar geliefde. De schoorsteenveger komt zijn belofte na en keert heelhuids terug, waarna hij trouwt met de herderin.
Lijst van vertolkers
Een (kleine) overzicht met een aantal vertolkers van het lied:
Externe link
Het lied "Étoile des neiges" op Allmusic.com
Frans lied
Single uit 1949 | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 2,997 |
Xylocopa amedaei är en biart som beskrevs av Amédée Louis Michel Lepeletier 1841. Xylocopa amedaei ingår i släktet snickarbin, och familjen långtungebin. Inga underarter finns listade i Catalogue of Life.
Källor
Snickarbin
amedaei | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 4,534 |
\section{Introduction}
The colorful Carath{\'e}odory theorem, discovered by Imre B{\'a}r{\'a}ny \cite{ba1982} (and independently in a dual form by Lov{\'a}sz), states that if $X_0$, $X_1$, $\dots$, $X_n$ are subsets in $\mathbb{R}^n$, each containing the origin in their convex hulls, then there exists a system of representatives $x_0\in X_0$, $x_1\in X_1$, $\dots$, $x_n\in X_n$ such that the origin is contained in the convex hull of $\{x_0, x_1, \dots, x_n\}$.
The classical Carath{\'e}odory theorem~\cite{car1911} is recovered by setting $X_0 = X_1 = \cdots = X_n$. There are several remarkable applications of the colorful Carath{\'e}odory theorem in discrete geometry, such as in Sarkaria's proof of Tverberg's theorem and in the proof of the existence of weak $\epsilon$-nets for convex sets. For further applications and references we recommend the reader to see Chapters 8, 9, and 10 in \cite{matousek}. We recommend the survey~\cite{eckhoff1993} for general background on Carath\'eodory's theorem and its relatives.
Recently there have been numerous generalizations of classical results from combinatorial convexity which focus on replacing convex sets by more general subsets of $\mathbb{R}^n$ which are subject to certain topological constraints (see for instance \cite{xavi-adv, xavi-arx, km2005, KMleray, montejano} and references therein). These generalizations usually require tools from algebraic topology. In this paper we also use such topological tools, but we do so in order to solve problems which are purely affine.
Our goal in this paper is to give an extension of the colorful Carath\'eodory theorem~\cite{ba1982} to the notion of strong convexity and strongly convex hulls. This also generalizes the (non-colorful) Carath\'eodory theorem for strong convexity from~\cite{kar2001car}. In fact, the proof presented here is very similar to that in~\cite{kar2001car}, using the colorful topological Helly theorem~\cite{km2005} instead of the original topological Helly theorem (see for instance \cite{debrunner}); but we reproduce some of its parts because~\cite{kar2001car} appears exclusively in Russian.
In order to state our results, we need some definitions on strong convexity from~\cite{pol1996,balashov2000}. Similar notions have appeared earlier, and we recommend the reader to~\cite{pol1996,balashov2000} for further references.
\begin{definition}
\label{definition:genset}
A convex body $K$ is a \emph{generating set} if any nonempty intersection of its translates
$$
K\gdiv T = \bigcap_{t\in T} (K - t)
$$
is a Minkowski summand of $K$, that is, $(K\gdiv T) + T' = K$ for some convex compactum $T'$.
\end{definition}
In~\cite{kar2001gen} it was shown that it is sufficient to test this property for those $T$ that contain two elements; but we do not need this simplification here. It is relatively easy to check that all two-dimensional convex bodies, Euclidean balls, and simplices in every dimension are generating sets (see for instance section 3.2 of \cite{schneider}). This property is also inherited under the Cartesian product operation. In~\cite{ivanov2007} a criterion for checking this property for $C^2$-smooth bodies was given, proving, in particular, that by sufficiently smooth perturbations of a ball one can obtain centrally symmetric generating sets which are not ellipsoids.
\begin{definition}
\label{definition:strongconv}
Let $K\subset \mathbb R^n$ be a convex body. A set $C\subset \mathbb R^n$ is called {\em $K$-strongly convex} if it is an intersection of translates of $K$, that is
$$
C = K\gdiv T
$$
in the above notation. The minimal $K$-strongly convex set containing a given set $X$ is called its \emph{strongly convex hull}, and can be found by the following formula
$$
\conv_K X = K\gdiv (K\gdiv X).
$$
\end{definition}
Note that the $K$-strongly convex hull is only defined for those $X$ that are contained in a translate of $K$.
In~\cite{kar2001car} it was shown, assuming that $K$ is a generating set, that the strongly convex hull of $X$ equals the union of the strongly convex hulls of all subsets $X'\subset X$ such that $|X'|\le n+1$; some particular cases of this were already proved in~\cite{balashov2000}. This is the Carath\'eodory theorem for strong convexity. Here we establish the colorful Carath\'eodory theorem for strong convexity. In fact, it is possible to state it without appealing to Definition~\ref{definition:strongconv}. Let us say that a translate $K-t$ \emph{separates} a set $S$ from the origin if $K-t$ contains the set $S$ and is disjoint from the origin.
\begin{theorem}
\label{theorem:colorfulcovering}
Let $X_0, X_1,\ldots, X_n\subset \mathbb R^n$ be finite sets and $K$ a generating set in $\mathbb R^n$. Suppose every system of representatives $x_0\in X_0$, $x_1\in X_1$, $\ldots$, $x_n\in X_n$ can be separated from the origin by a translate $K-t$. Then there exists a translate of $K$ that separates $X_i$ from the origin, for some $0\leq i \leq n$.
\end{theorem}
This can be related to Definition~\ref{definition:strongconv} in the following way: The hypothesis means that the origin is not contained in the $K$-strongly convex hull of any system of representatives $\{x_0, x_1,\ldots, x_n\}$, and the conclusion means that the origin is not contained in the $K$-strongly convex hull of one of the $X_i$'s. This precisely generalizes the colorful Carath\'eodory theorem~\cite{ba1982} to strong convexity, of course, assuming that $K$ is a generating set.
\medskip
Throughout the paper we will be working with topological spaces that are point sets in Euclidean spaces and use their \v{C}ech cohomology.
We denote the \v{C}ech cohomology of $X$ with coefficients in the constant sheaf $\mathbb Z$ simply by $H^*(X)$. We choose \v{C}ech cohomology because of its \emph{continuity property}, which we will use in the following form: If $Y\subseteq X$ is closed then $H^*(Y)$ is the inverse limit of $H^*(U)$ over all open neighborhoods $U\supseteq Y$.
Note also that in our (paracompact) case, \v{C}ech cohomology coincides with the sheaf cohomology (see Theorem 5.10.1 in \cite{godement1958}), this observation is frequently used in this paper. Let us make an explicit definition:
\begin{definition}
We say that $X$ is \emph{acyclic} if $H^0(X) = \mathbb Z$ and $H^k(X)$ is zero for $k>0$.
\end{definition}
Note that every contractible subset of $\mathbb R^n$ is acyclic, but the inverse is not true. For example, the closed topologist's sine curve, which shows that connectivity does not imply arcwise connectivity, is acyclic and demonstrates that acyclicity does not imply arcwise connectivity, and therefore does not imply contractibility.
\medskip
{\em Outline of the paper.} The proof of Theorem \ref{theorem:colorfulcovering} is given in Section~\ref{section:proof1} and uses the topological colorful Helly theorem due to Kalai and Meshulam \cite{km2005}. However, in order to apply their result we need a crucial lemma concerning the topology of sets of the form $K\setminus (K+T)$ where $K$ and $T$ are arbitrary convex compacta in $\mathbb{R}^n$. This is given in Lemma \ref{lemma:acyclic}, below. In Section~\ref{section:more} we prove a ``very colorful'' version of Theorem \ref{theorem:colorfulcovering} (see Theorem~\ref{theorem:strong-caratheodory} for the precise statement). This generalization also uses Lemma \ref{lemma:acyclic}, but needs some further topological machinery, which is given in Section~\ref{section:leray-link}. In Section~\ref{section:no-cara} we give a construction of a convex body $K$ in $\mathbb{R}^3$ for which the $K$-strongly convex hull has an unbounded Carath{\'e}dory number. This shows that it is necessary to make some assumption (such as the ``generating set'' property) on the convex body $K$ in our results. In Section \ref{section:topo} we establish a partial converse to the crucial Lemma \ref{lemma:acyclic} by giving a topological criterion for a convex body $K$ to be a Minkowski summand of an open bounded convex set $T$.
\subsection*{Acknowledgments.}
The authors thank Alexey Volovikov for his explanations about the topological facts used in Section~\ref{section:topo}, Imre B\'ar\'any for the discussion which resulted in the example in Section~\ref{section:no-cara}, and the unknown referee for numerous useful remarks.
\section{Proof of Theorem~\ref{theorem:colorfulcovering}}
\label{section:proof1}
We are going to utilize the colorful topological Helly theorem from~\cite{km2005} in the following form: Assume ${\mathcal F}_0, {\mathcal F}_1, \ldots, {\mathcal F}_n$ are finite families of subsets of $\mathbb R^n$ such that the intersection of the members of any subfamily $\mathcal G\subset \bigcup_i \mathcal F_i$ is either empty or acyclic, and every intersection $\bigcap_{i=0}^n F_i$ of a system of representatives $F_0\in \mathcal F_0, F_1\in \mathcal F_1, \ldots, F_n\in \mathcal F_n$ is nonempty. Then for some $i$ the intersection $\bigcap_{F \in \mathcal F_i}F$ is nonempty.
The above result is valid in the case when all the sets $F\in \bigcup_i \mathcal F_i$ are open. This case can be deduced from the combinatorial formulation in~\cite{km2005} by comparing the cohomology of the union of the family with the cohomology of its nerve. But we are going to apply this result to sets $F$ of the form $X\setminus Y$, where $X$ and $Y$ are convex bodies, $Y$ is fixed and $X$ depends on $F$, call it $X_F$. Such sets are neither open nor closed in general, so
some justification is needed.
First, we go to the manifold $\mathbb R^n\setminus Y$ and consider the sets $F=X_F\setminus Y$ as its closed subsets. The corollary after~\cite[Theorem 5.2.4]{godement1958} asserts that the \v{C}ech cohomology of the union of the family $\mathcal F$ can be calculated using the nerve of the family; so we can reduce the problem to studying the nerve combinatorially.
The next ingredient is the following lemma from~\cite{kar2001car}:
\begin{lemma}
\label{lemma:acyclic}
For two convex compacta $K, T\subset\mathbb R^n$ the set $K\setminus (K+T)$ is either empty or acyclic.
\end{lemma}
The proof of Lemma \ref{lemma:acyclic} was only published in Russian~\cite{kar2001car}, so we provide a sketch of the proof here for the reader's convenience.
\begin{proof}[Sketch of the proof] We start by making a series of reductions. First of all we may assume that $K$ has nonempty interior, or else we simply proceed within the affine hull of $K$. Next, we may assume that the interiors of $K$ and $K+T$ intersect, as the other case is evident.
Now we choose a point
$$
p\in\inte K \cap \inte (K+T).
$$
For a ray $\rho$ starting at $p$, the intersection points $\rho\cap \partial K$ and $\rho\cap\partial (K+T)$ depend continuously on $\rho$. This allows us to build a homotopy equivalence between $K\setminus(K+T)$ and $(\inte K)\setminus (K+T)$; this can be done in the intersection with every $\rho$ in a way which depends continuously on $\rho$.
In the same way, working in the intersection with every $\rho$, we can, for every neighborhood $U\supseteq K\setminus (K+T)$, construct a neighborhood $U'\supseteq K\setminus (K+T)$ contained in $U$ and homeomorphic to $(\inte K)\setminus (K+T)$. This shows that the singular cohomology of $(\inte K)\setminus (K+T)$ is the same as the \v{C}ech cohomology of $K\setminus (K+T)$, and the goal is therefore to establish acyclicity of the open set $(\inte K)\setminus (K+T)$.
For this open set, we may switch to singular cohomology and homology. It is now sufficient to represent this set as a union of an inclusion increasing sequence of acyclic open sets, since singular chains always have compact support and must fit in one of the sets of such a sequence. Represent $T$ as the intersection of an inclusion decreasing sequence of smooth and strictly convex bodies $T_k$. Then $(\inte K)\setminus (K+T)$ will be the union of the inclusion increasing sequence of sets $(\inte K)\setminus (K+T_k)$. This shows that it suffices to consider smooth and strictly convex bodies in place of $T$.
Now we represent $K$ as the union of an inclusion increasing sequence of smooth strictly convex $K_k$, so that
$$
K \subseteq K_k + B_{\varepsilon_k},
$$
where $B_{\varepsilon_k}$ denotes a ball of radius $\varepsilon_k>0$, for some sequence $\varepsilon_k\to 0$. We also consider $T_k = T+B_{\varepsilon_k}$. For such a choice, $(\inte K_k)\setminus(K_k+T_k)\subseteq (\inte K)\setminus(K+T)$, but the sequence $(\inte K_k)\setminus(K_k+T_k)$ is not necessarily inclusion increasing. Still, it is possible to show (we omit the details) that every compactum $X\subset (\inte K)\setminus(K+T)$ will be contained in some $(\inte K_k)\setminus(K_k+T_k)$ for sufficiently large $k$, thus reducing the question of acyclicity to smooth and strictly convex $K$ and $T$.
Now we consider the support functions
$$
s_K(p) = \sup_{x\in K}(p, x), \quad s_T(p) = \sup_{x\in T}(p, x), \quad s_{K+T}(p) = \sup_{x\in K+T}(p,x)
$$
and note that $s_{K+T}(p) = s_K(p) + s_T(p)$. Therefore $s_K(p) - s_{K+T}(p)$ is concave. Hence the set of $p\in \mathbb R^n$ such that $s_K(p) > s_{K+T}(p)$ is either empty (in which case $K\setminus (K+T)$ is also empty) or an open convex cone $C$. Consider the subset $K'\subset K$, where the linear functions $p\in C$ attain their maxima on $K$. From the smoothness and strict convexity it follows that this set is homeomorphic to an intersection of $C$ with the unit sphere, and is therefore contractible.
After this, for every $x\in K'$ it is possible to choose a ray $\rho_x$ from $x$ in such a way that it depends continuously on $x$, no pair of such rays intersect each other, every point in $(\inte K)\setminus(K+T)$ belongs to one such ray, and the intersection of $(\inte K)\setminus(K+T)$ with every $\rho_x$ is an interval depending continuously on $x$. This all allows to conclude that $(\inte K)\setminus(K+T)$ is homotopy equivalent to $K'$, and is therefore contractible.
The choice of $\rho_x$ in~\cite{kar2001car} was a bit lengthy, but here we want to outline a simpler construction. For any linear function $p\in C$, we take $x(p)$ to be the point where $p$ attains its maximum on $K$, and $y(p)$ to be the point where $p$ attains its maximum on $K+T$. The ray $\rho(p)$ will just start at $x(p)$ and pass through $y(p)$, it is easy to check that its direction is in the interior of the polar cone of $C$. For any two $p', p''\in C$ the two rays $\rho(p'), \rho(p'')$ do not intersect, in order to establish this it is sufficient to consider the projection of the picture to the two-dimensional plane with coordinates $p'$ and $p''$. The fact that every point $z\in \inte K$ has such a ray passing through $z$ is established by considering a homothet $H_z^{-t}(K+T)$ with center $z$ and big negative coefficient $-t$ and decreasing $t$ until $H_z^{-t}(K+T)$ touches $K$ at a point $x$, the point $y$ is then $H_z^{-1/t}(x)$. Eventually, we can retract the set $(\inte K)\setminus(K+T)$ to $K'$ (the set of all possible $x(p)$) along these rays to show its contractibility.
\end{proof}
\begin{proof}[Proof of Theorem~\ref{theorem:colorfulcovering}] Take a system of representatives $x_i\in X_i$. The assumption that $K-t\supset\{x_0, x_1,\ldots, x_n\}$ reads as $t\in K-x_i$ for every $i=0, 1,\ldots, n$, and the assumption $K-t\not\ni 0$ reads as $t\not\in K$. Now put
$$
F_{x_i} = (K-x_i)\setminus K.
$$
These sets form $n+1$ families $\mathcal F_i$ indexed by $i$. The hypothesis of the theorem now reads: For any system of representatives $F_i\in \mathcal F_i$, their intersection is nonempty.
Now we show that any intersection of $F_i$'s is either empty or acyclic. Indeed, this set is obtained as follows: First, we intersect a family of translates of $K$ to obtain $K\gdiv T$ (in the notation of the introduction); second, we subtract $K$ to obtain $(K\gdiv T)\setminus K$. But Definition~\ref{definition:genset} means that $K = (K\gdiv T) + T'$ for a convex compactum $T'$, and Lemma~\ref{lemma:acyclic} concludes that the set $(K\gdiv T)\setminus K$ is either empty of acyclic. Thus the colorful topological Helly theorem is applicable, and for some $i$, the sets $\{K-x_i\}_{x_i\in X_i}$ have a common point outside of $K$, which is equivalent to the conclusion of the theorem.
\end{proof}
\section{More Carath\'{e}odory-type statements}
\label{section:more}
It is possible to generalize Theorem~\ref{theorem:colorfulcovering} slightly, by replacing the requirement of not touching the origin with not touching a given convex compactum. Let us say that a translate $K-t$ \emph{separates} a set $S$ from a convex compactum $C$ if $K-t$ contains the set $S$ and is disjoint from $C$.
\begin{theorem}
\label{theorem:colorfulcovering2}
Let $X_0, X_1, \ldots, X_n\subset \mathbb R^n$ be finite sets, $K$ a generating set in $\mathbb R^n$, and $C$ a convex compactum. Suppose every system of representatives $x_0\in X_0$, $x_1\in X_1$, $\ldots$, $x_n\in X_n$ can be separated from $C$ by a translate $K-t$. Then there exists a translate of $K$ that separates $X_i$ from $C$, for some $0\leq i \leq n$.
\end{theorem}
\begin{proof}
The proof proceeds like the proof of Theorem~\ref{theorem:colorfulcovering}, putting
$$
F_{x_i} = (K-x_i)\setminus (K+(-C)).
$$
Again, any intersection of translates $K\gdiv T$ is a Minkowski summand of $K+(-C)$, thus the colorful topological Helly theorem is applicable.
\end{proof}
The following result improves Theorem~\ref{theorem:colorfulcovering} in the case when the union of the $X_i$ is covered by the interior of a single translate of $K$. In this case we obtain a generalization of the version of the colorful Carath\'eodory theorem (``very colorful theorem'') appearing in \cite{arocha2009very, holmsen2008surrounding}:
\begin{theorem}
\label{theorem:strong-caratheodory}
Let $X_0$, $X_1$, $\dots$, $X_n \subset \mathbb{R}^n$ be non-empty finite sets and $K$ a generating set in $\mathbb{R}^n$ containing the origin and the sets $X_0, X_1, \dots, X_n$ in its interior. Suppose every system of representatives $x_0\in X_0$, $x_1\in X_1$, $\ldots$, $x_n\in X_n$ can be separated from the origin by a translate $K-t$. Then there exists a translate of $K$ that separates $X_i\cup X_j$ from the origin, for some $0\leq i < j \leq n$.
\end{theorem}
The proof of Theorem \ref{theorem:strong-caratheodory} uses the following result, which is a special case from \cite{holmsen2013}. Let $\mathcal C$ be a simplicial complex. For a simplex $\sigma \in \mathcal C$, the link of $\sigma$ is the simplicial complex defined as
\[
\lk_{\mathcal C}(\sigma) = \{\tau \in \mathcal C : \tau \cap \sigma = \emptyset, \tau \cup \sigma \in \mathcal C\}.
\]
Here and in the following section we let $\tilde{H}_*(\mathcal C)$ denote the reduced homology with rational coefficients.
\begin{proposition}
\label{proposition:leray-link}
Let $\mathcal C$ be a simplicial complex on the vertex set $V$ which satisfies the following:
\begin{enumerate}
\item The vertices are partitioned into non-empty parts $V = V_0 \cup V_1 \cup \cdots \cup V_n$.
\item $\mathcal C$ contains every system of representatives (transversal for short) $v_0\in V_0, v_1\in V_1, \dots, v_n\in V_n$ of the partition. That is, every transversal $\{v_0, v_1, \dots ,v_n\}$ is a simplex in $\mathcal C$.
\item For all $i\geq n$, we have $\tilde{H}_i(\mathcal C) = 0$.
\item For every non-empty simplex $\sigma \in \mathcal C$ and $i\geq n-1$, we have $\tilde{H}_i(\lk_{\mathcal C}(\sigma)) = 0$.
\end{enumerate}
Then there exist indices $0\leq i < j \leq n$ such that $V_i\cup V_j$ is a simplex in $\mathcal C$.
\end{proposition}
Let us first show how to deduce Theorem \ref{theorem:strong-caratheodory} from Proposition \ref{proposition:leray-link}, the proof of the latter will be given in the next section.
\begin{proof}[Proof of Theorem \ref{theorem:strong-caratheodory}]
We define a simplicial complex $\mathcal C$ on the vertex set $V = X_0\sqcup X_1 \sqcup \cdots \sqcup X_n$. By this we mean that each point corresponds to a vertex, but we keep track of multiplicities in the sense that a point which appears in both $X_i$ and $X_j$ appears as distinct vertices in $V$. The simplices of $\mathcal C$ are the subsets of $X_0\sqcup X_1 \sqcup \cdots \sqcup X_n$ which can be separated from the origin by a translate of $K$.
Note that by the hypothesis we may assume that every point is distinct from the origin and can therefore be separated by a translate of $K$, so every point corresponds to a vertex of $\mathcal C$. We will interchange freely between referring to vertices of $\mathcal C$ and points in $X_0\sqcup X_1 \sqcup \cdots \sqcup X_n$. Note that the hypothesis implies that the simplicial complex $\mathcal C$ satisfies conditions (1) and (2) of Proposition \ref{proposition:leray-link}, so to complete the proof it remains to verify that $\mathcal C$ satisfies conditions (3) and (4).
For a point $x\in V$, let $K_x = (K-x)\setminus K$. As in the proof of Theorem \ref{theorem:colorfulcovering}, a subset $S\subset V$ is separated from the origin by a translate $K-t$ if and only if the set $\bigcap_{x\in S} K_x$ is non-empty. Thus, the simplicial complex $\mathcal C$ is just the nerve of the family $\{K_x\}_{x\in V}$. We now use the nerve theorem (justified in Section~\ref{section:proof1}) to verify conditions (3) and (4).
Condition (3): We know from Lemma~\ref{lemma:acyclic} that for any subset $S\subset V$ the set $\bigcap_{x\in S} K_x$ is empty or acyclic. Thus we may apply the nerve theorem, which implies that $\mathcal C$ has the same homology as $\bigcup_{x\in V} K_v \subset \mathbb R^n\setminus K$. This shows that $\tilde{H}_i(\mathcal C)=0$ for all $i\geq n$.
Condition (4):
For each $x\in V$ we define a subset $L_x$ contained in the boundary of $K$ as
\[
L_x = \left\{\pi(v) : v \in K_x \right\},
\]
where $\pi$ denotes the central projection from the origin to the boundary of $K$.
The crucial observation is that for any $S\subset V$ we have
\[
\bigcap_{x\in S} L_{x} \neq \emptyset \iff \bigcap_{x\in S} K_{x} \neq \emptyset.
\]
This follows because, for every $x\in V$, the translate $K-x$ contains the origin in its interior (this is assumed in the statement of the theorem) and every point in $\bigcup_{x\in V}K_x$ can be seen from the origin, that is, it is strictly starshaped. Hence the preimage of any $p\in L_x$ in $K_x$ under the map $\pi$ is a semi-interval starting from some $q\in\partial (K-x)$ and ending in $p$ (not containing $p$). Therefore, a nonempty intersection of several of $L_x$'s implies a nonempty intersection of the corresponding set of $K_x$'s; the opposite is trivially true.
Let $\sigma$ be a non-empty simplex of $\mathcal C$. The vertices of $\lk_{\mathcal C}(\sigma)$ correspond to the points $y\not\in \sigma$ such that $L_y \cap \left(\bigcap_{x\in \sigma}L_x\right) \neq\emptyset$. As before, we know that for every subset of vertices $S$ in $\lk_{\mathcal C}(\sigma)$, the set
\[
\left(\bigcap_{y\in S}L_y\right) \cap \left(\bigcap_{x\in \sigma}L_x\right)
\]
is empty or acyclic. So applying the nerve theorem to the family $\left\{L_y\cap \left(\bigcap_{x\in \sigma}L_x\right)\right\}$, where $y$ ranges over the vertices of $\lk_{\mathcal C}(\sigma)$, we see that $\lk_{\mathcal C}(\sigma)$ is homotopy equivalent to $\left(\bigcup L_y\right)\cap \left(\bigcap_{x\in \sigma}L_x\right) \subset \bigcap_{x\in \sigma}L_x$. Since $\bigcap_{x\in \sigma}L_x$ is an acyclic subset of the boundary of $K$, and the boundary of $K$ is homemorphic to $\mathbb{S}^{n-1}$, it follows that $\tilde{H}_i(\lk_{\mathcal C}(\sigma)) = 0$ for all $i \geq (n-1)$.
Now all the conditions of Proposition \ref{proposition:leray-link} are satisfied, so Theorem \ref{theorem:strong-caratheodory} is proved.
\end{proof}
\section{Proof of Proposition~\ref{proposition:leray-link}}
\label{section:leray-link}
For completeness, we now give a proof of Proposition~\ref{proposition:leray-link}. The main tool used in this proof is a Sperner-type lemma due to Meshulam \cite{meshulam2001}, which also appears in \cite{km2005}.
Let $\mathcal C$ be a simplicial complex with vertex set $X$ which is partitioned into non-empty parts $X = X_1 \sqcup X_2 \cup \cdots \sqcup X_N$. A \emph{colorful simplex} in $\mathcal C$ is an $(N-1)$-simplex which is a transversal of the partition. For a non-empty subset $I\subset \{1,2,\dots, N\}$, let $\mathcal C[I]$ denote the subcomplex of $\mathcal C$ induced by the vertices $\bigcup_{i\in I}X_i$. Meshulam's lemma gives a sufficient condition for the existence of a colorful simplex in $\mathcal C$.
\begin{lemma}
\label{lemma:meshulam-colorful}
Let $\mathcal C$ be a simplicial complex with vertex set $X$ which is partitioned into non-empty parts $X = X_1$ $\sqcup$ $X_2$ $\sqcup \cdots \sqcup$ $X_N$. Suppose for every non-empty subset $I\subset \{1,2,\dots, N\}$, we have \[\tilde{H}_i(C[I]) = 0 , \text{ for all } i \leq |I|-2.\] Then $\mathcal C$ contains a colorful simplex.
\end{lemma}
\begin{proof}[Proof of Proposition \ref{proposition:leray-link}]
Let $V = \{v_1, v_2, \dots, v_N\}$ denote the vertices of $\mathcal C$ and let $W=\{w_1, w_2, \dots, w_N\}$ be a disjoint copy of $V$. The partition $V = V_0\sqcup V_1 \sqcup \cdots \sqcup V_n$ induces a partition $W = W_0\sqcup W_1\sqcup \cdots \sqcup W_n$. Let $\mathcal D$ denote the simplicial complex on $W$ whose simplices consist of all partial transversals of this partition. Condition (2) therefore reads that for every simplex $\sigma_W = \{w_{i_1}, w_{i_2}, \dots, w_{i_k}\}$ in $\mathcal D$, the corresponding simplex $\sigma_V = \{v_{i_1}, v_{i_2}, \dots, v_{i_k}\}$ is in $\mathcal C$.
For a subset $S\subset V$ let $r(S)$ denote the cardinality of the inclusion-minimal subset $I\subset \{0,1,\dots, n\}$ such that $S\subset \bigcup_{i\in I}V_i$, that is, the minimal number of parts of the partition which contain $S$. The same notation will be used for subsets of $W$.
We prove the contrapositive. Suppose for every $0\leq i< j \leq n$ the set $V_i\cup V_j$ is not a simplex in $\mathcal C$, or equivalently, for every simplex $S$ in $\mathcal C$ we have $r(V\setminus S) \geq n$. We then show that there is a transversal of the partition which is not a simplex in $\mathcal C$, which violates condition (2).
Let $\mathcal C^\star$ denote the Alexander dual of $\mathcal C$, which is defined as
\[
\mathcal C^\star = \{S\subset V : V\setminus S \not\in \mathcal C\}.
\]
Define the simplicial complex $\mathcal B$ on vertices $X = V\sqcup W$ as the join of $\mathcal C^\star$ and $\mathcal D$, that is, $\mathcal B = \mathcal C^\star * \mathcal D$. The vertex set of $\mathcal B$ has a natural partition into $N$ non-empty parts $X = X_1 \sqcup X_2 \sqcup \cdots \sqcup X_N$ where $X_i = \{v_i,w_i\}$, that is, each part consists of a vertex from $V$ and its copy in $W$.
Our goal is to use Lemma \ref{lemma:meshulam-colorful} to show that $\mathcal B$ has a colorful simplex. This will complete the proof because a colorful simplex in $\mathcal B$ corresponds to disjoint subsets $I$ and $J$ such that $\{v_i\}_{i\in I}$ is a simplex in $\mathcal C^\star$, $\{w_j\}_{j\in J}$ is a simplex in $\mathcal D$, and
\[
I\cup J = \{1,2,\dots, N\}.
\]
However, $\{v_i\}_{i\in I}$ is a simplex in $\mathcal C^\star$ if and only if $\{v_j\}_{j\in J}$ is not a simplex in $\mathcal C$, which gives us the desired contradiction to condition (2) since $\{w_j\}_{j\in J}$ is a simplex in $\mathcal D$ and therefore a partial transversal of the partition $W= W_0\sqcup W_1 \sqcup \cdots \sqcup W_n$ (and therefore also of the corresponding partition of $V$). So it remains to verify that $\mathcal B$ satisfies the conditions of Lemma \ref{lemma:meshulam-colorful}.
For $\emptyset \neq I \subset \{1,2,\dots, N\}$ let $S = \{v_i\}_{i\in I}$ and $T = \{w_i\}_{i\in I}$. We want to show that $\tilde{H}_i(\mathcal B[I]) = 0$ for all $0\leq i \leq |I|-2$. If $S$ is a simplex in $\mathcal C^\star$, then $\mathcal C^\star[S]$ is acyclic which implies $\tilde{H}_i(\mathcal C^\star[S] * \mathcal D[T]) = 0$ for all $i$. So we assume that $S$ is not a simplex in $\mathcal C^\star$ and consequently $V\setminus S$ is a simplex in $\mathcal C$.
By the K\"unneth formula for the join, we have
\begin{equation} \label{eq:kunneth}
\tilde{H}_i(\mathcal B[I]) \cong \tilde{H}_i(\mathcal C^\star[S] * \mathcal D[T]) \cong \bigoplus_{k+l = i-1} \tilde{H}_k(\mathcal C^\star[S]) \otimes \tilde{H}_l(\mathcal D[T]) .
\end{equation}
Clearly we may assume that $\mathcal C$ is not a simplex, so Alexander duality implies
\begin{equation}\label{eq:alexander}
\tilde{H}_k(\mathcal C^\star[S]) \cong \tilde{H}_{|S|-k-3}(\lk_{\mathcal C}(V\setminus S)).
\end{equation}
Moreover, if $r = r(S) = r(T)$, then $\mathcal D[T]$ is a join of $r$ disjoint sets of isolated vertices, and consequently $\mathcal D[T]$ is acyclic or $(r-2)$-connected, and therefore \[\tilde{H}_l(\mathcal D[T]) =0 \text{ for all } l\leq r-2\]
We now consider two cases:
\begin{enumerate}
\item
If $I = \{1,2,\dots, N\}$, then $S = V$, so $\mathcal C^\star[S] = \mathcal C^\star$ and $\lk_{\mathcal C}(\emptyset) = \mathcal C$. By condition (3) we have
\[
\tilde{H}_i(\mathcal C) = 0 \text{ for all } i\geq n,
\]
so by Alexander duality \eqref{eq:alexander}
\[
\tilde{H}_{k}(\mathcal C^\star) = 0 \text{ for all } k\leq N-n-3.
\]
In this case we also have $T = W$, so $r(T) = n+1$ and $\mathcal D[T] = L$, which implies that
\[
\tilde{H}_l(\mathcal D) = 0 \text{ for all } l\leq n-1.
\]
Thus the K\"unneth formula \eqref{eq:kunneth} implies that $\tilde{H}_i(\mathcal B) =0$ for all $i\leq N-2$.
\item
If $I$ is a proper subset of $\{1,2,\dots, N\}$, then $\sigma = V\setminus S$ is a non-empty simplex of $\mathcal C$. By condition (4) we have
\[
\tilde{H}_i(\lk_{\mathcal C}(\sigma)) = 0 \text{ for all } i\geq n-1,
\]
so by Alexander duality \eqref{eq:alexander}
\[
\tilde{H}_{k}(\mathcal C^\star[S]) = 0 \text{ for all } k\leq |S|-n-2.
\]
Since $\sigma$ is a simplex in $\mathcal C$, it follows from our assumption that $r(S) = r(T)\geq n$, which implies that
\[
\tilde{H}_l(\mathcal D[T]) = 0 \text{ for all } l\leq n-2.
\]
Thus the K\"unneth formula \eqref{eq:kunneth} implies that $\tilde{H}_i(\mathcal B[I]) =0$ for all $i\leq |I|-2$.
\end{enumerate}
This shows that the conditions of Lemma \ref{lemma:meshulam-colorful} are met, and the proof is complete.
\end{proof}
\section{No Carath\'eodory-type theorem for arbitrary convex sets}
\label{section:no-cara}
The above proofs use the nontrivial colorful topological Helly theorem~\cite{km2005} and its relatives, like Proposition~\ref{proposition:leray-link}. It is interesting whether it is possible to make this argument more elementary, or give a different proof. For example, is it possible to prove such results with optimization ideas like in~\cite{ba1982}?
Moreover, we may ask whether the ``generating set'' property is really needed in the argument; the usage of such a property here was dictated by the topological Helly-type theorems which require us to have acyclic intersections.
In this section
we show that for dimension greater or equal to 3, the Carath\'eodory theorem does not holds for $K$-strong convexity when the set $K$ is an arbitrary convex body. In particular, for every positive integer $n$, we give an example of a set $X$ of $2n$ points and a convex set $K$ in $\mathbb{R}^3$ such that every proper subset of $X$ can be separated from the origin by a translate of $K$, but where no translate of $K$ separates the entire set $X$ from the origin. The convex set $K$ will be an epigraph of a function $f(x,y)$ and will therefore not be compact, but it is easy to produce a compact example by intersecting it with the halfspace $\{z \; : \; z \le C\}$ for a sufficiently large $C$.
Our point set $X$ will consist of the points for $k=1,\ldots, n$
$$
\xi_{\pm k} = (\pm k, 0, k^2).
$$
The point that we are going to test for containment in $\conv_K X$ and $\conv_K Y$ for proper subsets $Y\subset X$ is the origin $\xi_0 = (0, 0, 0)$.
Note that the set $X$ lies in the plane $\{y=0\}$ and on the parabola $z = h(x) := x^2$. We are going to consider $y$ as a parameter and describe how we choose the functions $f(x,y)$ of $x$ for given $y$. Let us choose them so that $f(x,y)$ is a $C^2$ smooth strictly convex (even with $f''_{xx} (x, y) \ge 1$) function of $x$, always satisfying the assumption
$$
f(0,y) = 0,\quad f(\pm k, y) \le h(\pm k) = k^2,
$$
for $k=1,\ldots, n$. When the equality in the latter inequality holds, we will call this ``\emph{$f(x,y)$ touches $\xi_{\pm k}$}''.
Now we require that $f(x,y)$ depends $C^2$ smoothly on $y$, is even in $y$, and satisfies the following assumption: $f(x,y)$ touches $\xi_{\pm k}$ precisely when $|y|\in [k-1, k]$ for $k<n$, and precisely for $|y|\in [n-1, +\infty)$ when $k=n$; moreover, let $f(x,y)$ be independent of $y$ for $|y|\ge n$. It is clear that such a family of functions exists and may be chosen twice continuously differentiable in $y$. The total function $f(x,y)$ is still not necessarily convex, but it can be adjusted to become convex after considering
$$
f(x,y) + Ay^2
$$
with sufficiently large $A$ instead. This adjustment changes the restriction to the plane $y=\const$ only by adding a constant, which is not relevant to finding $\conv_K X$, since $y$ is constant on $X$. So we prefer to consider here the non-modified and intentionally non-convex $f$ for clarity.
From the ``touching'' assumption it is easy to conclude that $\xi_0$ is in $\conv_K X$. Indeed, if the epigraph is translated with some value $-y$, then we actually consider the convex hull of the planar set $X$ with respect to the set $K_y$, the epigraph of $f(x,y)$ with fixed $y$. To put it clearly,
$$
\conv_K X\cap \{y=0\} = \bigcap_y \conv_{K_y} X.
$$
Again, from the ``touching'' assumption it is relatively clear that $\xi_0$ is in $\conv_{K_y} X$ for every $y$. But, the touching assumption also guarantees that for $|y|\in (k-1, k)$ the only thing preventing $\xi_0$ from getting outside $\conv_{K_y} X$ is the pair of points $\xi_{\pm k}$. In this range, if $\xi_{-k}$ and $\xi_k$ are in the translated $K_y$ then $\xi_0$ gets into this translate of $K_y$ as well. But, if we drop one of the points $\xi_{\pm k}$ ($\xi_k$ without loss of generality) then it immediately becomes possibly to cover $X\setminus\{\xi_k\}$ with a translate of $K_y$ leaving $\xi_0$ outside. This means that $\conv_K X$ fails to contain $\xi_0$ when any one of the points of $X$ is dropped.
\begin{remark}
The above example shows that the Carath\'eodory number is not bounded from above by a constant independent of the body $K\subset\mathbb R^3$. It can be modified by considering an infinite sequence
$$
\xi_{\pm k} = (\pm (2 - 1/k), 0, (2 - 1/k)^2),
$$
showing that for a particular body $K$ the Carath\'eodory number can be infinite.
\end{remark}
To conclude this discussion, we ask:
\begin{question}
Is the existence of a finite Carath\'eodory number for $K$-strong convexity equivalent to the \emph{generating} property of $K$?
\end{question}
\begin{question}
Is the property that the Carath\'eodory number for $K$-strong convexity equals $n+1$ equivalent to the \emph{generating} property of $K\subset\mathbb R^n$?
\end{question}
\section{Topological criterion for Minkowski summand}
\label{section:topo}
The crucial topological tool used in the proofs of Theorems \ref{theorem:colorfulcovering}, \ref{theorem:colorfulcovering2}, and \ref{theorem:strong-caratheodory} was Lemma \ref{lemma:acyclic}. In this section we investigate whether its converse also holds. Note that Lemma~\ref{lemma:acyclic} can be reformulated as follows: Assume a convex body $A\subset\mathbb R^n$ is a Minkowski summand of another convex body $B\subset\mathbb R^n$; then for every vector $t\in\mathbb R^n$ the set $(A+t)\setminus B$ is either empty or acyclic. In this section we are going to obtain a certain inverse theorem.
The crucial fact that we need is the following:
\begin{lemma}[Vietoris--Begle]
\label{lemma:leray-map}
Let $f : X\to Y$ be a proper continuous map between metric spaces such that for every $y\in Y$, the fiber $f^{-1}(y)$ is acyclic. Then $f$ induces an isomorphism of the \v{C}ech cohomology of $X$ and $Y$.
\end{lemma}
This is a well-known fact, see~\cite{begle1950,begle1955}; but we sketch the proof for reader's convenience. We remind the reader once again, that in our situation \v{C}ech cohomology is the same as sheaf cohomology.
\begin{proof}
Consider the Leray spectral sequence for the direct image of a sheaf with~\cite[Theorem 4.17.1]{godement1958}
$$
E_2^{p,q} = H^p(X; \mathcal H^q(f)),
$$
where the sheaf $\mathcal H^q(f)$ is generated by the presheaf $U\mapsto H^q(f^{-1}(U))$. This spectral sequence converges to $H^*(Y)$. But our assumption on the fibers together with the cohomology continuity property shows that the sheafs $\mathcal H^q(f)$ are trivial for $q>0$, and $\mathcal H^0(f)$ is the constant sheaf $\mathbb Z$. Hence in this spectral sequence $E_2 = H^*(X)$ and its differentials vanish, and therefore $H^*(Y) = E_\infty = H^*(X)$.
\end{proof}
Now we state the result:
\begin{theorem}
\label{theorem:acyclic}
Let $A$ be a convex body in $\mathbb R^n$ and $B$ be a convex open bounded set in $\mathbb R^n$. Assume that, for any vector $t\in\mathbb R^n$, the set $(A+t)\setminus B$ is either empty or acyclic. Then $A$ is a Minkowski summand of $B$.
\end{theorem}
\begin{proof}
Put $C = B\gdiv A$, we need to demonstrate that $A+C = B$. Evidently, $C$ is a convex open set.
First, we need to show that $C$ is not empty, that is, a translate of $A$ is contained in $B$. Put
$$
Z = \{(x, t) \in \mathbb R^n\times \mathbb R^n: x\in (A+t)\setminus B\}.
$$
Observe that the projection $\pi_1(Z)$ to the first factor is $\mathbb R^n\setminus B$, while its projection $\pi_2(Z)$ to the second factor is $\mathbb R^n\setminus C$.
The fiber of the first projection is $\pi_1^{-1}(x) = \{x\}\times (x - A)$, it is compact, convex, and therefore acyclic; the fiber of the second projection $\pi_2^{-1}(t) = ((A+t)\setminus B)\times \{t\}$ is compact and acyclic by the hypothesis. Also, it is easy to check by definition that both projections of $Z$ are proper maps. Thus Lemma~\ref{lemma:leray-map} applies to both projections and implies that both projections induce isomorphisms in cohomology. Since
$H^{n-1}(\mathbb R^n\setminus B) = \mathbb Z$, then we must have $H^{n-1}(\mathbb R^n\setminus C) = \mathbb Z$. Therefore the set $C$ must be nonempty.
Now we continue to work with $Z$ and consider its subset
$$
Z(\varepsilon) = \{(x,t)\in Z : \dist (t, C) < \varepsilon)\}.
$$
Obviously $\pi_2(Z(\varepsilon))$ is $C_\varepsilon\setminus C$; therefore its cohomology is the same as the cohomology of an $(n-1)$-dimensional sphere, that is $H^{n-1}(C_\varepsilon\setminus C) = \mathbb Z$. Lemma~\ref{lemma:leray-map} concludes that $H^{n-1}(Z(\varepsilon)) = \mathbb Z$ also.
Consider the commutative diagram:
$$
\begin{CD}
Z(\varepsilon) @>>> Z\\
@VV{\pi_2}V @VV{\pi_2}V\\
C_\varepsilon\setminus C @>>> \mathbb R^n\setminus C,
\end{CD}
$$
where the horizontal arrows are inclusions. Since the vertical arrows and the lower horizontal arrow induce isomorphisms in cohomology, the same is true for the upper horizontal arrow.
Now take a point $o$ in the interior of $B$ and consider the central projection to the unit sphere centered at $o$
$$
\phi : \mathbb R^n\setminus B \to \mathbb S^{n-1}.
$$
Note that $\phi$ obviously induces isomorphism in the cohomology. Hence the composition
$$
\begin{CD}
Z(\varepsilon) @>>> Z @>{\pi_2}>> \mathbb R^n\setminus B @>{\phi}>> \mathbb S^{n-1},
\end{CD}
$$
which we denote by $\psi$, induces an isomorphism $\psi^* : H^{n-1}(\mathbb S^{n-1})\to H^{n-1}(Z(\varepsilon))$. This implies $\psi$ must be surjective, because an inclusion $\mathbb S^{n-1}\setminus \nu \to \mathbb S^{n-1}$ (for any $\nu\in \mathbb S^{n-1}$) induces a zero map in $(n-1)$-dimensional cohomology.
Now let us decode the geometric meaning of what we have proved: For any unit vector $\nu$ the ray
$$
\rho_\nu = \{o+\lambda \nu : \lambda \ge 0\}
$$
intersects the set $(A+t)\setminus B$ for some $t\in C_\varepsilon$. Now we let $\varepsilon$ tend to $0$ and use the compactness to conclude that any $\rho_\nu\cap \partial B$ is contained in $A+t$ for some $t$ in $\cl C$, the closure of $C$. Since any point in $\partial B$ is $\rho_\nu\cap \partial B$ for a suitable $\nu$, we conclude that the convex set $A+\cl C$ contains the boundary of $B$ and therefore contains $\cl B$. From this it is easy to see that $A+C$ must coincide with the whole set $B$.
\end{proof}
To conclude let us put forth two conjectures. Lemma~\ref{lemma:acyclic} asserts that $A\setminus (A+B)$ is either empty or acyclic. Can one make an analogous assertion concerning the set $(A+B)\setminus A$?
\begin{conjecture}
Let $A$ and $B$ be convex bodies in $\mathbb R^n$. Then the set $(A+B)\setminus A$ is either empty, or acyclic, or has homology of a sphere of dimension $k\in [0, n-1]$.
\end{conjecture}
In Theorem \ref{theorem:acyclic} we needed $B$ to be open because it was convenient to have the sets $(A+t)\setminus B$ compact. Can one obtain the same conclusion assuming that $B$ is a convex body?
\begin{conjecture}
Let $A$ and $B$ be convex bodies in $\mathbb{R}^n$. Assume that, for any vector $t\in \mathbb{R}^n$, the set $(A+t) \setminus B$ is either empty or acyclic. Then $A$ is a Minkowski summand of $B$.
\end{conjecture}
| {
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{"url":"https:\/\/www.physicsforums.com\/threads\/decay-scheme-help-please.957935\/","text":"Apologies for this question, but I'm trying to understand what I'm looking at here and was unable to find an answer online.\n\nFrom my understanding, this is a decay scheme that shows the percentage of each energy level at which the disintegrated mother nucleus has reached after the disintegration has occurred. But what do the other numbers and arrows show?\n\nWhere I'm stuck is the symbols and numbers. I've tried to look in my textbook as well to no avail.\n\nI would really appreciate your help.\n\nMany thanks!\n\n#### Attachments\n\n\u2022 GuTnG.png\n58.5 KB \u00b7 Views: 905\nLast edited by a moderator:\n\nmfb\nMentor\nThe half-integer values on the left with the signs are spin and parity. At the right side you have the energies (in keV) and lifetimes of the excited states.\nThe arrows are possible follow-up decays of xenon. Their labels: Not sure what the first number is. Partial decay width would be reasonable but doesn't fit well. The second number is the energy difference, the third one tells you which type of decay it is.\n\nMahavir\ngleem\nStarting from left to right..The percentage under the I131 are the percentage of the beta decays that lead to the various energy levels of the daughter . The next number is the Log of the comparative half lives for the decays to the various levels. The comparative half live is proportional to the decay constant for that transition. The next number with the +\/- signs are the spin and parity of the Xe131 states. The numbers above the energy levels in Xe131 are the percent of total gamma decay for that transition, the next above is the energy of the gamma ray for that transition, and the M1, E2, M4 refer to the type of electromagnetic transitions, magnetic dipole, electric quadrapole and magenetic octopole respectively. The numbers to the right of the Xe131 energy levels are the energies and half lives of those states. The Q\u03b2- is he Q-value of the decay, the excess energy of the decay available to the beta particles as kinetic energy.\n\nEdit: The M4 term should have been hexadecapole not octopole.\n\nLast edited:\nMahavir\nStarting from left to right..The percentage under the I131 are the percentage of the beta decays that lead to the various energy levels of the daughter . The next number is the Log of the comparative half lives for the decays to the various levels. The comparative half live is proportional to the decay constant for that transition. The next number with the +\/- signs are the spin and parity of the Xe131 states. The numbers above the energy levels in Xe131 are the percent of total gamma decay for that transition, the next above is the energy of the gamma ray for that transition, and the M1, E2, M4 refer to the type of electromagnetic transitions, magnetic dipole, electric quadrapole and magenetic octopole respectively. The numbers to the right of the Xe131 energy levels are the energies and half lives of those states. The Q\u03b2- is he Q-value of the decay, the excess energy of the decay available to the beta particles as kinetic energy.\n\nEdit: The M4 term should have been hexadecapole not octopole.\nThe half-integer values on the left with the signs are spin and parity. At the right side you have the energies (in keV) and lifetimes of the excited states.\nThe arrows are possible follow-up decays of xenon. Their labels: Not sure what the first number is. Partial decay width would be reasonable but doesn't fit well. The second number is the energy difference, the third one tells you which type of decay it is.\n\nThank you both ever so much! It makes a great deal more sense.","date":"2022-06-25 19:56:28","metadata":"{\"extraction_info\": {\"found_math\": false, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.8257741928100586, \"perplexity\": 626.5961122709978}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2022-27\/segments\/1656103036099.6\/warc\/CC-MAIN-20220625190306-20220625220306-00690.warc.gz\"}"} | null | null |
{"url":"https:\/\/stats.stackexchange.com\/questions\/127298\/random-effects-probit-model\/127312","text":"Random-effects probit model\n\nI am currently using a mixed binomial model with the following specification in a paper I recently submitted (using lme4):\n\nm1<-glmer(y~X1*X2*X3+(1|Subject.ID),data=data,family=\"binomial\")\n\n\nX1 and X2 are binary predictors\n\nHowever, a reviewer has asked me to also include a random-effects probit model for the same analysis. What is the difference between a mixed effects model and a random effects model? Am I correct in thinking that a random-effects model would have no fixed effects and would thus be specified by:\n\nm1<-glmer(y~1+(1|Subject.ID)+(1|X1)+(1|X2)+(1|X1:X2),data=data,family=binomial(link=probit))\n\n\nIf so how do I interpret the output. All I get is the Std.Dev. for each random effect.\n\nAlternatively does it refer to a model where I would have a random slope for each of my predictors like:\n\nm1<-glmer(y~1+(X1|Subject.ID)+(X2|Subject.ID)+(X1:X2|Subject.ID),data=data,family=binomial(link=probit))\n\n\nm1<-glmer(y~X1*X2*X3+(1|Subject.ID),data=data,family=binomial(link=\"probit\"))\n\nas in your case only intercept is allowed to be random. I would make sure though, by searching whether random effects probit model can really be estimated with glmer, there might be some caveats related to exogeneity of regressors, which are ignored in glmer case.","date":"2020-02-28 02:49:54","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.6453412771224976, \"perplexity\": 585.0663369745789}, \"config\": {\"markdown_headings\": false, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2020-10\/segments\/1581875146940.95\/warc\/CC-MAIN-20200228012313-20200228042313-00558.warc.gz\"}"} | null | null |
Ex-Montebello councilwoman says city…
Ex-Montebello councilwoman says city can't be saved, drops out of special election
Vivian Romero did not mince words.
Former Montebello councilwoman Vivian Romero speaks during the groundbreaking ceremony at the Olson Company construction site on Emmet Williams Way in Montebello, Calif. on Thursday September 27, 2018. (File photo by Raul Romero Jr, Contributing Photographer)
By Mike Sprague | msprague@scng.com | Whittier Daily News
PUBLISHED: January 18, 2019 at 3:28 p.m. | UPDATED: January 18, 2019 at 5:31 p.m.
The field to fill the Montebello City Council seat vacated by former Mayor Vanessa Delgado is shrinking from three to two.
Former Montebello Councilwoman Vivian Romero, the city's first openly gay mayor, has dropped out of the special March 5 City Council election, saying there is no reason to run — the city can't be saved.
"I'm convinced this is a losing situation," Romero said in a Friday telephone interview.
"It does not matter who gets on the council," she said. "No new council member will be able to correct the deficiencies. There's too much mismanagement, waste and fraud. I say adios right now."
A state audit released in December warned the city of Montebello is on unsure financial footing as a result of relying on one-time sources of money, a lack of competitive bidding and running money-losing enterprises, such as its golf course, hotels and water system — all of which may need subsidizing.
Romero also has opposed bringing marijuana businesses to the city.
Romero's name is expected to remain on the ballot, along with former councilman Art Barajas and David Torres, a paralegal with the Los Angeles City Attorney's Office.
In an emailed statement, Torres wrote, "Vivian fought hard for her constituents and remained deeply committed to the betterment of Montebello throughout her term as councilwoman. As her competitor in both this race and last, I applaud her efforts, and as a resident I am grateful for her service to the city."
This woman is now Montebello's first openly gay mayor
Angie Jimenez wins third spot on Montebello City Council by three votes
In Montebello, it's already election season again: See who's running in the March special election
The state of California is very concerned about Montebello's financials
Montebello has a plan to address a critical state audit and solve its financial problems
More Montebello news
Barajas couldn't be reached for comment.
Romero said she now plans to go back to work — she's involved in the music business — writing songs and making music.
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Mike Sprague | Reporter
Mike Sprague has worked in the newspaper field since July 1977, beginning with the Huntington Park Daily Signal, and later moving to Southern California Publishing Co. where he was sport editor and editor of the Pico Rivera News. Mike began at the Whittier Daily News in April 1984. Since then, he has covered every city in the Whittier Daily News circulation area, as well as political and water issues. He has a bachelor's degree in communications and a master's degree in political science, both from Cal State Fullerton.
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San Gabriel City Council to fill seat vacated by recent Biden appointee Jason Pu
COVID: Why your free at-home rapid tests might take longer to arrive | {
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} | 7,090 |
\section{Introduction}
A central goal of the Learning Assistant (LA) model is to improve students' learning of science through the transformation of instructor practices \citep{Otero2016LearningNetworks}. Specifically, the LA model aims to leverage the additional in-class and planning supports that LAs provide to increase science instructors' uses of research-based pedagogies. To support LA and faculty collaboration, the LA model trains LAs in pedagogy courses and creates opportunities for instructors and LAs to co-plan for class each week. These structures support instructors to reexamine and refine their pedagogical practices and increase their effectiveness. This study sets out to examine whether instructor's prior experience teaching courses with LAs is associated with improved student learning.
\par The impact that K-12 teachers prior experiences have on their effectiveness, as measured by students' learning, has been the focus of significant discussion within the education policy communities \citep{StephenSawchuk2015,Ladd2015,Kini2016}. Researchers have repeatedly found strong links between teacher experience and improved student standardized test scores in math and reading \citep{Ladd2015,Kini2016}. The assumption that teachers' experiences improve their effectiveness has strongly influenced the creation of the K-12 salary schedules and is a significant source of inequity across school settings \citep{Rice2010}. While the impact of K-12 teacher experience on student learning of math and reading has been well documented, the impact of college instructor experience on student learning of physics (or science more generally) has received little attention.
\section{Background}
Increases in K-12 teacher effectiveness vary substantially across educational environments. The general trend within these settings is that teacher experience positively correlates with improved student performance on standardized math and reading tests \citep{Kini2016}. The effects of increasing teachers' experience is strongest over the first several years but continued throughout their careers. Teacher effectiveness was also found to improve most quickly when the teachers were in a supportive environment that facilitated peer collaboration \citep{Kini2016}. The impact of teacher experience on student math test performance was only half as strong in grades 6-8 than in grades 4 and 5 (Rice, 2010). Teacher experience was also associated with larger shifts on tests scores in math than in reading \citep{Kini2016}. Some studies have found that teaching effectiveness can decline over time, particularly in high school settings \citep{Rice2010}. These findings show that teacher experience can be an important factor in student learning, but there is considerable variability in how teacher experience relates to teacher effectiveness. Given the variation in impacts of teacher experience within K-12 educational environments and the substantial differences across K-12 and college systems, it is unclear how predictive the findings are of the impacts of instructor experience in college physics courses.
\par In one of the few examinations of physics instructor experience, Pollock and Finkelstein \citep{Pollock2012ImpactsPhysics} tracked eight years of student performance in first and second semester physics courses utilizing Peer Instruction \citep{Mazur1997PeerInstruction} and LAs. They categorized each of the 27 instructors in the study as Inexperienced, Experienced, or Physics Education Researcher (PER) based on their teaching and research backgrounds. Students in classes with Experienced and PER instructors outperformed their peers in classes with Inexperienced instructors. The three instructors initially identified as Inexperienced but who subsequently taught the course multiple times saw significant improvements in their students' performance. The three instructors identified as PER and who taught the course multiple times began with higher student performance but failed to show consistent improvement in student performance as they became more experienced. While the study was exploratory and did not have a control group of instructors not using LAs, it indicated that college physics instructor experiences may impact student performance and that these impacts may vary across instructor groups.
\par In an examination of the impact of LAs on instructor practices, Otero et al. \citep{Otero2010AModel} found that the 11 instructors interviewed reported that collaborating with LAs on planning lessons was instrumental in increasing their attention to student learning. The investigation, however, did not measure shifts in instructor effectiveness over time. While the support and collaborative aspects of the LA model align with the recommendations made in the K-12 literature \citep{Kini2016}, there are no large-scale studies that have empirically tested the impact of these practices on college physics instructors.
\section{Research Questions}
\par To investigate how interactions with LAs relates to physics instructor effectiveness over time, we investigated two questions:
\begin{enumerate}
\item What is the impact of instructor experience teaching introductory physics courses on student learning, if any?
\item Does an instructor's history of using LAs alter the impact of their teaching experience on student learning?
\end{enumerate}
\section{Methods}
The Learning About STEM Student Outcomes (LASSO) platform hosts, administers, scores, and analyzes student pre- and posttest assessments online to provide instructors with objective feedback on their courses. Instructors receive a report on their student performance and can access their students' responses. Data from participating courses are added to the LASSO database where they are anonymized, aggregated with similar courses, and made available to researchers with approved IRB protocols. This study used three years of introductory physics courses data from the LASSO database. We examined data from courses that used the Force Concept Inventory (FCI) \citep{Hestenes1992ForceInventory} or Force and Motion Conceptual Evaluation (FMCE) \citep{Thornton1998Fmce}. We did not differentiate between the FCI and FMCE in the models presented in this paper because our preliminary analysis indicated that doing so did not meaningfully change the model.
\par To clean our data, we removed assessment scores for students if they took less than 5 minutes on the assessment or were less than 80\% complete. We removed entire courses if they had less than 40\% student participation on either the pre- or posttest. After filtering our data was missing 15\% of the pretest scores and 30\% of the posttest scores. To address missing data, we used Hierarchical Multiple Imputation (HMI) with the hmi and mice packages in R. HMI addresses missing data by (1) imputing each missing data point \emph{m} times to create \emph{m} complete data sets, (2) independently analyzing each data set, and (3) combining the \emph{m} results using standardized methods \citep{Drechsler2015MultipleSimplicity}. The analysis used 10 imputed datasets. HMI is preferable to using matched data because it maximizes statistical power by using all available data \citep{Drechsler2015MultipleSimplicity}. After cleaning and imputation, our dataset included pre- and posttest scores for 4,365 from 93 courses.
\par When setting up a course in LASSO, each instructor answered a pair of questions on the number of times they had previously taught the course with LAs and the number of times they had taught the course without LAs. The majority (83\%) of the instructors reported having prior experience teaching their courses (Figure 1). Many of the instructors reported having always taught the course either with (24\%) or without (32\%) LAs.
\begin{figure}
\includegraphics[width=1\columnwidth]{color_graph.png}
\caption{Instructor's prior experience teaching their course with and without LAs. Sixteen courses were taught by instructors with no prior experience in that course.}
\end{figure}
\par To identify factors associated with differences in student performance, we developed 2-level HLM models using the HLM 7.01 software. These models nested student data (level 1) within course data (level 2). The multi-level nature of our models allowed us to quantify the impact of teacher experience in courses taught with and without LAs while accounting for inherent and unknown course-level variations (e.g. the time of day of a class and instructor backgrounds, which can lead to unforeseeable differences in student performance).
\par We developed our HLM models through a series of incremental additions of variables. In this paper we show the results from three models. Model 1 is the unconditional model, which predicts the student performance without level-1 or level-2 variables. Model 2 builds on Model 1 by including the student (level-1) variables (student prescore). Model 3 builds on Model 2 by including the course (level-2) variables and is shown below. Postscore is the outcome variable and is in level 1 because it was measured for each student. Level 1 also includes a coefficient for the intercept ($\beta_{0j}$), for the student prescore ($\beta_{1j}$), and for a random effects variable ($r_{0j}$). Each coefficient in level 1 has an associated level 2 equation. In the level 2 equation, the intercept is $\gamma_{i0}$, there is an associated coefficient ($\gamma_{ij}$) for each variable in the equation and $u_{ij}$ represents the random effect for the level 2 equations.
\\
\par
\textbf{Level-1 Equation}
\begin{eqnarray*}
(\text{Postscore})_{ij} & = & \beta_{0j} + \beta_{1j}*(\text{Student Prescore})_{ij} +r_{ij}
\end{eqnarray*}
\textbf{Level-2 Equations}
\begin{eqnarray*}
\beta_{0j}& = & \gamma_{00}+\gamma_{01}*(\text{Times Taught With LAs})_{j} +\\
& & \gamma_{02}*(\text{Times Taught Without LAs})_{j}+\\
& & \gamma_{03}*(\text{LA Supported})_{j}+\\
& & \gamma_{04}*(\text{Class Mean Prescore})_{j}+u_{0j}\\
\beta_{1j}& = & \gamma_{10}+u_{1j}\\
\end{eqnarray*}
\par We do not include LA-support in the level-2 equation for student prescore because the interaction between the variables is not of interest in our analysis. For ease of interpretation, student prescore is group mean centered, class mean prescore is grand mean centered, and all other variables are uncentered. These centerings simplify interpreting the model by shifting the model to predict posttest scores for average performing students in average performing classes. We included pretest scores in the model because they are strong predictors of student performance and improved the model's fit. Pretest scores are not the focus of this investigation so we will not substantively discuss them in our interpretation of the models.
\par To interpret the models we will first discuss the variance across the three models then we will look at the coefficients for each variable of interest. In discussing the variance, first we will discuss the Intraclass Correlation Coefficient (ICC) for the unconditional model (model 1) to compare the amount of variance in the data at the student versus course level. The ICC is a good indicator of the need for using HLM. Second, we will calculate the variance that the additional variables in each model explained by comparing the variances between the three models. Then we will discuss the model coefficients.
\begin{table}
\caption{Hierarchical Linear Models}
\begin{tabular}{p{2cm}ccp{.05cm}ccp{.05cm}cc}
\hline \hline
\rule{0pt}{3ex}&\multicolumn{8}{c}{Fixed Effects with Robust SE}\\ \cline{2-9}
\rule{0pt}{3ex} &\multicolumn{2}{c}{\underline{Model 1}}&&\multicolumn{2}{c}{\underline{Model 2}}&&\multicolumn{2}{c}{\underline{Model 3}}\\
&$\beta$&\emph{p}&&$\beta$&\emph{p}&&$\beta$&\emph{p}\\
For Intercept &&&&&&&&\\
~~Intercept &55.05&\textless0.001 &&55.04&\textless0.001 &&55.97&\textless0.001 \\
~~With LAs &-&-& &-&-& &0.02&0.974\\
~~W/o LAs &-&-& &-&-& &-1.18&0.01\\
~~LA Sup. &-&-& &-&-& &3.10&0.171\\
~~Class Pre. &-&-& &-&-& &1.05&\textless0.001\\
\multicolumn{4}{l}{For Student Prescore} &&&&&\\
~~Intercept &-&-& &0.55&\textless0.001 &&0.54&\textless0.001 \\
\hline
\rule{0pt}{3ex}&\multicolumn{8}{c}{Random Effect Variance}\\ \cline{2-9}
Intercept &\multicolumn{2}{c}{12.81} &&\multicolumn{2}{c}{12.98} &&\multicolumn{2}{c}{8.08} \\
Prescore &\multicolumn{2}{c}{-} &&\multicolumn{2}{c}{0.10} &&\multicolumn{2}{c}{0.10} \\
Level-1 &\multicolumn{2}{c}{20.14} &&\multicolumn{2}{c}{17.47} &&\multicolumn{2}{c}{17.43} \\
\hline \hline
\end{tabular}
\end{table}
\section{Findings}
The ICC shows that 39\% of the variability in student performance is between students within courses and 61\% of the variability is within students. This shows that course features are meaningfully related to student performance and HLM is an appropriate method of analysis. The reduction in level-1 variance (\textit{r}) from Model 1 to Model 2 (Table 1) shows that our student-level variable (Student Prescore) explains 13\% of the within-class variance in student performance. The reduction in level-2 intercept variance (\textit{u\textsubscript{0j}}) from Model 1 to Model 3 shows that our final model explains 37\% of the variance in mean performance across classes. This amount of explained variance indicates that Model 3 has strong explanatory power. As Model 3 is our most robust model, we will focus solely on it in the remainder of our findings.
\begin{figure}
\includegraphics[width=1\columnwidth]{ribbon_plot_rev1.png}
\caption{Predicted posttest scores for average students with instructors who habitually teach with or without LAs (95\% confidence interval).}
\end{figure}
\par Model 3 shows that as the number of times instructors have taught a course without LAs increases their posttest scores are predicted to reliably (p=0.01) decrease by 1.2\%/term (Table 1). This decline in instructor effectiveness is absent in LA-supported courses as instructor experience using LAs is not a reliable (p=0.974) predictor of student posttest scores. Figure 2 illustrates the longitudinal impacts of repeated teaching with and without LAs on predicted posttest scores for average students. When instructors have no prior experience teaching that course, our model predicts that the students in LA-supported courses will outperform their peers in courses without LAs by 3.1\%. As the instructors gain experience the predicted gap in student posttest scores grows. When instructors have 6 terms of experience teaching their respective courses (either with or without LAs), the students in LA-supported courses are predicted to outperform their peers by 10.3\% on their posttests.
\section{Discussion}
Prior research into the impact of experience on teacher effectiveness has primarily focused on K-12 settings. Existing research has found that teacher experience has differential impacts across grades and disciplines. Our investigation extends this work by examining the impact of teaching experience on college introductory physics instructor effectiveness. In answering research question 1, our analysis found a general decline in effectiveness over time for instructors who were not using LAs. In contrast, in answering research question 2, instructors who were teaching with LAs maintained their effectiveness. While the decline in student posttest performance associated with each term of instructor teaching experience without LAs (1.2\%) may not sound substantial, the losses are cumulative. Students in courses with instructors who have taught without LAs for 6 terms are predicted to underperform their peers in LA-supported courses by 10.3\% (7.2\% loss due to instructor experience and 3.1\% loss due to current lack of LA-support). Given that in our dataset the average student raw gains from pretest to posttest are approximately 20\%, losing 10.3\% of that gain represents losing approximately half of the student learning.
\par While our models cannot provide a causal mechanism for these observed declines in effectiveness we hypothesize that the shift may come from the lack of resources allocated to improving instructor pedagogical practices. In contrast to K-12 schools, the structures in colleges (e.g. incentives and funding) tend to value faculty's scholarly productivity over teaching effectiveness. Given the general lack of resources that colleges commit to supporting and improving faculty's instructional practices, it is not entirely surprising that college instructors do not improve their effectiveness in the same way as K-12 teachers do. In contrast to typical college instructors, instructors who use LAs have an entire network of resources (e.g. LAs, weekly LA co-planning meetings, LA pedagogy courses, LA program directors, and the LA Alliance) designed to support them in reflecting on and improving their teaching effectiveness. We propose that the additional resources provided by LA programs may help to fill the gap created by the colleges and preventing the decline in instructor effectiveness.
\section {Limitations and future work}
The LASSO platform was originally promoted to faculty in the LA Alliance, which likely skewed the courses to be ones that use research-based pedagogical practices whether they were LA-supported or not. Thus, the shifts in instructor effectiveness without LAs may not represent the shifts in traditional lecture-based courses. We expect that increased adoption of the LASSO platform will improve the generalizability of our findings. In our future work, we will use a meta-analysis of published results to further inform our analysis. This work was funded in part by NSF-IUSE Grant No. DUE-1525338 and is Contribution No. LAA-046 of the Learning Assistant Alliance.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 4,048 |
Robeson Extension is an unincorporated community and census-designated place (CDP) in Blair County, Pennsylvania, United States. It was first listed as a CDP prior to the 2020 census.
The CDP is in eastern Blair County, on the southern border of Catharine Township. It sits within a bend of the Frankstown Branch Juniata River, which borders to the community to the east, south, and west. Across the river are Woodbury Township and the borough of Williamsburg. High Street leads from Robeson Extension south across the Frankstown Branch into Williamsburg. To the north, High Street becomes Yellow Springs Drive, which leads north to U.S. Route 22 at Yellow Springs.
References
Census-designated places in Blair County, Pennsylvania
Census-designated places in Pennsylvania | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 4,304 |
Birmingham Royal Ballet, [Un]leashed, Hobson's Choice, Sadler's Wells
25 Jun 19 – 29 Jun 19
Birmingham Royal Ballet return to Sadler's Wells with [Un]leashed and Hobson's Choice, celebrating female voices in choreography and the company's outgoing veteran director
Birmingham Royal Ballet, The Nutcracker 2019, RAH
28 Dec 19 – 31 Dec 19
Birmingham Royal Ballet brings its much loved production of The Nutcracker to the Royal Albert Hall for a short run in this year's festive season
Taming the Wolf: Choreographer Ruth Brill Interview
As her choreographic career takes off, Ruth Brill talks to Culture Whisper about turning Prokofiev's Peter into a girl and working with the budding dancers of London Children's Ballet
International Draft Works, Linbury Theatre Review ★★★★★
11 Apr 19 – 12 Apr 19
The inaugural programme of the Royal Ballet's International Draft Works, at the Linbury Theatre, threw up a heady mix of new work from across Europa and America
BRB, La Fille Mal Gardée Review ★★★★★
01 Nov 18 – 03 Nov 18
Birmingham Royal Ballet bring their short visit to Sadler's Wells to a joyous end with their vibrant performance of Ashton's La Fille Mal Gardée
Sadler's Wells Spring 2019 – May/August Highlights
01 May 19 – 31 Aug 19
As Sadler's Wells moves into summer, so its programming becomes hot, hot, hot.... Here are some of the highlights
BRB Fire and Fury Review ★★★★★
30 Oct 18 – 31 Oct 18
Birmingham Royal Ballet's Fire and Fury, the first of two programmes in its autumn visit to Sadler's Wells, is inspired by France's Louis XIV and a painting by Turner
Christmas Dance Shows
There will be Nutcrackers aplenty, but more than that, Christmas Dance 2018 celebrates winter in all its forms. Here are the key shows for London families
Birmingham Royal Ballet, The Nutcracker, Royal Albert Hall
Following a hugely successful run last Christmas, Birmingham Royal Ballet returns to the Royal Albert Hall with its magical production of The Nutcracker
BRB, Polarity and Proximity Review
The second programme of Birmingham Royal Ballet's visit to Sadler's Wells, Polarity and Proximity, is a triple bill of deeply contrasting works
BRB, Romeo and Juliet Review ★★★★★
Birmingham Royal Ballet's brief season at Sadler's Wells kicked off with its own production of Kenneth MacMillan's masterpiece, Romeo and Juliet
Sadler's Sampled 2018 Review ★★★★★
02 Feb 18 – 03 Feb 18
Dance in all its dazzling variety is again on display in north London in this year's edition of the dance taster festival, Sadler's Sampled
Birmingham Royal Ballet, The Nutcracker Review ★★★★★
Birmingham Royal Ballet transform the Royal Albert Hall's rather unforgiving stage into a magical set for its production of the Christmas favourite, The Nutcracker
BRB, Aladdin, Sadler's Wells
31 Oct 17 – 02 Nov 17
Discover a family-friendly tale of magic, adventure and love triumphant when Birmingham Royal Ballet performs Aladdin at Sadler's Wells
Birmingham Royal Ballet at Sadler's- Shakespeare Triple Bill/The Tempest
Birmingham Royal Ballet invites dance fans across the capital to share in its celebration of William Shakespeare at Sadler's Wells this October
Birmingham Royal Ballet: Swan Lake/Triple Bill, Sadler's Wells
Birmingham Royal Ballet returns to Sadler's Wells with two programmes of classic and contemporary works.
Shadows of War, Birmingham Royal Ballet at Sadler's Wells
The Birmingham Royal Ballet present classic works from great choreographers on the theme of war and the shadows it casts over people's lives.
Beauty and The Beast, Sadler's Wells
A gorgeous Gothic fairytale choreographed by a master of narrative, the Birmingham Royal Ballet Beauty and the Beast is a much-loved classic. | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 4,863 |
Q: I'm getting a TypeError: The view function did not return a valid response from flask import Flask, request, render_template, redirect, flash, session
from flask_debugtoolbar import DebugToolbarExtension
from models import connect_db, db, User, Feedback
from forms import RegisterForm, LoginForm, FeedbackForm
from sqlalchemy.exc import IntegrityError
@app.route("/users/<username>/feedback/add", methods=["GET"])
definitely add_feedback(username):
"""Add feedback for specific user"""
if "username" not in session or username != session["username"]:
flash("Please login to leave feedback!")
return redirect(f"/users/{username}/feedback/add")
form = FeedbackForm()
if form.validate_on_submit():
title = form.title.data
content = form.content.data
new_feedback = Feedback(title=title, content=content, username=username)
db.session.add(new_feedback)
db.session.commit()
return render_template("/feedback/add.html", form=form)
Please help! I keep getting
TypeError: The view function did not return a valid response. The function either returned None or ended without a return statement. This is a get route, and should show the user a feedback form.
A: I just realized why I was getting this error. The indentation is wrong on the return render_template statement. I also changed the redirect url to "/login".
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 2,698 |
You can enable restrictions to stop your children from using specific features and applications on the Amazon Fire HD, including the ability to prevent purchases from content stores, access to age-restricted videos and movies and access to the camera.
An Amazon Account (email address and password).
Swipe down from the top of the screen and then tap Settings. Tap Parental Controls.
Tap On next to Parental Controls.
With Parental Controls turned on, enter a password, confirm your password and then tap Submit.
Enter the details of your child.
Click on 'Manage Your Content and Devices' to control what purchased content your child can access and on what device.
Open the Alexa App or echo.amazon.com on your smartphone and tap the menu icon.
Add a 4-digit pin and tap save to set up the pin. Alternatively, you can disable voice purchasing altogether by changing the setting on this page. | {
"redpajama_set_name": "RedPajamaC4"
} | 9,546 |
Astros, George Springer likely heading to arbitration
Sports // Astros
Chandler Rome , Houston Chronicle Jan. 10, 2020
George Springer, who hit a career-high 39 home runs in 2019, is asking for $22.5 million. The Astros are offering $17.5 million.
For a second straight offseason, the Astros will go to trial against one of their most sought after, soon-to-be free agents.
Houston could not come to an agreement with outfielder George Springer on his salary for the 2020 season on Friday, all but ensuring he will head to an arbitration hearing against the Astros in mid-February.
The gap between the two parties is seismic. Houston offered Springer a $17.5 million salary. Springer and his representatives requested $22.5 million. The team could not agree to terms with Aledmys Diaz, either, but reports state there is only a $600,000 gap between the two parties.
Two respected arbitration projection models — MLBTradeRumors and Cot's Contracts — predicted Springer to earn more than $20.7 million during this process.
If Springer's case goes to trial, arbiters will hear arguments from both parties before picking one of the two numbers presented. Typically, the Astros are a "file and trial" team, meaning it ceases negotiations after Friday's deadline and takes any unresolved cases to a hearing. Such a title does not necessarily prevent the two sides from speaking, though.
"The deals that we've done past the exchange date are usually deals that include option years or multi-year deals," general manager Jeff Luhnow said Friday. "There's always an opportunity to negotiate something like that but, otherwise, it's likely to end up in a hearing."
In Luhnow's first offseason without fired assistant general manager Brandon Taubman, the longtime spearhead for the club's arbitration process, the Astros took a team approach to the day. Luhnow was more heavily involved, as was assistant general manager Pete Putila, senior director of baseball strategy Bill Firkus and Senior Manager of Player Valuation and Economics Brendan Fournie.
Houston settled with four of its six eligible players. Closer Roberto Osuna headlined that group, receiving a $10 million salary, according to a person with knowledge of the deal. Brad Peacock got $3.9 million, and Chris Devenski netted a $2 million salary. Shortstop Carlos Correa, who took the Astros to a hearing last season, settled for $8 million.
Springer's case could headline the league's lineup of hearings. In Luhnow's tenure, the team has had little success against its players in arbitration. Astros players have won five consecutive hearings against their club. Houston has not won a hearing since 2016, when it went against former catcher Jason Castro.
"I'm not concerned about it," Luhnow said. "George is going to be playing for us this year; it's just a matter of how much we're going to be paying him."
The team lost both of its hearings last season against Correa and pitcher Gerrit Cole.
Cole and the Astros were $2,075,000 apart in their salary requests entering last season's hearing. The $13.5 million Cole won was the largest salary ever given from an arbitration hearing. Cole then authored one of the greatest seasons by a starting pitcher in franchise history, one he parlayed into a record nine-year, $324 million contract with the New York Yankees.
Springer could shatter Cole's arbitration record. Whether he replicates the on-field production and departs to free agency still remains to be seen. Springer is a logical candidate for a contract extension and intimated last spring he'd be open to discussing one. Houston's entire starting outfield — Springer, Michael Brantley and Josh Reddick — is scheduled to depart to free agency after the 2020 season.
During the best offensive campaign of his six-year major league career, Springer swatted a career-high 39 home runs last season and finished with a .974 OPS. He was seventh in American League MVP voting, hampered by a hamstring injury in May that sidelined him for a month.
Houston signed Springer to a two-year, $24 million deal in February 2018 that bought out each of his previous two years of arbitration.
Before Friday's deadline arrived, the Astros already had agreed to terms with two arbitration-eligible pitchers — Lance McCullers Jr. and Joe Biagini. McCullers will make $4.1 million in 2020, while Biagini will take $1 million.
chandler.rome@chron.com
twitter.com/chandler_rome
Chandler Rome
Follow Chandler on:
Chandler_Rome
Chandler Rome joined the Houston Chronicle in 2018 to cover the Astros after spending one year in Tuscaloosa covering Alabama football — during which Nick Saban asked if he attended college. He did, at LSU, where he covered the Tigers baseball team for nearly four years. He covered most of the Astros' 2015 playoff run, too, as an intern for MLB.com
Whistleblower Mike Fiers mum about Astros scandal; A's teammates support him
First Astros player apology comes from former pitcher Dallas Keuchel
Former Astros pitcher Dallas Keuchel apologizes for 2017 cheating scandal
Brad Ausmus, an Astros favorite, interviews for manager's job | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 8,001 |
\section{Introduction}
In a previous work \cite{cqg2} we proved that the static and axisymmetric solutions of the Einstein vacuum equations with a finite number or Relativistic Multipole Moments (RMM) \cite{geroch} can be described by means of a function $u$ which resembles exactly the Newtonian multipole potential if we write the metric in a so-called MSA (Multipole Symmetry Adapted) system of coordinates. In fact, this is properly the definition of these coordinates, which are constructed iteratively in terms of the Weyl coordinates.
The goodness of these coordinates arises from the fact that they allow us to generalize some theorems hold in Newtonian Gravity (NG) that establish the existence of certain symmetry groups of the equations satisfied by the classical potential whose group-invariant solutions represent the solutions with a finite number of RMM in NG \cite{cqg1}. The existence of these systems of coordinates is proved to be related with the fact that the relativistic equations analogously admit those symmetry groups that lead to the Pure Multipole Solutions in General Relativity (GR) (those with a finite number of RMM). In addition, the symmetry group for the case of spherical symmetry allows us to determine univocally the specific MSA system of coordinates by means of a Cauchy problem, whose solution provides the standard Schwarzschild radial coordinate.
These characteristics make the MSA system of coordinates become a very relevant reference to describe the gravity of stellar compact bodies whose multipole structure is known, or suitably estimated {\it a priori}, and differs slightly from the spherical symmetry. Moreover, a new feature of these coordinates reveals more relevance for the description of the Pure Multipole Solutions because they provide us with a procedure to establish measurements of high physical and astronomical interest about the behaviour of test particles orbiting into this kind of space-time.
Until now, only the spherical symmetry solution of Einstein vacuum equations has been written in MSA coordinates: this is the Schwarzschild metric in standard coordinates. But, do not we have a nonspherical axisymmetric solution written in these systems of coordinates, and it would be a very relevant success for the description of gravitational effects derived from deviations of the spherical symmetry. We are able to write explicitly all the metric components of a static solution characterized by any finite number of RMM, in particular the monopole, quadrupole and $2^4$-pole moments, in a system of coordinates such that the metric recovers the Schwarzschild limit when all RMM higher than monopole vanish. Hence, we are introducing a system of coordinates that generalizes the Schwarzschild standard coordinates and it can be used to study, in analogy with the spherical case, the physics of test particles in space-time slightly different from the Monopole Solution.
A very useful tool for the study of orbital motions in a classical gravitational problem is a second order differential equation called the Binet equation, from which the Kepler laws, for instance, can be deduced. From the geodesics of a space-time we can obtain a relativistic Binet equation whose resolution allows to determine relativistic corrections to Keplerian motion like the correction to perihelion and node line precession. The calculation of the Binet equation in an MSA system of coordinates is specially suitable to describe the influence and relevance of the different RMM in such corrections. It provides the gravitational effects due to deviation from sphericity when comparison with the Schwarzschild corrections is made.
As is known,(see \cite{goldstein} and references therein) the GR theory predicts a correction of the Newtonian movement which can be interpreted by means of a classical potential type $r^{-3}$. The Schwarzschild spherically symmetric solution of Einstein vacuum equations corresponds with a perturbed Hamiltonian in the Kepler problem. In fact, the Binet equation shows directly this relation between the orbital equation for geodesics in a relativistic space-time and the orbits obtained for a classical Hamiltonian dynamical system.
The question that promptly arises is whether any other solution of the static and axisymmetric Einstein vacuum equations can be identified with certain classical system by means of a suitable perturbative potential to obtain equivalent equations for the orbits. This is one of the purposes of this work which has been accomplished through the determination of the equivalent potential associated to a perturbed Kepler problem that leads to the same orbital equation as the one for certain geodesic of any static and axisymmetric space-time. In this scenario the study of geodesics of a test particle for a Pure Multipole Solution is particularly relevant, because the multipole characteristics of that solution allow identification the contributions of its RMM within a classical description of the problem. And here is where MSA coordinates become absolutely prescriptive.
Standard techniques for the study of the equivalent classical problem can be performed. In particular, the first order perturbation theory throw interesting results about relativistic corrections to the perihelion in Keplerian motion. As we will see, expectations arise from this study when the role of the quadrupole, and the magnitude of its contribution, are considered, because certain discrepancies are obtained with respect to other similar calculations \cite{leo1}, \cite{leo2}. In fact, experiments for the measurement of the quadrupole moment can be outlined from the contribution of the monopole and quadrupole moments to the perihelion shift at first order.
This work is organized as follows. In section 2 a procedure to write any Pure Multipole Solution in MSA coordinates is shown and, in particular, all the metric components of a static and axisymmetric solution with a finite number ($M_0$, $M_2$, $M_4$) of RMM are explicitly obtained. In order to do that, the MSA system of coordinates adapted to this kind of solution is previously calculated. The good behaviour of the metric and the structure of it, for a general case, is discussed.
In section 3 we calculate the geodesics of such a metric. We show that the restriction to the constant equatorial hyper-surface leads to a geodesic equation which can be written as a one-dimensional equivalent problem for an effective potential.
Section 4 is devoted to introduce the Binet equation from its classical derivation, and we show the relativistic Binet equation for the Pure Multipole Solution. We derive the perturbative potential that identifies the calculation of geodesics for any Pure Multipole Solution with the resolution of a classical Hamiltonian perturbation of the Kepler-problem.
In section 5 we show the relevance of the quadrupole moment on the relativistic correction to the perihelion for a test particle in a perturbed Keplerian orbit. We put our attention on the effect of the quadrupole moment at the same order as the monopole correction introduced by the Schwarzschild solution. This result suggests the possibility of measurement of the quadrupole moment through this contribution.
Finally, we discuss on the results obtained in a conclusion section.
\section{The Pure Multipole Solutions in the MSA system of coordinates}
The static and axisymmetric solutions of the Einstein vacuum equations with a finite number of Relativistic Multipole Moments (RMM) will be referred to as the Pure Multipole Solutions from now on. Some authors have devoted works on researching about those solutions \cite{varios}, \cite{mq1}.
The MSA (Multipole Symmetry Adapted) systems of coordinates were defined \cite{cqg2} as those that allow writing the metric component in terms of a function $u$ resembling the Newtonian gravitational potential, or equivalently, we can say that the expansion of that metric component ($g_{00}=-1+2 u$) in power series of the inverse radial MSA-coordinate provides a multipole Thorne structure with vanishing Thorne's rests \cite{thorne}.
The MSA system of coordinates belongs to a class of ACMC introduced by Thorne \cite{thorne}, with a suitable choice of asymptotical behaviour for the case of equatorial symmetry (the odd order RMM are null). The system of MSA coordinates $\{\hat x^{\alpha}\}=\{t,r,y\equiv \cos\hat \theta,\varphi\}$ ($\alpha=0..3$) can be constructed iteratively in terms of the Weyl coordinates $\{x^{\alpha}\}=\{t,R,\omega\equiv \cos\theta,\varphi\}$ as follows \cite{cqg2}:
\begin{eqnarray}
r=R\left[1+\sum_{n=1}^{\infty}f_n(\omega)\frac{1}{R^n}\right] \nonumber \\
y=w+\sum_{n=1}^{\infty}g_n(\omega)\frac{1}{R^n} \ .
\label{trans}
\end{eqnarray}
For the purposes of this work we consider the gauge (\ref{trans}) up to certain order of approximation $O(1/R)$, and we proceed to calculate the system of coordinates associated to a Pure Multipole Solution with the set of RMM desired. In particular, the constructive method showed in \cite{cqg2} is followed here to calculate the MSA coordinates associated to a solution only possessing the three first Multipole Moments of mass: $M_0\equiv M$, $M_2\equiv Q$ and $M_4\equiv D$. In the Appendix we show explicitly the expressions of the functions $f_n(\omega)$ and $g_n(\omega)$ up to order $O\left( 1/R^9\right)$ in the power of the inverse radial Weyl-coordinate $R$ (\ref{A1})-(\ref{A2}).
The solution managed can be considered an exact Pure Multipole solution in the sense that it only poses those RMM, but nevertheless the components of the metric are written in terms of a power series of the inverse radial coordinate $r$ up to the order of approximation of the gauge (\ref{trans}), except for the $g_{00}$ whose analytic expression is as follows:
\begin{equation}
g_{00} =-1+\frac2{c^2} \left[ \sum_{n=0}^N \frac{M_{2n}}{r^{2n+1}}
P_{2n}(y)\right] , \label{g00}
\end{equation}
where $N+1$ is the number of RMM of the Pure Multipole Solution selected ($N=2$ for our case) and $P_{2n}(y)$ stand for the Legendre polynomials depending on the MSA angular variable $y=\cos\hat\theta$.
We first need to perform the inverse change of coordinates (\ref{trans}) to write the metric in the MSA coordinates from the general Weyl line element of a static and axisymmetric vacuum space-time:
\begin{equation}
ds^2= -e^{2\Psi} dt^2+e^{-2\Psi+2\gamma} (dR^2+R^2d\theta^2)+e^{-2\Psi}R^2\sin^2\theta d\varphi^2 \ .
\label{dsweyl}
\end{equation}
The case of spherical symmetry is especially relevant because we know explicitly the sum of the series appearing in the gauge (\ref{trans}) and the standard radial coordinate of Schwarzschild is recovered (see \cite{cqg2} for details). The MSA $(\{r,y\})_{M}$ system of coordinates for the spherical symmetry is the following:
\begin{eqnarray}
r&=&M+\frac R2 (r_++r_-) = M(x+1) \nonumber\\
y&=&\frac{R}{2M} (r_+-r_-) =y_p \ , \label{msaM}
\end{eqnarray}
where $r_{\pm}\equiv\sqrt{1\pm 2 \omega\lambda+\lambda^2}$, $\lambda\equiv M/R$, and $\{x,y_p\}$ are the prolate spheroidal coordinates \cite{prolate}, \cite{algomio}. The inverse relations between these coordinates are given by the following expressions:
\begin{eqnarray}
R&=&r\sqrt{1+y^2\hat \lambda^2-2\hat \lambda}\nonumber\\
\omega&=&\frac{y(1-\hat \lambda)}{\sqrt{1+y^2\hat \lambda^2-2\hat \lambda}} \ , \label{weylM}
\end{eqnarray}
where $\hat \lambda \equiv M/r$.
By performing the change of coordinates in the line element (\ref{dsweyl}) we obviously obtain the known Schwarzschild metric in standard Schwarzschild coordinates:
\begin{equation}
ds^2= -\left(1-\frac{2M}{r}\right) dt^2+\left(1-\frac{2M}{r}\right)^{-1}
dr^2+r^2(d\hat\theta^2+\sin^2\hat\theta
d\varphi^2) \ . \label{dsweylmsa}
\end{equation}
The explicit expressions (\ref{msaM}-\ref{weylM}) are shown because we are able to recover these results from the general case of a Pure Multipole Solution by taking all RMM equal to zero except for the Monopole, as we will see in what follows.
The inversion of the series in the gauge (\ref{trans}) to obtain relations of the type $R=R(r,y)$, $\omega=\omega(r,y)$, for a general case, is a straightforward but cumbersome calculation. In the Appendix we show the inverse relations\footnote{It can be seen that the expansion of the expressions (\ref{weylM}) in power series of $\hat\lambda$ reproduces this results for the Monopole case.} (\ref{A3})-(\ref{A4}) corresponding to the previously calculated MSA coordinates associated to a Pure
Multipole solution only possessing the RMM $M_0$, $M_2$ and $M_4$.
The transformation of coordinates leads to the following components of the metric:
\begin{eqnarray}
g_{rr}(\hat x)&=&F(\hat x) \left[R_r^2+\frac{R^2}{1-\omega^2}\omega_r^2\right]_{x=x(\hat x)}\nonumber\\
g_{ry}(\hat x)&=& F(\hat x) \left[R_rR_y+\frac{R^2}{1-\omega^2}\omega_r \omega_y\right]_{x=x(\hat x)} \nonumber\\
g_{yy}(\hat x)&=& F(\hat x) \left[R_y^2+\frac{R^2}{1-\omega^2}\omega_y^2\right]_{x=x(\hat x)}\nonumber\\
g_{tt}(\hat x)&=&-e^{-2\Psi(\hat x)} \ , \ g_{\varphi\varphi}(\hat x)=e^{-2\Psi(\hat x)} \left[R^2(1-\omega^2)\right]_{x=x(\hat x)} \ , \label{ghat}
\end{eqnarray}
where $\displaystyle{F(\hat x)\equiv e^{-2\Psi(\hat x)+2 \gamma(\hat
x)}}$, and the subindices denote the derivative with respect to that coordinate.
By using the expression (\ref{A2}) into (\ref{ghat}) we obtain the following metric components, up to order $O\left(\hat\lambda^7\right)$ (although we only show here the first terms because the expressions are too large) in powers of the inverse MSA radial coordinate $r$ ($\hat \lambda\equiv M/r$):
\begin{eqnarray}
g_{rr}&=& 1+2 \hat \lambda+4 \hat \lambda^2+\left[8 +q(1-3 y^2) \right] \hat \lambda^3-\frac87 \left[-14 -3 M q(1-3 y^2)\right] \hat \lambda^4+\nonumber\\
&-&\frac{1}{28} \left[-896+d(2695 y^4 -2310 y^2 +231)+q(-240
+720 y^2)+\right.\nonumber\\
&+&\left.q^2(-2688 y^4 +2016 y^2 -224)\right] \hat \lambda^5+\nonumber\\
&+&\left[64+q \frac{56}{3}(1 -3 y^2)+q^2\left(\frac{76425}{154} y^4 -\frac{28935}{77} y^2+\frac{6161}{154}\right)+\right. \nonumber\\
&+&\left.d\left(-\frac{5075}{11} y^4 +\frac{4350}{11} y^2
-\frac{435}{11}\right)\right] \hat \lambda^6+O(\hat\lambda^7)
\label{metrica1}
\end{eqnarray}
\begin{eqnarray}
g_{yy}&=&\frac{M^2}{1-y^2}\left[\frac{1}{\hat\lambda^2}-2 y^2 q \hat\lambda-\frac{3}{14} q (5+7 y^2)\hat\lambda^2+\right.\nonumber\\
&+&\left.\frac{1}{35} \left[d(1715 y^4 -1785 y^2+210)+q(-42 y^2-94)+\right. \right.\nonumber\\
&+&\left.\left.q^2(-1848 y^4 +1890 y^2-182)\right] \hat\lambda^3+\right.\nonumber\\
&+&\left.\frac{1}{462} \left[d(89915 y^4-91560 y^2+10605)+q(-484 y^2-2508)+\right. \right.\nonumber\\
&+&\left.\left. q^2(
-99294 y^4+98616 y^2-9864)\right]\hat\lambda^4\right]+O(\hat\lambda^5)
\label{metrica2}
\end{eqnarray}
\begin{eqnarray}
g_{\varphi\varphi}&=&(1-y^2){M^2}\left[\frac{1}{\hat\lambda^2}+2 q(2y^2-1) \hat\lambda+\right.\nonumber\\
&+&\left. q \frac{1}{14}(87 y^2-51) \hat\lambda^2+ \left[(\frac{366}{35} y^2-\frac{46}{7}) q+\right.\right.\nonumber\\
&+&\left.\left.(-\frac{24}{5}y^4-2+\frac{54}{5} y^2) q^2+d(14y^4-21y^2+3)\right]\hat\lambda^3+\right.\nonumber\\
&+&\left.\left[ \frac{1}{21}(386y^2-250)q +\frac{1}{77}(-45y^4-362+2164y^2)q^2 +\right.\right.\nonumber\\
&+&\left. \left. d(\frac{1645}{66} y^4-\frac{580}{11} y^2+\frac{185}{22})\right] \hat\lambda^4\right]+O(\hat\lambda^5) \qquad ,
\label{metrica3}
\end{eqnarray}
where $q\equiv Q/M^3$, $d\equiv D/M^5$ are dimensionless parameters representing the quadrupole and $2^4$-pole moments respectively.
Let us briefly analyze these results:
\vspace{3mm}
{\it i)} First, we can see that the cross term of the metric $g_{12}$ vanishes up to this order of approximation, and in fact, the preservation of the diagonal aspect of the metric is a characteristic of the system of MSA coordinates. Supposing that the Jacobian of the coordinate transformation
is regular and the inversion of coordinates is able, i.e., $det\equiv |r_Ry_{\omega}-r_{\omega}y_R|\neq 0$,
it can be seen that the metric component $g_{ry}$ vanishes since we can write the following expression
\begin{equation}
g_{ry}(\hat x)=-\frac{F(\hat x)}{\left[(1-\omega^2)det^2\right]_{x=x(\hat x)}} \hat{LB}_1(r,y)_{x=x(\hat
x)} ,
\end{equation}
where $\hat{LB}_1(r,y)\equiv \eta^{ij}\nabla_i() \nabla_j()=R^2\partial_R()
\partial_R()+(1-\omega^2)\partial_{\omega}() \partial_{\omega}()$ represents the Laplace-Beltrami operator with respect to a 3-dimensional Euclidean metric (with axial symmetry) written in Weyl spherical coordinates (see \cite{cqg2} for details), and it was seen in \cite{cqg2} that the MSA system of coordinates fulfills the condition $\hat{LB}_1(r,y)=0$.
\vspace{3mm}
{\it ii)} Second, we can see from the expressions (\ref{metrica1})-(\ref{metrica3}) that the metric written in the MSA system of coordinates leads to the Schwarzschild limit by considering equal to zero all RMM higher than the Monopole, as well as that the MSA system, given by expressions (\ref{A1})-(\ref{A2}), recovers the standard Schwarzschild coordinates.
\vspace{5mm}
{\it iii)} And finally, the $g_{00}[x=x(\hat x)]$ metric component results to be equal to (\ref{g00}) as claimed by that system of coordinates.
\vspace{5mm}
A general expression for the metric components of the Pure Multipole solution with a finite number of RMM ($M$, $Q$, $D$) in MSA coordinates is the following:
\begin{eqnarray}
g_{tt}(\hat x)&=&-1+2 \left[ \hat\lambda+\frac{Q}{M^3}\hat\lambda^3 P_{2}(y)+\frac{D}{M^5} P_4(y)\right] \nonumber\\
g_{rr}(\hat x)&=&\frac{1}{1-2\hat \lambda}\left[1+(1-2\hat\lambda)\sum_{i=3}^{\infty}\hat\lambda^i
U_i(y,Q,D)\right] \nonumber\\
g_{yy}(\hat x)&=&\frac{1}{1-y^2}\frac{M^2}{\hat \lambda^2}\left[1+\sum_{i=3}^{\infty}\hat\lambda^i
D_i(y,Q,D)\right] \nonumber\\
g_{\varphi \varphi}(\hat x)&=&(1-y^2)\frac{M^2}{\hat \lambda^2}\left[1+\sum_{i=3}^{\infty}\hat\lambda^i
T_i(y,Q,D)\right] \ ,
\label{chachis}
\end{eqnarray}
where $P_n(y)$ stands for the Legendre polynomials, and the $U_i$, $D_i$ and $T_i$ denote polynomials in the angular variable $y$ of even order depending on the higher RMM ($Q$ and $D$ for this case).
\section{The geodesics of the Pure Multipole solutions}
We proceed now to calculate the geodesics of the metric associated to a Pure Multipole solution with mass, quadrupole and $2^4$-pole moments ($M$, $Q$, $D$ respectively) in the corresponding MSA system of coordinates.
The set of equations for the geodesics is the following
\begin{eqnarray}
&&\frac{d^2 t}{ds^2}g_{00}+\frac{dt}{ds}\frac{dr}{ds} \partial_rg_{00}+\frac{dt}{ds}\frac{d\hat\theta}{ds}
\partial_{\hat\theta}g_{00}=0 \label{te}\\
&&2\frac{d^2 r}{ds^2}g_{11}+\left(\frac{dr}{ds}\right)^2 \partial_rg_{11}+2\frac{dr}{ds}\frac{d\hat\theta}{ds} \partial_{\hat\theta}g_{11}-\left(\frac{dt}{ds}\right)^2\partial_rg_{00}+\nonumber\\
&&-\left(\frac{d\hat\theta}{ds}\right)^2\partial_rg_{22}-\left(\frac{d\varphi}{ds}\right)^2\partial_rg_{33}=0\label{erre}\\
&&2\frac{d^2 \hat\theta}{ds^2}g_{22}+\left(\frac{d\hat\theta}{ds}\right)^2 \partial_{\hat\theta}g_{22}+2\frac{dr}{ds}\frac{d\hat\theta}{ds} \partial_{r}g_{22}-\left(\frac{dt}{ds}\right)^2\partial_{\hat\theta}g_{00}+\nonumber\\
&&-\left(\frac{d\hat\theta}{ds}\right)^2\partial_{\hat\theta}g_{22}-\left(\frac{d\varphi}{ds}\right)^2\partial_{\hat\theta}g_{33}=0\label{teta}\\
&&\frac{d^2 \varphi}{ds^2}g_{33}+\frac{d\varphi}{ds}\frac{dr}{ds} \partial_rg_{33}+\frac{d\varphi}{ds}\frac{d\hat\theta}{ds}
\partial_{\hat\theta}g_{33}=0\label{fi} \ ,
\end{eqnarray}
where $s$ denotes the affine parameter along the geodesic. Since the metric is static and axisymmetric, both Killing vectors, $\xi$ and $\eta$, representing the corresponding isometries, remain constant along the geodesics, i.e., $\xi^{\alpha}z_{\alpha}=h$, $\eta^{\alpha}z_{\alpha}=l$, $z^{\alpha}$ being the tangent vector to the geodesic, $h$, $l$ are constants, and therefore the Eqs. (\ref{te}) and (\ref{fi}) become $\displaystyle{g_{00}\frac{dt}{ds}=h}$ and $\displaystyle{g_{33}\frac{d\varphi}{ds}=l}$ respectively. The norm of the tangent vector $z^{\beta}z_{\beta}\equiv\epsilon$ can be written as follows:
\begin{equation}
g_{11}\left(\frac{dr}{ds}\right)^2+g_{22}\left(\frac{d\hat\theta}{ds}\right)^2=k \label{ka} \ ,
\end{equation}
with $k\equiv\displaystyle{\epsilon-\frac{h^2}{g_{00}}-\frac{l^2}{g_{33}}}$, and hence, the geodesic equations (\ref{erre}) and (\ref{teta}) can be written as follows:
\noindent \begin{eqnarray}
&\displaystyle{\frac{d^2r}{ds^2}+\left(\frac{dr}{ds}\right)^2\partial_r
\ln\sqrt{g_{22}g_{11}}+\left(\frac{dr}{ds}\right)\left(\frac{d\hat\theta}{ds}\right)\partial_{\hat\theta}\ln g_{11}=\frac{1}{2 g_{11}}\left[\partial_rk+k\partial_r \ln g_{22}\right]}\nonumber\\
& \label{p1}\\
&\displaystyle{\frac{d^2\hat\theta}{ds^2}+\left(\frac{d\theta}{ds}\right)^2\partial_{\hat\theta}
\ln\sqrt{g_{22}g_{11}}+\left(\frac{dr}{ds}\right)\left(\frac{d\hat\theta}{ds}\right)\partial_{r}\ln g_{22}=\frac{1}{2 g_{22}}\left[\partial_{\hat \theta}k+k\partial_{\hat \theta} \ln g_{11}\right]}\nonumber\\
& \label{p2}
\end{eqnarray}
Let us consider now the case of geodesics with constant $\hat\theta$ and $\displaystyle{\frac{d\varphi}{ds}\neq 0}$, i.e., they are not radial geodesics but those constrained to a constant hypersurface ($\hat\theta=\hat\theta_0$) with coordinates $\{t,r,\varphi\}$. This restriction is compatible with the Eq. (\ref{p2}) since it leads to
\begin{equation}
\left[\partial_{\hat\theta}k+k\partial_{\hat\theta} \ln
g_{11}\right]_{\hat\theta=\hat\theta_0}=0\label{condi} \ ,
\end{equation}
which is fulfilled at the equatorial plane ($\hat\theta_0=\pi/2$ or equivalently $y=0$) because the expressions (\ref{chachis}) allow us to hold\footnote{Let us note that we have considered equatorial symmetry and hence $g_{00}$ only contains even order Legendre polynomials, and the polynomials $U$, and $T$ depend on even powers of $y$.} that $(\partial_yg_{00})|_{y=0}=(\partial_yg_{11})|_{y=0}=(\partial_yg_{33})|_{y=0}=0$.
Therefore, with respect to the relevant geodesic (\ref{p1}), and by using the Eq. (\ref{ka}), we obtain on the equatorial plane the following expression:
\begin{equation}
\frac{d^2r}{ds^2}+\frac 12 \frac{k}{g_{11}} \partial_r \ln \left(\frac{g_{11}}{k}\right)=0 \ . \label{p1f}
\end{equation}
This equation can be written as follows:
\begin{equation}
\left(\frac{dr}{ds}\right)^2+V_{eff}=C \label{ocho} \ ,
\end{equation}
$V_{eff}$ being a so-called effective potential which can be obtained by integration as follows
\begin{equation}
V_{eff}=\int \frac{k}{g_{11}} \partial_r \ln\left(\frac{g_{11}}{k}\right) dr = -\frac{k}{g_{11}} \
.\label{eff}
\end{equation}
As can be seen, the Eqs. (\ref{ocho}), (\ref{eff}) reproduce the Eq. (\ref{ka}) for constant $\hat\theta$.
\section{The Binet equation}
As is known, the classical problem of Kepler consists on determining the movement of a test particle within a gravitational field generated by a potential of the type $V(r)\sim \mu/r$. Since this potential is conservative and leads to a gravitational force orientated towards the center of the source, the conservation of the energy $E$ for a particle with mass $m$ and orbital angular moment $\vec J$ is followed ($\mu\equiv GMm$):
\begin{eqnarray}
&&E=\frac 12\left(m\dot r^2+r^2m\dot \theta^2+mr^2\sin^2 \theta\dot\varphi^2\right)-GM\frac mr\nonumber\\
&&\vec J=m\vec x\wedge\vec v \Rightarrow \vec x \cdot \vec J = 0 \ , \label{conser}
\end{eqnarray}
and the particle moves on a constant plane $\theta=\pi/2$. Hence, one may define an effective potential in the following way
\begin{equation}
E=\frac 12m\dot r^2+\Phi_{eff}(r) \qquad , \qquad \Phi_{eff}\equiv \frac{J^2}{2mr^2}-GM\frac mr \ ,
\label{esta}
\end{equation}
and the equations of motion are the following:
\begin{equation}
\dot r^2\equiv\left(\frac{dr}{dt}\right)^2=\frac{2E}{m}-\frac{J^2}{m^2r^2}+\frac{2GM}{r} \qquad , \qquad
\dot \varphi \equiv \left(\frac{d\varphi}{dt}\right)=\frac{J}{mr^2}. \label{conser2}
\end{equation}
Consequently, the equation of the orbits is given by the following expression in terms of a variable $u\equiv 1/r$:
\begin{equation}
\left(\frac{du}{d\varphi}\right)^2+u^2=\frac{2m}{J^2}\left(E+GMm u\right) \ , \label{bipre}
\end{equation}
and from it we can easily obtain (by deriving with respect to $\varphi$ the Eq. (\ref{bipre})) a second order differential equation for the orbit of the test particle:
\begin{equation}
\frac{d^2u}{d\varphi^2}+u=\frac{GMm^2}{J^2} .
\label{binetcla}
\end{equation}
This is the Binet equation which can be solved to derive the three laws of Kepler concerning the orbit of a test particle describing a closed ellipse around the source, for the attractive case $E<0$.
Let us consider now a perturbation of the Newtonian potential of the type $-\alpha/r^3$. It is straightforward to see that a generalization of the Binet equation is obtained for this case as follows:
\begin{equation}
\frac{d^2u}{d\varphi^2}+u=\frac{GMm^2}{J^2}+3 \frac{\alpha m}{J^2} u^2 .
\label{binetper}
\end{equation}
Since the corrected potential, i.e., $V(r)=\displaystyle{-\frac{GMm}{r}-\frac{\alpha}{r^3}}$ does not depend on the angular variables hence, the gravitational force is still central and conservative and we can go on considering the conservation of the orbital angular moment of the particle moving along the orbit on a constant surface.
If we calculate the geodesics of the Schwarzschild metric in standard coordinates (\ref{dsweylmsa}) we obtain, for a constant angular variable $\hat\theta=\pi/2$, the following equation:
\begin{equation}
\left(\frac{dr}{ds}\right)^2+\left(1-\frac{2M}{r}\right)\left(\epsilon+\frac{l^2}{r^2}\right)=h^2 \quad
,\label{schwar}
\end{equation}
where $h$ and $l$ are constants, derived from the isometries as mentioned in previous section, that represent the energy and the angular moment per unit mass respectively. In fact, this Eq. (\ref{schwar}) is exactly the Eq. (\ref{ocho}) with the effective potential for the spherical symmetry case given by the following expression:
\begin{equation}
V_{eff}(r)=\left(1-\frac{2M}{r}\right)\left(\epsilon+\frac{l^2}{r^2}\right) \quad .\label{potM}
\end{equation}
From the Eq. (\ref{schwar}) the orbit of the particle is described by the following equation
\begin{equation}
\frac{d^2u}{d\varphi^2}+u=-\epsilon\frac{M}{l^2}+ 3 M u^2 \ ,\label{binetrela}
\end{equation}
$u\equiv1/r$ being the inverse of the standard-Schwarzschild radial coordinate. Since $l$ is considered to be the angular moment of the particle per unit mass ($l=J/m$) we can hold by comparing this equation with (\ref{binetper}) the following statement \cite{goldstein}:
{\it The orbit on a constant surface $\hat\theta=\pi/2$ corresponding to a timelike geodesic ($\epsilon=-1$) of the Schwarzschild space-time is given by the same equation as the Binet equation corresponding to the Newtonian Kepler problem with a perturbed potential of the type $-\alpha/r^3$ with $\alpha=J^2 M/m$}.
\vspace{2mm}
As is known \cite{leo1}, \cite{leo2}, the {\it relativistic} Binet equation (\ref{binetrela}) allow us to calculate corrections to the Newtonian orbit even for the motion around a spherical distribution of mass, which is no longer closed. In particular this relativistic effect has been tested in our solar system and it amounts to a slow precession of the perihelion of the orbit of Mercury. Predictions of the General Relativity correcting the classical gravity, as the precession of the perihelion or deflection of light, arises from the resolution of Binet equation and constitute the well known ests of GR.
\subsection{The generalized Binet equation}
We want to extend the above-mentioned statement to any static and axisymmetric space-time corresponding to a nonspherical mass distribution, by means of a generalized relativistic Binet equation. Of course that RMM higher than the mass will also contribute to the precession effect and, in principle, these moments could be calculated by measuring the precession of a certain number of test particles orbiting at conveniently different distances from the gravitational source. We will devote last section of this work to discuss this point.
Therefore, we need to compare the relativistic Binet equation with a classical Binet equation corresponding to certain gravitational potential. According to Eq. (\ref{ocho}) we can define an effective potential in such a way that the orbital equations (on the equatorial plane) corresponding to geodesics of any static an axisymmetric space-times are exactly given by the classical Binet equation related to some perturbed Kepler problem.
Hence, we have established a relationship between the equation for geodesics in a relativistic space-time and the orbital equations for an associated Newtonian potential. But moreover, since we have constructed Pure Multipole solutions with a meaningful physical interpretation in terms of their finite number of RMM as successive corrections to the spherical symmetry, the Binet equation for these solutions will provide us with the contributions of the different RMM to the relativistic effects correcting the Newtonian orbits. In order to support this assertion, we must remind that the MSA system of coordinates used to write the metric and its geodesics are adapted to the set of RMM of the solution, and these coordinates recover the standard Schwarzschild coordinates in the limit $M_{2n}=0$, $\forall n>0$.
In fact, from Eqs. (\ref{ocho}) and (\ref{eff}) we have that
\begin{equation}
\left(\frac{du}{d\varphi}\right)^2=\frac{k}{g_{11}}\frac{g_{33}^2}{l^2} u^4 \ ,
\end{equation}
where the notation $u\equiv 1/r$ is used again. Finally, the derivative of the above equation with respect to the azimuthal angle $\varphi$ leads to the following equation:
\begin{equation}
\frac{d^2 u}{d\varphi^2}=\frac 12
\frac{d}{du}\left[\frac{g_{33}}{g_{11}}u^4\left[\left(\epsilon-\frac{h^2}{g_{00}}\right)\frac{g_{33}}{l^2}-1\right]\right] \ . \label{binetrelacomplet}
\end{equation}
For the case of a Pure Multipole solution with a finite number of RMM ($M$, $Q$ and $D$) this equation provides the generalized relativistic Binet equation, for the orbit on the equatorial plane ($y=0$) of a test particle moving along a timelike geodesic ($\epsilon=-1$), as follows:
\begin{eqnarray}
\frac{d^2
u}{d\varphi^2}+u&=&\frac{M}{l^2}+\left[ 3M +\frac {3Q}{2 l^2} (5+6 h^2) \right]u^2+\frac {6}{7 l^2} M Q (-3+25 h^2) u^3\nonumber\\
&+&\left[-\frac{30}{M l^2}Q^2(1+h^2)-\frac{15}{56 l^2} 4Q(-7 l^2+2M^2(3-22 h^2))+\right.\nonumber\\
&+&\left.D(133
+140 h^2) \right]u^4+O(u^5) \quad ,\label{miembrodcha}
\end{eqnarray}
where terms in powers of $u$ higher than $5$ have been neglected. As can be seen, if we take all RMM higher than monopole equal to zero the relativistic Binet equation (\ref{binetrela}) is recovered.
Finally, we want to obtain explicitly which is the perturbed Kepler problem associated to this relativistic Binet equation. As we already saw, a perturbative potential of the type $-\alpha/r^3$ leads to a classical orbital equation (\ref{binetper}), that reproduces exactly the orbital equation corresponding to a timelike geodesic of the Schwarzschild metric on the equatorial plane. In analogy with this result, if we handle with a Pure Multipole solution with a finite number of RMM, a suitable perturbed potential to the Kepler problem can be selected to obtain a generalized Binet equation that equals the Eq. (\ref{miembrodcha}). Nevertheless, despite the spherical symmetry case, we will see now that this potential is given up to a suitable order of approximation in the power of the variable $u$.
Accordingly to Eq. (\ref{esta}) let us consider now a generalized effective classical potential $\Phi_{eff}(r)$ given by this expression:
\begin{equation}
\Phi_{eff}\equiv \frac{J^2}{2mr^2}-GM\frac mr +V_p(r) \qquad , \qquad V_p(r)=-\frac{\alpha}{r^3}+V_p^{RMM}(r)\ ,
\end{equation}
where $V_p^{RMM}(r)$ denotes the new perturbation considered in addition to the previously studied. The comparison of the resulting Binet equation with the expression (\ref{miembrodcha}) will supply us with the perturbed potential that provides different contributions due to the RMM higher than monopole. The conservation of energy $E$ and the orbital angular momentum of the particle $J$ lead to the following equation for the orbit\footnote{Let us note that (\ref{defi}) can be obtained from Eqs. (\ref{conser2})}:
\begin{equation}
d\varphi=\frac{J/r^2 m}{\sqrt{2/m(E-\Phi_{eff})}}dr \ ,\label{defi}
\end{equation}
or equivalently, we can write the following generalization of the Eq. (\ref{bipre}):
\begin{equation}
\left(\frac{du}{d\varphi}\right)^2+u^2=\frac{2m}{J^2}\left(E+GMm u+\alpha u^3-V_p^{RMM}(r)\right) \ ,
\label{bipregen}
\end{equation}
and therefore, the generalized classical Binet equation is
\begin{equation}
\frac{d^2u}{d\varphi^2}+u=\frac{GMm^2}{J^2}+3 \frac{\alpha m}{J^2}
u^2-\frac{m}{J^2}\frac{d}{du}V_p^{RMM}(r) \ .
\label{binetclagen}
\end{equation}
By comparing this Eq. (\ref{binetclagen}) with (\ref{miembrodcha}) we can hold the following statement:
{\bf Proposition:}
{\it The classical Kepler problem for a mass distribution $M$, with total energy $E$ and orbital angular momentum $J$, perturbed with a potential given by this expression:}
\begin{eqnarray}
V_p(r)&=&-\alpha u^3-Q m G (\frac 52+3 h^2) u^3+Q M m
G(\frac{9}{14}-\frac{75}{14} h^2)u^4+\nonumber\\
&+&\left[-\frac {3}{2m} Q J^2-6 \frac mM G (1+h^2) Q^2
+(\frac{57}{8}+\frac{15}{2} h^2) m G D+\right.\nonumber\\
&+&\left.(\frac 97 -\frac{66}{7} h^2)m M^2 G
Q\right]u^5+O(u^6)
\nonumber\\
\label{vpr}
\end{eqnarray}
{\it provides (up to the desired order in the power of the variable $u$) the same orbital equation for a test particle of mass $m$, as the corresponding orbital equation for the timelike geodesic on the equatorial plane of the relativistic Pure Multipole solution with a finite number of RMM if the following values of the parameters are considered}:
\begin{equation}
l=\frac{J}{mG^{1/2}} \qquad , \qquad h^2=-\frac{2E}{mG}-1 \qquad , \qquad \alpha=\frac{M J^2}{m} \ .
\label{vpr2}
\end{equation}
Let us note that the above expressed potential can be written in terms of the dimensionless parameter $\hat\lambda\equiv M u=M/r$, which controls the perturbational character of it, as follows:
\begin{eqnarray}
& &V_p^{RMM}(r)=-mG\left(\hat\lambda^3 \frac q2 (5+6h^2)+\frac{3}{14} \hat\lambda^4 q (-3+25h^2)+\right.\nonumber\\
&+&\left.\frac{3}{14} \hat\lambda^5\left[q\left(44 h^2-6+7\frac{J^2}{M^2m^2G}\right)+28q^2(1+h^2)-\frac 74 d(19+20h^2)\right]\right) ,\nonumber\\
\end{eqnarray}
where $q\equiv Q/M^3$ and $d\equiv D/M^5$ denote for dimensionless parameters associated to the quadrupole $Q$ and $2^4-$pole moment $D$ respectively.
Consequently, the Binet equation is given by the following expression:
\begin{eqnarray}
&&\frac{d^2u}{d\varphi^2}+u=M \left(\frac{m}{J}\right)^2 G+\left[(\frac{15}{2}+9h^2) \left(\frac{m}{J}\right)^2 G Q+3 M\right]u^2+\nonumber\\
&+&\left[M Q G \left(\frac{m}{J}\right)^2\left(-\frac{18}{7}+\frac{150}{7}h^2\right)
\right]u^3+\nonumber\\
&+&\left[\frac{15}{2} Q+\left(\frac{m}{J}\right)^2G\left(30 (1+h^2) \frac{Q^2}{M}
+M^2 Q \frac{15}{7}(-3+22 h^2)+\right.\right.\nonumber\\
&+&\left.\left.\frac{15}{8}D(20h^2+19)\right)\right]u^4 \ .
\end{eqnarray}
\section{Measuring the quadrupole moment}
The Eq. (\ref{vpr}) shows that a quadrupole contribution arises at order $u^3$, the same order as the known Schwarzschild correction due to the monopole. The role of the quadrupole becomes relevant enough when the relativistic correction to the perihelion of a test particle orbit is calculated. Hence, let us consider the above potential (\ref{vpr}) and let us develop up to first order of perturbation theory the following perturbed kepler problem (for $n=3$):
\begin{equation}
V=-GMm\frac1r-\frac{\xi}{r^n} \quad , \quad H=H_0+\xi H_1 \quad , \quad H_1\equiv -\frac{1}{r^n} ,
\end{equation}
where $\xi$ is a small parameter, and $H_1$ is the perturbation of the Hamiltonian $H$.
According to the standard theory of perturbations \cite{goldstein} within angular-action variables, the averaged rate of secular precession due to the perturbation is given by the following expression:
\begin{equation}
{\bar{\dot \varsigma}}=\frac{1}{\tau}\int_0^{\tau}\frac{\partial H_1}{\partial J}dt=\frac{\partial}{\partial J} \bar H_1 ,
\end{equation}
$\tau$ being the average time interval considered, in particular the period of the nonperturbed orbit; $\varsigma$ stands for the angular position of the periastron on the orbit plane, and $\bar H_1$ is the time-averaged perturbed Hamiltonian which can be calculated by using the conservation of the angular moment ($J=mr^2\dot \varphi$=cte) as follows:
\begin{equation}
{\bar H_1}=-\frac{1}{\tau}\int_0^{\tau}\frac{1}{r^n}dt=-\frac{1}{\tau}\frac{m}{J}\int_0^{2\pi}\frac{1}{r^{n-2}}d\varphi ,
\end{equation}
where $r$ can be expressed in terms of $\varphi$ by means of the nonperturbed orbit:
\begin{equation}
\frac1r=\frac 1p(1+e \cos\varphi) ,
\end{equation}
$e$ being the eccentricity and $\displaystyle{p\equiv\frac{J^2}{m^2MG}}$ is the so-called ellipse's parameter.
Therefore, the averaged rate of precession is given (for the $n=3$ case) by
\begin{equation}
{\bar{\dot \varsigma}}=\frac{6 \pi}{\tau}GM\frac{m^3}{J^4} \xi=\frac{6 \pi}{\tau}\left[GM^2\frac{m^2}{J^2}+QG^2 M\frac{m^4}{J^4}\left(\frac 52+3h^2\right)\right] \ .
\label{aver}
\end{equation}
The first term of (\ref{aver}) is the monopole contribution already known, which is provided by the Schwarzschild solution, whereas the second term is the correction to the precession due to the quadrupole moment. If we take into account the value of $h$ (\ref{vpr2}) and consider $J$ and $E$ in terms of the eccentricity $e$ and the semimajor axis $a$ of the orbital ellipse, i.e., $J^2=a(1-e^2)GMm^2$, $|E|=GMm/(2a)$, we have that
\begin{equation}
\bar{\dot \varsigma}=\frac{6\pi}{\tau}\left[\zeta+\zeta^2 q\left(-\frac 12+3\frac Ma\right)\right] \ ,
\label{averdef}
\end{equation}
where $\displaystyle{\zeta\equiv\frac{M}{a(1-e^2)}}$ is a dimensionless parameter\footnote{Let us note that $M$ must be considered in length units ($M\rightsquigarrow\frac{GM}{c^2}$). For the case of the Sun the value of this {\it length} is about $1.476$ km, and hence $M<<a$ for any planet of the solar system.} less than $1$, the quadrupole contribution is of order $\zeta^2$ and its sign depends on the relative value between $M$ and $a$:
\begin{equation}
\zeta^2 q\left(-\frac 12+3\frac Ma\right) \left\{\begin{array}{ccc}
<0&\leftrightarrow&M<<a\\
\geq 0&\Leftrightarrow&6M>a .
\end{array}
\right.
\end{equation}
In \cite{leo1}, \cite{leo2} the authors look for patterns of regularity in the sign of the contributions for different RMM, ending up the conclusion that the linear quadrupole term is negative for a positive quadrupole. This pattern is verified by our calculation except for the case that $6M>a$, i.e., a test particle closely orbiting around a strong gravitational source. The discrepancy arises because in \cite{leo2} the authors do not obtain\footnote{Let us note that our parameter $\zeta$ is exactly equal to the parameter $\epsilon^2$ used in \cite{leo2} to develop the expansion series.}, up to this order in the parameter $\zeta$, the relativistic contribution $\displaystyle{\frac{3M}{a}}$ appearing in (\ref{averdef}) and the contribution of the quadrupole at order $\zeta^2$ is given only by the Newtonian term $-1/2$.
Since the first contribution of the quadrupole moment to the perihelion shift appears at the same order in $\hat\lambda$ as the monopole contribution, this calculation provides a procedure for measurement of the quadrupole moment. In principle a test particle conveniently far away ($\hat\lambda<1$) from the source should be affected only by the monopole and quadrupole contributions which are the only effective corrections at that distance (contributions higher than $\hat\lambda^3$, in the first order of perturbation theory, are considered negligible). Dropping any other external effects, for a suitable isolated source-particle system acting on the perihelion precession of the orbit, the quadrupole contribution can be estimated to obtain a tentative measurement of the quadrupole moment since the monopole correction is well known. In fact, the relative value between both corrections at this order of perturbation theory is the following:
\begin{equation}
\Delta\equiv\frac{Q^{term}}{M^{term}}=\frac{\zeta^2q\left(3\frac Ma-\frac12\right)}{\zeta}=\zeta q \left(3\frac Ma-\frac12\right) \quad . \label{delta}
\end{equation}
Let us calculate an estimate of this relative value for the orbit of Mercury. As is known, Einstein's theory of gravity leads to a relative correction of the Newtonian value for Mercury's secular perihelion drift of $42.98^{\prime\prime}/$century \cite{soffel}. The rate of precession for the relativistic monopole (Schwarzschild correction) can be calculated from the first term of our Eq. (\ref{averdef}) to obtain\footnote{The quantity $(6\pi/\tau) \zeta$ provides an estimate of the Schwarzschild correction, with the following values of the parameters: eccentricity of the orbit $e=0.2056$, the semi-major axis of the orbit $a=6.4529 \times 10^{7} km$, $M$ being a half of the radius of Schwarzschild for the Sun $M\equiv GM_{\odot}/c^2$, and period of the Mercury's orbit $\tau=7600428 s$.} $38.01^{\prime \prime}/$century.
The quadrupole contribution can be calculated from the second term of the Eq. (\ref{averdef}), and hence, the key point of its estimate, as well as that of the relative value (\ref{delta}), depends on the dimensionless parameter $q$ related with the quadrupole moment of the Sun. This is a matter of increasing research\footnote{The gravitational multipole moments describe deviations from a purely spherical mass distribution. Thus, their precise determination gives indications on the solar internal structure. It is difficult to compute these parameters and the way to derive the best values and how they will be determined in a near future by means of space experiments is the aim of several works \cite{rozelotpiro}.}, because the quadrupole moment is a relevant quantity for a lot of related measurements; in fact, the evaluation of the solar quadrupole moment still faces some controversy: on one side, the theoretical values strongly depend on the solar model used, whereas accurate measurements are very difficult to obtain from observations, in particular the value of the quadrupole moment can be inferred to be in agreement with the experiment observations of precisely the perihelion advance of Mercury (see \cite{pirozelot} and references therein).
Different estimates of the quadrupole moment of the Sun \cite{pirozelot}, \cite{rozelotpiro}, provide a range of values from a theoretical determination $J_2=(2\pm 0.4)\times 10^{-7}$ to another bounds around $J_2=(1.4 \pm1.5)\times 10^{-6}$ \cite{soffel}; nevertheless, the quadrupole moment of the Sun may not exceed the critical value of $J_2=3.0 \times 10^{-6}$ according to the argument given in \cite{rozbo}, based upon the accurate knowledge of the Moon's physical librations (these data reach accuracies at the milliarcsecond level).
The factor $M/a$ for the Mercury's orbit is about $2.257\times 10^{-8}$, and the parameter $\zeta$ strongly depends on that value, since $1/(1-e^2)$ is around $1.04415$, and so $\zeta\simeq2.356\times 10^{-8}$. Therefore, Eq. (\ref{delta}) for the relative value of the quadrupole contribution with respect to the Schwarzschild correction leads to the following estimate:
\begin{equation}
|\Delta|\simeq 1.18 \times 10^{-8} q \label{deltaest} \ ,
\end{equation}
or equivalently, the rate of precession due to the quadrupole contribution is estimated as follows:
\begin{equation}\displaystyle{\bar{\dot \varsigma}_Q=\frac{6\pi}{\tau}\left[\zeta^2 q\left(-\frac 12+3\frac Ma\right)\right]}\simeq 4.48 \times 10^{-7}q{}^{\prime \prime}/century. \label{myestimate}
\end{equation}
This result
is perfectly in agreement with the current predictions of measurements and values of the advance of Mercury's perihelion deduced from observational data: As is known \cite{pirozelot}, once correcting for the perturbation due to the general precession of the equinoxes and for the perturbation due to other planets, the advance of the perihelion of Mercury is a combination of a purely relativistic effect and a contribution from the Sun's quadrupole moment. One may compute the corrective factor to the prediction due to General Relativity ($42.98^{\prime \prime}/$century, the Schwarzschild contribution, which does not include the quadrupole correction): this factor, i.e., the relative value of the solar quadrupole correction with respect to the Schwarzschild contribution is
\begin{equation}
2.821 \times 10^{-4} (2.0\pm 0.4) \label{deltadato} \ ,
\end{equation}
for a value of the quadrupole moment $J_2=2.0\times 10^{-7}$, or equivalently, the correction to the
perihelion precession due to the quadrupole moment is about
\begin{equation}
2.425 \times 10^{-2}{ }^{\prime \prime}/century \label{quadrudato} \ ,
\end{equation}
These calculations are done within
the Parameterized Post-Newtonian (P.P.N.) formalism describing a fully conservative relativistic theory of gravitation (see Eq. (1) in \cite{pirozelot}), and they are in accordance with our Eqs. (\ref{deltaest}) and (\ref{myestimate}) respectively by taking into account the appropriated relation between the parameter $J_2$ in P.P.N. formalism and the relativistic multipole moment $Q$ defined by Geroch \cite{geroch}, i.e., $|Q|\equiv M R_{\odot}^2 J_2$. Hence, from (\ref{deltaest}) we have that
\begin{equation}
|\Delta|\simeq 4.45 \times 10^3 J_2 \simeq 8.9 \times 10^{-4} \ ,
\end{equation}
where a value of $J_2=2.0 \times 10^{-7}$ has been used, or equivalently, Eq. (\ref{myestimate}) leads
to the predicted relations between observational or
theoretical quadrupole moment and the quadrupole correction to the perihelion precession of Mercury's orbit: \begin{equation}
\displaystyle{\bar{\dot \varsigma}_Q\simeq 4.48 \times 10^{-7} J_2 \left(\frac{R_{\odot}}{M}\right)^2} \simeq 1.12 \times 10^{5} J_2 {}^{\prime \prime}/century \simeq 2.24 \times 10^{-2} {}^{\prime \prime}/century.
\end{equation}
\section{Conclusion}
In this work we have tried to show the relevance of the MSA system of coordinates for the description of static and axisymmetric vacuum solutions with a finite number of RMM, particularly for those which are slightly different with respect to the spherically symmetric solution. In \cite{herrera} the authors study the behaviour of different geodesics of quasispherical spacetime, for example the case of self-gravitating sources with the exterior gravitational field of the $M-Q^{(1)}$ solution \cite{mq1}.
First, we have explicitly written a static and axisymmetric vacuum solution with a finite number ($M$, $Q$, $D$) of RMM in MSA coordinates. The expressions obtained for the metric components are approximated because the MSA system of coordinates are constructed iteratively by means of a power series. But, these results allow us to handle with the Pure Multipole solutions as generalizations of the Schwarzschild solution in the sense that each one of the metric components are written as a series whose first term represents the monopole solution and the following terms provide the successive corrections to the spherical symmetry due to the other multipoles (\ref{chachis}). Furthermore, the $g_{00}$ metric component is calculated to any order and it resembles, as it was desired, the formal expression of the classical multipole potential. Since these solutions are static, we are actually giving the Ernst potential \cite{ernst} of the solution in such a way.
Until now, no other solution has been written in MSA coordinates except for the Schwarzschild solution. The expressions obtained for the metric are supported by the calculation of the MSA coordinates in terms of the Weyl coordinates (as well as the inverse relations). We are providing a system of coordinates that generalizes the standard Schwarzschild coordinates for the cases of Pure Multipole solutions.
Second, we have used this system of coordinates to study the behaviour of test particles orbiting in a space-time described by a Pure Multipole solution. Two results seems to be specially relevant:
One of them is the possibility of finding an equivalent classical problem; we are able to write the orbital equation associated to geodesics in the equatorial plane identically equivalent to the Binet equation obtained from a classical perturbed Kepler problem. In other words, we can describe the orbital motion of a test particle in the same way as it is studied the classical field equations for a problem of a conservative potential endowed with certain perturbation.
We calculate explicitly this perturbative potential in terms of the physical parameters of the virtual Hamiltonian dynamical system (energy $E$, particle mass $m$, orbital angular momentum $J$...) and the RMM of the vacuum solution.
This relationship between the resolution of a classical dynamical system and a geometrical description of the problem by means of an associated riemannian metric is an analogous result to the prescription derived from the Maupertuis-Jacobi principle \cite{maupertuis}: the trajectories of a mechanical system, with a natural Lagrangian function $L=(1/2) g_{ij} \dot q^i \dot q^j -V(q)$, are geodesics of the Jacobi metric $g^J_{ij}=2(E-V)g_{ij}$ for a fixed total energy $E$ of the system. Possibly be some connection between those schemes can be explored.
The other important result of this study of the geodesics in MSA coordinates is the calculation of high order relativistic corrections to Keplerian motion. In particular, we have calculated the perihelion shift due to the correction of the quadrupole moment in addition to the Schwarzschild contribution, and it is shown that both corrections arises at the same order in the perturbed potential. Classical techniques of perturbation theory can be used to make this calculation since the description of the relativistic motion is made from the equivalent Newtonian problem.
In \cite{leo1}, \cite{leo2} the authors develop a calculation of relativistic corrections to Keplerian motion; the advantage of our work is that we do not need to introduce a parameter {\it ad hoc} to perform the expansion series, because the MSA system of coordinates itself leads to geodesics of the solution written in such a way that the corrections due to any RMM are clearly distinguished.
The estimate of the quadrupole contribution leads to the conclusion that it is small compared with the Schwarzschild correction for the case of Mercury's orbit, but it is perfectly detectable by present experiments, since one of the techniques used for measuring the quadrupole moment of the Sun is just by means of the perihelion precession of the orbit \cite{rozelotpiro}, \cite{pirozelot}.
Comparison between both corrections (\ref{delta}) leads to the conclusion that the quadrupole contribution to the perihelion precession may be quantitatively significant with respect to the Schwarzschild correction for scenarios with a very massive source and test particles closely orbiting around: Eq. (\ref{averdef}) shows that it is important not only the value of the quadrupole moment but also the factor $M/a$. So, if we think about an experiment or astrophysical system with a test particle closely orbiting around a strong gravitational source we could handle with a value of the factor $M/a$ which may compensate the factor $q$ whose value is rather small for standard astrophysical systems (except for compact binary systems).
A future generalization of our results to a stationary and axisymmetric case will provide us with a more realistic scenarios, and the estimates will become very relevant if the calculation is applied for instance to an axisymmetric spinning star.
For example, neutron stars are extremely compact objects typically around $1 M_{\odot}$ or $2 M_{\odot}$ compressed in a radius of a few kilometers, and hence, the corresponding value of $M/a$ for a test particle orbiting closely around a neutron star can be near to $10^{-1}$.
In addition, some works have studied the central role of the innermost stable circular orbit (ISCO) in the relativistic precession of orbits around neutron stars \cite{stergi}, \cite{morsink}. Strange stars has also been considered as relevant sources (of QPOs for example \cite{gourgou}); Strange stars are objects with two main characteristics: they are made of a mixture of quarks and they have no minimum mass. It has also been shown in \cite{stergi},\cite{gourgou} that ISCO is located outside the strange star for relatively high mass (ranged from 1.4 to 1.6 solar masses depending on the different EoS) even at very high rotation rates, this fact being the main difference with respect to neutron stars.
In \cite{ss} Shibata and Sasaki calculated analytically the ISCO of neutral test particles around a massive, rotating and deformed source in vacuum, including the first four gravitational multipole moments (following the scheme given by Shibata the authors in \cite{sanabria} extend it to the electrovacuum case.); it is possible to study the role of the quadrupole moment of mass related to the neutron stars, whose value is not constrained to be small, and the factor $M/a$ can be considered for hypothetical orbits nearby the ISCO ($r\approx 6M$).
\section{Appendix}
The gauge (\ref{trans}) is defined in terms of series, up to order $O(1/R^9)$, with the following functions $f_n(\omega)$ and $g_n(\omega)$:
\begin{eqnarray}
f_1(\omega)&=&M \quad , \quad
f_2(\omega)=\frac 12 M^2 (1-\omega^2)\quad , \quad
f_3(\omega)=\frac 12 Q(1-3 \omega^2)\nonumber\\
f_4(\omega)&=&M Q\left(-\frac 54 \omega^4-\frac{19}{28} +\frac{39}{14} \omega^2\right)+M^4\left(\frac 34 \omega^2-\frac 58 \omega^4-\frac 18\right)\nonumber \\
f_5(\omega)&=& \frac{Q^2}{M}(1+12 \omega^4-9 \omega^2)+M^2 Q \omega^2(2-3 \omega^2)+D\left(\frac{45}{4} \omega^2-\frac{105}{8} \omega^4-\frac{9}{8}\right)\nonumber\\
f_6(\omega)&=&Q M^3\left(\frac{73}{168}+\frac{705}{56} \omega^4-\frac{361}{56} \omega^2-\frac{45}{8} \omega^6\right) +\nonumber\\
&+&M^6\left(\frac{35}{16} \omega^4-\frac{15}{16} \omega^2-\frac{21}{16} \omega^6+\frac{1}{16}\right)+\nonumber\\
&+&M D\left(\frac{191}{88}-\frac{1965}{88} \omega^2-\frac{21}{8} \omega^6+\frac{2485}{88} \omega^4\right) +\nonumber\\
&+&Q^2\left(-\frac{1247}{616} +\frac{10347}{616} \omega^2-\frac{13089}{616} \omega^4-\frac{15}{8} \omega^6\right)\nonumber\\
f_7(\omega)&=& Q^2 M\left(\frac{61}{28}-\frac{2711}{140}\omega^4-\frac{38}{5} \omega^2+\frac{81}{2} \omega^6\right)+\nonumber\\
&+&M^4 Q\left(-2 \omega^2
+\frac{17}{2} \omega^4-\frac{15}{2} \omega^6\right)+\nonumber\\
&+& M^2 D \left(\frac32 \omega^2+\frac{85}{2} \omega^4-\frac 32-\frac{105}{2} \omega^6 \right)+\nonumber\\
&+&\frac{Q D}{M}\left(-3+154 \omega^6-195 \omega^4
+60 \omega^2\right)+\nonumber\\
&+&\frac{Q^3}{M^2}\left(
-\frac{144}{5} \omega^2+\frac{981}{10} \omega^4-\frac{414}{5} \omega^6
+\frac 32\right)\nonumber\\
f_8(\omega)&=&\frac{Q^3}{M}\left(\frac{52341}{520} \omega^2-\frac{138851}{24024}-\frac{13553439}{40040} \omega^4+\frac{892359}{3080} \omega^6\right)+\nonumber\\
&+&D Q\left(-\frac{84665}{176}\omega^6+\frac{646781}{64064}+\frac{19850195}{32032} \omega^4-\frac{280173}{1456} \omega^2-\frac{675}{64} \omega^8\right)+\nonumber\\
&+&Q M^5 \left(
-\frac{383}{1056} -\frac{4897}{112} \omega^4+\frac{4825}{462} \omega^2+\frac{1595}{28} \omega^6-\frac{715}{32} \omega^8\right)+\nonumber\\
&+&M^8\left(-\frac{5}{128}-\frac{315}{64} \omega^4+\frac{35}{32} \omega^2
+\frac{231}{32} \omega^6-\frac{429}{128} \omega^8\right)+\nonumber\\
&+&M^3 D\left(\frac{445}{2288}+\frac{3890}{143} \omega^2+\frac{3171}{22} \omega^6-\frac{159915}{1144} \omega^4-\frac{273}{16} \omega^8\right)+ \nonumber\\
&+&M^2 Q^2\left(-\frac{936731}{672672}-\frac{1143841}{140140} \omega^2
+\frac{34285679}{560560} \omega^4-\frac{4121}{77} \omega^6-\frac{715}{32} \omega^8\right)\nonumber\\
\label{A1}
\end{eqnarray}
\begin{eqnarray}
g_1(\omega)&=&0 \quad , \quad g_2(\omega)=(1-\omega^2) (-\frac 12 \omega M^2)\nonumber\\
g_3(\omega)&=&(1-\omega^2) (-Q \omega)\nonumber\\
g_4(\omega)&=&(1-\omega^2) \omega(-\frac{1}{56})\left[ M^4 (49 \omega^2-21)+ Q(70 \omega^2-78) M \right]\nonumber\\
g_5(\omega)&=&(1-\omega^2) \omega \frac{1}{10 M} \left[D M(-105 \omega^2+45)+Q M^3( -30\omega^2+8)+Q^2 (96\omega^2
-36)\right]\nonumber\\
g_6(\omega)&=&(1-\omega^2) \omega (\frac{-1}{3696}) \left[M^6(7623 \omega^4
-6930 \omega^2+1155)+\right.\nonumber\\
&+&\left.Q M^3(25410 \omega^4+7546 -34188 \omega^2)+D M(9702 \omega^4 +27510-69580 \omega^2)+\right.\nonumber\\
&+&\left.Q^2(6930 \omega^4+52356\omega^2-20694)\right]\nonumber\\
g_7(\omega)&=&(1-\omega^2) \omega(\frac{-1}{490M^2}) \left[D Q M(-64680 \omega^4+54600 \omega^2-8400)+\right.\nonumber\\
&+&\left.Q^2 M^3(-19845\omega^4+7024 \omega^2+957)+Q M^6(
4410 \omega^4-3038 \omega^2+336)+\right.\nonumber\\
&+&\left. M^4 D(25725 \omega^4-13475 \omega^2-210)+Q^3(34776 \omega^4
-27468 \omega^2+4032)\right]\nonumber\\
g_8(\omega)&=&(1-\omega^2) \omega \frac{1}{1921920M} \left[Q^3(417624012 \omega^4-327877128 \omega^2+48074796)+\right.\nonumber\\
&+&\left.D Q M(-20270250 \omega^6-693406350 \omega^4+595505850 \omega^2-92457090)+\right.\nonumber\\
&+&\left.Q M^6(-58558500 \omega^6+100720620\omega^4+4832100-45945900 \omega^2)+\right.\nonumber\\
&+&\left.M^9(
-10735725 \omega^6+15030015 \omega^4-5780775 \omega^2+525525)+\right.\nonumber\\
&+&\left.M^4D(-37837800 \omega^6+226746520\omega^4-137167800 \omega^2+12251400)+\right.\nonumber\\
&+&\left.M^3Q^2(-49549500 \omega^6-83972460 \omega^4+63989772\omega^2-4272228)
\right]
\label{A2}
\end{eqnarray}
The following expressions show the relation of Weyl coordinates $\{R,\omega\}$ in terms of the MSA coordinates $\{r,y\}$ up to order $O(\hat\lambda^9)$:
\begin{eqnarray}
\omega&=&\omega(r,y)=y+\frac 12 y (1 -y^2) \hat\lambda^2+\left( (1-y^2)+q (1-y^2)\right)y \hat\lambda^3+\nonumber\\
&+&\left[(-\frac94 y^2+\frac{15}{8} +\frac38 y^4)+q(-\frac54 y^4 -\frac{5}{14} y^2 +\frac{45}{28})\right] y\hat\lambda^4+\nonumber\\
&+&\left[(-5 y^2 +\frac 72 +\frac32 y^4)+q (-\frac{22}{35} y^2 +\frac{92}{35}-2 y^4)+d(15 y^2-\frac92 -\frac{21}{2} y^4)+\right.\nonumber\\
&+&\left.q^2 (-\frac{66}{5} y^2+\frac{18}{5}+\frac{48}{5} y^4)\right] y\hat\lambda^5+\nonumber\\
&+&
\left[(\frac{75}{16} y^4-\frac{5}{16} y^6+\frac{105}{16} -\frac{175}{16} y^2)+q (-\frac{39}{8} y^4+\frac{15}{8} y^6+\frac{715}{168}-\frac{211}{168} y^2)+\right.\nonumber\\
&+&\left. q^2(\frac{9179}{616}+\frac{26617}{616} y^4-\frac{15}{8} y^6-\frac{34641}{616} y^2)+\right.\nonumber\\
&+&\left.d(-\frac{1325}{88} -\frac{8197}{264} y^4-\frac{21}{8} y^6+\frac{12865}{264} y^2)\right] y\hat\lambda^6+\nonumber\\
&+&
\left[(-\frac{15}{8} y^6 +\frac{105}{8} y^4-\frac{189}{8} y^2+\frac{99}{8} )+ q(\frac{1893}{280} +\frac{57}{8} y^6-\frac{463}{40} y^4-\frac{647}{280} y^2)+\right.\nonumber\\
&+&\left. q^2(\frac{412336}{2695} y^4-\frac{929517}{5390} y^2+\frac{116833}{2695}-\frac{239}{10} y^6) +\right.\nonumber\\
&+&\left. q^3(\frac{4446}{35} y^4-\frac{450}{7} y^2+\frac{288}{35}-\frac{2484}{35} y^6)+\right.\nonumber\\
&+&\left. d(-\frac{9981}{88} y^4+\frac{86511}{616} y^2-\frac{24729}{616} +\frac{105}{8} y^6)+\right.\nonumber\\
&+&\left. q d(-\frac{1704}{7} y^4+\frac{900}{7} y^2-\frac{120}{7} +132 y^6)\right]y \hat\lambda^7+\nonumber\\
&+&
\left[(\frac{35}{128} y^8+\frac{2205}{64} y^4 +\frac{3003}{128} -\frac{1617}{32} y^2-\frac{245}{32} y^6)+\right.\nonumber\\
&+&\left. q(-\frac{15119}{560} y^4+\frac{54881}{5280}-\frac{32327}{9240} y^2+\frac{1257}{56} y^6-\frac{75}{32} y^8)+\right.\nonumber\\
&+&\left. q^2(\frac{165}{32} y^8+\frac{272710509}{560560} y^4-\frac{416569}{3080} y^6-\frac{130608551}{280280} y^2+\frac{122863527}{1121120})+\right.\nonumber\\
&+&\left. q^3(-\frac{1144047}{2464} y^6+\frac{26397765}{32032} y^4-\frac{13183965}{32032} y^2+\frac{21543}{416})+ \right.\nonumber\\
&+&\left. d(\frac{938}{11} y^6-\frac{1241945}{3432} y^4+\frac{316955}{858} y^2-\frac{221363}{2288}+\frac{63}{16} y^8 )+\right.\nonumber\\
&+&\left. q d(\frac{273111}{352} y^6-\frac{22394167}{16016} y^4+\frac{3333245}{4576} y^2-\frac{556299}{5824}-\frac{675}{64} y^8) \right] y\hat\lambda^8
\label{A3}
\end{eqnarray}
\begin{eqnarray}
R&=&R(r,y)= r \left[1-\hat\lambda-\frac 12(1-y^2) \hat\lambda^2+\left(-\frac 12 (1-y^2)-q\frac 12 (1-3 y^2)\right) \hat\lambda^3+\right.\nonumber\\
&+&\left.\left((-\frac58 +\frac34 y^2-\frac18 y^4)+q( -\frac{9}{28} +\frac{3}{14} y^2 +\frac54 y^4)\right) \right.\hat\lambda^4+\nonumber\\
&+&\left.\left((-\frac38 y^4 -\frac78+\frac54 y^2)+q(2 y^4 -\frac{5}{14} y^2-\frac{3}{14})+q^2(9 y^2-12 y^4-1)+\right.\right.\nonumber\\
&+&\left.\left.d(-\frac{45}{4} y^2 +\frac{105}{8} y^4 +\frac98 )\right)\hat\lambda^5+\right.\nonumber\\
&+&\left.\left((\frac{21}{16}-\frac{15}{16} y^4+\frac{35}{16} y^2+\frac{1}{16}y^6)+q(-\frac{1}{168} +\frac{219}{56} y^4-\frac{11}{8} y^2-\frac{5}{8} y^6)+\right.\right.\nonumber\\
&+&\left.\left.q^2( -\frac{1525}{616}-\frac{21099}{616} y^4+\frac{15525}{616} y^2+\frac{15}{8} y^6)+\right.\right.\nonumber\\
&+&\left.\left.d(\frac{205}{88}-\frac{1995}{88} y^2 +\frac{21}{8} y^6 +\frac{2135}{88}y^4)\right) \hat\lambda^6+\right.\nonumber\\
&+&\left.\left((-\frac{33}{16}+\frac{5}{16} y^6-\frac{35}{16} y^4+\frac{63}{16} y^2)+q(\frac{155}{336}+\frac{4363}{560} y^4 -\frac{1973}{560} y^2-\frac{33}{16} y^6)+\right.\right.\nonumber\\
&+&\left.\left.q^2(-\frac{1651}{308}-\frac{135637}{1540}y^4 +\frac{91493}{1540} y^2+\frac{287}{20} y^6)+\right.\right.\nonumber\\
&+&\left.\left.d(\frac{829}{
176}+\frac{10735}{176} y^4 -\frac{8631}{176}y^2-\frac{63}{16} y^6)+q d(3 +195 y^4-154 y^6-60 y^2)+\right.\right.\nonumber\\
&+&\left.\left. q^3(-\frac{3}{2}+\frac{414}{5} y^6+\frac{144}{5} y^2-\frac{981}{10} y^4)\right) \right.\hat\lambda^7+\nonumber\\
&+&\left.\left((-\frac{429}{128} -\frac{5}{128} y^8+\frac{35}{32} y^6 -\frac{315}{64} y^4+\frac{231}{32} y^2)+\right.\right.\nonumber\\
&+&\left.\left.q d(\frac{722587}{64064}-\frac{113533}{176} y^6 +\frac{675}{64} y^8 +\frac{25975585}{32032} y^4 -\frac{360285}{1456}y^2)+\right.\right.\nonumber\\
&+&\left.\left.q^2(-\frac{661565}{61152}-\frac{120202913}{560560}y^4-\frac{55}{32} y^8+\frac{45937}{770} y^6+\frac{18225373}{140140} y^2)+\right.\right.\nonumber\\
&+&\left.\left.d(\frac{506395}{3432} y^4 +\frac{20849}{2288} -\frac{1897}{66} y^6-\frac{21}{16} y^8 -\frac{14745}{143}y^2 )+\right.\right.\nonumber\\
&+&\left.\left.q(\frac{1571}{1056}-\frac{159}{28} y^6 +\frac{15}{32} y^8 -\frac{2689}{330}y^2 +\frac{26459}{1680} y^4)+\right.\right.\nonumber\\
&+&\left.\left.q^3(-\frac{149437}{24024} +\frac{1206969}{3080} y^6 +\frac{71211}{520} y^2 -\frac{18927009}{40040} y^4 )\right) \hat\lambda^8\right]
\label{A4}
\end{eqnarray}
\section{Acknowledgments}
This work was partially supported by the Spanish Ministry of Education and Science
under Research Project No. FIS 2009-07238, and the Consejer\'\i a de Educaci\'on of the Junta de Castilla y
Le\'on under the Research Project Grupo de Excelencia GR234. We also want to thank the support of the Fundaci\'on Samuel Sol\'orzano Barruso (Universidad de Salamanca) with the project No.FS/8-2009.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 3,381 |
module ShortScaleNums
VERSION = "0.1.0"
end
| {
"redpajama_set_name": "RedPajamaGithub"
} | 6,125 |
{"url":"https:\/\/electronics.stackexchange.com\/questions\/239260\/output-impedance-of-the-current-output-dac\/239264","text":"# Output impedance of the current output DAC\n\nAs known there are two types DAC using R-2R ladder. One is voltage output and another is current output. The voltage output type has a constant output impedance which equal to R. The current output type has a input code dependent output impedance. Then how the output impedance dependent on the input code? Are there a mathematical function, such as $$R_{out} = f(n)$$ in which n is the input code, to show this?\n\nRefs:\n\nThe output of a current-output R-2R ladder must be connected to a virtual ground, such as the inverting input of an opamp whose non-inverting input is grounded. Call the feedback resisor RF.\n\nYou can think of the circuit overall as \"amplifying\" the fixed VREF with a variable gain that is equal to\n\n$$A = -\\frac{R_F}{R_{OUT}}$$\n\nand\n\n$$V_{OUT} = -V_{REF}\\frac{R_F}{R_{OUT}}$$\n\nWe know that\n\n$$I_{OUT} = \\frac{n}{2^N} \\cdot \\frac{V_{REF}}{R}$$\n\nand\n\n$$V_{OUT} = -R_F \\cdot I_{OUT} = -R_F \\cdot \\frac{n}{2^N} \\cdot \\frac{V_{REF}}{R}$$\n\nIt's easy to set these two equations equal to each other and solve for ROUT:\n\n$$-V_{REF}\\frac{R_F}{R_{OUT}} = -R_F \\cdot \\frac{n}{2^N} \\cdot \\frac{V_{REF}}{R}$$\n\n$$R_{OUT} = R \\frac{2^N}{n}$$\n\nWhen the input code is all-zeros, none of the R-2R legs are connected to the output node, so ROUT is infinite. When the input code is all-ones, ROUT is nearly equal to R.\n\nIt really doesn't matter, though, since as we said before, this output node needs to be connected to a virtual ground, so ROUT is in parallel with an impedance that is effectively zero. It's actual value has no effect on the rest of the the circuit.\n\nTo use either a voltage output R2R DAC or a current output R2R DAC properly you have to use it in such a way that the output impedance of the DAC does not matter.\n\nFor the voltage output DAC it is the same as how you would want to measure a voltage inside a circuit. You want to use a high impedance to measure it. So at the output of the voltage output DAC you will want to connect a high input impedance buffer amplifier, example:\n\nFor the current output DAC it is the same as how you would want to measure a current in a circuit, you want to use an impedance as low as possible so that the current can flow through an impedance with the lowest voltage drop possible. Here you want to use a current input amplifier or a current to voltage converter. That can be a circuit as simple as:\n\nThis circuit has an input impedance of almost zero ohms. It multiplies the input current by the value of Rf and that will appear at the output as a voltage.\n\nThe trick with using such circuits is that it eliminates the influence of the (change in) output impedance of the R2R network. That way, you can forget about that output impedance also it does not introduce any errors anymore.\n\nIf you do not use an R2R DAC as I explained, the output impedance will matter and errors will be introduced.\n\nUsually you can get reasonably small errors if you make the load impedance of the R2R DAC significantly higher (for voltage output) or significantly lower (current output) than the resistors used in the network. So if the network has 100 kohm resistors, for a voltage R2R load it with 10 M ohm. For a current output load it with 1 k ohm (so a factor 100 larger\/smaller).\n\nBut the opamp solutions are more accurate !\n\n\u2022 I liked your second-to-last paragraph and expanded on that in my answer :) \u2013\u00a0Marcus M\u00fcller Jun 5 '16 at 13:01\n\nI think I should expand on what Fake Mustache said about low frequency \/ DC design for DACs:\n\nYou do not generally prefer the opamp output stage. This gets increasingly important with the bandwidth of the signal you want to generate.\n\nFor example, see the schematic (p.1) of this high-rate DAC'ing software defined radio peripheral.\n\nThe idea behind these devices is that the DAC sits on the motherboard, and you use interchangeable daughterboards to take the generated signal, and filter it, mix it up to some RF, amplify etc it. That means the signal has to travel a bit and cross a connector before it reaches the relevant analog circuitry. Here, the design choice was hence to use a current DAC.\n\nThe AD9777 DAC's analog outputs get directly fed into the daughterboard connector:\n\nThen, on the daughterboard (let's talk about the WBX here, schematic):\n\nwe see that\n\n\u2022 we match the 50 Ohm of the transmission line, which is necessary to get the most energy out of the DAC into our daughterboard (and corollary, the least reflections\/distortions and\n\u2022 no active parts whatsoever involved in buffering what the DAC produces.\n\nSo, the DAC here runs at 100MS\/s, which means that it's already wise to not think of the signal as \"current flowing through a piece of metal\", but to layout the differential lines from DAC to connector as microwave lines, i.e. microstrip etc, and commit to the fact that the fields around these conductors will carry the energy. In this scenario, capable opamps are hard to find, harder to get linear and even harder to get linear enough not to waste expensive DAC bits.\n\nOf course, a DAC for these rates is specced with an output impedance that allows for correct transmission line impedance and termination impedance design. Which also means that for the 50 Ohm termination used here, Analog guarantees driving capabilities. From the AD9777 datasheet, p. 46:\n\nNote that the output impedance of the AD9777 DAC itself is greater than 100 k\u03a9 and typically has no effect on the impedance of the equivalent output circuit.\n\nhence, we're pretty much in the case where \"ok, you've got a sink impedance in the range of 100\u03a9, but the source impedance is much much higher, so don't you worry\". Of course, p. 47 also explains how you can use an Opamp as output buffer:\n\nYet the text mentions explicitly the disadvantages and design restrictions this has:\n\nThe common-mode (and second-order distortion) rejection of this configuration is typically determined by the resistor matching. The op amp used must operate from a dual supply since its output is approximately \u00b11.0 V. A high speed amplifier, such as the AD8021, capable of preserving the differential performance of the AD9777 while meeting other system level objectives (for example, cost, power) is recommended.\n\nSince Opamps are never perfect, you infer a lot of additional problems. Just think about parasitic capacitance in the feedback line, inclucing the 500 Ohm resistor, or the fact that resistors and package pins have inductance, that change the phase of a signal depending on the signal's frequency... suddenly, your broadband DAC has a less-than-flat buffer, and changing that might not be trivial, lest you reduce the bandwidth to something manageable.\n\n\u2022 Actually I think you don't disagree with my answer but my answer refers only to the DC \/ low frequency case and you look at the case where the behaviour of the opamp limits the performance. So I think your answer is an addition to mine. \u2013\u00a0Bimpelrekkie Jun 5 '16 at 13:22\n\u2022 @FakeMoustache true. 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Latest solar cell breakthrough a nark's worst nightmare
October 29, 2012 2019-07-09T12:40:04 by Staff Writer 474 Comments
Nanosilicon contacts like these can go underneath the solar cell instead of on top where they block some of the sunlight. Pic: Bandgap Engineering
It must be really depressing being a solar nark these days. With the increased popularity of solar power throughout Australia and the world, and regular announcements of improvements in technology, better storage capacity and cheaper prices, solar power is going through the roof (or on the roof). The more the narks whine about what they see as the limited capacity of solar, the more breakthroughs in technology occur to push back the possibilities of clean, solar, renewable energy future for our world.
One of the key developments in recent times has been the drop in cost of solar cells along with improvements in the generation of power by each solar cell. The latest breakthrough in this latter category comes from innovative U.S startup company Bandgap Engineering.
Using nanotechnology, the firm is looking to develop a "super" solar cell that could eventually generate as much as twice the power as conventional solar cells. Double the power? Yes, but that's not all folks as the technology will also reduce the cost of solar cells. According to this October 16 MIT Energy Review article, the firm will develop "…silicon nanowires that can improve the performance and lower the cost of conventional silicon solar cells".
These "super" solar cells — surely a narks worst nightmare — are planned for the not-too-distant future but Bandgap is developing a version of the technology which will have an almost immediate impact. Using existing manufacturing technology the company says it's nanowire-improved silicon cells with help boost the power output of solar cells by increasing the amount of light the cells can absorb.
"For example, by increasing light absorption, it could allow manufacturers to use far thinner wafers of silicon, reducing the largest part of a solar cell's cost. It could also enable manufacturers to use copper wires instead of more expensive silver wires to collect charge from the solar panels," said the MIT article.
The money pitch is that these changes could see "solar panels that convert over 20 percent of the energy in sunlight into electricity (compared with about 15 percent for most solar cells now) yet cost only $1 per watt to produce and install," as a mid term goal, and a long term goal of efficiencies over 30% according to Richard Chleboski, Bandgap's CEO.
So there you have it solar fans, the latest in what is the latest in a continuous line of technological breakthroughs in relation to clean energy. Congratulations to the team at Bandgap, this is great news …unless of course you're a member of that rapidly diminishing group the solar narks.
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Filed Under: Solar Panels Tagged With: Solar Technology
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RobbieJ says
So a "nark" is someone who questions and decides not to go solar due to the impact on the environment in making and later disposing of limited life solar panels. Got to love how "the greens" vilify anybody who has a different opinion to theirs.
Mmm there's so many political parties in history that have done just that and ended up being vilified themselves. German socialist party for one.
Finn Peacock says
Thank you Robbie for proving Godwin's Law
Robbie did prove the law but his point about being derogatory about the anti solar lobby is valid. The term "nark" is loaded.
Sorry Kim but the very definition of Godwins Law states that Robbie invalidated his entire argument by invoking the Nazis.
Although I have to concur with you, even as die-hard solar user/supporter, that the use of the word 'nark' to describe (I assume) the anti-solar pro-oil lobby (prefer the term 'Kocheads' myself) does detract from an otherwise informative article.
Phil La says
well you could consider the term "nark" a let of when you consider implications of failing to adapt in addition to the already current effects on life quality – especially in the case the science and the proof has now long contradicted comments of these "narks", or perhaps better described 'pessimist'
TG says
I think your preferred term could also apply to someone who can turn an article about a wonderful breakthrough that could potentially make solar a economically viable alternative into a childish "nah nah" rant.
Is this really where journalism is going these days.
John Galt (@nos235) says
Godwin's Law is not a law – just as Murphy's LAw is not a law – it's just a quaint little internet tactic used by those without any understanding of history or politics (i.e all greenies)
Lindsay says
John Galt: I love the irony in your choice of handle. I wonder if you appreciate it too?
Trim says
Luddite's would be a better term. Even so, the reality of solar is found in some very simple calculations found here: http://ergobalance.blogspot.com.au/2006/06/slim-chance-for-solar-energy.html
Hmmm, Written in 2006, he's been proven wrong on pretty much all his predictions since then.
The CO2 debt of worldwide solar panel production has already been paid off by PV generation worldwide. The PV industry is saving more CO2 than it generates. Details here:
http://www.solarquotes.com.au/blog/newly-crowned-as-net-producer-pv-looks-to-full-payback-of-dirty-energy-debt/
I notice he also predicts that the price of polysilicon will increase! The price has fallen off a cliff in the last 6 years.
Well Finn, as a sailor, I'm a fan of solar. I've lived off of it exclusively for many years. However, I'm also an engineer, and I know the only energy source capable of meeting the exponential growth in demand is nuclear. When peak oil comes, and it will, it will not be able to close the gap…not even at 35 or 40 efficiency. Do you think I'm wrong?
I'm a big fan of nuclear power. Most engineers are because they look at it rationally not emotionally. My first job was designing control systems in a nuclear power station. Unfortunately the world isn't building nuclear and there's not much I can doi to change that!
We are on the same page then. My basic felling is that petroleum is far too vital for other important aspects of life like textiles, drugs and chemicals to be burning it as an energy source. I firmly believe a energy mix of solar, nuclear and ethanol will eventually meet the needs of the global demand for energy, however that realization will only come after it is too late and massive upheaval in economies and society are forced to make the change. It seems to be the human way.
Richard Boult says
No need for nuclear. Solar Thermal, with storage, is a proven technology already producing 24hr energy on an industrial scale, in Spain and USA. No need to go nuclear, and much quicker to build, and economically competitive with coal over the total life of a project. Producing more jobs too!
There is a Melbourne university based group of engineers who have developed a fully costed and peer reviewed solution for repowering Australia with Solar Thermal and Wind in just 10 years.
All that is lacking is the political will.
Get informed at Beyond Zero Emissions – http://bze.org.au/
airtonix says
I'd like to see more work in the liquid thorium salt reactor (LFTR) area .
But there won't be because it's not easy to make weapons grade uranium with those reactors.
Uranium Willy says
Trim, I am for nuclear as well but, nuclear has problems with limits in some of the materials need to build nuclear power stations. I think the future is going to be a mix of technologies depending on the location.
Just to be fussy. The National Socialist German Workers Party (renamed Nazis by the British) were just one party at that time to include Socialist in their name, one of the others the Social Democratic Party of Germany is still a major political party to this day (wouldn't want them to take offence would you).
So the term social or socialists was more in reference to people than a style of politics, the right wing lie of Nazis being left wing.
Hugh Jarse says
I nark fart in your general direction
KG says
How very convenient..
"Godwin's Law" is no such thing…merely a useful device invented by lefties in order to avoid (often justified) comparisons with Nazis. (aka the National SOCIALISTS).
dabbles says
Well said, KG.
A nark is a nark is a nark, to (mis)quote Gertrude.
What's in a name? ~ Shakespeare.
If the cap fits, wear it ~ Someone or other.
topcu says
"German socialist" is a bit opaque, but much more likely to refer to left-wing politics than Nazism, hence Godwin is not triggered.
Marvin Lightfoot says
sO Too be Trendy tehn use street names like nark so sounds tough huh. well I just may like 10 million in jail for narcotics offences, whilst u sleep under silly cones and hope the wooorld goes goody too shoes. Reform inhumane treatment of your fellows photon lovers. Or else and do a telsla and suck on a pidgin. U will all stuff it anyway there is absolutely no hope when treaviality reigns with language like nark..when us should have said tard.
Peter Kroll says
Wow! I'm sure you said something really powerful, Marvin. Unfortunately it all got lost in the badly developed irony and ridiculous generalizations. But I do like 'Suck on a pidgin'. If only it wasn't so hard to suck.
Will not submit says
@ Finn Peacock:April 25, 2013 at 9:25 am.
Nothing wrong with invoking Godwin's Law if the comparison is appropriate. After all, that "law" was invented by leftist progressives for self protection by pre-empting, through implied ridicule, of such obvious comparisons. It is a fascist tactic of the worst sort It is rebutting an argument by simply calling upon Godwin's law by the use shallow ad hominem self-defense strategies that are bereft of any substantial content. .
Ozzy says
Interesting juxtaposition of Socialist and Fascist in your statement Finn. Considering Socialism is (ostensibly) left of centre and Fascism is extreme right politically. I can't see fascists invoking Godwins "law" because it is completely inappropriate for them to do so as their views are diametrically opposed to the socialist position and Godwin's "law" would be anachronistic to their politics. They already are not associated with socialist politics by definition.
luther says
All this political hair splitting, left and right, it's really not important, just a big act and maybe people are starting to realise that?
Man made climatic catastrophe is of course real, it's proven here.
And as for left and right, it was Mickey Gorbachev wasn't it who reckoned man made climatic catastrophe was the key to unlocking the new world order.
And the greens, you can't say they're left or right, which is meaningless anyway, but they were formed after ww2 with their buddies from the Nazis and the commies getting together to do their thing. and for that matter, people are starting to ask about things, like the Japanese bombing pearl harbor on second thoughts, I mean after the twin towers, starts to have an eerie kind of common contrivance going on there to it?
So, saying the sky is falling or whatever, la la la, it's not a new thing to have this climate thing. that's the ozone layer, cfc, carbon dioxide, greenhouse gas, but not a greenhouse, really subatomic generation of heat that has no scientific basis, kind of climate change right?
Whether y'all understand what's really wrong with your sick little hippy minds, not sure. but it's of little consequence, right now the world is changing. not that climate change is the problem, but oxygen deficit units might be seen to be better applied in parks and wildlife rejuvenation products with a focus on nitrogen enrichment.
Graeme Cant says
No, Finn. Godwin's Law is about reference to the Nazis in debate. Nazis were the National Socialist Party. He referred to the German Socialists – a very different group.
Good catch, but my guess is he meant to write National Socialists. Hardly anyone knows of the German Socialists.
GregW says
I suppose that if you were present when the Wright brothers made their first flight, you would be busy telling everyone that it will never catch on. The passengers would get cold sitting out in the breeze, it's too slow, insufficient range, unable to go to the toilet whilst flying, and will never be able to take enough passengers to be viable. Ditto with the first steam engine.
The world is full of Narks, all deserve to be denigrated for being clueless mental pigmies.
MonkeyMadness says
That's not fair on the pigmies
CyrilH says
I do not think that the Wright Bros business model included having the Government steal large amounts of money from the tax payer to fund your un economical business. If all subsidies for this useless and uneconomic form of generation were removed all of these solar companies would go broke. This already happening by the way with the largest manufacturer of panels in China just declaring bankruptcy.
Wow – that's rich.
Did you not realise that:
* Every coal fired power station in Australia was paid for by taxpayers (I'm talking 100% paid for, not subsidised).
* All the transmission lines in the pre-wind/solar age were paid for by taxpayers (as opposed to today when the wind or solar farm pays for its own transmission line).
* coal is (even now) subsidised by taxpayers (due to the deals done when the coal stations were privatised).
But other than that I'm sure you're right.
There are quite a few coal-fired power stations which were entirely paid for by private investment. And of the majority of them, I am assume you are refering to the ones built by the old State electricity authorities. Those were paid for by electricity consumers, not taxpayers. None of those authorities relied on general taxpayer revenue, they borrowed their investment capital on the bond market and paid it all back with revenue from electricity consumers.
Solar and wind farms do not pay for their own transmission line, they only pay for the line to connect to the existing grid nearest to their facility. The electricity grid network is used to convey their power to the customers. The electricity grid network is also paid for by electricity consumer, not taxpayers, and not the solar and wind farms.
Virtually every new technology that is deemed to be useful is supported by government in the start up stages. Canals, Railroads, Roads for motorists, airports for air transport, etc.
One problem we have now for solar is that, despite being a profitable Cash Cow, the fossil fuel industries are still massively subsidised by government, due to the power of their lobbying.
Fossil fuel's rearguard action now is only about continuing profits for as long as possible. In the medium to long term fossil fuel burning will have to be banned.80% of the stuff we know about has to stay in the ground,or the planet will simply be cooked, populations decimated. check out what the International Energy Agency has to say on the matter.
So for the sake of continuing and more profit$ for a few billionaires like the Koch brothers, we are delaying properly addressing a truly life threatening situation, possibly beyond the point of no return.
Koch bros and mates should be spending their money on getting into renewables, instead of denying the inevitable, and funding the obscurement of the suicide track the human race is currently on. But Koch bros and mates are not entrepreneurs, innovators, They are simply stand over merchants who threaten politicians unless they get what they want.
Fossil fuel industries are basically global drug pushers. They don't care the harm they are doing, just about the profit$.
MacGregor Scott says
@mich. Your deceptive attempt to distinguish electricity users and tax payers as seperate when referring to the revenue raised for power stations, is weak and argumentatitive. There is little dfference between the two catagories. Tax payers use most of the electricity created and are therefore the same people you claim to be electricity users only.
micko says
It is so mich…….. They paid for a small % of their own stuff the rest is covered…. Like always….
Cyril Fletcher says
Cyril, your uninformed, if the subsidies paid to the oil companies were also removed and they damn well should be, youll be paying £10 a gallon for petrol if you could get it, this then level playing field would shake down to natural energy as it would be cheepest, cleenest, and inexaustible,. also keep in mind, if the Earth continues to warm and it will with fosil fuel, and the ice cap on Greenland melts, never mind the poles, just Greenland, then the Earths seas will rise 24ft world wide, bang goes your holiday in sunny bloody Blackpool mate and Skeggy, well its gone so yeah remove the subsidies on solar panels but also remove the subsidies on oil.
Josephus says
I live too far from the beaches. I need a beach to come to me. Melt baby melt. Long live CO2.
Uninformed, I am pretty sure everything you just stated was false.
weterpebb says
Absolute nonsense. The oil industry is massively taxed. The wholesale cost of production of petrol in Australia (and the UK is similar) is about $US 0.50 per litre. The retail price of about US$ 1.30 per litre includes $0.60 excise (tax). In the UK, you pay even more for petrol, because you have even higher taxes on petrol and diesel. In the US, prices are lower again, because taxes are lower again.
If there were no taxes on petrol, it would retail for the world parity price of approximately 60c per litre.
So, fossil fuels (petrol and diesel in particular) are massively taxed; solar energy is massively subsidised. And still solar energy is not cost effective for grid power.
We keep hearing of these breakthroughs which will dramatically reduce the price of solar power. And it is still many, many times more expensive than coal. If solar energy actually becomes cheaper than coal, then people will build solar plants. Please let us know if and when that happens; at the moment, it is just another failed technology.
mcmontecarlo says
@ Weterpebb: If solar is "just another failed technology" then kindly ask China why they've built the world's largest solar farm.
@waterpebb…. Failed? it is bloody amazing you could do your part and put some on your roof, Stop being useless and do something rather then just cry about what you do not know…
Narks! Narks everywhere says
But if someone is talking about alternatives to optic fibre then it's okay to be a Nark.
Andrew T says
PV panels for on-grid use are a little like the Concorde (or TU144). It was a technological breakthrough however they were also expensive to run and could not carry a lot of passengers ect. Once the race had been "won" there was little point in spending more money to further the technology.
The word "nark" generally means someone who unpopularity tells of others misendeavours. In the case of the Concorde the "narks" told of the huge cost of running these planes so therefore they only saw limited use and did not become a mainstream option used by most airlines.
I am a huge fan of the Concorde and the history of it however I think it would have been a massive waste of money to ensure that most commercial flights were with this type of plane and then to try and subsidise the costs of that with rebates and subsidies.
PV panels should be paid for by the end-user entirely and if any taxpayer money is going to be used it should be into research of new/improved technologies or building CSP projects (large mirror arrays that concentrate and collect the suns energy).
I do have to agree with the article in say that the narks are doing a good job of ensuring that PV technology continues to improve by scrutinising its ROI and demanding better products instead of blindly subsidising immature technology that has a negative overall effect on the environment.
Yes Minister says
Its interesting that opponents of subsidies conveniently ignore the massive savings from not having to build horrendously expensive power generation facilities. In Queensland particularly, PV systems make a significant contribution to electricity supply when homes & businesses have airconditioners running full-bore. Without all those PV systems, the local grid couldn't hope to cope with the load, resulting in the need to purchase excess electricity from interstate grids at a cost many times what is given to PV system owners.
Warwick says
Andrew T,
your comparison with the Concorde is very appropriate.
Aeronautical enthusiasts would conceivably have demanded that governments subsidize supersonic passenger craft but commonsense prevailed.
Wind and solar power, however, are articles of faith with the green religion, and whenever religion is involved the faithful will use any falsehood and any logically corrupt argument to push their cause.
We saw the same with both communism and fascism. The Marxist true believers, and the media and academic worlds are full of them, still push their beliefs. They maintain that every form of actually existing communism was a corruption of the true faith, just like some Christian fanatics maintain that Christianity has never been tried.
Ecofanatics who push wind and solar power, as well as other forms of self-sufficiency and sustainability, are motivated primarily by their faith.
And you do a great service in revealing the falsity of the rationalizations they employ to cover their illogical religious belief.
Warwick, you do realise that you response is motivated essentially by your dislike for green policy. Progressive technology in itself is not the bastion of Green or Left politics. It has just been co-opted because the outcomes are compatible with their politics. Why not look at it from another angle?
By locking down your world view you essentially kill any libertarian motivations of self sufficiency and personal choice.
I'd rather invest in solar tech and reduce my reliance on the grid. I smooth out price fluctuations and create jobs which are service based and are not geo located to brown coal deposits.
An investment in Solar is shared amongst franchises for service and installation. Look at it from a point of a network, with power stations controlled by a single entity you have one path to failure. With everyone generating and battery tech, plus solar thermal (molten salt batteries) the technology to manufacture the PV can be shared across multiple manufacturers and will improve possibly in the same fashion as Moore's law. Within a generation there will be a service fee for grid connection in your new home and if you chose to disconnect, then your energy costs at home will be almost nil. You will pay a sparky to service it once a year and maybe a local guy who comes in cleans your gutters and squeegees your PVs clean.
To all of you invoking Godwins law and claiming renewables are greenies in control, try flipping the conversation and take ownership of your own environment. By arguing for coal burning and gas burning you are essentially the marketing and PR for some very big foreign companies who love the fact you don't want to leave them.
I want to capture and filter my own water and pay a small service fee to a local business to maintain it once a year. I want to capture and store my own energy and pay a small service fee to a local business to maintain it once a year. When a river floods a brown coal open cut in Gippsland I don't want to explain to my customers why I can't deliver the goods
Who's with me?
Ner of BVT says
Andrew, I am with you all the way. And many will stay the same as you. It is now time to rethink of our future, not to mention, the future of the one and only earth we have. Be the alternative is more expensive financially (as what the anti solar group say), many will still go to solar and other clean alternative source of energy. Money is nothing compared to clean air and water.
enno says
How's the progress on getting electricity from moonlight ?
Thought so.
Rhino says
Solar cells can generate electicity from moonlight as it is reflected sunlight. Maybe you should have thought about that.
I have thought about it, and they don't. The intensity of moonlight is only about 1/100000 th part of the intensity of sunlight.
ninerocks says
While a solar panel will produce energy even if you shine a torch on it at night, I've done this myself and seen the (very small) numbers on a multimeter, it is so small as to be irrelevant. Just how much power do you think a 100W panel produces under moonlight Rhino? That was a very silly "comeback" as I am sure you know very well that PV is useless at night, and even an overcast day dramatically reduces their performance.
Fact is that solar is a very, very long way from ever being a replacement for fossil/nuclear energy. Energy storage for use while the sun is not shining being one of the big stumbling blocks, as well as the general inefficiency of PV cells (yes, of course that will get better over time, but just how much time?).
Add to that the fact that some of the biggest solar manufacturers are going broke (http://www.economist.com/news/business/21574534-troubling-bankruptcy-troubled-business-sunset-suntech) or shutting up shop after huge losses (http://www.pv-tech.org/news/bosch_shuts_down_solar_division_total_loss_amounts_to_2.4_billion) and the future looks a little bumpy for PV industry.
FYI: I will soon be relying on a stand-alone PV system and am not against PV tech at all, I just don't like unreasoned PV evangelism that trumpets PV as a replacement for our current mainstream/base load power supply. It is quite clearly nonsense.
If you look into the background of most of these renewable energy fanatics it is notable how few have an engineering background.Except for the experimenters , the supporters seem to be of the same ilk as
the UFO believers.The Greens , if they have any higher education at all, are mostly from the "Yarts".
The Labour Party members are similarly untechnical, but this does not keep them from pie-in-the sky promotions.
Like all the scientists that design them, all idiots I suppose. yawn
Last time I checked I was a chartered electrical engineer, who has built, nuclear, coal, wind and solar. I've done the math, I've designed the power plants, and I have decided that solar is the way forward.
Almost every engineer I know (except a few very old school die-hards) support renewables.
You have built nuclear power stations? I very much doubt it.
You may "have done the math" but you don't produce it when asked. That *you* have decided that "solar is the way forward" is hardly proof.
And almost everybody in the world "supports renewables", but that doesn't mean that they agree with any assertions you have made concerning the costs of solar energy.
You are one step away from being in breech of the Trade Practices Act. That one step is that you never ascribe the savings to a particular product; as long as you never mention a specific product name as meeting these claims you are within the law. So you can lie all you like. As you have obviously worked out for yourself.
I find it sad and depressing that someone who presumably got into this for the best of motives is now reduced to telling some pretty obvious porkies to drum up business. Ends justify the means, I guess.
Wow, you really are a deeply suspicious and angry fella.
I have physically built control systems inside real nuclear power stations. Is that so hard to believe? Yes I have actually designed and physically wired up their control systems with my own bare hands deep inside the reactor building. That's generally the kind of work that real engineers get paid to do. But hey – you don't have to believe me.
Your misspelt ramblings are getting tiring. The calculator here, which is available for everyone to use:
http://www.solarquotes.com.au/calc3/indexsavings.php
shows real, dollar savings for any good quality solar system. I really can't be any more transparent than that.
The costs of solar systems in Oz are here:
http://www.solarquotes.com.au/how-much-do-solar-panels-cost.html
If you doubt these costs, please feel free to get 3 quotes through this site.
I have a 6kW Tindo solar system (solar bridge microinverters) on my roof and the LCOE is 12.8c per kWh. It is guaranteed for 25 years with <1% degradation per year. You are welcome to come and inspect it. Alternatively, just look on 1 in 10 roofs in Australia if you want to see real solar systems, in the real world paying for themselves. Yes they do exist - get out of your cave and you'll see them.
The calculator you provide shows savings only if you get a healthy feed-in tariff. This is only apparent if you click "advanced options". Set the amount sold back sold back to the electricity company as zero, and the cost of the electricity doubles and exceeds retail. Very deceptive.
But your sales pitch is that solar is economic even in the absence of feed-in tariffs. Your own calculator shows this is false. It produces a figure of about 34c per kWh, more than double what you claim as the cost of solar power. This 100% difference between what you claim in the text and what your own calculator shows is not explained. Imagine a car company that quoted a certain fuel efficiency in their advertisements which was double what their own calculator showed as possible.
I don't just doubt the costs of solar; I doubt the benefits. How many of these companies will give me a guarantee of total kWh per year? How many actually believe in their product enough to install it on my roof and charge me for the electricity I use? None.
I can't see 1 in 10 roofs in Australia "in the real world paying for themselves". I can't see dollars being produced and consumed from the street. I can see lots of comments here and elsewhere from people who have installed it, that domestic solar is not cost effective in the absence of feed-in tariff. You have never produced a worked example showing solar is a good investment in the absence of feed-in tariff.
You try and present yourself as a scientific/engineering person. But you blogs are pure sales and marketing. Instead of worked examples we get shonky calculators. Instead of analysis which is based on measured energy outputs of installed and commercially available domestic solar systems, we get unexplained infographics from other companies which also appear to be based entirely on wishful thinking.
If you were directly selling some system and claimed the benefits that you do (eg electricity generation at 16 cents per kWh) you would be subject to the Trade Practices Act. Because you cannot demonstrate the savings to be true, it would be deceptive and misleading advertising. If the product didn't produce electricity for 16c per kWh, consumers would be entitled to a refund of purchase price. But as you don't claim any specific system will produce electricity at this cost, you avoid the Trade Practices Act.
Doesn't it worry you that your advertisements are highly misleading? That you cannot sustain them with a single example of anybody who has ever installed a domestic PV system which produces electricity for 16c per kWh?
You may once have been an engineer. Now you are a sales guy trying to drum up support for a product you are involved with. To do this you lie about what the product can do (eg this 16c per kWh fiction). If you want to be considered as an engineer, start telling the truth.
Please provide a screenshot of the calculator giving an LCOE of 34c per kWh.
(Also to repeat myself a third time "THE SOLAR SYSTEM SITTING ON MY ROOF IS AN EXAMPLE OF AN LCOE BELOW GRID COST". You are welcome to look at the online monitoring to see the kWhs, and see how much I paid for it ($15,000) and do the maths yourself. It is not a complicated sum.)
Unfortunately, I can't show screen shots in a text newsgroup.
But here you go again, claiming that you have a system which is cost effective, telling me that I am welcome to inspect it and do the math for myself, but alas you don't actually provide the numbers from which the "math" can be calculated. In fact you never do. You love your shonky calculators and infographics, but never want to actually provide real production numbers so we can check for ourselves.
So, have you ever been involved with a domestic solar system which generated energy for 16c per kWh as you claim?
If so, you should give us the numbers so we can all see the savings. How much did it cost to buy and install, how much is the manufacturer's annual maintenance, what energy does it produce by time of day per day on average (so we can compare with typical tarrifs), what degradation should we expect, and what is likely to need replacement over the lifetime of the system, when and at what cost?
If not, and you have never been involved in a domestic PV system that generated electricity for 16c per kWh as you claim, then frankly you shouldn't make that claim. It is lying.
So, still looking for a real life example of a domestic solar user producing electricity at a net cost of 16c per kWh. Are you going to back up your claims with an example of a single person who has ever achieved these savings, or are you going to keep making claims you can't substantiate? Engineer or shonky salesman?
Yawn. This is the last time I am going to repeat myself:
How much did it cost to buy and install: $15,000 (similar setups now cost under $12,000)
How much is the manufacturer's annual maintenance: $0 (apart from feeding the communist pixies making the electricity!)
What energy does it produce by time of day per day on average: 28kWh per day, typical solar generation profile as per this graph:
http://www.solarquotes.com.au/do-i-get-paid-for-my-solar-energy.html
I will post the URL of the live monitoring system with minute-by-minute data soon.
What degradation should we expect? 0.5% per year
What is likely to need replacement over the lifetime of the system? Nothing. If it does – I have a manufacturer's 25 year full replacement warranty. So cost to me will be zero.
BTW: Google "Sungevity" if you want to lease a system in Australia with guaranteed kWh per year output and pay the installer for the electricity generated at less than current retail cost per kWh. All maintenance included.
Gee, another "typical" energy graph. Not real numbers.
And the graph shows that about half the power is exported to the grid. It is your claim that solar is cost-effective even in the absence of a feed-in tariff. Unfortunately your "typical" graph is more of a cartoon than a graph; it does not actually even specify what proportion of the energy is used and what has to be on-sold through a feed-in tariff.
Why are you so unwilling to produce figures which can actually be used to verify your claim that domestic solar is cheaper than grid? Why not simply produce an actual real-life home configuration, document its cost, document the energy output by day and the profile of the household use of electricity usage so we can work out how much of this energy is used by the house and hence the cost of each unit of energy?
It won't be 16 cents per kWh as you claim. I do look forward to some calculation from you which produces some actual figure for the cost of solar energy. So far, you haven't provided a single calculation showing any costs at all for domestic solar on kWh basis (which is how I buy grid energy).
If you claim that domestic solar has a production cost of 16 cents per kWh, and that it is cheaper than grid power even without a feed-in tariff, then you should be able to substantiate these claims. You haven't because you can't; its nonsense. You haven't even tried.
Ohh, and you were wrong about Sungevity. They will not install a solar system on my roof and allow me to just pay for the electricity I use at a fixed rate. Because they could never make money that way; the cost of production would exceed the retail cost of electricity and nobody would buy it. Of course, if solar actually was cheaper than grid power this would be a great business model. But all solar companies are very, very careful to transfer all financial risk to the purchaser. They know that the systems are not cost effective replacements for grid power, so they won't sell you the electricity that their panels produce for less than grid rates, or at any fixed rate. They will only sell you the panels so you are taking the financial risk. If solar companies know enough to not guarantee their energy is cheaper than grid by selling it to you for less than grid, I suggest you should assume its not until demonstrated otherwise.
For your curve, the yellow bit is the solar power that you can directly use. It represents about 40% of the area under the blue line (total household power consumption). About half of the area under the yellow curve is shoulder usage (before 2:00 pm) and about half at peak rates.
I pay $1600 pa for electricity. According to your curve, my bill should go down by about 0.4 x $1600 = $640 pa.
The system according to you costs (if you bought it now) $12,000 pa. Cost of capital is about 8%, to buy this on a 25 year lease would cost $1,440 pa on normal rates. Add in a very modest 5% pa for maintenance (as you would hopefully be aware, most maintenance packages on hardware is 15% – 18% pa, even for equipment in controlled environments) and this works out at about $2,000 pa. Which is three times the cost of buying this energy off the grid. Indeed based on the average of shoulder and peak costs for grid power, the three times greater cost works out at about 70 cents per kWh. Which is a lot more than your claimed 16 cents per kWh.
Your own figures show the cost to be almost five times greater than you claim.
So where on earth did you get this ludicrous figure that domestic solar power works out at 16 cents per kWh (its many times that), and the ridiculous assertion that its cheaper than grid power (when on your figures it is at least three times as expensive)?
Maybe you should post the calculations which showed that it costs 16c per kWh? Or maybe somebody just invented this number? Or maybe the calculations are so obviously wrong that you don't think you can get away with posting them? One thing I am certain of is that you cannot and will not produce a reasonable analysis showing domestic solar works out at 16c per kWh, because pretty obviously the real figure is many times higher.
Bit sad when you have to lie to sell your services. I assume that you do this because you think it will save drowning polar bears, and the ends justify the means. Maybe you should go back into engineering, where you presumably didn't have to lie to make a living. Indeed, after Saturday we may have an economic rationalist government, and the raft of subsidies that prop up this inefficient industry (particularly MRET)will start to be rolled back and electrical energy prices may actually start to fall, and you might have to go back to building conventional power stations for a living. As I have pointed out in the past, only a fool makes a business decision based on the belief that government subsidies will last forever. They don't.
kimalice says
The whole argument is academic anyway as those who think they are saving the planet by putting solar panels on their roofs are only fooling themselves.
To be truly Solar one must bite the bullet and pay through the nose for batteries, store their output and use it at night instead of relying on dirty coal power to light, heat and entertain them when it is most needed, after the sun goes down.
Until that time it doesn't matter how many graphs you produce you are still reliant on mainstream power most of the time and the monetary bonus you get doesn't even compensate for the carbon released in the manufacture and installing of those or so delightful panels on your roofs. Talk about living in a fools world.
Oksanna Zoschenko (@OshZosh) says
Dear weterpebb, and anyone else who can bother replying. I am confused. I have read a bunch of stuff on solarquotes about how to get the latest whizzbang panels, – question is…do I need them? My bi-monthly electricity bill is horrendous..around $700 to $800 for 60 days. Five in the household, two fridges, aircon the usual nightmare. These bills are ruining me. Well, recently had a windfall. If I don't spend the money on a score of solar panels it will surely get spent on something else, and I'll still be stuck with the big bills. House empty most days, all working (so less usage during daylight hours). So, who is right, you weterpebb with your paltry annual electricity bill, or solarquotes? Help! (I am in Perth)
If your house is empty during the day, then solar is of very little direct use. It generates all of its energy during the middle of the day (when you are using almost no power) and zero in the evening when you actually need it.
It might be a worthwhile investment if you can sell your power back to the grid. To make sure this is a good investment, you will need two things. Firstly, the solar cell provider must guarantee that your panels will generate a certain amount of energy (in kWhs) over the course of the year. You also need a contract which guarantees your local electricity distributor will rebuy this power at an attractive rate over a long period of time (years).
Then you can work out whether the profit you make per kWh multiplied by the number of kWhs your solar supplier will guarantee your panels produce. If this income works out to exceed the capital and running costs, then it is a good financial idea.
I doubt very much the numbers will work out. The price paid per kWh by electricity companies for domestic solar electricity has crashed as government rebates have been wound back. It is quite possible that you may not be able to sell your excess electricity (basically all of it) at any price in the future; many electricity companies might consider this whole business to be more trouble than its worth and reduce the buyback to zero.
If you still live somewhere with a heavily subsidised electricity buyback, you could make money in the short term. But it is an incredibly risky investment in this form; all that has to happen is a government official to decide your scheme is too generous, wind it back to zero, and your expensive solar installation will be doing little more running your fridge during the day.
Caveat Emptor.
Barry Nielsen says
Hi Oskanna, I think you've missed the boat, but I suggest you go to a company to get your budget sorted before anything else. The very generous subsidies for solar (thanks, taxpayers) meant my 5kW system was bought and installed for $4,900 (amazingly, within 48 hours of ordering, it was producing power) and I get to feed excess power to the nice electricity company (who get re-imbursed by the government – thanks again taxpayers!) at a whopping 50c per kWh – and until 2028!! In summer my bill goes to zero and is halved in winter. Family of four, with AC, but we try to avoid using it. Just installed heat pump hot water including reduced cost installation ($700) for RECs, so expecting to reduce annual power consumption further. Switching to LED bulbs… and low power pool pump (more RECs…). The motivation has nothing to do with reducing emissions – which is negligible on a world stage. Australia could reach it's emissions targets overnight by halving agricultural exports. Like most easy solutions, the issue is noone wants the financial impacts. France got it right with nuclear – 20c/kWh and too much power, they have to export it, and a robust distribution network which is ripe for electric car introduction. In Aus we're spending untold billions on a new broadband network and still have electric wires strung along the streets on wooden poles – go figure.
Just Defiance says
Good comment from one who knows.
But don't mock yes, a pricey NBN, pls?
I assert that these types of "leftie" [right-of-centre left] infrastructure projects are subverted by right-of-right-of-centre right wing fanatics across these types of industries, those who have grown into their respective trades and professions from church schooling, so from an inherently self-centred, right wing indoctrination, almost all of the "sub-contractor" self-interested class.
The NBN if ever finished, is a, if not the best type of telecomms and internet infrastructure we could have, and, if there IS life after about 2020, will serve the whole polity very well – until the next "best invention", that-is.
It's key problem, is that the polies are not techies, nor engineers, at the levels we need to decide and ensure a smooth and fault-free construction. That doesn't make the project itself bad.
All the delays are quite deliberate subterfuge, and is the way things are now, with everyone fanatical for their own beliefs system and cult, so ready to do the subversion for their own mobstas.
Thanks Barry and weterpebb.
20 individual AC 250W of those South Australian panels each with microinverters produce 5000 watts (5kW) (or average around 22kW/hs per day? with North facing roof, some minor occlusion from the West) and will cost $13,000 after federal rebates to install.
(W.A.govt) Synergy's sad RESB buyback rate for residential is only just under 9 cents/kWh.
I use around 2900 units every 60 days or 2900 kW/hs.
Cost (charge) is around 23 cents per kW/h. Around $760 every two months.
That equals 48 kW/h per day. Up there with Al Gore.
As I said, have two fridges, and security cameras 24/7 but much of the use is at night.
I have no idea how to do the calculations properly but looking here and there on the web expect to save around $1250 off my annual bill, at a guess. My $760 bill will reduce almost $200 for two months period. Sound about right?
Bill before =$ 4560 p.a.
Bill after = $ 3438 p.a.
It will only take a mere eleven years, including State Govt setup costs, for the system to pay for itself 🙁
Question is, do you think my guestimates are overly optimistic? If they're about right, I am still going ahead to get quotes 🙂 What do you say, Finn?
No, I don't think your calculations are correct.
Solar electricity you use yourself "earns" you 23 cents per kWh through cost avoidance. Electricity you sell "earns" you 9 cents per kWh through the feed-in tarriff. So the percentage you can use and the percentage you have to sell makes a huge difference. And its not in your favour.
Your unit produces 5 kW peak. You house is unattended Mon to Fri during the day, when you are producing solar power, no way you will be using anything like 5 kW. So virtually all of your solar power during the week will have to be sold. Even on the weekend, your average daytime use will be far lower than 5 kW. If you have a pool, you can reprogram the solar heating and recirculation to occur during the day, which will productively consume some of your daytime power, but nothing like 22 kWh per day.
So you have to assume that the majority – 80% or more – of your solar energy will be sold at 9 cents per kWh, as you simply have no use for 5 kW in the middle of the day.
The figure of 22 kWh per day seems way too high for an average figure. I suspect this is the output on cloudless days. If this is what the solar company is telling you, get them to supply a figure for the energy produced each year, and get it in writing. This is the important number, and I suspect their figures for energy production are massively inflated by telling you daily production on sunny days instead of the average production across a year.
Even going with these figures, 22 kWh/day x 365 days/year x $0.09 per kWh
= $722 per annum
It costs you $13,000 after Federal rebates. Even if the system never cost you another cent – and you will be up for maintenance charges – and you got a 0% interest loan to pay for it, it would still take you 18 years to repay the capital cost.
Realistic figures for energy production would increase this payback period. Realistic assumptions about maintenance would increase this payback period. And nobody is handing out 0% loans.
On the figures you have given, and the usage profile you have provided (ie little use for power during the day), and at a feed-in tariff of $0.09 per kWh, this is a long, long way from being a good financial investment. Do it for other reasons if you wish, but be aware these other reasons are costing you a *lot* of money. You would be far better financially off sticking the $13,000 into a fixed term investment and continuing to use the grid for all your electricity.
I checked my figures on Finn's calculator, numbers crunched out the same as my guesstimate:- eleven years to pay back the $13,000, and save a couple-hundred each two-monthly bill. Also, I was surprised that the cost of the new mini-inverters on the South Oz-made AC panels was not much more (maybe $3,000 more) than the same 5kw setup with old style DC panels plus big inverter. However, I am extremely grateful for weterpebb's challenge to this modestly optimistic scenario, and will consider his words carefully before any purchase. Am now looking at our usage and ways to reduce it. Nevertheless I am concerned not to miss out, if there is any cut in federal solar installation subsidies by Abbott, and also Barnett's plan to privatize our WA generators after improving their saleability (read: improve bottom line by jacking up everyone's power bills). Thanks to all.
enno you muppet…strangley enough it can still be windy at night and waves still roll in and tides still change…oh…there is also this amazing thing called a battery…welcome to the 21st century mate…did you just unbury your head from the sand for one second this century?
Batteries? They are the thorn in the side of any stand-alone PV system owner, especially if you live in a cool/cold climate. And the article is talking about a "clean, solar, renewable energy future for our world" which presumably means PV replacing fossils on a large scale. Just how big will these battery banks be, and how enviro friendly? Or are we going to go down the inefficient road of having hundreds of thousands of stand-alone systems powering individual homes?
Even if PV cells were 100% efficient, battery/storage tech is the bottleneck and still needs to come a very long way, and as a stand-alone PV system user I wish it would hurry up and happen.
Does noone know that the snowy hydro scheme has 4000MW of ready made , rapidly dispatchable, and complimentary generation capacity . If this was used to cover those times when solar and wind power are inactive then far more cheap but intermittant solar and wind could be installed. In fact with a relatively small investment the snowy hydro scheme could be modified to provide pumped storage facilities.
And indeed we have many coal powered power stations that could be run at night. But that is the unfortunate thing about solar power – you have to build two power stations (solar+hydro, or solar+coal) to do one job – doubling the capital cost.
Indeed, the highest power consumption occurs from 6pm to 7pm each evening, when solar power is useless. Even with very significant use of solar, we still have to build sufficient power stations to cater for the 6pm peak (when solar doesn't work), so solar power does not reduce our need to build conventional power stations at all. We have to build two power stations to do one job.
Yes, we could use some form of battery (eg pumped storage as you suggest), but this is very expensive – both in capital and running costs. No, we can't use the Snowy scheme for this; the 4 GW available from the Snowy is already used to cater for peak use periods. If you want to rely on being able to use 4 GW from the Snowy to backup solar, you need to build in another 4 GW of generating capacity and the capability to pump water uphill during the day. This would be like building a second Snowy scheme.
The fact that solar only works during the day and peak consumption is in the evening means that solar is spectacularly poorly suited to provision of baseline loads. The economics of solar come nowhere near adding up.
Bruce Miller says
The hardest thing for a peon soaked in the "U.S. psychology" to understand is the notion of "renewable = perpetual" energy! For as long as your current, and very temporary, natural gas abundance flows, and long after it it all gone, the Solar, Wind, Wave, Hydro, Tidal, Geothermal, Biological, renewable, domestic systems will still be there, as the very backbone of your economy, and unlike nuclear by Uranium Enrichment, offer no hidden, humanocidal waste disposal expenses, no harmful leaks to clean up, no high and hidden decommissioning costs, no anti-terrorist security costs, lower initial installation costs. Even China's thrust towards Thorium LFTR technologies promise better than the American Nuclear Experience, is plutonium free, and cheaper, safer and easy to fuel. U.S. peons, caught in an 'economic energy trap', corporately controlled for the shareholder's benefit, not designed to build a strong nation, not designed to build a strong people, not designed for a safe and secure future for progeny, not designed to produce a strong infrastructure, not designed to produce or accommodate a well educated population, Strictly and legally limited to shareholder benefits. The "Post WWII German psychology", is very different. They rejoice when a car made from renewable power is sold, realizing the 100% profit in benefits to the general populace of Germany. They understand an austerity not yet suffered in the U.S.A. They see gains in an educated working population, They require for their very survival, well educated, hard working, frugal, people. They defend cleanliness and environmentally proper care of their "Father Land", they feel a certain responsibility for their own. Canadians have developed similar sentiments for their environment and 'Fellow Canadians". Americans seem weak in these areas, and more concerned with Capitalist and Corporatist, shareholder values? My Question: Is this the work of the Great Corporate American Propaganda Whore and her moanings, persuasions, illusions, on the American people? To maximize shareholder's stakes even at the expense of the peon's stake? In the new 'Corpocracy" that America has become? The reason why, in 1999, Thorium was rejected, even though proven safer, saner?
CRISP says
So researchers are "looking to develop…". " It could allow developers to…". We "could see solar panels that cost $1 per watt." Could. Might. Perhaps.
Why don't you write about this when it has actually happened, not the same pipe dreams they were writing about in the 70's.
In the real world, governments are forcing those without solar panels i.e. those on social welfare, renters, itinerants, the low-paid to subsidise the electricity bills of rich middle-class hypocrites. Utterly immoral.
Ali Cat says
I totally agree. I'm a low income renter, my energy bill is around $2,000 in arrears and growing despite paying $60/fn, more than 10% of my income.
No one seems interested in helping us become green, gov and landlord too busy feathering their nests and green washing the climate warnings written on the wall.
havasay says
So you've got a problem with the Government and the Corporate fossil fuel dinosaurs not with the green lobby – you need to vote accordingly
Mythbuster says
Sigh, and the source for your last statement is? Maybe you should look at the facts (the real "the real world") of where solar panels are being installed: http://www.energymatters.com.au/index.php?main_page=news_article&article_id=3392. Turns out "A broad range of communities have accessed solar under the RET scheme and the figures explode the myth that the RET is supporting metropolitan middle class welfare and is evidence of the RET's equitable effectiveness".
(itinerants?? you mean tenants?)
Also, the actual component on our electricity bills of how much we pay to subsidize people with solar panels is tiny (a few percentage points max). Check AEMC sources for that.
Ali,if you are really that keen to become greener you should do your own homework. There is lots of information available, even from government. What do you expect? That they come in every night and switch off your appliances and lights for you?
Why do people have to turn these issues into an "us vs them" battle? Stop whinging and start taking actions that will save you money.
Fungal says
@Ali Cat: It seems you have other issues like turning on aircon and heaters instead of opening a window (or turning on a fan) and putting on a jumper.
If you are paying more that ($60/fn ~ $120/month = $360 per quarter) $360 per quarterly bill then you need to look at turning off the second and third fridge also…. unless you are a hydroponic type of person and the business has not kicked off yet?
Seriously you are saying you pay more than what 3 adults living in a unit pay per quarter (over several years our highest was $320 and we used the drier and heater)? and the only income is less than $600 / fortnight? something does not add up. Maybe you need to provide more details before complaining about green policies.
It may pay to switch off everything and have a look at the meter to see if it is still spinning as you may have an earth leakage….
Chris Sherlock says
Actually, one of the problems might be her hot water system. I've found that most units without gas hot water have small, inefficient tanks in them that cost an absolute fortune to run.
Well I'm a landlord and a solar generator and frankly it's the same dumb schmucks that pushed for these stupid "green" policies that are now pissing and moaning because they can't afford to benefit from them.
Frank says
Ah but $1 per Watt is happening now, in fact wholesale prices are at about 50 cents per Watt, with system prices, that includes installation and all the hardware like the inverter at about $1.5 per Watt. Return on investment can be achieved in 3 years, and then free power from then on. That is the reality.
Your numbers on the cost per Watt are correct, but not the return on investment – at least in Victoria. As I am retired , I used our "smart meter" to record the hourly consumption through the day (in Jan this year with an aircon on sometimes in the afternoon), and compared that to the generated power estimate for a 1.5Kw North west facing system (provided by quotes i had requested). Given the 8 cent feed in tariff that now applies here in Vic, the payback period was between 12 and 15 years which is probably outside the life of the system – and certainly nothing like 3 years. probably much more effective to swap over my halogen downlights with LED ones as and when they need replacing?
I too went solar (I live in a block of units: yes it was much easier to get approval than I expected as most Strata managers and *MOST* installation companies can handle the paperwork and are happy to help) and found the bill drop by around 1/3 we were not big users but seeing a $300 a 1/4 bill drop to around $200 means the investment of around $2600 will be recovered in around 6.5 years… HOWEVER, we tend to use more power now, just during the day instead, so effectively saving even more and we are about to come to the anniversary of the install and although Mark Group were not the cheapest BUT they were one of the most professional I dealt with as the original company I was trying to work with suddenly became busy and could not fit me in as a unit would take longer to do than a single storey dwelling… ie the installers would do 2 houses compared to 1 unit.
If I had known it was so easy to get approval in a unit I would have done it when the 60c/kw was offered here in NSW and started making money, but alas 6.5 years is still a good ROI.
Of course, the only reason that you get a 6.5 year payback is that the electricity company is buying your excess electricity at a massive loss. They are required by law (the MRET scheme) to do this. The savings on your bill derive from the higher costs that other electricity consumers must pay to subsidise MRET. It simply wouldn't be cost effective without this mandated subsidy.
@weterpebb – close, but not quite… the excess is not at a loss, as they don't sell green energy at $0.077 per kwh (aka 7.7cents!). The lower cost is actually the energy used during the day, I do not know why people will try and put down solar with these types of arguments.
Either way if I did or did not have solar, they would still charge me the same amount per kwh, I now use around 2/3 of what I used to use from the grid… that is where the savings are ROI come in.
I get a little bit more back. Given a good quarter, its more like a $2000 rebate 🙂 🙂 🙂
Just to rub more salt into the wound, I'm looking at getting another 6 – 8 panel off-grid system to run the house so I can sell the whole output of the big system to the grid for 52c per unit.
Anyone who lacked the foresight to get a solar power system when the time was right need not blame me, I merely accepted a business proposition that entailed mutual obligations & which was made freely available to any who chose to accept.
Well, that is one of my points, if I had known it was so easy to put on the roof of the units then I would have done it when NSW was offering 60c/kwh + the normal feed in tariff, but alas I found out after the fact, but still got the green rebate off the price selling the credits to an energy provider.
I'd originally intended getting a 5kw system but after doing the numbers it appeared 10kw would pay for itself inside 4 years (better payback than smaller system due to more excess to attract 52c FiT). Anything more than 10kw would have needed 3 phase power but then there was no more room on the north-facing 22 degree roof. The off-grid panels I'm contemplating will need to go on the 10 degree veranda & get jacked up to the optimal 22 degree angle. That gives me another 40 odd square metres, heaps to run a house that only costs me about $150 per quarter in electricity. Idea is that the $150 I'm using would be worth $300 to AGL & $1200 per year will go a long way to paying for a decent off-grid system. Doesn't really need to cover all costs, I'll do it just to spite the parasites.
MarkB says
I think payback calculations by weterpebb are not taking into account of income tax, inflation and the fixed or floating FIT rate over the lifespan of the unit when commenting on the commercial viability of a homeowner investing in a PV system.
For example, if you invested the capital cost, say $10k, in a fixed term deposit then your current nett after tax and after inflation return can be as little as $150 p.a (assuming highest personal tax rate) to off set a grid only consumption bill. Not even an eighth of some householder's bills.
Conversely, as no income tax is paid on the reduction in your electricity bill, then (assuming the highest personal tax rate) nearly half of what is saved can be considered tax free income as the after tax dollars that would have paid that portion of the bill can now be spent on something else. It's like the benefits of salary sacrifice without having to enter into a novated lease.
With the effect of inflation, If you are on a long-term contracted fixed FIT rate, then over time the increasing price of electricity will decrease the difference between your FIT and the retail Kw/h rate. This means that the best economic returns are are the beginning of the contracted period.
Conversely, with a non – fixed 'going market' rate for exported electricity, inflation means the rate paid will go up and so the system will earn more in the out years Thus more rapidly paying itself off towards the end of its economic life. Of course the payback calculations have to take into account that any borrowings are outstanding for longer and therefore will cost more in interest. But this is somewhat offset by having your future bills reduced in future dollars for the own consumption component. Eg a system bought today saves around 25c KW/h for power not bought from the grid. In say 2024, the system could be saving you 50c KW/h for power not bought. Yet at that time the principle and interest repayment is the same $ amount as in 2014 thus reducing any out of pocket difference between the two amounts in the future.
As you can see, there are more factors at play than just the system cost and it's ROI.
The real problem, from a strict investment perspective for people with PV systems, is that with an average time between selling and moving house at 7 years, only a very few will own their system long enough to actually get any ROI. Real Estate agents tell me that, like pools, a PV system may make one house more desirable over another for the right buyer but it won't translate into a higher sale price for the vendor. Thus the vendor walks away from the capital investment and the buyer gets the benefit of reduced electricity bills.
Joseph B says
Another example of tall poppy syndrome that holds Australia back. The poor do not subsidise the rich and middle class who pay high taxes to support your Centrelink benefits.
Solar power is good for the environment, good for Australia, and means fewer coal powered generators have to be built. Get a job and save your money, solar power is not that expensive and will pay itself back in a few years.
mary wiseman says
HIGH TAXES? joke , "your" centerlink benefits , ? solar we agree on ,
Priit says
I agree with the facts that Solar Power is good for everyone. Currently the problem is that people renting can not get Solar as they do not own the place and may not be able to stay in the same place long enough even if the landlord agreed to allow putting the solar in if the tenant pays for it.
The solution for this situation could be that the power companies who already own solar farms could sell people slots at their solar farm (expand their farms by allowing individuals to purchase extra solar panels, expand their inverters) meter those slots separately and deduct the power collected by those purchased slots from the individuals power bills. This way if a person moved, their power bills would still get the benefit from the solar panels.
Nick says
You can already buy "green" electricity from power companies. They "guarantee" that it comes from renewable sources. (Not sure how they sort clean green electrons from dirty black coal ones inside the copper wires, but I'm sure they have a clever way to do it.
Anyway, even Renters can do this.
trouble is, it costs more than normal electricity…
Fred Bloggs says
My neighbour pays a couple of cents more per kWh for 'green energy'.My power comes off the same line. I don't pay extra, but still get the 'green power'. How does my neighbour benefit?
If logic like that is typical of Australians, its no wonder we are going down the gurgler.
This "green" electricity is simply an accounting trick. You do not get or use any more renewable energy than the person living next door.
The amount of renewable energy available in the network is a tiny bit more than the minimum required by MRET. As renewable companies cannot charge any more for this additional energy than market price for coal energy (maybe 5c per kWh), renewables companies sell it for much the same cost as electricity from coal. As this small bit extra energy is not required to meet MRET, they can lable it as renewable power and sell it at a slight premium to people foolish enough to buy it.
It is the proper function of the serfs and slaves to suffer in the service of their superiors
to achieve great things. The Pyramids and countless other great works of civilization since would never have been built without the iron heel of the ruling classes upon the necks of the underclass whingers and would-be welfare recipients.
My Other Head says
Ken, to extend your very fine argument, use could be made of the prison population to generate electrical power by pedalling on a stationary bike coupled to a generator.
Yeah, and the slaves revolted, took off across the Red Sea, proliferated to maximum population, spread west and north, then everywhere else, plundering everything along the way, developed the MAXIMUM CONSUMPTION zionist culture, whence they had to program up an Einstein and Oppenheimer to split atoms and now sunlight, to cater for the over-consuming WRONG WAY-ists of us, who cannot be happy with a nice river, bark canoe, a fishing line, or net, spear and boomerang [still one of the most brilliant weapons ever "divined"] made of natural materials, to knock down a 'roo, and the sharing of resources in the perennial extended families, model of True Culture.
All mentioned energy producing concepts, are but band-aids over the terminally-errant whiteguy culture.
There is no energy-efficient means, other than dropping all our crazy insatiable desires and, going semi-naked, on foot, and return to the ways of "Eden", by Communal, "Luddite" if-you-like, Extended Family Communalism, finding our pleasures with nature and relationships other than technological.
hedeho.
Getting used to it now, makes it easier for the future generations who will have no alternative.
As all the arguments and counter-arguments in these many many comments attest to, in the end, no modern options add-up, or save anything worth saving, long term.
But I'm all for employing whichever "labor-saving" devices we can afford, personally and governmentally, to get through the times now.
It's just that we really are better fools if we try our best to not destroy everything getting and using them.
By the time the present generation of Solar panels are due for decommissioning, the energy used to recycle etc should be from clean renewables. The production of panels these days should also be from same.
Whether it is or not, particularly the cheaper panels from China, is another thing.
The term nark is somewhat pejorative but if it means somebody who objects to something without sufficient real knowledge of all the details around it, or nitpicks negative or magnifies missed details in order to criticise rather than constructively comment, so be it.
The antisolar lobby try so hard to undermine clean energy efforts, we have to wonder who/which of them are plain "useful idiots" and who are paid shills of dirty carbon (look up Koch brothers)
But "nark" doesn't mean "somebody who objects to something without sufficient real knowledge of all the details around it, or nitpicks negative or magnifies missed details in order to criticise rather than constructively comment". It means nothing like that.
People aren't trying to "undermine clean energy efforts"; they are pointing out solar energy is very, very far from being a viable alternative for base load power, and is unlikely to ever become one. It is similar in this respect to nuclear fusion based power stations; great idea, but not economically viable.
Indeed, you will find many people (including me) who believe that solar power is a technological dead-end for baseload generation but are very enthusiastic supporters of other clean energy sources, particularly hydro power. That somebody is critical of solar power does not mean they are undermining or against clean energy; it just means that they have done the sums and realised that solar power is never going to cut it for the grid.
To try and make the argument that anybody who does not believe solar power is viable must therefore be against clean energy is patently wrong. I don't believe solar power to be worthwhile for grid generation but I am a big supporter of clean energy. To suggest people criticise the economics of solar because they are being bribed to say so is ludicrous. I thing solar is a dead-end for grid generation, but I am not directly or indirectly paid by fossil fuel companies. Your argument is patently false.
'That somebody is critical of solar power does not mean they are undermining or against clean energy; it just means that they have done the sums and realised that solar power is never going to cut it for the grid'. Never? Thats an extremely conservative statement from someone claiming to be broad-minded when it comes to renewable energy production, and seems to bely the claim of an un bias stance. Surely experts in the field are the most qualified to make such definitive statements, and even then should be
treated with reasonable skepticism?
Fair enough. "Never" is too strong a word, and "solar power" encompasses a lot of technologies that haven't even been thought of. I was speaking colloquially, and using a colloquial expression.
I could quite believe that in 20 years time we will be using oil extracted from bio-engineered algae pumped through plastic pipes on large energy farms. You could argue that this is "solar power".
Andrew Richards says
The thing is that when people say "solar" they invariably mean photo-voltaic energy collection and maybe a tiny bit of thermal, all from a terrestrial collection point. The fact is that if you were to build a large array in the middle of the desert, you could maybe look at powering the entire country that way, but even forgetting about issues with transmission losses, you're still removing all redundancy from the system and you're one blackout away from crippling the entire country. Either ay it's far from the way of the future in terms of the wider grid.
In fact what we need to start doing is associating solar with nuclear. Such a paradigm shift would mean not only changing just what energy we harness from the sun, but where we harness it from. Such a move would mean orbital energy collectors and terrestrial receivers – with a wide variety of energy cllectors, ranging from thermal, to optical, to electromagnetic.
Such a move would have interesting implications and if any type of solar power application has merit in terms of large scale power generation, it would be that approach.
Just noticed the date on this article.
And the second to last paragraph surely only applies to their proposed stop-gap solution.
Darren says
Solar panels that cost $1 per watt, but are sold on to Australians for significantly more than that I bet…
Only because we have 'sold out' with manufacturing which means R&D also gets off-shored as the CEO of Ford US rightly pointed out with the US economy.
We need to push to get manufacturing back here… how about charging a 'carbon tax' for all imports to counteract the carbon used to manufacture the item overseas? Maybe that would level the playing field… but it needs to take into consideration the OH&S costs they save on in developing countries as well, this would make it easier, even with a strong dollar, to at least be self sufficient.
Vote for Big Clive in September, he's got a few quite well thought out plans for bringing business back to OZ, in fact he might well bankroll halfway intelligent ideas. No point asking the RAbbott for business assistance unless you are a multinational.
I don't think that the Pile of Blubber would have any ideas about saving the planet unless he was the number one recipient of any advantages thus generated
Unfortunately there are far too many devoted supporters of Red Headed Witches & Wacky Wabbots in this country.. Is it any wonder we are in deep diabolicals !!
Fred Smith says
RobbieJ enno and CRISP have it right.
Don't get me wrong, it is great to see R&D into potential improved efficiencies of PV solar technology, but this whole article comes across as nothing more than reinterating the clickbait headline.
PV solar has its place, but overall from a grid stability and general consumer perspective, it is not in the grid connected arena. CRISP summed up the second point, as this will still not be economically viable without being subsidised by government/taxpayer.
As for grid stability, there are serious issues with a high percentage of grid connected PV solar in a given area and the base load generation required to cover this when something out of the ordinary happens, such as when a cloud goes over. This only becomes noticable once you get over 10% generation as PV solar. Typically the base load generation cannot increase output fast enough to pick up the slack and brownouts occur.
Solar has its place in stand alone and pumping applications, however, for grid connected situations (without storage) it is more trouble than it is worth once it becomes common.
If you are looking for a clean, safe, environmentally friendly source of power generation for the future look no further than nuclear power – specifically Thorium based reactors that cannot melt down.
I was just going to leap in and say Thorium nuclear, but you bet me too it.
Very interesting comments about grid–tie-in solar and brownouts. I did not know that.
Unfortunately the 'brownouts' assume everyone is home using 1.5kwh (or more for larger units) of power and all homes in the area are covered by the dense cloud cover, it is like saying evolution is true as it just has to happen once… there are brownouts already without solar in some areas so what is the difference?
Power suppliers are the ones responsible for monitoring the loads and they too have access to weather forecasts… so I can not see where there is an issue, unless it is privatised and they start cost cutting to make more profits for bonuses and dividends… whoops… forgot that was on the card as the NSW government wanted to push through the NW rail link at any cost….
frank…lookup DYESOL….works under cloud cover…wow…progress hey…now we just need a product called Ceramic Fuel Cells for home micro generation using natural gas at 60% improved efficiency compared to using large power stations to generate…and maybe chuck in your own small personal windmill and hey presto…
stop making excuses use whats available the market will push prices down and efficiency up if we can somehow not let the manufacture and development become monopolized. we have solar and dont have bills except for the installation costs and admin. the sooner we can get ourselves off grid the better and supporting good changes creates further good changes all the cynics need to get a life
Tjilpi says
To me, this is an entirely new use of the word Nark. I read the entire article thoroughly, wondering why a word used as a derogatory term for a police informer, fink or spy was used in this context, and wondering how it came to be connected to critics of solar power. I am still wondering …
My parents (born 1920's rural Victoria) used to use the word nark in the same way as the author of this article. I think a word like 'naysayer' would be better. Same meaning but more mainstream English.
@jeff. Thanks for that. I agree 'naysayer' would have stopped me looking for some connection to a snitch, fink, grass, spy or dog. Of course there is also the word "narky" as in "Don't get narky with me young lady" meaning upset or moody, and the slight hint of a possible reference to a narcotic addiction. I'll have to admit it: As far as the use of Nark goes in this context, I'm a Naysayer 🙂
Tom Anderson says
For context, this is a purely Aussie slang term:
4. nark. noun– Australian term — one who complains and spoils other people's enjoyment http://www.urbandictionary.com/define.php?term=nark
Julian Clark (@Mostlegendary) says
It must be specific to a region within Australia… I've never heard it while living in WA & QLD.
I have heard 'narky', but never nark.
PiDstr says
Ditto for Victoria.
Narky for someone being snide,.. Sure.
But 'nark', that's a police informant.
I read the article thinking the journo didn't know what the work usually means.
Betting it's a Sydney-Centric thing, like a lot of the slang that you see reported as 'colourful Aussie colloquialisms' in international press.
Isn't it "narc"? As in, derived from the word narcotics?
Or am I nitpicking?
Shelberight says
Thorium is the safer nuclear option.
Australia has estimated 30% of worlds thorium.
Thorium repeating myself.
Can you provide any links to mainstream policy discussion about Thorium reactors. I hear about them a lot in blog comment threads but i have never heard about them from anybody who, you know, counts.
Where are these utopian power generators being installed?
I hope I don't sound like a "nark" (ha ha) I would love to hear news of a sustainable practical power source.
mills says
"generate as much as twice the power as conventional solar cells"
"convert over 20 percent of the energy in sunlight into electricity (compared with about 15 percent for most solar cells now) "
I know I am not a math whizz, but anyone else see this?
Hi mills,
Good spot! I've edited the post to include their long term goal:
"[20%] as a mid term goal, and a long term goal of efficiencies over 30%"
Whilst I can't wait for Solar becoming more prominent (Japanese investments in space based solar is pretty exciting), the tone of this article is nothing short of juvenile. In fact it's almost counterproductive …
I'm confused, you blame the complaints of narks on the progress of solar technology:
"The more the narks whine about what they see as the limited capacity of solar, the more breakthroughs in technology occur"
Surely this cause and effect you've identified is a good thing and you should encourage narks to step up the complaining?
Logic Bot says
That is a loose use of the word 'prove'.
The cleanser says
Since 1980 when solar panels appeared in bulk on the market in NZ , I've been waiting for such improvement and I'm certainly not a nark ,all rather weird when there was an abundance of hydro power that was cheaper anyway.My green party believed the dams altered the climate and could burst, but I enjoyed cleaning my gutters,windows and car with boiling hot water anyway.
I love the derogatory comment. I have a small holiday shack on off grid solar. I am a solar nark because I cannot afford to pay for the full system I require. I am a nark because I resent taxpayers money subsidising systems for those that can afford it. I am a nark because I resent people like the article's author's condescending attitude to the not so well off like me. When solar gets cheaper, a lot cheaper such that the subsidies stop, then I will stop being a nark.
Myles says
The 36 Megawatts used to process layers of sand and charcoal over 3 days to make basic Silicon glass will never be recovered in the life of a solar cell. Of course further refining is necessary using more energy. The protective glass is also energy hungry to produce, much the same for the aluminium for the frames. Alumina is heated by megawatts to melt and then electricity is passed through electrodes to extract the aluminium ..
A solar cell has no moving parts, and aside from exposure to the elements, shoddy (insecure) installation or large airborne debris damaging it…
My question is, how does one determne the "life of the cell"?
If, as I suspect, the life of each cell is indefinite, one could see the energy required to produce it as an investment. Of course, that invested energy may well have been "green" in nature but I concede this is unlikely.
You determine the life of a cell by measuring the rate at which its efficiency drops over time. All solar cells degrade in this manner, as the constant exposure to sunlight causes chemical changes in the material. Just like paint fades over time.
Your suspicion is incorrect. The life of each cell is not indefinite. They age, and get less efficient. Eventually they become useless. Different manufacturers provide estimates of how quickly their cells will degrade over time. You can look it up.
Thanks for the concise explanation.
DannyDix says
Reading some of the posts, I now understand that there are increasing balance issues related to any rising percentage of solar input to the grid. As solar input becomes more substantial, juggling the somewhat random solar injection is difficult given the lag in ramping up the base load supply.
I was wondering if an over-supply of power could be used to store energy to be converted to current at high demand periods later in the day?
Please don't crucify me for making a suggestion. I'm no engineer, just a dreamer, and besides, its a while since I did a pee.
Here's my idea for storing energy. Create a very large circular pool with a low-drag high gloss interior. Minute air injector holes cover the interior of the perimeter vertical wall to introduce a fine foam to reduce skin friction. At several points around the vertical wall. (At different depths) tunnels or pipe inlets run away from the wall at an angle. These pipes contain impellers attached to large pump/generators. The other end of these pipes are re introduced to the pool at a corresponding angle. The pool is filled with water. Excess electrical energy from the grid is fed to the pumps which then serve to rotate the water in the storage pool by injecting water at pressure through multiple angled jets around the perimeter. On site solar arrays could maintain or boost input to power the pumps. Over a period the body of water is moving briskly and the water level around the perimeter wall is higher than that at the centre. When power is required in the grid, the return injectors are closed, and the exhaust water from the pumps is redirected under the whirlpool through pipes to the centre of the pool and re introduced through the floor into the shallows. Power to the pumps is shut down and the impellers in the pipes now power generators. Deflector panels are opened into the water flow at the tunnel entrances to increase flow to the impellers. Fine foam injected through the millions of fine holes in the outer perimeter wall reduce skin friction, maximising the vortex action. Water exiting the impellers is drawn back to the low pressure area in the centre, reducing back pressure on the rear of the impeller blades. As the main body of water finally slows, larger blades could be lowered into the water from above the pool to harness the stored energy, almost to a stop in water flow. This may provide a coal fired power station some breathing time to ramp up when caught short on input. Anyway, I need to go take that pee.
What's wrong with a mechanical flywheel?
The solution you are looking for is already proven in industrial scale use.
Solar Thermal plans (as in Spain, USA) use hot liquid salt (heated to ~600deg by concentrated solar) to store energy in a massive thermally insulated reservoir. Heat is drawn from this store to drive traditional steam turbines.
This has a big advantage over burning coal, as the draw from the heat source can be adjusted very quickly, whereas coal-fired boilers tend to run at one rate, and can only be slowly adjusted, becoming less efficient in the process. The solution the industry uses presently is to flog electricity cheap at night to encourage use!!
The whole concept of baseload power goes away. We have FREE energy from the SUN, cheap and massive storage of energy, on demand energy availability, supplementing other variable sources such as wind and wave power. Combined, these power sources can provide power as reliably as coal-fired power, without all the wastage and CO2 involved with coal.
Check out the fully engineered, peer reviewed plan at BZE.org.au
I don't understand kW's, nanotechnology, yada, yada.
I DO understand that my current coal-fired electricity provider is charging me up to 3x what they're buying electricity for, and alternative suppliers are all about the same.
Technology to cut these b….ds out, bring it on!
duncano says
I think you're all missing the point. The current solar cells are useless and doubling their capacity will only make them slightly more effective, but, still useless. It's good to see they're trying though.
I think perhaps you are concerned about solar cell efficiency, being only around 15% – 20%.
But efficiency is meaningless when the input (Solar radiation) is FREE.
The real measure is the $ investment per megawatt-hours of production over the lifetime of the system.
Low efficiency units can be winners if they don't cost much. Such as coating surfaces that are needed anyway, such as roofs and windows and walls.
What a rubbish article. It was really just a veiled attempt to introduce a new derogatory term. This is the standard tactic of the Maoists though. They cannot win a n argument with facts or logic so resort to name calling.
Typical climate denier
Peter Burgess says
I have been looking for someone else to raise this question. When one uses solar power, the planet stays the same. When one uses fossil fuel, the planet has less resources. A fossil fuel company calculates its profits by reference to price and cost … but the cost does not include the depletion of the planet's stock, just the amortization of the money costs incurred. With thinking like this, fossil fuels are a whole lot more expensive, and solar becomes the better buy without the distortion of subsidies!
The proce of fossil fuels is set by a world-wide market based (in part) on the costs of finding and producing new resources, from a finite (but large) base. The cost of depletion is already built-in.
BTW there is hundreds of years supply of coal, so the price won't rise in a hurry because of depletion. There may be other reasons to use "price signals" to reduce coal consumption.
Oil and gas – perhaps 100 years supply but everything has been thrown open by shale gas and shale oil technology.
The real costs of fossil fuel need to include the cost to the commons of dumping the CO2 into our atmosphere, and the subsequent damage through Climate Change.. If these real costs, "externalities", were charged properly to dirty fuel industries, they would be out of business in a very short space of time. And how about withdrawing the subsidies governments still give to fossil fuel industries all over the world.
No good having 100's of years of coal, when solid calculations show that we cannot afford to burn more than 20% of fossil fuel reserves!
Rob Dunne says
a "nark" is a police informer. It is derived from the Romani word "nak" meaning "nose", an informer being a person who is too nosy about things that don't concern them. It has shifted meaning in America where it is used to mean a DEA agent as in "Norbert the Nark". Your usage is just confusing.
Nark says
So, these new solar panels… They work at night time?
Alex_D says
Yes they do.
But only if you BELIEVE they do.
Billnix says
Solar power can be generated 24/7 because the sun always shines on some part of planet Earth. The problem is that to make solar power 24/7 feasible without the need for back up fossil fuel or nuclear power, a transcontinental grid distribution system joining all the globe would be needed. This is unlikely to ever occur because of political, technical and economic factors. The technology of transmitting large amounts of power over long distances still poses a major hurdle so remote sites where renewable energy could be generated by example using hydro power are in many cases not utilized.
Solar Thermal, with storage, is a proven technology already producing 24hr energy on an industrial scale, in Spain and USA. No need to globally connect, just store the energy, with liquid salt stored as thermal eneergy being the preferred choice, but better batteries are also coming along.
Quicker to build, and economically competitive with coal over the total life of a project. Producing more jobs too!
Bigpfella says
You can make solar cells as efficient as you like but until you can use the power when the sun isn't shining you don't have a viable technology. I live off grid and recently replaced my solar array for less than $2K (bought the cells from a Chinese supplier and soldered them together myself). The commercial panels I started with lasted only 12 years and though guaranteed for 25 neither the distributor or manufacturer are still in business. To replace my Lead/ Acid batteries with the more environmentally sound and much longer lasting Nickle/ Iron batteries will cost more than $10k. That, though is considerably cheaper than the 120K+ quote for connection to the coal fired grid. Original and now backup power is an Indian built 22HP Lister diesel which runs on filtered sump oil and 10% diesel or kerosene driving a US surplus Lincoln welder alternator. Flat out at 1000rpm it uses around 3 litres an hour and it is very quiet. So quiet that it would probably be viable in suburbia and we don't have any transmission losses.
Personally I don't give a rats whether the 'experts' are in favour of PV power or otherwise, I'll never need to concern myself about electricity company price gouging and thats more than sufficient reason for me to have a BIG system on my roof. In fact I'm on another non-grid-connect system on which to run the house so I can sell ALL the power generated by the big system. Anyone content to chuck money at the Newman / Seeney / Nicholls dictatorship, Origin, AGL, etc is welcome to do so. Even if some bright spark beancounter trots out figures 'proving' solar power is financially unviable, its still well worthwhile to spite the bloodsucking parasites. .
What's a Nark says
Where is everyone getting those cool little piccies from? I'm very new to this argument, but its very informative! So far I've learned what a nark is, Goodwin's Law, Greenland's heating effects and a whole load of not so useful information. Keep it up! 🙂
Mr Bruce says
MagLev Conical Solar Generators …. I suggest checking them out. Mr Bruce
Philosopher King Socrates III says
Interesting scientific development.
Steph Graham says
Interesting article but if you want to be a journalist you at least need to know where apostrophes go. "Nark's worst nightmare" (ie possessive: worst nightmare belonging to the nark; "its nanowire improved silicon cells" (ie a personal pronoun does not take a possessive apostrophe). It's not rocket surgery.
But is it rocket science?
Lowie says
The only bloodsucking parasites around here are those leaches that were able to take advantage of the commie/green labor turds in the previous government who created a system where low income earners (I am not talking about unemployed) pay for the power systems of the bloodsuckers. Those that generate excess power and sell it to the power companies should get the wholesale price, no more. Those that are growing fat on the low income earners are filthy bloodsucking leeches, full stop. Rot in hell.
Firstly, you've been sucked in by the lies of various bloodsucking parasite politicians, even according to the stacked Competition Authority, PV power only contributes a few percentage points to power prices & without all those private rooftop systems, the state would be up for megadollars for new power stations. Imagine how much MORE they would cost !!
Secondly, people who purchased PV systems made a commercial decision that entailed a mutually binding contract. Nobody got their system for free, in fact mine cost me over $30,000 in addition to the $11,000 odd federal subsidy
Thirdly, the REAL cause of power price escalation (ueensland) is the billion per annum the gubmunt rips out of Energex / Ergon plus the four billion squandered on Origin / AGL / etc faccats, shareholder dividends & operating profits. Thats five billion extra because of privatization, or average $2500 per electricity connection on Queensland.
Spoken by a true them-and-us unionist.
If you are sufficiently indoctrinated to believe even one word expelled from General Disaster than I pity you. remember we are talking about the same bottom-feeding grub who masterminded the tunnel disasters, who ignored conflicting evidence from his own tame Competition Authority showing clearly that PV owners have stuff-all impact on retail electricity price, who invented the gold plated poles & wires porkie after he'd already sacked most of the electricity workers, and who blamed the 10% carbon tax for 50% electricity rise. The ONLY thing at which the despicable little worm excels is divide and conquer, ie pitting one sector of the community against another when in reality we all need to unite against Newman and the rest of his clowns.
Patrick Reagan says
Interesting reading.
No mention of pumped storage: boiling fluids rich in salt; and only a passing reference to Geothermal?
What stupid, loaded premise for an article. Everyone wants it to work. They just don't want to hear breathless gush by some fly-by-nighter installer who is only in business because of a prevailing Govt Incentive. And won't be there when the cells fail to reach the Warranted Lifetime.
We each need 2-4 affordable directly-charged storage cells that you just pick up and use in your electric car. Drive away, leave 1-2 charging from the Roof Panels, Petroleum Game Over (mostly).
How hard can it be?
Very difficult.
Do some sums. The batteries will be too heavy to lift; you will need some machine to remove and replace them. About 70% of the cost of a pure electric car is batteries; you have just made the cars 50% dearer by duplicating the battery pack. And if you want to travel any distance, you will need lots and lots and lots of very expensive solar cells for recharging. All with significant capital and associated costs.
Electric cars are a very marginal economic proposition even when recharged with cheap grid electricity. To saddle them with the additional higher costs of solar power won't help.
If you have solar panels on your roof, the best strategy is to not use the electricity for any practical purpose – you should sell every kwh back to your electricity company in the middle of the day when your power consumption is low. No need for batteries. You can sell solar power to electricity companies for maybe 60c per kWh. You can then buy the electricity back later from the grid for 15-25 cents per kwh depending on the time of day. If you had an electric car and solar panels, the best thing to do would be to sell the solar power (energy, actually) at 60c per kwh, then buy it back a couple of hours later for 25c per kwh, and pocket the profit. If you use it directly to charge your car batteries you miss out on this profit, which is the only thing that makes solar panels cost effective in the first place.
@weterpebb – where will you get 60c/kwh these days? I know almost all of the state government incentives have evaporated, hence I get 7.7c/kwh, yes still cost effective over a longer term, it was never meant to be a get rich quick scheme from tax payer funded incentives, people like that don't deserve to call Australia home as they have too much of an attitude of 'entitlement'… and entitlement for doing what? sweet FA!
Most with that type of attitude tend to have just arrived and were not brought up in this country and see the Australian government for what it is, foolish! Next time you receive your government payment, ask yourself… what did I do to deserve it? In some cases people have paid taxes for years and fall on tough times and I respect that, unfortunately they are in the minority.
people like that don't deserve to call Australia home as they have too much of an attitude of 'entitlement'… and entitlement for doing what? sweet FA!
I'm a second generation Australian with a 10kw PV system giving me 52c per unit and I have no issues whatever with accepting the income guaranteed by a formal contract, My outlay was considerable & only entered into as a commercial decision underwritten by the contract. In fact I'll be the first to sign up for a class-action lawsuit against any bloodsucking parasite politicians who attempt to change the rules. For that matter, I'll gladly accept every possible handout available to me, after all if the country can pay red-headed witches & KRudds a half million per annum, it will have little difficulty with the meagre few dollars I can siphon off. Have you ever considered what all those illegals are getting & they aren't even citizens ?? Personally I believe the best response to the bottom-feeding elected representatives is a HUMUNGOUS bulk-purchase of PV systems for every residence in the country, Cut the income from the likes of Energex / Ergon to half & watch the slimeballs sit up and take notice. It should be patently obvious that ***NO*** politician can be trusted to make a significant difference to electricity prices, if they were even remotely serious they would be re-establishing public sector retailers and admitting their rake-off from generation & wholesale facilities. Whatever, I'll never pay for electricity, get too greedy and I can get batteries and disconnect from the grid within days. What does annoy me however are the 'divide & conquer' episodes used to divert the attention of the sheeple from the lowlife scumbags in Canberra, George Street Brisbane & wherever. Solar vs non-solar are only part of the story, we also have public servants vs private sector, big schools vs little schools, ratepayers vs renters, cyclists vs motorists etc etc. The sheeple need to awake to the realization that the REAL battle is between citizens & bloodsucking parasite politicians of whatever colour.
Misa says
You seem quite upset, toplel.
The only thing about which I'm really upset is the utter duplicity of the bloodsucking parasites we've elected to look after our interests. These bottom-feeders have concentrated on feathering their own nests whilst keeping their own snouts firmly lodged in the feeding troughs and ensuring they stay on the gravy-train in perpetuity. None of them have any right to the 'honorable' title, in fact the words 'honorable' & 'politician' are mutually exclusive. Siphoning a billion per annum out of Energex / Ergon whilst ignoring the four billion cost of the privatized retailers is not only inequitable but its intentionally deceptive. Electricity price could EASILY be brought under control within weeks by any halfway honorable government, all thats required is a reduction in the squandering of public money to offset the billion dollar rip-off, and re-establishment of a public retailer. There is no need or justification for compensation to Origin, AGL etc as those companies don't enjoy protection, in fact it would be unconstitutional for any government to guarantee private company monopoly, hence there is no real impediment to creation of a genuinely public owned essential services entity.
From what Ive read of your posts it would seem that you really dont give a rats about Solar as long as you can have a rant agianst Politicians. Second generation, probably Pommy extraction as they are the only ones i know who whinge like that incessantly. As for the rebate being given to those who had the money to pay for panels why should those who couldn't afford them pay anything towards those that counld. That's not the Australian way, the Australian way is that everybody pulls together and shoulders the costs to gether instead of some being disadvantaged by those who think they are above the others. I dont give a rats as i am 100% solar and need no subdises because I for one look after myself without being a burden on sociaety like some.
I seriously doubt that anyone would have borrowed over $32,000 for the 10kw grid-connect system or an additional $11,000 for the planned 2.5kw off-grid system had they not been serious about the PV scene. Furthermore, every property owner in the country had exactly the same opportunity as I was offered & they have only themselves to blame for ignoring the chance to kick the politicians & power company grubs in the privates. There is a very simple reason why I continually bash politicians, ie they are the ones totally responsible for electricity price escalation & rather than fess up to the electorate for their duplicity, they persist in inventing ever more fanciful lies which they hope will divert attention elsewhere. To date, the Newman dictatorship in Queensland has peddled three distinct flavours of male bovine dropping, firstly the gold plated poles & wires, secondly 'solar people are evil' and thirdly carbon tax. Note that one of Newmans first actions after getting up was to sack a significant number of those capable of doing any 'gold plating' & subsequently to dramatically wind down even essential maintenance. The 'solar people are evil' con is exposed instantly by looking at the figures produced by his own tame Competition Authority, and the 10% carbon tax clearly could not cause anything remotely like a 50% price increase. The 'REAL' truth about electricity price escalation is the billion per annum rip-off from Energex / Ergon and the four billion dollar cost of running Origin / AGL / rats & mice retailers, but then we really can't expect a bunch composed largely of failed lawyers (who spent their previous lifetime inventing porkies) to suddenly start telling the gospel truth. I will refrain from getting into discussion of my ancestry, suffice to say its both completely irrelevant and very different to your proposition. .
What household PV systems do that no large scale alternative energy technology could ever begin to achieve is to allow the sheeple a measure of control over what they pay for electricity. Certainly a commercial size installation would possibly / probably be more 'efficient' in terms of operating cost relative to output, however any savings would be merely soaked up by big business & a big chunk would end up padding the already criminally exorbitant fatcat salaries. Furthermore, most if not all other power generation technologies are totally impractical for home use.
Interesting reply. (Lithium car batteries are that heavy?)
So that would mean the 60-24c = 35c differential is actually subsidised by tax revenue? As soon as most people are doing it, it will be withdrawn?
In any case, once most people are doing it, who will be consuming the electricity being sold into the grid?
Risk Rarius says
So let me get this straight. If you have an engineering background, and can prove the inefficiency of Solar, Wind, Wave or whathaveyou through basic math. You are hereby automatically a "Nark" and are cast out to be a Pro-Oil Pro-Coal anti-green sustainable or renewable energy? Give me a break. Furthermore, 0.60c a KW? Give me a a break. Re supplying the Grid, now that is an even bigger farce. I have a 5KW system on my roof. I do not want a bloody thing for the so-called power I create which incidently does as much to help the grid out as sticking your finger in a GPO. Here is where they get you. You create for example 1000 KW for your bill period. As you are Not allowed and enforceable by government in NSW to store the excess power your excess goes directly to the grid (Basically shunted to earth). So at night while you are not using your own stored energy you take back from the grid. Let's say in the billing period you sucked in 200 KW for your hours of darkness use. By that measure you are 800KW in front yeah? Hell no you are not. They charge you circa 22-26cents per KW for your use, then pay you your 6.7 cents for "Your Excess" then they do the subtraction. The only time you are actually winning is when you are creating your own power during the day. if your usage does not exceed it or there is a storm on top of you then kiss that days total collection goodbye. I love Solar as much as most people. But it is inefficient, yes I'm sure it will get better eventually like most things with private enterprise. I would rather granny down the road has her air conditioner on when its 45.1 Degrees, than she die of exposure because some twat thinks she is being selfish and should be ashamed of herself. So quite frankly, I am disturbed at anyone playing the Hegelian Dialectic in any discussion. And by the way, Socialism/Marxism/Fascism/Communism, it doesn't matter. When you have people with guns pointed at your heads who want to dictate what you are going to like , who gives a shit! One can still debate the efficiency of a system, and have a valid point. The fact this article is on a Site called Solar Quotes says it all. The thread is compromised. Oh and by the way, it never escapes me, the hypocrisy that most Solar advocates live in verticle high-rises and are in the top 1% of this country's rich. I would gladly place another 5KW inverter and subsequent panels on my roof in a fit, but only if I get to store it myself. I do. to want anything from the grid. I do not want to get paid for a lie either. I would rather granny get a free heater and the power to run it. By subsidising anyone, you are simply taking the money from those who least can afford it. But that has always been what they wanted.
John Ward says
Nothing will change until all of you who have Paradigm Paralysis die out.
O Lly says
>> yep Bandgap Solar did win an award once, but that was for their "Power"Point Presentation (not sorry, bad pun intended).
I was installing PV solar systems back in 1990, stopped after a couple of years, it's all a green lie.
There ain't no silver (or gold) in them panels guys & girls, that is the truth, not the ones they put on the average roof any-ways.
PV solar systems may be part of the answer if you are not connected to the grid, but to save the world from flushing it's self down it's own dunny (toilet) you have to stop worrying about the dollar return to yourself and reduce your personal consumption of what precious little remains of our one and only mother earth.
Start thinking of our earth as your children's life capsule not a bottom less wallet you can flog stupid.
Thank you for your attention and reading this far <<
PELOHA – Olly (ex Country Technical Services/FNQ/Australia)
Who gives a rats whether its the truth or a lie, and whether whatever it is is green, purple, blue with yellow spots or fuschia !! What solar power means to me is that not only will I never pay another power bill but I also get an ongoing income & a tax break from depreciation. Furthermore I'll do everything in my power to organize bulk-purchases to that everyone who doesn't wish to bankroll the power barons can bypass their rorts. Those with shares in Origin or whatever are quite welcome to their skyrocketing electricity bills.
You are the one rorting the system. You get paid more for your energy than it costs to buy retail off the grid. Which us other customers have to pay for. You are the one overcharging for power and making unreasonable profits, not the utilities. Please, don't boast about how everybody else has to pay more for electricity in order to subsidise your scam. In fact, please don't sell your electricity at all; I am sick of my power bills being inflated to pay you more than your electricity is actually worth. What you are doing may be legal, but it is immoral.
Nonsense !! Even the tame 'Competition Authority' only attributes 4% of electricity cost to PV systems, a miniscule figure compared with the cost of the couple of mega-power stations that would be needed without all the rooftop systems & a mere fraction of what is paid for interstate power. I have no qualms whatever about accepting exactly what the formal contract provides. Wh3en its all said & done, the billion dollars per annum siphoned off Energex / Ergon & the four billion per annum cost of privatization are infinitely more iniquitious than what PV system owners get. No bloodsucking parasite CEO is worth remotely near the ten million per annum awarded to Origin / AGL fatcats.
To Olly
Can you say more about your perceptions? Re Green Lie?
Legend_of_Aus says
So a major barrier to understanding this article is the term 'Nark'. From the title onward, this term is not properly explained, defined or contextualised. What it does tell us is that by descending into Name-Calling, the journalist loses objectivity and credibility in an otherwise constructive argument.
My 1.5KW solar system cost $1500, or $1 a watt. Did the writer get his numbers wrong?
The $1500 you paid was not the true cost of the system. The installer will have claimed $1000's in rebates on your behalf. So the actual cost was much more (depending on which solar credits multiplier you got)
Julius Thomas says
?NUCLEAR -emotions, yeah when people suffer radiation induced injuries and deaths, there is some emotion involved , if your human?, if one get paid i guess that rational gets the boot, anyhow nuclear waste makes the industry economically and politically (no one wants it!) unviable!
Julius, your response is essentially the equivalent of the argument that all cars should be banned because dragsters have unstable fuel systems.
If you were to limit your argument to rod-core, water cooled reactors, then I would be in complete agreement with you. However when you take the broad brush argument and apply it to all types of nuclear reactors, you simply come across as uneducated.
The fact is that your argument soon falls apart when you start to look at pebble bed reactors. Pebble Bed reactors use less fuel, can run on thorium (meaning no weaponisation and only a 500 year half life compared to the half a million year half life of uranium), are much cheaper to build and most importantly, cannot melt down (the reactor works on a principle known as doppler broadening where the fuel "pebbles are geometrically aligned so that should the coolant fail, the temperature only rises to 1600 degrees before naturally cutting out – 400 degrees below the melting point of the graphite fuel cell casing).
Granted, you still have the issue of waste half lives, but there are already reprocessing technologies out there- such as hybrid reactors where electron bombardment based fusion reactors to dramatically lower the half lives involved. Furthermore what is to say that we wont perfect incredibly effective waste reprocessing techniques if we actually invested in researching them.
Off course this ignores the fact that fission should be merely a stepping stone to fusion, where the half lives, even without reprocessing, are in the vicinity of around 12 years.
In fact the biggest problem with the whole nuclear debate is just how uneducated people are on just what nuclear entails and base their entire understanding of nuclear power on the likes of 3-Mile Island, Chernobyl and Fukushima.
http://www.newscientist.com/article/dn23770-renewable-energy-to-eclipse-gas-by-2016.html
According to the latest projections from the International Energy Agency, by 2016 global electricity generation from renewable power will exceed that from natural gas – and should be double that provided by nuclear. We don't need nuclear its so 1950's. we have a huge fusion power source operating at a nice safe distance. We should be using that.
What's really needed is a generator that runs on smug self-satisfaction and pretension.
I'm pretty sure that is what powers the Toyota Prius.
I wonder how many of those frantically attempting to find arguments to discredit PV systems are motivated by their discovery that their fence-sitting back when the feed-in tariffs were sufficient to render investment in a system attractive has left them vulnerable to the scandalous electricity price escalation we've seen in recent years. I contend that rather than admitting their earlier mistake, they now choose to invent all manner of arguments to justify their unbridled hatred of those insulated to some extent from the avarice of bloodsucking parasite politicians and their power-baron cronies. The reality is that even a small (say 1.5kw) PV system combined with careful attention to power conservation can still provide for a zero electricity bill without requiring a dark-age lifestyle. Obviously one wouldn't run a humungous airconditioner or other high use devices 24 x 7, but its still possible to have a refrigerator, freezer, television, PVR, computer, washing machine & reasonable lighting. Many of these little systems have paid for themselves within four to five years. Bigger systems generating nett income sufficient to attract the attention of the ATO can be depreciated, thereby further reducing the payback period. I've attempted to arrange bulk-purchase of PV systems in quantities sufficient to get the price down however I keep getting told there isn't sufficient margin for further price reduction. Whatever, its quite obvious that no bloodsucking parasite ALP or LNP politician will ever produce more than hot air re containing electricity price rises. I've tackled QLD energy minister McArdle re supporting community solar farms (as per other states) however he isn't prepared to do anything that threatens the Newman / Seeney / Nicholls dictatorship revenue from Energex / Ergon. Their lies about PV system owners causing the majority of the price rises conflicts with the figures produced with their own tame competition authority, furthermore they conveniently ignore the massive savings due to the state not needing to build at least two mega power stations thanks to the contribution made by all the rooftop PV systems. Contrary to what many would have us believe, daytime PV output is actually significant in Queensland at least because of the almost universal use of airconditioners. Not too far back, Energex & Ergon needed to run supplementary generators in the suburbs during summer to prevent a melt-down of the mainstream generation system, however that situation has now been largely resolved as a result of the increase in the number of PV systems installed.
I have a dear neighbour who does have an electric car, and we get on well. But I punctured his personal radius by asking where did the electricity come from that goes to the wall socket that then goes into his car ( night time recharge ). Alas he then thought that because he paid his power distributor ( this is Victoria, so there are many of them quite separate from the generation entities ) a premium price to select/support 'green' generating methods. He went back to closely look at the explanatory notes ( asterisk near the tick-a-box for 'renewable sources' on his contract ) to find that the phrase 'when available' was present. Thus in fact there was no actual requirement for his 'green' wishes to ever be met. Meaning that renewable sources could in fact never be drawn upon by the distributor, and this would not be a breach of supply contract.
At this point he admitted that he'd initially chosen such things ( electric cars, green renewable premium on power ) because he felt better for 'doing his bit'. At no small expense of his it is worth mentioning, what with buying an overpriced car ( comparing to features and performance of competitors ) and overpriced power. On inquiry he found that the distributor 'could not provide' detail of their renewable sourcing, either in the specific or the generality.
So we both reasonably concluded that given the significant price excess of some renewable methods over, say, coal fired generation ( which is why the green option existed on the contract ), then the distributor has a huge incentive to never touch such modes. Remember they've already got his money and his signature, and there is no legal foul if his 'intent' is not realised.
My reason for presenting this anecdote is my suspicion that I don't this type of scenario is at all uncommon.
As regards doing your own home solar power and feeding into grid ( offsetting drawings from same, but at a discounted rate ), many I've chatted to feel ( there's that emotional word again ) that it will be much like car LPG gas conversions : the rebate for the conversion does not lesson consumer cost ( increases to the converter's profits ), and with general uptake LPG consumers get milked as per other fuels.
As for the use of 'nark' here, this language technique is borrowed from the climate crowd in order to deflect ( in advance ) critical query and thus debase discussion to group thinks and unnecessary adversarial stances, straw men etc. The ancient Greeks kicked this off long ago with their schools of rhetoric, but I guess each generation has to learn such hazards anew.
Some new news : Germany has/is winding down it's solar power subsidies recently :
http://www.thelocal.de/money/20130709-50753.html
I guess one has to view this within the convoluted EU system – and German politics – so the lessons don't necessarily translate. But I think there is an overall warning here regarding how green intentions may lead to misdirection, specifically : pollution 'costs' during production have been moved out of jurisdiction, and the lower quality ( you will get what you pay for ) will make the amortised position rather shaky.
Harry says
I have to respond to your lpg put down. For a start it all comes from Australia, we only have one major refinery left, most is imported. good for the reefs when they have accidents. And the balance of payments ( that probably made no sense if moneys not your thing) Having driven an lpg car for the last 15 years on the saving alone I have saved my self almost 40,000 and the cars 2 of them cost me about 35,000. 2 free cars over petrol. I sold one car at 350,000 so I don't know if they don't last as long as a petrol guzzler.
Emmanuel Goldstein says
Bah to your guvment subsidies, and "lobbyist" is another word for bribery. You all realize that none of this will get sorted so long as the criminals' gang in parliment is running the show.
You green folk want solar, then buy it fit it and maintain it without having your buddies point guns at me and steal my money for your cause.
Matter of fact, any solution that you come up with that requires your thug friends to extort more of my hard earned, is a bad solution.
If you all stop arguing over who should wield the fist of power and just realize that the market will solve all problems if you let it, we might have a chance at saving our planet.
What the bloodsucking parasites have succeeded in doing is to set one section of the community against another section when we really should be uniting against politicians at all levels. They are the bottom-feeding grubs who caused price escalation, not PV system owners. Privatization would NEVER have resulted in lower priced electricity because the privately owned retailers want to make a profit, their avaricious fatcat executives believe they are worth ten million per annum, the shareholders expect dividends & the slimeball politicians siphon money out of the wholesale industry. In Queensland, corporatization & privatization costs us five billion per annum, thats $2500 average per electricity connection …. other states are probably in a comparable situation. Its high time we targeted the grubs responsible.
Agreed @Yes Minister, but have you ever noticed the politicians as soon as they come into office put forward a pay rise for themselves, and for the opposition (so it gets passed without objection). Also privatization looks good for the budget for THAT year… then they justify their bonuses and pay rises based on their financial budgets, yes they are crooks, no wonder the last election came down to 3 independents, because no one wanted any side!
The slimeballs have the temerity to crap on about the ostensibly 'independent' renumeration tribunal which involves a tame and totally compliant governor-general appointing a tribe of known politician-friendly drones who would never dream of not pandering to the wishes of the bloodsucking parasites. Queenslanders have also seen General Disaster creating another 'independent' tribunal, this one controlled by one of his cronies. GRRRRRRRRRRRRRR If the judiciary and / or the governor had the slightest semblance of decency, they would scream blue murder. One can't expect any interest from the Queensland watchdog since the dictator had it de-fanged & emasculated. What really gets my blood boiling is the use of the 'honorable' title when in reality, the words 'honorable' & 'politician' are mutually exclusive.
Factually incorrect. Australian federal politicians' pay is set as fixed ratios of the pay of senior public servants, which in turn are set by an independent body (the Remuneration Tribunal). It doesn't matter what the federal opposition thinks (or even the Government); the salaries of senior public servants and federal politicians are set by regulation (not legislation) and hence don't even go through Parliament. No involvement from politicians at all, and certainly no need for them to vote on it. So it works pretty much exactly opposite to what you have claimed. You should be happy to be mistaken.
The point is that the renumeration tribunal is stacked with drones who know they will be dispensed with the instant they buck the system, mind you it would never come to that because the selection process weeds out anyone with a shred of nous..
Tgon says
Can anyone explain the etymology of the term 'nark' as used in this article?
I only ask because the only time I have heard a similar term being used (narc), it was in reference to a narcotics officer and used to describe a person who reports the 'crimes' of another person to some form of authority.
Exactly. Rich Bowdon uses it as a derogatory term for those whose opinions are not as desperate as his own. Must make him feel superior, but it doesn't disguise the fact that he's the one who is whining.
I noticed that the technology mentioned here is, at the moment, only aspirational. Not really a time to be celebrating. Not until they actually make the new 'super' cells using the new ideas that they are thinking about potentially developing.
Its always aspirational. PV cells were invented in 1839 (a far older technology than say nuclear power) and despite almost 200 years of research and billions of dollars in R&D they are always 10 years from being cost competitive with traditional power. Reminds me a lot of nuclear fusion based power stations – always just around the corner, never actually here. PV should be added to the long list of technologies that looked promising initially but turned out to be technological dead-ends.
For a 'technological dead end' it works fine for me. Not only will I never get another electricity account but I also get an income & a tax rebate from depreciation. All luddites are welcome to keep supporting bloodsucking parasite politicians & their avaricious power retailer cronies but I for one have chosen to opt out of their rorts. Given the repeated posts from weterpebb, one has to wonder for whom he / she / it / whatever works, my guess is some entity that profiteers from the mainstream electricity industry.
It works "well for you" because your costs are being heavily subsidised by taxpayers and other electricity consumers. The wholesale cost of electricity is about 12c per kWh; most jurisdictions will buy electricity off consumers at about 4 or 5 times this cost. The electricity companies do this (pay hugely more for your power than it is worth) because they are required to do so by law. They pass the much higher wholesale price onto regular consumers (like me).
If the people using PV panels on their roofs were to stop selling their power back into the grid, the cost of electricity to everybody else would drop. The people who are "bloodsucking" are the people who force electricity companies to buy their massively overpriced solar energy (who have no choice; they are required to by law).
Please, don't boast that you can force electricity companies to buy your massively overpriced power and hence make money. I am the consumer at the other end who eventually has to pay the difference in costs between wholesale grid power (maybe 12 cents per kWh) and your power (maybe 50 cents per kWh). You are ripping off other consumers and boasting about it. Not a good look.
So, who is the bloodsucker, exactly? The entities supplying electricity at 12c per kWh, or the entities who are exploiting badly devised legislation to force electricity retailers to buy the same electricity for 50c per kWh, and then boast how are they are ripping off the system?
And no, I have nothing to do with the energy industry in any way. I do however have a pretty good understanding of economics, sufficient at least to know if one supplier is charging 12c for something and another supplier is charging 50c for the same thing, then the 50c is the ripoff, not the 12c.
Use solar PVs all you like. But don't force consumers to pay 4 or 5 times the market rate for your power in order to line your pockets at everybody else's expense. What you are doing is bloodsucking; worse, you are boasting about it.
I've posted the following points a hundred times but obviously I need to do so again .
Firstly, I presume you comprehend the finer points of a legal contract ?? Every person in Australia was offered the chance to partake of same re PV systems and in fact a few million did so (as was their right). A number of fence-sitters chose not to (as was their right), however now its become obvious that jumping on the good ship solar was a very good move, the fence sitters have chosen to find every argument in the book and a few more besides to demonize the smart ones, Since there is a proper legally binding contract in place to back up a commercial decision involving many thousands of dollars invested in Pv systems, do you seriously expect us to throw the contract out the window ?? Personally I'll be one of the first to join any class-action lawsuit needed to belt any bottom-feeding politicians who attempt to meddle. General Disaster tried that in Queensland and promptly changed his mind when threatened with a 400,000 plus plaintiff lawsuit.
Secondly, PV systems in Queensland have saved the gubmunt building two power stations to run all the daytime airconditioners. The gubmunts own tame competition authority tells us PV systems constitute a mere 4% of electricity prices, whereas two new power stations would constitute well over 20%
Thirdly, PV system detractors conveniently ignore the billion dollars per annum siphoned off Energex / Ergon by the past three gubmunts, plus the four billio0n per annum cost of privatization. Thats FIVE BILLION per annum additional cost purely because of corporatization & privatization, an average $2500 per annum (note **AVERAGE**) per electricity connection.Obviously a lot of connections don't even use $3500 per annum but a lot of factories use tens of thousands per month, hence the AVERAGE. That makes the 4% associated with PV systems too trivial to mention .
Finally, have you gone to the trouble to check the price paid for spot power from the interstate grids ?? To save you the trouble its a wee bit higher than the 52c per unit I get, like several times higher !!
The entities you should be bagging are the bottom-feeding slimeballs infecting parliament house and the avaricious fatcats running Origin, AGL etc.
Hugely misleading statistics.
Firstly, you state that the existence of domestic PV systems has eliminated the need to build two coal power stations. This is not true. Because solar power is intermittent (doesn't work very well on cloudy days), we still have to have sufficient traditional plants to meet peak demand on cloudy days. Solar doesn't eliminate the need to build traditional power stations; it potentially reduces their load factor when the sun is shining.
Subsidising solar may add 4% to electricity costs, and two new power stations may have increased electricity costs by 20% (both very dubious statistics), but you haven't described how much base load power is generated by PV versus two new power stations. Two new power stations would probably have added about 2 GW continuous to base load power. On most days, the peak energy demand is about 6:00 pm when lights, heaters, TVs and ovens start getting turned on. How much power does PV contribute at these peak times? 0 Watts?
Yes, you entered into a legal contract where the Utilities are forced to pay you far more for the electricity you generate than the wholesale cost from traditional power stations. Which of course the rest of us to pay for in higher electricity costs. So congratulations, you have signed up for a scam where you are overpaid for the electricity you generate, and the rest of us have to foot the bill. I can understand you want the scam to continue. But please don't boast that you are forcing Utilities to buy your over priced electricity which the rest of us have to pay for; as a person who eventually has to buy your over-priced power I am not happy that I have to subsidise your inefficient electricity generation.
I would of course be very happy for you to go completely off-grid; then I wouldn't be subsidising your electricity generation. But that's not cost-effective for you, is it? These systems are only cost-effective if you can force somebody else to subsidise your electricity. The large majority of electricity users would be better off financially if you weren't leeching the system. As one of the people being leeched, I find your boasting about it somewhat offensive.
You've clearly bought the utter crap being peddled by the lunatics we unfortunately elected … I'll happily debate this subject all day with anyone but a person who believes ***ANYTHING*** uttered by a politician. For what its worth, the statistics I provided came straight from General Disasters own tame Competition Authority so if you dispute them I suggest you take it up with the grubby little man himself. Suffice to say PV systems can in fact give decent output during cloudy periods although nobody who hasn't had a few could be expected to know that. Queenslanders use a **LOT** of power during daytime to ruin airconditioners & before all the PV systems were installed, Energex used to run mobile generators in many areas during the summer to supplement supplies.All that aside, I suspect the main reason you seek to demonize PV system owners is that you lacked the foresight to get them when the time was right and now you have no option but to pay through the nose …. tough !!!
@Yes Minister regardless of whether politicians say it or not, it's still a fair comment. You seem to be forgetting that individual solar systems are going to fail from time to time and you're also going to have issues with weather (which I can attest to growing up with a Solarhart on our roof). In those cases, you need the grid to provide redundancy. That's far from political spin, that's just common sense.
huxman says
If you research it without bias, then Solar is uneconomical, most times comical exaggerations..
But Id rather subsidize not quite there solar tech now so its refined and as good as it can get before the oil crisis to come. But we do need to stop pretending solar is somehow carbon neutral and "there yet".
give the manufactures incentives to refine the tech, not just subsidize home owners for imaginary power output as they do in Australia.
Solar is good, great and here to stay, but don't pretend its good enough to replace coal gas nuke yet.
Call me a Nark if I think we should be driving solar research, instead of settling for its current level.
Kermit says
Silly misuse of the word nark, which is a narcotic's agent or informer, which simply distracts the point of the article.
May I suggest a better term Eco-Reactionary. A weird collection of resenters who reject anything green on a "never liked it never will", for no particular reason other than maybe they just love being dirty, wasteful and generally dupes of large corporations.
I use 100% off grid solar to power my house and that cost about $10,000 less than putting electricity on but still ran out at about $45,000.
Not cheap and this system is just enough to run a basic home for two people. Add to this amount the $1000 a year that I have to put away to replace the batteries when they die, $16,000 for a set and its not even economical. Now if you add to that the cost of manufacturing the Solar Panels, the batteries including the power needed then Solar is a dud.
If I want to use power tools then its start up the old generator or go without. Solar is usefull but not the answer. Nuclear is the answer but the Green's and those opposed to anything that works properly break out in hives when anybody mentions it.
Just because junk food is heavily marketed and always put in easy reach doesn't make it GOOD for you!
First step is to reduce the dependency on dirty coal, which has massive subsidies built in. Over time Renewables will become more competitive and catch up.
I am in 2 minds over nuclear but it would only be a stop gap. There simply isn't enough nuclear fuel to go round and its byproducts are incredibly poisonous. Fukujima and Chernobyl show how people are the biggest flaw in nuclear safety, it only takes individual or group stupidity to take hold and the consequences are awful. What has been the cost of the land lost, poisoned environment, deaths, disease and poisoned food from just those 2 "accidents"? Who factored those into the cost of nuclear power?
Pollution and any clean-ups are taken to be free or swept under the carpet when you aren't looking.
I detect the Lazy Man's "Blame the Greens" for trying to do something. The Greens I know are really trying to balance the best of all options, when there are no perfect choices.
Watched Dick Smith's doco on energy last night and his interviews with typical families. As an architect I am constantly amazed how the elephant in the room never gets a mention. The totally wrong houses we keep building 60, 70 years on from it being obvious which way they should face, be shaded and open up to the sun. Far from learning anything, the MacMansions have just grossed out to be morbidly obese monuments to our on-going stupidity, ludicrously far from work, facilities with no alternatives to the God Car.
Lets face it, we are where we are because we just want to pig out and bugger the consequences.
Thank you Kermit, I agree with (almost) everything you say especially the elephant in the room!
I forgot to mention that coal in itself releases radioactive side-products as well as heavy metals and other carcinogens. It is wrong, filthy and dangerous on SO many levels.
The bill, which they didn't tell you about, for coal's side effects is now being delivered and everyone wants someone else to pay for it. As usual it will be hoisted on the poor, even those rich buggers in their waterfront properties will find ways to get the government or insurance companies to foot the bill for their choices.
Just put your head around the fact that once we have finally bitten the bullet (probably too late) and shifted our economies to clean renewables and seen yet another lift in our standard of living, (which always seems to happen after these continental shifts in the way we do things) everybody will claim they were all for it all along.
Just like with democracy, the end of slavery, female emancipation, public health and education, the end of child labor, the 40 hour week, widows pensions, immunisation, fluoridation of the water supply, compulsory seat belts, the breathaliser, smoking bans and all the other changes that were going to be "The ruin of us all!" The Tony Abbotts will be with us forever.
At 8 star rated, my house is arguably the most energy-efficient in Australia & its paying off handsomely with heating / cooling costs. For example the average abode in my area uses 5 tonnes of wood in a winter (approx $1000 worth) whereas my usage is just over one tonne per annum. According to electricity retailer AGL, electricity bills in the area ivary between $1200 – $1600 per annum whereas mine is approx $600 which I don't pay out of pocket anyway thanks to $7000 – 8000 PV system income. The only significant fuel cost is for petrol but I figure a battery-electric car with 200k range will fix that, especially if I add another few kilowatts of PV power. For the benefit of the peanut gallery, PV output does drop 40 – 50% during prolonged periods of overcast, typically thats 3 – 4 months per annum based on personal experience over a few years.,
Al says
So how exactly is a press release a basis for informed product research?
enotsyaj says
This is old technology that has not been used because of cost. The theory was developed for solar panel application when carbon nanotubes were born.
george riszko says
An interesting article (f factually true) but needlessly inflammatory. I wonder how he treats his wife. What is wrong with objecting to wealth transfer by paying middle-class users of solar power when the costs was 20-40 times the cost of coal? If the technology becomes efficient enough to be competitive, I will switch, but not until then. Why should I sponge of lower income workers so that I can bathe in my own smug feeling that I am saving the world?
Chron_reader says
The derogatory use of the word "nark" just lost you a couple of Brownie points, you radical hippy you!! Seriously though, solar will keep improving. Let's just hope batteries do too. Efficient, cost-effective, environmentally-friendly and long-lived storage is the big hurdle that solar power needs to overcome.
Um, yeah. The word is used completely incorrectly. A "nark" is a type of informer. Such as " Thanks for being a Nark, John. I thought you'd keep quiet about my crack habit." In this article he's using the word as if it means detractor or no-believer.
Narn says
I agree, I have always understood nark to mean dob or tell on. Maybe he means wowser?
Alena says
Exactly……..
Garratt - Kustcom says
A "narc" is American slang for a narcotics agent. NSA.
A "nark" is Australian and British slang for "an annoying person" according to Webster's dictionary.
However I've never heard anyone use it in such a way, it's always been used to describe people who dob to authorities. An informant.
@Chron_reader actually the biggest problem that solar has nowhere near the energy density of thorium based pebble bed reactors, or when we finally crack it, fusion (at which point our fuel comes from the ocean itself and mining giants no longer dominate the energy sector). After all, the achilles heel of solar has always been that it taps into a narrow bandwidth of electromagnetic energy resulting from a nuclear reaction collected from such a distance that the vast bulk of the energy has dissipated in other directions (compounded by losses due to the magnetosphere.
In solar's defence, recent projects such as orbital collectors coupled with tight beam microwave transmitters ill give higher yields, however the transmission process can also then be affected by bad weather.
The fact is that realistically, solar will only ever serve in an auxiliary, rather than base-load capacity, however in that auxiliary capacity, it definitely has merit and will hopefully continue to improve with time.
Brett Allen says
Oh, this guff again? For 15 grand i took my business off grid 3 years ago, and I am avoiding costs of about 4,000/year by doing so. I cannot get a return like that from a bank or from the stock market. And i have not yet had a single blackout.
A solar panel is now about the same price as a window of similar size. "density" doesn't mean a damn to me, the real estate on my roof is not otherwise useful. And I don't see a Thorium Pebble Bed Reactor for sale at Harvey Norman.
@Brett Allen "Oh, this guff again?" Which is an utterly ironic post considering that your post is pure logical fallacy that just makes you come across as utterly ignorant. To begin with you're equating an auxiliary solar power application (which with the exception of being aware of certain potential issues that may crop up, I have never argued against the viability of) to a baseload power scenario, demonstrating that when it comes to understanding the realities of just what is required from a baseload power grid.
Of course you well and truly nail your on coffin shut and destroy your credibility when you claim that electrical appliance retailers supply governments with large scale power solutions such as coal fired power stations through ignorant and uneducated statements such as "And I don't see a Thorium Pebble Bed Reactor for sale at Harvey Norman".
Oh and fyi, in terms of small scale power applications, I seem to recall that CERN was currently working on a throium powered car which if successful, would make the internal combustion engine a thing of the past. See it's amazing hat happens when you actually both educating yourself rather than making utterly ignorant statements which just make you come across as uneducated.
Alan Buchbach says
It's not CERN that is working on the Thorium car, a private US company called Laser Power Systems is working on it. Prototype available in ~2 years. 🙂
The 8g of Thorium in the engine should power it for over 100 years… but I'd take the $2000 engine out and use it to power my house for at least 30 😉
Although you are quite correct that Switzerland, among other nations, has been researching thorium power as a long term replacement for coal or uranium quite intently.
Oh, that sorts it. You called me Uneducated, guilty of Logical Falacies and Ignorant? QED. You must be right.
But you need to prove me wrong before you insult me, matey.
Density is a non issue at present PV efficiencies. The Sun striking an average house (let's guess 250M2, shall we?) in Sydney, Australia (our biggest city) is well over 1000kWh of radiation/day, at a yearly average of around 4kWh/M2/day. The average energy usage is around 30kWh/household/day. Please do me the kindness of looking at a table of Daily Insolation Rates by Lattitude to confirm this for yourself.
I am intimately aware of the functioning of the National Energy market, because its what I look at every day. I am a scientist with a degree in Energy Management consulting to industry.
With technology as it presently exists we can integrate far more renewables into the grid than we now have in Australia, as they already have in Spain, Portugal, Scandanavia, Germany, and even the UK have brought significant wind resources online in recent years.
Even very small grids can hold far more than what we have in Australia. Check out Esperence in WA, or the Bass Straight Islands in Tas.
And I am sorry mate, but I see no good reason to wait for a Nuclear Powered car, or an orbiter with a microwave beam, or Pebble bed Reactors. I dig Thorium, and support research into it, and would support the construction of a plant in my baxkyard. But this in no way precludes the use of solar on rooftops, which these days just makes financial as well as environmental sense.
The only people I hear rabbiting on about "density" these days are Cittizens Electoral Council/LaRouche types, and your good self, sir. Are you of their number, by chance? And what is your background, please, as it is surely the basis on which you call me uneducated?
Kieran Revell-Reade says
Brett Allen stops your little anti solar rant in its tracks and you resort to name calling, sad mate, very sad. Brett makes his point "You can't find a Thorium Pebble Bed Reactor for sale at Harvey Norman." quite clear, if you want to help yourself and the environment at the same time, then solar can be a viable option and his experience proves it (in his area, for his purposes).
If you want to be able to call someone ignorant when talking about the practical and real world operation of a technology, show us an example of where you have used it first hand and how it failed you. Until then, I'll take Brett's example as the more informed.
Brett and Keiran, you have no valid response and if you believe you do then you are simply demonstrating your ignorance, especially when Keiran, your response is that of some pseudo religious zealout effectively throwing around accusations of heresy (especially when besides pointing out some potential pitfalls to be aware of, I have never said that solar wasn't a viable option for an auxiliary power generation application) .
Brett, your response has merely proved my point. What you are discussing there are household applications and small grids as opposed to large power grids. There is a vast difference between baseload power applications and auxiliary power applications. The needs of someone hooking up a solar power array on a factory or a house (which provided you're aware of potential problems and are fundamentally different to power needs of a state government trying to cover an area of hundreds of square kilometers. As someone who has electrical engineering qualifications, I can honestly say that if you cannot understand the fundamental differences in requirements between baseload and auxilliary power generation, then you are completely ignorant on the subject.
Furthermore involving availability from a standard electrical retailer in an argument on baseload power, just destroys any crediblity that someone might have- especially when anyone who knows what they're talking about knows that you're dealing with firms who specialise in large scale power generation needs the moment you start talking about building a power station to deal with large scale baseload needs.
In fact the only nation in the world who may be on the verge of making solar viable at a baseload level are the Japanese who are developing orbital solar power applications, which significantly increases the energy density involved (although you will still get some losses from the microwave power transmissions). However the fact is that there is simply no getting away from the fact that solar is essentially incredibly inefficient nuclear fusion based power and that the moment you need to supply a large enough area, you run into significant physical constraints.
Righto, Mr Andrew Richards. Have at you.
1. I have given you examples of grids both large and small with significant renewable penetration, as the most cursory reading of my post will inform you.
2. Baseload. We have no shortage of it. Look at the NEM price for energy at 4AM, what you will see is a few aluminium smelters paying very low rates for energy. No-one is gunning for that market segment. Existing infrastructure is already in excess of present needs.
3. Density. This is an absurd LaRouchian myth. The area required to capture the entire annual energetic pruduct of the country, at an array efficiency of 10%, is significanlty less than the area already under roof in Australia.
There is no density constraint. If you wish to make an economic argument, I am ready. But desist with assertions that simple arithmetic can disprove.
4. No serious solar proponent of whom i am aware is proposing a 100% solar supplies mix. This is a stupid straw man argument, seeking to avoid the reality that the rooftop 'real estate' is unutilized and the generation from solar is presently economic at retail electrical prices, solar capital costs and the prevailing costs of capital. Companies purchasing solar are perfectly aware of solar's lower capacity factor, and even allowing for this it remains competitive.
If we run our existing installed conventional capaity less, this is no bad thing. I am confused as to why you allege that I desire to remove infrastructure that is already built and paid for, which I do not. You are attacking a straw man, and i find it odius, sir.
5. I suggest you desist from calling me ignorant. It it very poor form.
RJ says
dont feed teh angry troll.
Brent, I'll deal with point 5 first. If you don't want to be accused of being ignorant, then don't make idiotic arguments about not being able to buy certain types of power stations from the likes of Harvey Norman when electrical retailers have never been in the business of providing them. Such arguments just make you look uneducated and ignorant and destroy your credibility.
Now to your points.
1. By your own admission in point 4 no serious proponent of solar would argue in favour of solar being the core of a grid, but rather serving in an auxiliary capacity. Funny how I've never argued against them being used in that capacity with the exception of in areas where polarisation issues affect local wilflife.
2. Existing infrastructure is a joke- having been left to rot and rust over more than 20 years of maintenance being determined by economic rationalism rather than in the iterests of keeping the power grids of this country at peak efficiency.
3. The fact is that whichever way you slice it, different power sources are going to have different efficiencies. Harvesting a tiny fraction of an output from a nuclear reaction where the output is already attenuated to hell by the inverse square law, is going to give you far less bang for your buck than harvesting the full spectrum of energy at a much closer proximity to the reaction. Likewise, energy produced by a chemical reaction is generally speaking, not going to give the same yields as a nuclear chain reaction.
4. You accuse me of attacking a strawman, yet that is the position you adopted from the outset. I made it clearthat I had issues with solar being used in a primary baseload capacity, while at the same time recognising that provided you're aware of the pitfalls from things like dodgy panels and dodgy installs ( plus ensuring that there's sufficient roof access in the case of fire) that solar certainly has merit in an auxiliary capacity, such as residential applicatios and small business. If your position is that it merely forms part of the grid and is perfectly fine for small scale power needs- rather than forming the foundation and majority source of say, the entire power grid for the bottom half of Sydney's Central Coast for example, then why did you respond to me in a way that did come across as being in favour of baseload?
Brett and Kieran, don't argue with id1ots, they'll drag you down to their level and beat you with experience.
Paul, if you were trying to engage in irony by calling me an idiot, then congratulations, you just succeeded in spades.
ppl says
What a useless, worthless article. I don't know what 'nark' means and i'm confused the way the word is used in the article. What a waste of time writing rubish.
Good lord ppl – it's called sarcasm. Get over it.
Paul Tyrrell says
Loved it. The sooner we learn to focus on Solar tech for our energy needs the better. The sooner we make some hard choices to move quickly, the less we and future generations will suffer from the greed and short termism of large corporates, the sooner we move to solar the quicker we can get away from corrupting Oil and Mining power, and the poor decisions of weak government. We don't need more breakthroughs we need more guts to go solar now, and largely relegate the coal and oil companies to history with horse drawn carts and steam power.
Bring on the solar generation. Lower pollution, improved health, sustainable energy, fairer power supply.
Where is my damned country going to get it's power from, will I invade a poor country and steal their oil, or will I open my eyes and look up and see the sun above, will I take some intelligent but tough decisions to fight against corrupting corporations and weak government.
It is our world, we will get what we fight for.
"Where is my damned country going to get its power from?"
Well, that depends on what country you are from. If you are an Australian, we don't have to worry about that. We have massive resources of oil (the tar and shale oil sand reserves in QLD exceed the oil reserves of Saudi Arabia), coal, natural gas, and Uranium. We are a massive net exporter of energy. Indeed, the Ranger Uranium mine on its own provides the energy for about 5% of the world's electricity generation.
You are quite welcome to use solar power if you wish. It is a very expensive and inefficient means of generating electricity. But if your motivation is that we are running out of traditional sources of energy, the short answer is that we aren't. In 1920 the world's proven resources of oil were sufficient for 15 years at constant consumption. Now its about 50 years. Thanks to new technology (eg for extraction of natural gas from coal deposits, oil from shale and tars etc) the world's reserves are increasing much faster than we are consuming them. We are further away from running out of traditional energy sources (oil, coal, gas, Uranium) than we have ever been in history.
So if you want to use solar because of possible future resource depletion, don't bother. The world's reserves have been increasing far faster than we are consuming them. Worrying that civilisation will come to an end because we are running out of oil makes about as much sense as the 19th century notion that civilisation could not further expand because there was insufficient whale oil to provide indoor illumination for the developing world (thought to be a prerequisite of civilisation). Then they invented kerosene and nobody cares in the slightest any more about the world's whale oil supply.
If you think growth in the Western world will be constrained by resource depletion, provide a single example (over the thousands of resources that we have relied on) where this has actually come to pass in the Western world. This argument that we are resource constrained has been proven wrong a thousand times in a row, and it is certainly just as wrong now.
A well considered response.
However, if "peak oil" never happened, explain the ballistic rise in energy prices (that happened to shadow oil prices). Or is that issue simply a multi-pronged conspiracy to prevent the masses switching to lower cost sources?
Aside from which, who ever said sustainable energy sources were needed as a sole response to peak oil?
What about the primary concern? Or has everyone forgotten that among the bickering over efficiency and subsidies?
CO2 emission reduction. Anyone remember that?
Peak oil hasn't happened. We continue to consume more oil each year, which means we produce more oil each year. This will continue well into the future with the economic growth in China, India, Brazil and in many other emerging economies.
And energy prices have not "gone ballistic". Energy costs as a share of world GDP has been dropping for 100 years; in the US (for example) oil consumes about 1.2% of GDP, versus 2.2% 30 years ago (see http://one-salient-oversight.blogspot.com.au/2011/10/cost-of-us-oil-consumption-as.html)
Proven world reserves of all fossil fuel types are increasing, not only in absolute terms (tons), but also in years of reserves. In 1920 the world had only 7 years proven reserves of oil at then current consumption levels; by 1980 it was 29 years and currently stands at 42 years (see http://chartsbin.com/view/t3t). Reserves have been increasing faster than consumption – in the case of oil, a lot faster. And the same is the case with nuclear fuels; we haven't even begun to exploit Thorium reserves (thought to be much larger than Uranium reserves, which are themselves huge).
There may be arguments for reducing our use of fossil fuels, but running out of traditional fuels (fossil and nuclear) is not one of them. We are not supply constrained, and won't be for a very, very long time – hundreds of years.
Midge says
That isn't what peak oil means.
"Peak oil, according to M. King Hubbert's Hubbert peak theory, is the point in time when the maximum rate of petroleum extraction is reached, after which the rate of production is expected to enter terminal decline."
Source: http://en.wikipedia.org/wiki/Peak_oil
So yes, that is what "peak oil" means.
David Sparkman says
The rising cost of energy is mostly optical. As was pointed out, as a percent of GDP it is declining. But inflation caused by overspending governments cause the perceived price to increase. Add to that, the fact that energy taxes are a major resource for governments, and like the golden goose, governments want to keep increasing their revenue so they keep increasing their taxes on energy.
Currently Solar is mostly for the well to do that can afford the investment. It is neat to be able to not pay taxes on energy just like it is neat to grow your own food and be independent of Government regulations and ersatz foods that have been over cooked, over salted, and oversold. But for solar to succeed, it needs to become cheap enough for the masses at which point I am sure the government will step in and start taxing sunshine. Hey Government employees have to eat too, right? And we need more government employees, right? So when you want government to help you out, with those " narks" just remember one day your friendly government will be taxing your sunshine.
(I assume the term "nark" comes from those who make "narky" remarks. The term Nark originally was used to refer to a drug enforcement officer – someone unfriendly to those who smoked weed.)
Rick Jensen says
taxing sunshine was back in the dark ages when people were charged for the windows they had in their houses…It's been done. What I would like to know is why Australia charges it's customers some of the highest rates for electricity in the world ?. Why if I install solar panels, I would now get only 8c/kwh for the electricity I produce, but pay 30c/kwh for the electricity I use.
Why we pay around 90c/litre for lpg when China pays 7c/litre for our lpg.
Rick:
Three different questions.
Firstly, "why does Australia charge some of the highest rates for electricity in the world"? I'm not sure we do, but high wage costs and high levels of environmental legislation (eg MRET) both contribute to higher costs.
Secondly, the reason that electricity cost 30c per kWh retail but you get paid 8c per kWh for solar is because the wholesale price of electricity is about 5c per kWh. You actually get paid more for your solar energy than the distribution companies pay for energy from a traditional power station.
Thirdly, the reason you pay 90c per litre for lpg at the pump (much higher than the wholesale price) is due to fossil fuel taxes in Australia (lpg is taxed under the fuel excise scheme); as China does not have fossil fuel taxes on lpg, the price of Australian lpg is much lower in China.
The spot price for electricity on the National Electricity Market actually fluctuates between zero cents and $13.10 per kWh depending on demand and supply. So there will be instances where the spot price is $13.10 and solar owners are getting $0.08 per kWh exported.
Solar supply has massively reduced the peaks on hot days where the spot price can get up to $13.10 per kWh, reducing the average wholesale price and really hurting the incumbent generators profits. This is all documented by the AEMO, NEM and others.
Good description of NEM operation: http://en.wikipedia.org/wiki/National_Electricity_Market
Wow 30c per Kwh for electricity and 90c per litre for lpg at the pump, ramping to extreme. China fuel price is the same as everyone else. The benchmark price set in Singapore is us$900 per tonne, do your sums, 7cents per litre is BS. Having just returned from China I can confirm the price's same as ours(oz) less taxs.
Finn:
The peak price is meaningless, as it occurs for only an extremely short period of time. The meaningful figure is the average price. From a coal powered power plant, it is 5c per kWh. A rebate of 8c per kWh is paying more than the average wholesale price of 5c. Other electricity users are subsidising higher rates for solar.
And as for your comment:
You forgot entirely to provide documentation of that fact by AEMO, NEM, or others. It sounds very unlikely to me. Electricity demand has been falling since 2007, and so has the spot price. An increase in solar generation should have little effect in the face of falling demand, particularly as it is the most expensive source of electrical energy available to distributors.
Could you please provide a reference to where AEMO and NEM say that solar supply has massively reduced the peaks on hot days and are really hurting incumbent generators profits? I know total demand is falling and hence so are spot prices, but where do AEMO and NEM say what you claim they do?
The peak price is meaningless in such a non-linear system? I thought you were a mathematician?
The generators that make 25% of their profits from 36 to 100 hours of peak electricity prices per year would beg to differ with your analysis.
What the heck. We have infinite resources, just pollute away.
The oceans can absorb it all. Oh, its growing more acid and destroying shellfish and making the oceans fit only for jellyfish.
The atmosphere can absorb it all. Oh, the CO2 has more than doubled and temperatures are starting to steadily rise. A little heat and tropical diseases are good for you.
The forests will grow faster with more CO2. Oh, if only we weren't chopping them all down!
The ice can absorb all the extra heat. Oh, the glaciers are rapidly shrinking, and we will have major floods followed by water shortages in the major population centres that depend on the summer melts.
The sea level can rise all it wants. Oh, low lying fertile deltas and mega-cities along with Venice etc will be inundated, no big deal.
So now's the time to frack the water tables and fertile farmland. A little industrial poisons in your water supply and food never hurt anyone, especially if there is some gas and oil in it for the multi-nationals.
…all so you can sit in your car for the endless slow commute from the outer suburbs, because you NEED the space to stash all that cheap stuff that you use to take your mind off just how shitty you are making everything else.
This might be a bit of a diversion from mainstream solar power stuff however I believe its relevant as my interest is reducing reliance on bloodsucking parasites (whether gubmunt, bureaucratic or corporate) as far as is humanly possible. I'm effectively self-sufficient in energy & 80% so with food, next thing is transportation. Its a pity nobody is selling battery-electric cars at a halfway sensible price (remember they are infinitely simpler than petrol or diesel equivalents & the techology isn't exactly rocket science). Seems the most cost-effective solution available at present is the plugin / extra battery conversion Prius, reportedly 200k EV only range. Been looking at electric bikes too however I need more than the 250w legal power to get up hills around here … anyone know how diligent the QLD blue-uniformed fundraisers are about checking the power of electric treadlies ??
Peter Stanton says
I assume you avoid using any facilities supplied by these bloodsuckers such as schools, hospitals and roads.
Know what I object to most with the rush to fracking?
The fact that the States assert ownership to the resources under privately owned land. Farmers/owners should be within their constitutional rights to deny access.
I sure hope the courts agree!
Hear hear,
Although it depends where you live. In Australia a residential / agricultural lease only extends 6′ into the substrate. If you want mineral / resource rights then you need a different (& expensive) mineral lease.
Different circumstances to the US given Aus was initially and largely settled via state sponsored /forced migration vs the freeholder tradition and private investor settlement in the Americas.
Senne Kuyl says
https://www.google.com.au/url?sa=t&rct=j&q=&esrc=s&source=web&cd=2&cad=rja&ved=0CDUQtwIwAQ&url=http%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3DumFnrvcS6AQ&ei=pPCXUsGvIcSAiQeU3ICYCA&usg=AFQjCNE6Sa9L_NviilCGGPm6Wid6qzaNfg&sig2=aa1eiYlGy4uJsOLd1ZSzXg&bvm=bv.57155469,d.aGc
Ugh. Obviously there was supposed to be more content to my reply. It is obvious weterpebb doesn't understand exponential functions. We, after all, know the volume of the earth and subsequent layers on which we reside. Then we get to the faulty premise of 'technology will save us (if x really is a problem).' The above video covers both those issues very well.
Infinite resources. :sigh:
I understand exponential functions extremely well (I'm actually a mathematician). But I also understand history and evidence.
Putting aside the unusual and controversial example of Easter Island, humans have never had a problem with resource depletion. And this is across thousands or tens of thousands of resources which have at various times been strategic or economically important. This is because of resource substitution and technological development.
About 1 million years ago, parts of planet earth were running out of triangular shaped stones suitable for spear heads. Quite possibly, somebody pointed out that the number of humans increases geometrically and faced with a finite supply of triangular stones we won't be able to make enough spearheads to be able to feed everybody. This lead to a new technology (stone flinting) and ultimately resource substitution (metal spearheads). Triangular stones are no longer a strategic resource.
And this has been happening for a million years. We didn't run out of wood to build ships. We didn't run out of whale oil to power lanterns. We didn't run out of hemp to make ropes. We didn't run out of peat for fires. E didn't run out of bees wax to make candles. We didn't run out of lead and tin to make cans. We didn't run out of Potassium Nitrate to make gunpowder. We didn't run out of horses for transport.
This exponential argument sounds convincing, right up until you see if it could possibly be true. And its not. We have been dependent on thousands of different resources over thousands of years, and resource depletion has never been a problem. According to the theory in the video, it should always have been a problem. The error is that the video does not consider market forces and in particular new technology and resource substitution. These are so powerful that rather than resource depletion always being a problem, in practice it has never been much of a problem.
We are at less risk of resource depletion than at any previous time in history. We have good substitutes for almost every resource we use. If oil really does start to be depleted, then we will convert our cars to run on synthetic oil made from coal. We have had this technology for 60 years, and there is plenty of coal. Compare this to (say) wood in the 17th century, which was needed for weapons, transport, and construction – a very finite and in some cases unreplaceable resource which was shrinking fast. Then along came the substitutes. Wood isn't even a strategic resource any more. Any more than are triangular stones. Even though our population has increased exponentially since those times.
Ezra Bowen says
weterpebb, I agree we are aware of more resources now then we ever have been aware of in the past, however If I'm not mistaken in say the 1920's with 1 barrel of oil you could mine 50 barrels, in this day and age with 1 barrel of oil you can only mine about 5 barrels, and is including how efficient machines are becoming, so what will it be in 10 years then? with 1 barrel you can get 2 barrels of oil, now fuels are getting expensive.
Ezra:
This raises an interesting but seldom discussed aspect of future energy mix. Shale oil deposits can need 50% of the power from the shale to power the extraction process. The Canadians are considering building a nuclear reactor on top of their shale oil deposits. The nuclear reactor would directly provide the heat needed to extract the oil from the rock. This means 100% of the oil is available. And as their tars are in mostly remote places, the nuclear reactor is well away from population centres and NIMBYism.
The interesting twist is that even if the process consumes more energy than it produces, it can still be economically viable. Energy in the form of oil is a lot more valuable than energy in Uranium (or coal for that matter) as it can be used for transport. In a situation where energy consumed by the mining and extraction process is the same as the energy in the oil which is produced (ie net energy production is zero), shale oil become a means of converting electrical energy into oil. The medium term problem is not a shortage of energy, it is more likely to be increasing costs of liquid/gas fuels for transport. Shale oil solves this problem.
What REALLY amazes me is the news that ex QLD Premier Peter Beatty (AKA Teflon Pete) is standing in the federal seat of Forde and more so that some utterly mindless dumbclucks are actually planning on voting for the clown. Remember that he was the 'brains' behind retail electricity privatization (and hence the massive price hikes), the abortive super-councils, the health department payroll disaster, and his chosen protege GoAnna the Blight (easily the most inept Premier in recorded history) one would think those little issues would disqualify the galah from ANY political position.
Solar panel could be 20% efficient in"nearest future" (10? 20? 50 yers later?) but always will drop the efficiency to zero as panels will (and ARE everywhere where they are installed!) cover with dust,carbon and other smog residue!
Those who advertize SP never mention about this factor!
Your local solar installer can, today, sell you a panel with an efficiency of 21% (sunpower 327).
Your devastating problem with solar panel technology can be solved with a high tech device known in the trade as a 'wet sponge'.
Wow, you should go into engineering! Absolutely no-one has ever thought to clean or maintain the solar panels once installed!
Oh, wait I just got this flyer in my letterbox offering to clean solar panels.
RepatMatt says
I'm confused, are there really people out there informing the police about people with solar panels on their rooves? I understand that there is some way to get in trouble if you power your own requirements first, and put excess back to the grid, instead of the way the electricity companies want it, but are neighbours informing the police often about this?
FatherJon says
So, where does that leave those of us who wasted 5 grand on solar 2 years ago for a promised 'good deal' which has been very disappointing.
Do we now have to spend another 5 grand to upgrade our existing system for more supposed benefits?
Count me out!
It's interesting to see how many people will spend a lot of money generating extra electricity, but almost no money reducing the amount of electricity they consume. In Victoria Smart Meters are here and yet most people are unaware that they can be used to save power. I think I've saved more money with a $100 in home display from mysmartmeter than I did with a Solar installation.
Smart meters are for idiots! Why would you need to spend 100 bucks to help regulate your use of electricity? Can't be that smart, when common bloody sense tells you that a switch means OFF as well as ON. Regulate your own use and keep the money in your pocket.
On your second point, I'm one of the ignorant masses with regard to the smart meter savings. It was already here when we moved in about two years ago, but there was no documentation provided. It uses a pre-paid card and has a few buttons on it and an LCD display, so I can only assume it's a smart meter.
Your first point…yes!
When "Australia's largest solar company" (TVS) saturate with TV ads such as "Families are missing out on trips to the movies, eating at restaurants and taking holidays, just to pay their increasing power bills…" Well, really?
They're talking about discretionary spending. Anyone who knows how to budget will prioritise and save for such things. And these tales of woe come to us from within a McMansion with its typical vast, open areas that take more energy to heat and cool!
Their other ads practically encourage entrenched high consumption behaviour with phrases like "Protect your lifestyle" and "Our lifestyle protection package". What I find most offensive about these jokers is this: their business would be a tiny fraction of what it is today were it not for the Rudd/Gillard subsidies.
They showed their appreciation by echoing the LNP fear campaign in the lead-up to…"THE CARBON TAX IS COMING!!!". They continue to sound like an LNP slogan parrot.
Oh, and let's remember they're major sponsors of…
Essenden 😮
All very confusing ! – keep getting the feeling that I should hold off because panels are getting ridiculously cheaper and better ??
Also, there was recent press about when the use of private solar panels reaches a level ( approx. 30%) within a certain …area there is a real risk of voltage surges within that network area, damaging appliances etc.
The article concluded that the real future for solar power lay not in the installation of panels on private homes, but in the creation of distinct solar power stations which then feed into the network – as per existing power stations. ???
That makes commonsense, having a central solar power station instead of us all uglifying our rooftops with heaps on panels that need occasional cleaning and are vulnerable to hail storm attacks.
That sounds like utter twaddle to me. Firstly the power companies gladly accept all the solar farm power however they don't pay **ANYTHING** for it, at least in Queensland. Yes Martha I HAVE looked at that for people who haven't got their own PV system and that incomparable idiot McArdle advised me that the Queensland gubmunt wouldn't provide any assistance whatever. Given that politicians everywhere are duplicitious self-serving bottom-feeding slimeballs, I doubt any other states are more enlightened. On the other hand, those of us who paid ridiculous prices (by todays standards) for PV installations will never pay for electricity while they stay above ground levels (ie they aren't pushing up daisies). Dunno about the 'narks' but I know what works better for me. All that aside, I'm absolutely ropable about the elected scum who fabricate whatever crap in order to support their own male bovine dropping. Furthermore, the extent of their opposition to genuine cost-saving endeavours I've investigated on behalf of non-PV folk is absolutely amazing. Moral of the story, politicians are easily the lowest lifeform in creation. !!!
But the point of the article I was quoting had nothing to do with aesthetics or politics, just better technology !
i.e. > 30% household 'suppliers' to grid = voltage surges = damaged appliances
therefore large distinct Solar plants = way to go, NOT EVERYONE having panels…
Happy to hear if this is correct or not
You may well be correct on a purely technical basis however after fifteen years and three PV installations, I've never encountered as much as a hint of voltage surge trouble. Mind you I always have professional quality surge protection installed in my switchboards to protect computer equipment (couple of servers & related stuff). My primary reason for criticism however was / is to do with the untold avarice of both the bottom-feeding scum we elect & their various cronies / hangers-on. Unfortunately any solar-farm (in Queensland & probably every other state for that matter) will never result in financial benefit for consumers whereas a home PV system certainly will to some extent depending on system size, power usage patterns etc etc. Personally I view the exponential escalation of retail electricity prices as a massive social issue that will never be properly addressed by either ALP or LNP. Sure RAbbott & KRudd will crap on as is their wont, but the point is they will never do anything bar padding their own pockets. Some of us were fortunate enough to bypass the system but many others missed the boat. Recently I attempted to establish a solar farm to provide cheaper power to those in my community who for one reason or another couldn't install their own PV system … predictably the bloodsucking parasites in gubmunt put every possible obstacle in the way. Note particularly the blatant lies being spread about PV systems causing the price rises when corporatization & privatization (in Queensland) added five billion total per annum, or an average $2500 per connection per annum to power bills. (five billion divided by 2 million connections. And yes Martha, I do realize not everyone pays over $2500 per annum but a lot of businesses pay tens of thousands per month, hence the **AVERAGE** figure.
This whole thing is geting out of hand. Firstly people are saying that if they, remember they, put solar panels on their roofs the Government should pay for it or at least subdisie it and then that they be paid better than the 8c now offered for their power. What ever happened to paying for ones own decisions or is that asking too much. No people now expect the Government to subsidise each and every personal decision that they make up to and including solar panels, maternity leave, first home buyers grants and the list goes on an bloody on.
I also noted with satisfaction the WA has passed a bill cutting the rebate allowed for power back to the grid and wonder how long before other states follow suit and those being provided for by the Tax Payer pay thier own way again.
Firstly, governments actively encouraged homeowners to install PV systems because it obviated the need for governments to build a bunch of power stations. Particularly in Queensland, daytime use of electricity for airconditioners was such that Energex / Ergon emergency generators were run in many suburbs simply to stop the grid crashing. You won't hear that from the bloodsucking parasites in George Street, but then neither will you hear about the five billion per annum additional cost of corporatization / privatization.
Secondly, installation & FIT subsidies were needed at the time many of us purchased PV systems at around twice the current price, otherwise we wouldn't have been convinced to assist governments to avoid their responsibility to build power stations. Whether or not the previous level of assistance should be provided for installations now is another question. All that aside, formal contracts must be honored otherwise the biggest class-action lawsuit in recorded history will eventuate. For what its worth, I understand that the WA government has been forced to back down after being threatened with a lawsuit from Solar Citizens similar to the threatened one that convinced Queenslands General Disaster to pull his head in. Note particularly the FIVE BILLION additional cost Queenslanders have been slugged as a direct result of corporatization / privatization …. thats where price escalation REALLY originates. Unfortunately our politicians being the duplicitous lying slimeballs they are, obfuscation takes precedence over truth.
The domestic solar energy schemes had nothing to do with eliminating the need to build additional power stations. Domestic solar installations generate a tiny amount of electricity, and on cloudy days almost none at all, and don't meaningfully reduce the requirements for reliable grid power. In States other than QLD, solar could not possibly reduce the requirement for generating capacity, as this peaks at 6:00 pm – 7:00 pm when solar contributes nothing.
The various governments introduced the scheme to buy Green votes. Far more cost effective than building a large solar plant; lots of people make money from it (always a vote buyer) and as people can see the installations on roofs they act like billboards advertising the government's Green credentials.
The schemes are being wound back because they were massively over-generous, and people now obviously care somewhat less about climate change and the environment generally than they did a decade ago when these schemes were introduced.
As to the people who put solar on their roofs in the expectation of continued large government handouts – well, relying that government handouts would continue forever is a bad business model. If your solar installation is not a good idea without continued government handouts, you shouldn't have done it. If it was a good idea even without continued government handouts, then you really haven't got a problem.
'If your solar installation is not a good idea without continued government handouts, you shouldn't have done it.'
Too late now, we're stuck with the bloody system. I certainly shan't be servicing it or buying any attractive 'add ons' in the future. Just put it down to another expensive white elephant. There's a new scam every day.
PV panels are indeed getting cheaper, I could replace my 3 year old system for half what it cost me, nevertheless its not only provided me with FREE electricity for the time I've had it & its already 75% paid for itself. Had I opted to sit on the fence and wait for prices to reduce, I'd have forked out several thousands for my electricity and would not have a nearly paid-for system that should keep producing a meaningful income for another twenty years. All that aside, the opportunity of subscribing needlessly to the parasitic establishment was more than sufficient motivation to install a PV system although it must be said that three years ago I had little concept of how avaricious the politicians & power retailers would become. Its clear that we can expect escalating greed in the near future, especially with LPG, petrol & diesel fuel pricing, consequently I'm planning on solar hot water to replace the instantaneous gas system & battery-electric car to replace the ICE ones. Thumbing my nose at the establishment looks more appealing with every passing day.
Just waiting for Graphene tech to get off the ground, 60% efficient at the moment, works at any angle to the sun and 1/1000 the weight of silicon panels. graphene can also make super batteries. I did have silicon panels, moved, and now I'm prepared to wait 5 years to see how graphene goes.
China is the current source of 90% of the worlds graphene. A graphene/silicon price war ?
As always, weterpebb hasn't a clue what he / she / it is on about. Firstly, at the time the Queensland Solar Homes Program was rolled out, the **official** reason was to avoid the state incurring the cost of building additional power stations. You could easily verify that by reference to newspaper advertizments posted at the time. Secondly, PV systems do in fact produce meaningful output when its overcast. For example, during the first quarter 2013, my area was consistently cloudy / raining for the entire period, nevertheless PV output was still slightly more than 50% of what I get during a completely sunny quarter (as demonstrated both by the number of units exported and the amount deposited in my bank account), And yes, the meter **IS** read (not estimated) every quarter, as is standard practice with every PV installed property that consistently returns a negative bill. Thirdly, before large scale uptake of home PV systems in Queensland, it was necessary for Energex / Ergon to run their mobile emergency generators in certain suburbs right through the summer. This hasn't been necessary for some years & no new power stations have been built, in fact the daytime output has been scaled back in many cases. Fourthly, the people who installed PV systems in the past made a commercial decision backed up by a formal contract … but then I don't suppose you have any more idea what a formal contract implies than you do about PV output in cloudy conditions.
Of course that was the ***official*** reason.
You don't really think they would state the official reason is "we are trying to buy Green votes through a massively expensive energy program which has the sole benefit of advertising our Green credentials through lots of rooftop installations visible to lots of other voters" ?
This argument that there was a net economic benefit to the subsidisation of solar doesn't bear scrutiny. Firstly, they don't want you to scrutinise the argument, which is why they publish no figures on how much power that domestic solar injects into the grid at daily peaks, or how much the government is paying for it. In fact at the moment it is precisely zero; the peak consumption in QLD currently occurs at nightfall (around 6 pm) when domestic solar contributes nothing. But of course, they won't publish the figures; they don't want their customers to know how much money is being wasted in this way.
And if the idea is to minimise energy costs, as solar is many times more expensive than coal plants, electricity companies would build more coal plants if their motivation was cost. They are forced to buy uneconomic power through the MRET scheme, and that is the reason they subsidise solar.
Ohh, and your argument about cloudy days doesn't hold water. Sure, over a period of weeks or months, these average out. But weather patterns (being overcast) can affect a large geographic area (eg the whole of Brisbane) for hours or days at a time. This reduces solar cell output at that time (when it is cloudy) to almost zero. So if we were relying on that power – for factories, offices etc – then these would have to shut down when its cloudy. And if we aren't relying on this power, then we have built sufficient generating capacity to handle peaks even without domestic solar, and hence solar has not reduced our need for traditional power stations.
Solar is a joke for grid power. Its not reliable (doesn't work at night or properly on cloudy days). So it has to be backed up by something which is reliable. Like a coal power station. Or we get brownouts when its cloudy, and blackouts at night.
Its obviously escaped your notice that Queenslanders use airconditioners during the day & funnily enough those things use electricity at exactly the same time PV systems are working at peak capacity. You only need to check with Energex & Ergon to see what contribution PV systems have made although anyone who has driven around the suburbs with their eyes open would have noticed the absence of the emergency generators that used to be a common feature during summer.With that in mind, Blind Freddie could see how PV systems have seen how additional power stations have been avoided. I don't intend to buy into the relative economics or coal vs PV generation on a commercial scale, or even solar farms for that matter …. what matters primarily to me is my cost of living, and thanks to an investment in solar power, I'll never need to pay for electricity again. Even if the numbskulls in George Street manage to stuff-up something, I'll only need a few batteries and the system can go to Hell. Furthemore, if the parasites we elect had and semblance of decency, I'd establish a solar farm for residents of my community who for one reason or another can't have their own PV systems.Even if a coal-fired community power generator was 'cheaper', (highly doubtful on a small scale) environmental considerations would quite obviously prevent it being allowed in a 'green' area. Point is the parasites don't want the sheeple to have cheap power, and given your closed-mind attitude toward breaking the price nexus, its blatantly obvious that you prefer to support avaricious power retailers & the politicians who pander to them rather than embracing presently available and cost-effective solutions which allow the hoi-polloi to maintain some quality of life & at least some independence from those which regard them as simply milch cows to be exploited.
No, you can't ring up the electricity companies and ask them the contribution made by domestic solar at times of peak demand. (The peak demand determines the total generation equipment required, which you argue incorrectly is reduced by solar). They don't keep these statistics. They don't need to. The answer is zero.
On the Australian grid (which QLD is connected to), the peak demand for power is between 6:00 pm and 7:00 pm, when ovens, TVs, and domestic lighting gets turned on and many offices have not yet turned their lights off.
So the contribution of solar to peak network demand is zero, as the peak occurs as it gets dark when solar produces nothing.
So the total generation capacity required by the network (which is capacity needed to met peak demand at 6:00 pm to 7:00 pm) is completely unchanged by the existence of solar power, which contributes nothing at times of the peak demand.
All those rooftop PV systems are a terrific advertisement for the Green credentials of the State Government, and the government is prepared to subsidise home owners heavily to have such advertising on their roofs, but they do zero to reduce infrastructure (eg generation) costs of the network. Well, not quite zero; as PV power is nowhere near as clean as generator power, PV solar slightly increases infrastructure costs for power companies as they need to provide additional filtering and conditioning hardware.
Its a nice little scam between the government and home owners. The government appears to be green; home owners get money from the government and power companies. The losers are of course the taxpayer and normal electricity users. Congratulations to you for exploiting this little scam, but as one of the people paying for it, excuse me if I think that publicly boasting about it is a little tasteless.
"Well, not quite zero; as PV power is nowhere near as clean as generator power"
Does that include coal-fired "generator power". Very sad assertions there, not knowing anywhere near as much as you seem to. But it'd help it if you defined "generator power", pls?
The power coming out of coal fired power stations using traditional generators is far cleaner than out of a PV system. Traditional power stations produce a rock steady 50 Hz sine wave with effectively zero impedance. Solar cells produce intermittent power which usually looks very little like a sine wave, is not closely phase locked to the grid, and has transients. This needs to be fixed by the electricity company before it can be resold. This produces higher infrastructure costs for the energy distributor. Large scale generators (eg in coal fired plants) produce very clean power without anything like the same conditioning costs.
All costs born by regular electricity users to subsidise inefficient domestic solar systems.
I'd describe an average 25kwh per day exported to the grid during months of consistent heavy overcast as something slightly better than 'not working properly'. Sure its less than I get during periods of bright sunlight, but its still far more than needed to give me a meaningful rebate at the end of the billing period. Vehement opponents of PV systems love to throw up all manner of poorly researched arguments that don't hold water. 'Backing up' doesn't necessitate coal-fired power stations, even stone age lead acid batteries suffice on a domestic scale & sodium technology batteries promise far more cost-effective energy storage than we've ever seen previously. A number of associates have gone completely off grid even with their stone-age batteries and still manage to have most of the trappings of modern society without having to run a generator for more than a few hours per year. That to me constitutes an infinitely greater advancement than supporting the bottom-feeding establishment. Sure there may be bigger & fancier ways of generating electricity in the future, but its inconceivable that any will allow ordinary folk to escape the clutches of power barons to the extent that PV systems have done. 'Efficiency' isn't necessarily the same to everyone … personally I much prefer a lower efficiency arrangement that results in lower cost of living, but then I've never been one to support corporate profitability / globalization or whatever. Those who subscribe to those schools of thought are welcome to their beliefs, just don't expect me to follow.
"I'd describe an average 25kwh per day exported to the grid during months of consistent heavy overcast as something slightly better than 'not working properly'".
I doubt very much if you actually get months in a row when it is always overcast. The issue is short term loss of power due to it being overcast, lasting minutes or hours. Over the long term (months) this average out, but this doesn't help during those minutes and hours when it is heavily overcast.
So I don't understand why you keep using this misleading and irrelevant fact that over a period of months it averages out. That's not the issue.
Why don't you just wait until it actually is heavily overcast, and them measure the power output of your panels? How much are they contributing to the grid? This is what the electricity companies can be sure to get from domestic solar, and all the rest they need alternative generating capacity for, because people still use electricity even if it is cloudy. I bet you get very little power from your PV when it is heavily overcast, so the electricity company still has to supply the same total generation capacity whether PV is used or not.
As always, you are unbelievably thick !!! It just so happens that Queenslanders have a lot of airconditioners and these things not only get turned on during daylight hours but they also use a lot of electricity at exactly the same time that PV systems are producing peak output. Since I not only live in Queensland but also have business connections with Energex / Ergon, I'm aware that its no longer necessary to run the mobile emergency generators all summer, as used to be the case before all us evil people installed PV systems.Strangely enough, there hasn't been any other power input to the grid in living memory and the population has increased significantly. Whether or not daytime constitutes 'peak' electriciy usage is immaterial, PV systems are producing sufficient to power stuff that used to require a bunch of diesel generators. Whilst it is certainly possible for Queensland to purchase electricity from interstate, the cost of this is vastly more than whats paid to PV system owners (check the QCC report for details). I suggest you have a close look at the QLD governments billion dollar rip-off from Energex / Ergon and the four billion dollar annual overheads of Origin . AGL / rats & mice retailers before you crap on about PV costs.
Peak power consumption on the grid occurs between 6:00 pm and 7:00 pm. PV cells don't operate at this time. The existence of domestic PV does not change the traditional generating capacity required for peak times at all.
"weterpebb says:
And when everyone is on the smart meters, will they use the air con more during peak times or off-peak? Smart meters WILL change the way people use power and when if they all go to 'time of day' usage model.
so… you maybe correct for the short term (maybe not) but long term (which Australians seem to forget about hence we are no longer manufacturing much and importing cheap crappy reject food) it will have a dramatic effect.
Jeffrey Rush says
Omg solar cells is as good as communismm.
Solar cells are ***MUCH*** better than communism. Whereas communism or indeed any political system invariably provides disproportionate benefits for bottom-feeding parasites who consider themselves 'leaders', together with the ability to concoct all manner of justifications for their utter ineptitude, PV systems allow any of the hoi-polloi to avoid at least some of the male bovine excreta produced by the 'leaders'. Note that all of the political persuasion adopt the 'honorable' title when in fact the terms 'honorable' & 'politician' are mutually exclusive.
[bottom-feeding], [bloodsucking]
Could you dig up some new adjectives please? It's getting boring.
If / when our elected representatives demonstrate they are worthy of being respected, I'll be only too happy to do so. Unfortunately they constantly prove beyond any shadow of doubt that all of the above apply. In short. the words 'politician' & 'honorable' are mutually exclusive.
It seems you've forgotten theold axiom:
We get the politicians and governments we deserve.
They pander to the lowest common denominator; the swinging voter, aka Bogans of every stripe. Is it any wonder they play us like the fools we are?
The last "time" the "west" had "Communism" was before the "fall" from the Garden of Eden. Using the word "Communism", when referring to any system we can only read about, in seriously "winner-writes-all" historical documents and DVDs, fails the word's user, for their shallow political understanding of the human being and of history.
A society/nation/planet run by modern, free-market-gushing geeks with outright rejection of the depths of insight into human psychology, and of how good governance works, as found and expounded by the likes of Karl Marx, Henry George, David Ricardo, Et Al, is a failed society/nation/planet. :]
Basically, that's where the world is headed, for anonymous smart-arses and modern technology.
"Good governance" is a contradiction in terms. Anything truly 'good' doesn't need the coercion of 'governance'.
Over 4 billion years the only consistently effective guiding principle (providing survival) has been the evolving of instincts in each evolving species. That would still be the way today except that our species has outlawed the operation of Natural Selection.
Hence we arrive at 'Democracy':- the brainless concept that two morons are smarter than one genius. And the natural evolution of that little sideshow has inevitably produced endless streams of politicians who in their turn have given us coal-fired power stations.
The more profound question ~ raised here previously ~ is why do the voters continue to vote for them and submit to the extortion of taxation to pay for the bastards?
….oh, wait! I forgot! Two out of three of those voters are NOT geniuses.
Here's an option: a friend of mine recently interviewed by the ABC:-
https://open.abc.net.au/explore/82086
captain obvious says
So why would I invest in solar cells now when I could wait and get double the power later? Maybe even octuple the power further down the road?
I should say thank you to the early adopters I guess….
Why would you buy a computer/ipad/iphone now when you could wait and get double the processing power in 12 months?
http://en.m.wikipedia.org/wiki/Moore's_law
Ipads and computers are not designed to generate power.
If I believed they were only going to cost half as much in 12 months time, I would definitely wait.
And yes of course if the solar PV cells were (effectively) only going to cost half as much in 12 months time, then you would be better off waiting. There is no way the "savings" from operating a PV system 12 months earlier could possibly offset the 50% saving in cost from waiting a year.
You keep claiming the argument for solar is based on financial considerations, but you provide no financial information. As soon as a comment comes close to being about financial issues – like this argument that you would be better off waiting – you run away from the financial argument and start talking about iPads. As if iPads had anything to do with it.
I guess if you have no objection to paying the utterly scandalous prices demanded by Origin / AGL / rats & mice retailers for however many years then you certainly should wait as long as it takes, mind you one would probably pay for a few PV systems in the meantime. Personally if I was building a new house in 2013, I'd certainly include off-grid PV whether or not the technology will improve in the future, but then I've never been one for subsidizing grossly overpaid fatcat CEO types. That said, I have no problem with others doing their bit for the poor dears if such is their wont. My present grid-connected PV system will be switched to off-grid the day it becomes financially advantageous for me to do so.
Whether my PV system produces one milliwatt or a hundred megawatts at any one point in time is the very least of my concerns. What does matter to me is the size of the FIT rebate I receive quarterly, and that halved in the first quarter this year when the weather was consistently overcast, and yes it was 'consistently overcast' as is typical for the particular location at that time of year. For what its worth, certain places relatively remote from the rat-race / industrialization enjoy largely similar weather patterns year after year. The profitability and / or the output of whatever power grid players does not, and never will even figure on my radar. Those don't give a rats about my financial position so why FFS should I give a rats about theirs ?? I have no interest in energy shares, in fact the more I can do to detract from their profitability the more I like it.
basil says
READ THE ARTICLE – THEY HAVE NO PRODUCT.
Just spruking for investors.
Instead of lobbying for "silver bullet" new energies. Lobby for NO 4WDs and other large motors in major cities. Limit plane travel (see CO2 a return trip to London creates). Ban large yachts and fishing boats for the rich. My mate uses $1500 fuel just on saturday fishing trip offshore……..because they are rich enough to do so. And that is only a $700,000 boat.
ITS ABOUT HOW WE USE OUR ENERGY IS WHERE the argument needs to go !!
I had an argument along those lines with the local authority. I'd just about finished a new house that in all respects bar one was / is arguably the most energy efficient one in Australia. The sticking point was a 160 litre hot water system that was judged 'not energy efficient'. Mind you I export an average 50 – 55kwh per day to the grid so I provide many times more 'green' electricity than I ever use. The 'experts' wanted me to purchase a horrendously expensive 'energy efficient' hot water system that would have given me well over twice the hot water I need IF it worked in my area (which it wouldn't for various reasons). To keep the lame-brained ones happy, I installed a quick recovery gas system however I'll eventually switch to solar once I sort out a logistical issue. Point is I have a tiny carbon footprint compared with most, but thats clearly something beyond the comprehension of the shiny-bums.
Good On Yer, Baz!
All the geeks, while lost in their own buzz-headed electro-opinion wars for and against solar, miss that point entirely, aye?
Energy supply/demand = satiation v insatiability = techno v natural jollies = lost tribes of whiteguy v the Wise Tribes.
Troglodyte says
The issue for me is nowhere near as esoteric as some have sought to make it. As far as I'm concerned, the entire political / bureaucratic / media / energy establishment is corrupt beyond imagination & as such I'll do everything in my power to reduce my reliance on parasites which exist only to siphon off as much as they can. I'm about 90% self-sufficient in all other areas except transportation & I'm currently assessing options to avoid having to make contributions to camel-herding terrorists & oil barons. As with PV systems, there are members of various peanut galleries wont to crap on about irrelevant male bovine dropping, none of which bothers me one iota … the exercise is purely about telling the parasites to rack-off hairy legs.
CHEM5 says
pineapples are a good food, maybe we should power the world with them?
savenaturefree says
warming Australia and fires question for Tony
I just watched abc news about the hottest year on record frightening fires and Tony Abbott plan to cut climate change action funding. He will have a good time convincing me this is the right course of action. Try Googling me "savenaturefree" we are number 1 on Google search with just over 500 members.
2012 (the last year we have figures for) was far, far from the hottest year on record globally. Although measurements differ, that honour probably belongs to 1998.
And, I might point out, in these bushfires one house was destroyed and nobody died. Nothing very "frightening" about that. Bushfire death rates have to do with suburban encroachment into bushland and regulations concerning land use and clearing. They have almost nothing to do with climate change.
Some years ago I was in Adelaide & had an opportunity to drive through the Hills District. Its not difficult to see why there was so much devastation there, Houses perched right on top of ridge-lines with thousands of acres of tinder-dry timber on the slopes below. makes for a very effective bonfire. I doubt that even a rigorous scheme of back-burning would be effective in that particular area. That said, if perchance climate change causes rainfall patterns to alter to the extent that dry periods lengthen, particularly in summer, then bushfire rates must increase. Mind you that doesn't by any means excuse people building houses in extremely dangerous locations. I live in a rural area too however the vast majority of the forest is wet, and what little flammable area exists here is regularly burned off by the rural fire service.
Be pleased to be advised otherwise, but I certainly can't remember bush fires this big this early
A Dose of Reality. says
I think everyone misses the main point (in "fossil fuels v renewables"), consistently.
Fossil fuel entrenches the "infrastructure" model, where a "supplier" sells a product (energy). The majority of solar research is geared towards the "self sufficiency" model, where a household can produce it's own.
As such it is not a question of the raw cost of power generation that is the question or "battle" – it is the very relevancy of the "grid". If every household could generate enough power for it's own use (and adequately/efficiently store excess for later use) then the "grid" is irrelevant.
That's an awful lot of capital that'd become VERY expensive to upkeep and less profitable, at exponential rates. Who that capital represents – your end opponent to the renewables effort – is a rather more than considerable grouping.
"…enough power for it's own use (and adequately/efficiently store excess for later use) then the "grid" is irrelevant."
Interesting comment for someone using this name ! – technology to store excess is a long way off
Forgive me for making you look foolish because of your ignorance, but home battery technology is available right now, not a long way off, this is in fact that next big wave in home energy supply improvements, and it is a big problem for the grid people, because as they gnash and gnarl (raise prices, reduce FiTs), it becomes ever more compelling to ditch the grid completely.
I do believe this isn't necessarily a good development, but the responsibility lies squarely with the utilities they have no one else to blame.
And there are things that can be done, other than sticking your head in the sand, just as an example: Energy network company Vector in New Zealand is offering leases for solar panel combined with battery storage to householders.
http://reneweconomy.com.au/2013/future-grid-networks-focus-on-solar-storage-for-consumers-66152
Your argument is that it is less capital intensive to construct lots of self-contained solar systems with batteries than it is to use centralised grid infrastructure.
This is nowhere near correct. And it will never be correct. There are huge economies of scale in using shared centralised power stations, deriving from what are called aggregation gains. Basically, the peak power usage of 10 houses is far less than the sum of the peaks of the 10 houses, because people have different usage profiles. These "aggregation gains" are why we centralise infrastructure where we can, and is why you don't have a dam in your backyard, a heliport on your roof, an airport in your front yard and a mobile phone tower down the side of your house.
Come back when you actually can produce a self-contained solar power system which caters for the same power demands as the grid for a typical hone at lower cost. Its a dream. A very implausible one.
As always, weterpebb chooses to totally ignore the reality that big companies invariably regard their own profit as the ONLY thing that matters. Whilst its possibly true that a centralized PV power station could possibly be more economical to construct than a zillion itty-bitty ones, there is simply no way known that consumers would ever benefit. If there were savings realized, those would only result in even bigger bonuses for the already grossly overpaid grubs at the top of the pile. On the other hand, privately owned PV systems allow the average person to insulate themselves to lesser or greater extent from the predations of avaricious fatcat CEOs & bottom-feeding politicians. The utter crap peddled about private PV systems being responsible for electricity price escalation conveniently ignores the billion dollars per annum successive governments since that of Teflon Pete have ripped out of Energex / Ergon and the four billion cost of supporting AGL, Origin & the rats and mice retailers. The Murdoch press (never one to let the truth get in the way of a 'good' story) recycled the same tired old 'PV system owners are evil' claptrap in the Sunday Mail yesterday claiming PV systems cost everyone else a whopping $32 per annum. Gee whiz, personally I would have thought a five billion dollar per annum impost rated a tad more significant, but then Rupert would never dream of allowing any story detrimental to his grubby LNP mates.
*roll eyes*
no that is not my argument
maybe you should read my post again because you're clearly reading something into that isn't there
kimalicet says
Before you get all gooyey about batteries here are a few things you should know.
Firstly they are expensive, both to buy and to manufacture and in their manufacture they create an inordinate amount of polluting gases. A small household of two people usually needs about 12 x 4vDC x 1030AHr batteries to make it through the day and night with each and every appliance checked for the amount of power they use during the day. A set of batteries will cost about $16,000 and have a life of between 10 and 15 years before needing replacing. Then add the extras like wiring, installation, special cabinets to hold the batteries, regulator and the list goes on and on. It all sounds nice to have ones own power factory but even this system has its limitations and the reliance on coal fired power is still there or a dirty back up generator and battery charger. What makes me laugh is these sanctimonious clowns that rave about solar power but still rely on coal fired power to get through the day and night. If you are really that keen bite the bullet disconnect from the grid and live on 100% solar as we do or shut up.
Batteries are indeed a costly thing. I'm working through a lot of options right now & part of my solution is reducing electricity load as much as is humanly possible in order to minimize battery requirements. I don't believe I'll need anything like the capacity suggested as the house is arguably the most energy efficient in Australia. Mind you cost isn't necessarily the ONLY motivation for me …. there wouldn't be another person in the country with a lower regard for energy companies & their political compatriots, consequently reducing my reliance on these bloodsucking parasites is just as much a factor as cost-effectiveness. I see the price of LPG is also set to escalate by 300% or whatever, maybe that will give Murdochs lazy reporters something else to write about instead of bashing PV system owners.
well that's the thing, even in your overpriced scenario, $16,000 over 10 years is a good deal, if say you were to contemplate building a house that costs $400,000 and instead of of putting Italian marble in the bathroom, you merrily have some tiles, and put the difference into a system that will isolate you from energy utility shenanigans for ever it doesn't sound so painful.
If you spend a little more on panels and batteries, and an electric car, you can even immunize yourself from bowser shock.
Do I think if everybody becomes self sufficient is the ideal outcome? no I don't, the best case scenario is, as always, when the most number of participants are reasonably happy.
The grid is a very valuable (and not just in money terms) public good, even if it is owned by private companies, so what needs to happen, is that people who have invested in their own generating capability are treated fairly, those with batteries be connected to the grid so this storage capacity can be used to buffer against the peaks are also treated with respect, which presents the greatest cost in infrastructure investment by the utilities, which also need to be reimbursed by higher electricity prices, while they also write off the value of their assets. And this is not negotiable because the only alternative for the utilities is the death spiral.
What overpriced scenario, that's the cost as I can attest and that's just for a modest home where we don't use an electric kettle and a toaster at once, where we don't have every light on , where we turn off everything that has a standby every night, where we don't have a millions gadgets that need constantly charging overnight, where we don't have children that need to be"entertained" with TV, Games Consoles and the like, where we don't have air conditioning. Have a good look at some of the prices being charged for homes with stand alone power that use the average power consumption per day of an Australian household and the price will triple, quadruple or even more.
As for people who have invested in their own generating capability being treated fairly are you alluding to those that have by virtue of being able to afford Panels on their roofs forcing the price to those who cant afford it up and up. Its time this farce was scrapped and the most that people putting power back into the grid should be paid would be a quarter of the price that Power Companies charge the regular consumer or put the tariffs up for those people on the .44c buy back so that they are indeed paying an equivalent to those not so fortunate.
The idea of being 100% Solar is to be self sufficient and not be connected to the grid in any way shape or form and on looking at the habits of a typical Australian family, 2 adults, 2 kids there is no way that they have the self control to actually make this work and the screams when the power fails would be almost human.
Yes Minister, Yes batteries are indeed an expensive item but not just in the purchasing of them . They are also detrimental to the health of the planet as the raw materials needed have to be mined, then they have to be processed into the final article all taking coal powered power to make, then fuel to transport and deliver. Add to that scenario and the cost of just letting ones guard down for a moment can be costly as well. I deliberately ran my home as most people would run theirs, lights on, standbys left on more appliances etc, etc and in one week the batteries were so low that I couldn't run my refrigerator and freezer all night without the power shutting down (and they are the most efficient items of that nature that are available),that it needed 15 hours of generator charging to get them back to a suitable standard to run the house again. The maintenance is always ongoing, not costly but has to be done religiously or the batteries will not last the required time and more expense will fall upon those who have this idea that 100% solar is a doodle and trouble free.
This argument about people with PV systems forcing the price up is as fallacious as the concept of politicians being 'honorable'. Even the QLD governments own tame Competition Authority admits that only an infinitesmal component of electricity price is due to PV systems. What is ***NEVER*** admitted is the billion dollar per annum ripoff from Energex / Ergon & the four billion dollar per annum cost of private sector retailers. That five billion dollar per annum surcharge is ***INFINITELY*** more significant than all the PV systems on the planet. Furthermore, the price paid for interstate power is also many times that of even the highest FiT. Whats really going on here is a gubmunt orchestrated attempt at 'divide & conquer'.
Better batteries might not actually be beneficial for the solar power industry.
The issue is that low cost batteries would probably have a more beneficial effect on traditional power costs than on PV power. Coal plants have to run all night. Because of low demand at 2:00 am, energy is cheap at that time which explains why off-peak power rates are much lower. If we had cheap efficient batteries, the most cost-effective use would be in conjunction with coal plants. Charge up the batteries at night when energy is cheap, and discharge them at times of peak demand when prices are highest. This would very significantly reduce the amount of generation capacity we would need (as coal plants could operate at near full load 24 hours per day) and hence electricity costs.
Off-peak water heaters use a similar principle, but they store the electrical energy as heat in the water, much easier/cheaper than storing it as electrical energy.
Better batteries would change the world in many ways. Yes, they would improve functionality of PVs, but they are just as likely to reduce costs for traditional power, negating any competitive benefit for PVs.
Two problems I see with ditching the grid. Firstly it is the height of foolishness to remove such a fundamental level of redundancy (although if it were reduced to a backup, then it ceases to become economically viable for profiteers and instead becomes state owned)- especially when it is environmentally irresponsible to use them in areas where their polarisation will affect breeding cycles of fauna which lay their eggs on water.
Secondly, the notion that pv-based terrestrial solar collection is the ideal approach is shortsighted and farcical thinking when you start talking about baseload power (ie supplying 30k-50 k properties). The fact is that solar has always had 2 glaring flaws. The first is due to losses resulting from distance and the inverse square law. There is no way around that. The second though is that due to our magnetosphere (which as an aside, has been known to be in a weakened state for some time and a major cause of the radical climate change we are currently experiencing- compounded by cosmological issues due to our galactic orbit), the very radiation filtering by the upper atmosphere that makes life so desireable, also rips the guts out of the efficiency and effectiveness of solar power. The fact is that optical energy is merely a fraction of the solar energy which can be harvested. The moment you move from a terrestrial collector to an orbital one and move beyond the sole use of pv collection, you're suddenly looking at a vast increase in energy collection. Such an approach would still use pv collection, but it would also collect and up/downmix and convert all of the accessible em radiation (such as microwaves and xrays), beta radiation and gamma radiation (even if only using a steam turbune) into a tight beam transmission and beam it to ground based receivers.
Of course the irony is that at that point, you cease dealing with solar power and instead are in the realm of nuclear power (gasp shock horror). At that point you also discover just how much of an effect the inverse square law has had and how large a grid an orbital fusion collector can power. However such a paradigm shift really is a game changer in terms of the viability of solar power in any kind of baseload capacity.
beeden says
Nuclear, another finite resource for rollercoaster prices(that's just for the fuel supply), the industry is still "cleaning up" after Chernobyl, Three Mile Island, and with Fukushima currently/blithely polluting the coast of Eastern Japan/Pacific Ocean(still no idea when and how the disaster site will be contained), and 60+ years down the track, "Where the hell are we going to store these millenial unsafe nuclear fuel waste products?", did I mention the massive time it takes to build a nuclear plant and their ginormous cost to build? Nuclear fuel for the future, you have got to be kidding!!!
beeden, sadly yours is the very type of ignorant response to nuclear which due to just how common it is, is precisely the reason why there has never been an educated debate on nuclear power in this country. Noone with any level of common sense would allow dragsters with unstable fuel systems to be driven on our roads. Likewise noone with any level of common sense would suggest that because dragsters with unstable fuel systems should be kept off our roads, that we should ban all cars. Yet analogously speaking, that has been the state of play and the later of the two is analogously speaking, exactly what you have argued here.
To begin with we never would have had the disasters you mention had the world gone with high temperature pebble bed reactors. Yet as per usual with these things, the reason we got the rod core, water cooled reactor was because it was better suited to nuclear powered submarines. Then the very testing phase which would have proved the design was a ticking timebomb was circumvented because of cold war propaganda needs. Never let it be said that military intelligence isn't an oxymoron.
The fact is that we never would have had "three mile island", "chernobyl" or "fukushima" had the world gone with pebble bed reactors as they are quite literally meltdown-proof. By all means research this for yourself and educate yourself. A great starting point is a wired magazine article from 2004 which last I checked was easily found by typing "wired let a thousand nuclear reactors bloom". The moment you shift to that style of reactor, your entire argument about safety goes right out the window.
Then you have the fuel argument. I completely agree that using uranium was a completely shortsighted move. Between the half million yearhalf life and the weaponisation aspects of it, it was only ever going to end in pain. Conversely thoruim only has a 500 year half life and cannot be weaponised. That's ignoring waste reprocessing techniques such as hybrid fission-electron bombardment fusion reactors which dramatically bring that half life down.
Furthermore you don't merely stop at perfecting fission but then look at perfecting fusion, whereby you're dealing with helium3 amd deuterium. We already know there are rich helium3 deposits on the moon and besides the fact that deuterium makes up 1/6000 of seawater, the gas giants may well prove rich fuel sources for it.
In short, by all means we should have a serious and informed debate about nuclear power before we implement it- comprehensively weighing up the pros and cons. However that means calmly weighing up the facts objectively as opposed to having a "discussion" along the hysterical and uneducated more reminiscent of the likes of the Salem Witch Trials.
Tony Lear says
The "Narks" are utterly correct when they say Solar must compete economically with fossil fuel before it can be adopted. Get it right Solar and you will be number one but until then stfu because you will break our economies with your fantasies.
gary may says
I like the idea of solar power….but….your not going to get the full benefit from any solar panels for one important reason. If you know whats happening in our skys u will know that the sun is being deliberately blocked out most days by toxic chemtrails that turn into toxic chem clouds, so u end up with very little sun & as you know solar pannels need direct sun to work best. If you don't know anything about chemtrails you best google it & find out all u can about it because the media is gagged from informing people.
Male bovine dropping. During the first quarter this calendar year, my area experienced almost exclusively heavy overcast for the whole period, nevertheless PV output was still 50% 0f peak. Narks are quite welcome to dream up all manner of fanciful nonsense but just remember they don't have any effect on reality.
If the peak power production of your PV cells is only twice what you get on heavily overcast days, then there is something wrong with your setup. Peak power should be many, many times higher than what you experience when it is heavily overcast.
NotaNarkJustaRealist says
What do you mean by many times WeterPebb. If there is a %50 reduction in the incident solar radiation then, then you would get twice as much out at optimum solar flux. If it is a %80 reduction, then you get five times as much. The point is you don't get peak output apart from 1-2 hours a day and if you don't have an energy storage system you can't use the energy generated at the peak output. Peak output does not correspond with peak consumption in time which is generally between 4pm and 8 pm at night.
There is a considerable daytime spike in electricity consumption due to the almost universal use of airconditioners in both homes & businesses. Funnily enough, this just happens to be the exact same time when PV systems are operating at close to peak efficiency. Some years ago, it was normal practice for Energex / Ergon to trot out their fleets of 300kva / 500kva / 1100kva emergency generators & park them in high consumption areas for the duration of the summer. Since the widespread installation of PV systems, this is no longer necessary. Note particularly that the generators were ONLY necessary during daytime, whilst they were left in place, they were only turned on in the mornings and off in the afternoons. As for the claim that peak PV output is only achieved for 1 – 2 hours daily, that is probably true with systems facing east or west, however a system sited for maximum yield ie due north at a 20 degree angle, will give close to maximum output for many hours. Whilst I've never felt the need to inquire in detail, I suspect photovoltaic cells work with a relatively wide spectrum of radiation, not necessarily the visible component, hence the higher output than expected by some when the sun isn't shining..
Yes Minister:
1. There is no daytime spike in power consumption. I have already posted the figures for NSW power consumption over a 24 hour period (and I believe other states are similar) which clearly shows daily maximum consumption occurs in the early evening. When the most lights are on. Because it is getting dark. At which time solar produces nothing.
2. Energex didn't stop deploying emergency generators because of the widespread installation of PV systems. They have stopped doing it because total demand for electricity in Australia is decreasing, and has been since 2007. We are, as a nation, producing and consuming less power than we have in the past, so there is no need for emergency generators. So more expensive facilities – such as emergency gas turbine generators – are being phased out as demand falls. Nothing to do with solar power increasing supply; the driver has been increased energy efficiency reducing demand. We now have plenty of conventional power stations for our needs.
There is no daytime spike in power consumption.
Hmmmm, and I always thought airconditioners used electricity, Maybe the ones you have in NSW are steam powered !!!! Interestingly, I've seen the electrical load figures for south east Queensland and believe it or not, there is indeed a very significant ramp up corresponding with all the airconditioners getting turned on. Furthermore i have regular contacts with Energex management and am more inclined to accept their explanations rather than those of some clown known to invent fairy stories.
Yes Minister.
Yes, there is a considerable ramp when airconditioners get turned on. But the peak use of electricity occurs in the early evening. When the Sun doesn't shine.
See for example http://energyaction.com.au/peak-demand-what-is-it which shows average power consumption by time of day. Note the peak occurs on average from 6:00 to 6:30 pm, at which time households are using almost the most energy (people come home and turn on lights) and commercial use has not ramped down much for the evening.
Perhaps if your "regular contacts at Energex management" could supply a graph of average daily peak use by time of day which you claim to have seen, as I have done? So we aren't relying on your recollection of some conversation which turns out to contradict published sources?
In any event, we no longer have problems with daily peak power. Electricity consumption in Australia has been falling for 7 years in a row. On the east coast of Australia (which is connected into a grid) we now have excess generation capability. So more expensive means of generation designed to handle peak loads – such as gas turbines – are effectively being mothballed; in the face of decreasing demand we have no need for additional generation equipment. The crazy MRET scheme is forcing companies to subsidise additional (and extremely inefficient) generation equipment when we already have more than we need. MRET is economic lunacy in the face of falling demand.
In any event, solar does not help us with daily peak loads. Firstly, solar doesn't operate during the daily peak (which occurs as the Sun sets in the evening, when people need artificial lighting). Secondly, as demand for electricity is falling, we already have more generation capacity than we actually need.
By all means install solar power for yourself. I don't care how you generate electricity. But don't kid yourself that you are doing the rest of us a favour; you are not. And in particular, if you use a feed in tariff of more than the wholesale price of electricity (maybe 8c per kWh) you are simply ripping-off other customers who are forced to buy your more expensive electricity. Just because this FIT scam is legal doesn't make it morally justified.
For my system to produce more than twice the output on a clear day as it does with heavy overcast, it would require a 10kw installation to generate something like 20kw output, or in excess of 100kwh per day. Unlike a few self-proclaimed 'experts', I'm in the situation of having actually owned a few PV installations over many years, consequently I've had the opportunity to observe what really happens under different climatic conditions. For what its worth, it doesn't necessarily conform with the beliefs of solar philistines.
you are playing with words …. makes me think you've worked in the legal area perhaps because twisting words is typical of legal practitioners. Who gives a flying f**k when 'peak' usage occurs !!, My point remains that PV contribution to the grid is CONSIDERABLE at the very times all the airconditioners are running full blast. During Queensland summers, it would be difficult to find even one house or business premise which doesn't have airconditioning running & they certainly aren't all 1kw units !!.
But don't kid yourself that you are doing the rest of us a favour;
I never at any point suggested I was into doing favours for ANYONE. My objective was simply to insulate myself from the predations of greedy politicians & their corporate mates. As for 'ripping-off other customers', thats far from correct & nothing more than parroting the verbal diarrhea from General Disaster & Co. Even the QLD governments own tame Competition Authority identifies only a tiny contribution to electricity prices from PV system owners despite the politicians choosing to crap on as if the major cause of price escalation is PV power. What they will never confess to is the five billion dollar per annum cost of corporatization & privatization, a figure VASTLY higher than that due to PV systems. Furthermore, the price paid for power from the interstate grid is many times that paid under even the highest FiT, but again the philistines invariably ignore that as well.
MsBridgit says
NARKS? I have heard of Coppers Narks.
janet patzwald says
when are they going ti invent a super storage that would replace all those battery banks i have solar thats connected to the grid so dont have batteries
Great question – it has already been invented and proven: molten salt.
http://www.solarquotes.com.au/blog/solar-storage-breakthrough-spoil-narks-party/
W Stuart McCann says
Finn, I am somewhat bemused at the lack of discussion on CSP. Back in 2006 on the 27th Nov an article by Ashley Seager in the Guardian caught my eye "How mirrors can light up the world" It was a fascinating read, not least the part about the development of HVDC cables which can transfer power over a distance of a thousand kilometers for a loss of a mere 3%. The thought of a chain of CSP powerstations across North Africa connected together covering several time sections of the globe and across the Mediterranean to Europe, made me think of what could be done across Australia with such a system. PV panels are great but real power from the sun requires CSP to produce enough to power communities. The sun is always shining somewhere. The problem is sending the power to where the sun doesn't shine. (Try to resist a smart remark) I am tempted to send the whole article to you but it might take up to much space, Cheers!
Good idea in theory, however any community based endeavour that bucks the established system to the extent that it costs some major entity money, is guaranteed to be a failure. I attempted to establish a solar farm in my area however the 'renewable energy division' of the state government advised there would be no assistance or incentives (in reality the clowns took action to render the project unviable) …Reason given for the concerted opposition was that such a project had the potential to reduce the profitability of the government controlled power generation & wholesale businesses. So much for a mob supposedly into 'renewable energy' !!!
As far as I'm aware its not available commercially as at October 2013. I recall speaking to some professor mit funny name (russian perhaps ??) supposedly at a southern university a few months back & he said its quite functional … he's got some tribe working on commercializing the project. Hopefully it won't get bought out by the power company parasites and/ or their grubby mates.
To begin with, Godwin's Law doesn't apply here because the historical record shows that the remnants of the Nazi party (such as Prince Phillip), the SS (such as Prince Bernhard) and the British Eugenics Society (Sir Juylian Huxley) all fled to and founded the modern environmental movement. In fact, the fact that the modern environmental movement in essence argues for mass genocide (in fact it is on record as wanting to "combat overpopulation" to the point of reducing the human race to under a billion- ie committing genocide against over 5 billion people) rather than on space colonisation and exploration and developing the high level technologies to make it possible for the bulk of the human race, speaks volumes in that regard.
Of course the fact that the average person associates what is actually eugenics with being a solely Nazi ideology, solely associates the Holocaust with the Jews (which made up just over half of the victims of Hitler's genocide programs) and solely associates it with the Nazis, rather than organisations like the Fabian society (which funnily enough was the impetus for the Stolen Generation and which by at least 2010, Julia Gillard was still officially a member of- in addition to the likes of Obama I might add), is the reason why we will never come up with the high technology we need.
To take it back to the technical debate though, here's an interesting breakdown someone laid out on comparitive energy densities (Megawatts per square meter):
Solar–biomass .0000001
Solar–Earth surface .0002
Solar–near-Earth orbit .001
Fossil 10.0
Fission 50.0 to 200.0
Fusion trillions
Notice that on the figures there, that to be competitive, Solar-Earth Surface, which is the type of technology in question, has 50,000 times less energy density than fossil fuels, which are your baseline. Even if you double that, then you're still out by a factor of 25,000.
Don't get me wrong, Solar has auxilliary uses, but considering the energy losses due to the inverse square law that Solar is plagued by (essentially you're siphoning fusion power at an incredible distance from the reactor with solar), it's highly unlikely it'll ever have the energy density to be a reliable baseload source – not unless you destroy large tracts of land to facilitate a power plant hundreds of times the size of a standard coal-fired power station to make it work.
Yes you have solar-thermal, but even then you still need a significantly larger power plant to make it work and there are still issues with QC in practice on solar cells.
As others have said, nuclear fission is the likely immediate solution, but even that should be a stepping stone to fusion.
The fact is that nuclear has never been properly done in the modern age save for Germany in the 80s, South Africa and China. The original pebble bed reactor was scrapped in favour of the rod core reactor because of the needs of nuclear submarines, was never properly tested due to cold war propaganda, is dirty, unstable and for anyone looking at the technology and its history, Fukushima, 3-Mile Island and Chernobyl were foregone conclusions.
The fact is that we need to look to pebble bed reactors as the next step to mass power. Not only is it impossible for them to melt down (due to the laws of physics [the 'melt down' temperature is 1600 degrees, but the graphite casing on fuel cells has a 2000 degree melting point] as opposed to the walls and walls of systems and redundancies on rod core reactors), but they use far less fuel than rod core reactors due to doppler broadening.
The moment you switch to thorium as a fuel your half life drops to 500 years down from half a million years. Then you have waste reprocessing techniques that can radically speed up that process, such as using electron bombardment fusion reactors (not yet self sustaining or cost effective, but operational enough that we could use them in this capacity).
As others have said, we need to take another look at nuclear for baseload power- but a serious and genuine look at it.
However the ultimate goal has to be fusion power. If we can get fusion working, not only does tritium (the waste product) have a half life of 12 years, but deuterium makes up 1/6000 of our oceans, making extracting it (and again, safe extraction methods could be found) quite possible for most nations on the planet (those without coastlines could even look at offshore extraction plants) and giving them energy independence.
However such an outcome is unlikely. The same big oil who pushes fossil fuels are controlled by the big banks – who are run by the very types of individuals who are ultimately calling the shots of the environmental movement and have absolutely no interest in a thriving, intelligent, high-energy, high-technology society.
Alternative / renewable technologies are certainly unlikely to be properly implemented on a large scale for exactly the reasons mentioned, however they are nevertheless still quite viable on a small scale even though the ultimate 'efficiency' may not be realized. Those of us with an all-abiding contempt for the parasitic establishment choose to take advantage of alternative technologies that reduce our reliance on the system that exists purely to extract the absolute maximum from us whilst returning the absolute minimum possible. Reducing ones carbon footprint also reduces ones cost of living, and reducing ones cost of living significantly reduces the number of pre-tax dollars one requires in order to maintain a desired lifestyle …. the fact that this 'bucks the system' is a very good thing when one has as low a regard for the political / bureaucratic / multinational establishment as I do.
"Yes Minister", as I said, solar works in an auxilliary capacity.
Although given issues with solar panels and fire, as well as solar panel QC issues, we should be encouraging people to not mount them on their roofs, but ideally on slabs in the backyard with some kind of isolation in the event of shorts and fires.
Regarding things like carbon footprints though, we need to realise that while climate change is real, the evidence points to cosmic forces being far more of the problem than human activity.
The big problem we have currently is our weakened magnetic field, making us more prone to cosmic radiation, which in turn is causing additional tectonic activity- which the Haiti earthquake of 2010 proves we have a flawed understanding of – or the model would have been right. It's no coincidence that in light of that and the natural disasters we've faced, that the rim of fire is currently active.
Of course, what is compounding this is our current galactic orbit. Currently the solar system has crossed the galactic plane and is at a sinusoidal peak in its orbital path- an event which happens every 62.5 million years. The problem with this peak is that we no longer have other star systems shielding us from extra-galactic radiation.
In fact the fossil record has been found to contain records of mass extinction events to corresponding to this orbital movement. If we really want to save the planet, then we need to focus on expanding our cosmological knowledge and applying those understandings technologically in ways which assist our magnetic field and actually minimise the effects of the current cosmic phenomenon on the biosphere.
Hypothetically, an increasing solar magnetic field could deflect galactic cosmic rays, which hypothetically seed low-level clouds, thus decreasing the Earth's reflectivity and causing global warming. However, it turns out that none of these hypotheticals are occurring in reality, and if cosmic rays were able to influence global temperatures, they would be having a cooling effect.
http://skepticalscience.com/cosmic-rays-and-global-warming-advanced.htm
The article is seriously flawed. It contains the following: "between 1970 and 1985 the cosmic ray flux, although still behaving similarly to the temperature, in fact lags it and cannot be the cause of its rise."
However, ice core records also shows that CO2 increases lag temperature increases in a similar manner. This is entirely discounted by the climate "science" community, who say that this inversion of cause and effect proves nothing.
Yet, in a slightly different context, this inversion is taken as "proof" that cosmic ray flux has not contributed to increased temperatures.
Climate "scientists" cannot use one argument when it suits them and the exactly the opposite argument to prove the opposite when it suits them. Well, they can, but they shouldn't expect people to believe them. Which is what is happening.
Overall, about 90% of the global warming occurred after the CO2 increase (Figure 2).
Figure 2: Average global temperature (blue), Antarctic temperature (red), and atmospheric CO2 concentration (yellow dots). Source.
The problem with that article Finn, is that it hasn't looked at the whole picture and has taken far too simplistic an examination of the problem. For starters, you need to look at what the fossil record is telling us- namely that there's a 62 million year mass extinction cycle and that we're currently approaching the next one.
As for external forces themselves, "cosmic radiation" is not the only type of stellar force you have to deal with. Currently the Milky way is being pulled towards Virgo on it's northern side (which we're exposed to at the sinusoidal peak of the Solar system's orbit) which in turn creates bow shock. This distortion, which affects gravity, would not only have an effect on the planet's tectonics, but affect solar activity. which would in turn affect the planet's temperatures.
That can't be a coincidence in light of volcanic activity under the poles and the string of natural disasters that have taken place over the past few years that have correlated with the rim of fire being active.
I suspect you'll find the following article and the comments section listing further reading on the subject, most eye opening:
http://www.centauri-dreams.org/?p=1378
This graph was actually from the skepticalscience web site that you love to quote; it is quite misleading. A lot of what they say is. The graph only goes back 22,000 years. The age of the earth is 4,300,000,000 years. They have selected a slice which is 1/200,000th of the earth's history.
Fortunately, elsewhere on the skepticalscience site they have graphs which represent more than 1/200,000th of the data. For example, http://www.skepticalscience.com/co2-lags-temperature.htm has proper graphs covering a significant fraction of the earth's temperature history and states "However, based on Antarctic ice core data, changes in CO2 follow changes in temperatures by about 600 to 1000 years, as illustrated in Figure 1 below."
So on one page, and based on 1/200,000th of the data, skepticalscience claims that temperature follows CO2. On another page, which doesn't have a narrow timeslice carefully cherry-picked, skepticalscience points out that CO2 follows temperature by 600 to 1,000 years.
Its not science. It is badly written propaganda which nobody bothered to proof read to see if it was even internally consistent. And you use this site as an authority?
Your link is the page I took the graph from. Have you actually read the page that you link to? It completely demolishes your argument.
To make it easy for you, just watch this – no reading required:
http://youtu.be/8nrvrkVBt24
Your mention of solar panels & fire is the very first time I've heard of it. I've owned a number of properties with PV installations & have regular contact with many other owners, none of whom have ever mentioned their systems catching fire. Furthermore, no insurance company I'm aware of charges any extra for properties with solar power & given the propensity of those bottom-feeders to charge for everything imaginable, I'm certain there would be a penalty if indeed there was any risk involved. The nearest I've heard of are rumours of issues with lithium batteries however I doubt that would amount to any significant number given that the vast majority of hybrid / off-grid systems still use lead-acid batteries for cost reasons.
"Yes Minister" if you're using dodgy panels or use a dodgy installer, you wind up with a nasty trifecta of issues. If you use dodgy panels, then the panels can be prone to shorting out and due to the high voltages involved, causing electrical fires. If you use a dodgy installer then not only can you not have things like isolation switches installed, but dodgy wiring itself can cause an extreme fire risk.
The problem that you have is when a building does go up (and not even in terms of the solar panels starting fires themselves), solar panels in some cases can actually make roof access to a building impossible and in some cases it has resulted in the policy of buildings being left to burn down in the case of fire due to the extreme risk of injury to firefighters.
Here are a few articles on the subject I found with a quick google search (and yes I am aware that one of them is Fox News heh):
http://www.heraldsun.com.au/archive/news/danger-fears-over-solar-panels-in-fires/story-fn7x8me2-1226167564759
http://www.triplepundit.com/2013/09/rooftop-solar-panels-really-hinder-firefighters/
http://www.foxnews.com/us/2013/10/02/firefighters-alarmed-by-dangers-posed-by-rooftop-solar-panels/
As an aside, solar panels actually kill off insect populations due to the polarisation of the panels playing havoc with insect breeding cycles (confusing them for water and laying their eggs on panels instead.
I'm by no means saying solar should be avoided. However it's something which people need to go into with their eyes wide open on.
Also if we're keen on preserving the environment, then there needs to be some factoring in of where not to allow solar panels in terms of disrupting insect breeding cycles.
Cara says
Nark? As in slang for a narcotics agent or someone who works as an informer for them? What's that got to do with solar power? Next time don't embarrass yourself by using slang you don't understand.
ye olde cultural whazzat??
Australia—nark = irritated complaint.
narked off = annoyed.
narky =in a bad mood and picky about it.
America—-nark = federal or state narcotics agent, da fuzz.
all this is a bit likeAustralia
wowser = prude, wet blanket, Mr and Mrs Grundy, spoilsport,
pain in the neck or arse.(an ass is a donkey)
wowser +yippee, yay and so forth.
goddit?
Shona Duncan says
A very appropriate use of the word Nark, many energy companies that know this tech is on the horizon are flogging off their old stocks more quickly than you can say 'nano tech'. Nano tech has also been subverted by the military as a biological weapon with a kill switch.
Frank Flobster says
Whatever the waffle, I live in a notoriously wet part of southern Victoria and I haven't had an electricity bill for 15 years. I did replace my batteries two years ago (under $5000). For a couple of weeks around the shortest day (which is shorter here than in Qld) I have to watch my electricity usage. I could just buy a few more panels but it isn't worth the trouble.
What batteries were / are in the $5000 battery bank & how old were the previous ones ?? According to advice I've been receiving, battery price is expected to drop dramatically in the next five years so if thats true, there isn't much point buying top of the range ones now.
I only have grid-connect at present but hope to get an off-grid system installed in the new year. Whilst i have a substantial excess of power so no bills for me & a handy income, I'm still 'using' electrons that I could sell for more $$$$ than the ones for which I would otherwise pay, consequently the off-grid system will pay for itself albeit not quickly. Output does drop during long periods of heavy overcast but typically only to about half. I've done a lot of investigation of the pros & cons of whacking more panels onto the grid -connect system as opposed to a different off-grid system. Whilst its a lot cheaper to just add panels, I'm advised they would probably shorten the life of the inverters, thereby reducing the viability of that option. A complete off-grid system is obviously far more expensive with (probably) a longer payback but shouldn't have any reliability issues.
Pejay Kilroy says
And here was i thinking Nark was a Narcotics Officer, and that, cointerpoised with a bed of what look like Hypodermic Needles,… oh never minds I was obviously wrong.
drdingo says
Pejay, you win, it's only taken 6 months for someone to answer the original question !
LOL, Bazinga.
Talking to a very well respected installer of Solar last night and its very disturbing. He is saying that the panels now being put on roofs are so badly made that they are falling apart as we speak, or type. People say their panels are german or swiss but have a good look and they are made in China or indonesia. Some panels being installed have only a 12 month warranty and are being slipped into the system illegally and sold to unsuspecting people who pay top dollar for shoddy panels and installation and when they fail have no recourse as the installer wont even answer the phone and the manufacturers warranty isn't worth the paper its printed on.
As in every industry there are good installers and bad installers. The CEC has actually done a fantastic job with their accreditation and Australian Standards for Installation. But yes there are some companies that cut corners. And yes – some shonks try to pass off Chinese made panels as German:
http://solarquotes.com.au/panels/german/
That is why I am so fussy about who I let quote through SolarQuotes. I have turned down hundreds of solar companies because I don't believe they will give the service befitting of a SolarQuotes installer. So rest assured, kimalice, if you get solar through this site you will end up with a well installed system. 🙂
If you want to know the truth about solar warranties this will help also:
http://www.solarquotes.com.au/blog/your-solar-panel-warranty-what-you-need-to-know/
Yet Finn, this is the exact type of nuanced debate we don't tend to have with the issue of energy sources. We tend to have an attitude of nuclear="evil"; solar="sacred magic bullet" where dogma, far more than beliefs, tends to rule the discussion.
The fact is that as your own post here proves, while solar certainly has merit on a small scale, it's not without it's share of pitfalls. Where is the public discussion on issues with panel QC issues, installer issues and in issues of fire, roof access/safety issues in terms of firefighters? Where is the discussion on nuclear which actually factors in HTPBRs? Where is the discussion on the limitations of a solely PV based approach to solar, as opposed to a comprehensive, nuclear power approach to solar where we look at collecting more than just optical energy from the sun (dramatically increasing the output of solar in the process)?
Surely with something as critical to modern society we need to move toward such a measured and rational approach as to what is feasible and where, the limitations of various approaches and here each power application will give society the optimal result.
kerry says
lets hope this system doesnt end up like the 100 miles per gallon carburetor the fuel companies bought out and destroyed
I'm in the process and panels are so cheep now that I intend not to use the hot water converter but rather use surplus electricity to heat my water. We get diddly squat for putting it into the grid so why not hot water, why not 2 tanks, 3 tanks whatever and this is then in effect a way to store energy without batteries.
What do you do with all the hot water? I was wondering the same thing, if only you could heat water and then use that heat energy at a later date, say at night – but how?
You can't. There are theoretical limitations to the efficiency of heat engines which means that even a perfect heat engine couldn't extract more than 10% of the energy used to heat water for a domestic hot water system. And even this would require a heat sink capable of absorbing the energy without appreciably warming, fine if you have a backyard swimming pool but otherwise impractical. (For a mathematical treatment of this, Google "Carnot cycle").
In practice, reliable heat engines which operate at low temperature differentials do not achieve anything like the theoretical efficiency, low that this is. You would be lucky to get a few percent of the heat out as electrical or mechanical energy.
Which is a huge pity. If we could build efficient, reliable heat engines which operate with low temperature differentials, our energy problems would be solved. We would simply pump up cold water from 100m below sea level (uses very little energy as the density of sea water at 100m is the same as the density of water on the surface) and use the heat engine to transfer heat from warm surface waters to the colder water from deeper in the ocean. This energy is free and essentially unlimited. The only thing making it impractical is the fact that we haven't got/invented suitable heat engines.
As I keep saying, the world is awash in energy resources. 50 years from now oceanic heat engines may well be the cheapest way of producing electricity. They operate 24 hours a day, require no fuel, and the only pollution is very localised cooling and warming of oceanic waters – which occurs with all thermal power plants anyway. The only impediment is technology, and that is something we humans are good at.
Stephen Lipshus says
To Andrew Richards and Weterpebb, thank you for a very interesting read tonight.
I wasn't aware of a these things you mentioned, but will now go and investigate.
Thanks again for sharing your knowledge.
As for the rest of you, please refrain from commenting on such trivial matters, forget about "Nark" as clearly there are more important things to discuss.
Murray says
Geo Thermal Energy is the go, still works when it's dark. A good base load energy source.
Geothermal definitely has merit, however last I checked, weren't there issues with exactly where you could put a geothermal tap (without doing a stack of drilling to manufacture one that is). Ultimately, we need to head towards fusion. Even if it doesn't get used much on the planet itself; at some point we'll need to look at colonising space, and helium3 holds the most promise in terms of a fuel source for interplanetary travel. That of course ignores the usage of iy in being able to recycle 100% of all landfill.
I'd dearly love a geothermal setup in my backyard but even if I could afford to pay for a couple of thousand metre deep drillhole, I don't believe the equipment is available on a small enough scale for home use. These kinds of technologies are all very well but they don't take account of the main reason most people install PV systems, namely to minimize their reliance on greedy energy companies & duplicitous politicians.
"minimize their reliance on greedy energy companies & duplicitous politicians."
See these types of arguments are precisely why our infrastructure is in a mess. Never mind the fact that what we need on macroscopic level is for the national grid to return to a place where it, like other pieces of infrastructure exists for the sake of the general welfare of the people and to facilitate industry and business as opposed to existing for the sake of economic rationalisation. Never mind the fact that the system clearly needs to be held to account and needs everyone to demand it en masse. No, instead what you have responded with here is the cynical equivalent of the very "she'll be right mate" attitudes which are the very reason for the very state of play you claim to take issue with.
Any personal power generation a person can safely and effectively use will always be a bonus, however this notion that we should move away from having a grid on the sole grounds that the administration of it has become corrupted, is utterly ludicrous and completely irrational.
I'd love nothing more than to see the utterly crooked system cleaned up and in particular, all essential services returned to their rightful public control. Unfortunately I cannot imagine that occuring as long as the present culture of corporate greed & political male bovine dropping is tolerated. As I've commented countless times, the concept of large scale alternative energy technologies are all very commendable however its inconceivable that consumers will ever see any benefits, in fact I can well imagine arguments being mounted for significant price increases. That in a nutshell is why I am far from convinced that there is any point in pursuing alternative energy on a macroscopic level. We've already see the results of allowing big business get its grubby claws on essential services and nobody in their right mind could possibly support any expansion of this nonsense. It may well be that stifling innovation is the result, but there is nothing new about limiting new technologies when they threaten the profitability of multinationals.
Many years ago there was a statement made about the love of money being the root of all evil & the significance of that was never more obvious than it is today. Blind Freddie can see that corporatization / privatization of essential services must inevitably lead to MASSIVE operating cost escalation regardless of any possible 'efficiency' increase. Public companies exist only to make an operating profit whereas the original concept of public sector entities was to minimize overheads by ensuring they remained 'non-profit organizations. Politicians as a race (being mostly failed lawyers with all the 'interesting issues' endemic to that mob) are experts at stuffing their own pockets with public money whilst avoiding any possible semblance of accountability / responsibility, hence the headlong rush to flog off every asset not securely bolted down. It matters not that the sheeple are expected to pay extremely dearly for the aspirations of those they appoint to look after their (ie the sheeples) interest.
There seems to be this idea that somehow Governments are going to have to fund alternative power generation when in reality it is the so called grubby industrialists that will be doing it. Government cant afford the outlay and the ongoing costs of maintenance whilst big business can. This fact and this fact alone should tell people that alternative power will be more expensive than what we have now as big business is not going to outlay billions upon billions of dollars without making a profit. Only those who live in lala land would think anything different. The cost of power whether coal fired, nuclear or alternative will get more and more expensive not cheaper as that is the way of things. The only real alternative is to do what we have done, 100% solar power and a backup generator for when the sun doesn't shine for a couple of days but of course there will be those who think the Government should pay them to do this. Take resonsibility for yourselves and stop expecting the tax payer to fund a lifestyle that you choose.
Yes Minister, the problem with that response is that it's precisely everyone responding that way and giving up which allows that very status quo to continue. Often people say "I'm just one person, what can I do?" The answer is, that if you and everyone else ho felt that way got together and saw what you could do collectively, your mind would most likely be blown.
Kimalice, your claims about governments being able to fund large scale infrastructure are a myth. In fact the Commonwealth Bank as initially set up to do just that. The fact is that if our government looked at the resources it owns (including mineral resources and its capacity for growth and generated that credit to itself as a loan (much like a business getting a loan) then that issue would soon go out the window. Need 100 billion for a national high speed rail network? Done (the railway pays for itself both directly and indirectly in terms of the commerce it facilitates). Same goes for any kind of infrastructure project you can name, including power generation, big water projects and low interest loans for things like manufacturing. The truth is that contrary to the myths of politicians, we don't need big business to fund infrastructure- just that by having backroom deals, politicians can secure post political retirement jobs for themselves, as well as jobs for the boys.
Need 100 billion for a national high speed rail network? Done (the railway pays for itself both directly and indirectly in terms of the commerce it facilitates). I don't think so. Most of us would be dead and buried before any government spent that amount of money on something that just might make money but probably wont because the cost to the customer would be prohibitive.
Look at the money spent on Tunnels in Brisbane and the failure one after the other where the expected usage came in so far below that they couldn't even service their debts. Their initial solution to the problem was typical, bump up the price to the consumer and that will fix everything except as usual it didn't .
Here's another doozie, in Queensland we were told by the then Premier that because our Climate Change Commissioner had, using the best science available concluded that we would never have enough water to ever fill our dams again so we would embark on a water infrastructure scheme to drought proof Queensland, meaning the South East. So we spent billions on a pipeline that now sits idle and has never been used, we spent billions on a desalination plant that sits and rusts and take millions each year to maintain and you go on about Government financed infrastructure. More infrastructure like that and this whole state would be broke.
That's the way Government do anything and that's the way Tax Payer money is wasted hand over fist. Your hypothesis sounds great but fails miserably when there is any Government or Government entity involved.
Yes Ministerno says
In response to Andrew Richards, I am in fact active in a number of consumer groups which have achieved a measure of success, however I don't rely on pressure groups to 'fix' everything. I also attempt to get elected officials to extract their digit & whilst there are a few who make at least a token effort, the majority are nothing but overpaid oxygen bandits. Personally I won't take on a political position until / unless they are made voluntary / unpaid (as was the case with many local authorities not that long ago) .The system of paying top money to attract top people has obviously never worked, all that does is encourage the kind of grubs we've had for the past twenty years or more whereas voluntary / unpaid positions would appeal to those with a genuine interest in their community. There is no shortage of highly capable folk with the ability to provide a few days per week without expecting a kings ransom in return (as is the case with the present crop of incompetents).
Criticisms of public sector failures are generally justified & the dismal lack of accountability is certainly deplorable. On the other hand, it can't be denied that Energex / Ergon in Queensland were infinitely more cost-effective electricity retailers than the AGL, Origin, rats & mice retail entities with which we are presently saddled. Same goes for the local authority water entities compared with the ostensibly 'more efficient' corporatized replacements. Essential services don't need a greedy ten million dollar fatcat, they don't need a bunch of shareholders all clamouring for dividends and they really shouldn't be regarded as profit making centres. Had successive politicians not decided to get their grubby claws into power and water, the issue of privatization with all its nasty side-effects would never have arisen. Furthermore, the retail electricity price wouldn't have risen dramatically if at all, and the ne3ed for PV installations on every second house in the country would never have existed.
kimalice, all you've done here is show that you are incapable of grasping the practical realities of building large scale infrastructure. If we followed you line of argument to its ideological conclusions, then we'd have demolished and completely rebuilt the Sydney Harbour Bridge ten years ago. After all, by your argument infrastructure should only last less than a lifetime and pay for itself in less than a lifetime.
Sydney's Rail Network was built 150 years ago for example and it has only been in the process of being reconstructed as of the past decade. Why does something that lasts 100-150 years need to be paid for quickly, or even make a profit as opposed to breaking even. Furthermore let's run the sums on what it would need to break even.
Suppose you have 20 million people with access to the network. Over the hundred year period, ignoring income from commercial sources like fright and supposing that that revenue had to come solely from private citizens, you would need to recoup $50,000 from each person on average for it to break even. Let's take that over a 100 year time frame for example. If each person spent an average of $10 in rail fares each week, that works out as being $500 a year, or $50k over 100 years. Considering the current cost of the average rail fare, that $10 is incredibly conservative. Again though, that also ignores streams of revenue such as freight, which on high speed rail, is far more competitve than road. Yet according to you, this is an unfeasible option? Your anti-governemnt dogma has clouded your reasoning skills here.
You say you hate govt involvement in infrastructure and make it clear you are pro-privatisation. Let's take a good look at what deregulation and economic rationalisation (including privatisation) has done to this country. Our roads are in a mess, our manufacturing industry is almost extinct, our police are underfunded, organisations like DOCS are so underfunded that the system has more cracks and holes in it for victims of abuse to fall through than a giant block of Swiss cheese, our education system is in tatters, our power grids are on their last legs due to poor maintenance and our hospitals have record high waiting lists. All of this caused by the dogma of privatisation and economic rationalistion completely taking over state and federal governments for the past 30 years.
Let's take a good look at what deregulation and economic rationalisation (including privatisation) has done to this country. Our roads are in a mess, our manufacturing industry is almost extinct, our police are under funded, organisations like DOCS are so under funded that the system has more cracks and holes in it for victims of abuse to fall through than a giant block of Swiss cheese, our education system is in tatters, our power grids are on their last legs due to poor maintenance and our hospitals have record high waiting lists. All of this caused by the dogma of privatisation and economic rationalisation completely taking over state and federal governments for the past 30 years.
Let's see, our roads are Government funded, not privately funded, our manufacturing is in such a mess because the Unions have demanded and got, through intimidation, wages that verge on the ridiculous. Take a Holden worker just as as an example. He or she is paid 3 times the normal wage for the work they do and that's before the 26 special conditions are bought into play. Now the Unions are backed by the various Labor Governments that have blighted this land over the last 50 years so there is another example of Government stuffing this country.. Everything that you have shown as examples of Privatisation is actually Government funded so your whole argument backs me up completely, thanks.
Privatisation without Government interference is the way to go. Wages have to be curbed and the power of Unions stopped as this is what is making Australia a laughing stock and forcing our manufacturing overseas or to close down.
I was an employer who had workers on wages and was getting crucified by the Union demands that were backed up by the Government so I sacked the lot and took them back as contractors. Not only did they make more money but they turned out more product with less faults as they were paid per item, I made heaps extra and everybody except the Unions were happy, that's how private enterprise should work and work well.
kimalice your statement about the roads of this country is completely false. In fact it's an open secret in that Sydney for example, that the owners of the vast bulk of major roads are none other than Macquarie bank, while the railways are also now privately owned here.
As for the rest of your argument (or is it Marie Antoinette), attitudes like yours are precisely why this once great country has been destroyed over the past 30 years. Firstly, working conditions and the unions have nothing to the collapse of manufacturing. Working conditions here are due to union influence were alive and well prior to the 1980s along with that high standard of living and our manufacturing industry thrived.
What killed our manufacturing industry was throwing tariffs out the window where our own workers were forced co compete with places where workers are paid $2 a day and the vast majority of the population lives below the poverty line – to the point where we now have, as you yourself demonstrated, governments subsidising them to keep them in the country, to overcome a problem in terms of the local market, that was never there when import tariffs were in place to begin with.
Yet here you are arguing for this country to take a leaf out of Gina Rinehart's book and have people on $2 a day when the cost of living in this country is out of control and families are already struggling with the cost of living as things stand (funnily enough, due to duopolies and deregulation where it is big business that has all the power)? Do I even need to point out the glaring flaw here.
Finally, the net end of privatisation is government control of assets going right out the window- where they are bought, paid for and run by big business whose primary aim is maximising their profits from them, regardless of the net effect it has on both the well being of that area's people and the productivity of the nation. If you cannot grasp the basic fact that privatisation is the government selling off infrastructure which is then bought and owned by private companies, then you just destroyed any and all credibility you have on this subject.
Colin Spencer says
Base load is Coal, in this country. And it should be that way. We don't import coal, we export it. Our infrastructure has been developed around the cheapest energy source available – coal. We can use natural gas, but it is supplementary to coal fired turbines and that is exactly how the other power sources fit into our base load system. Wind turbines, natural gas, domestic and commercial solar, geothermal, wave power are all in the same category. Each is important in its own right, and each one of them contributes to a cleaner energy outcome by replacing some of the coal base load power supply.
This is not rocket science, everyone should understand it. Although some people read the words Commercial Solar and imagine that it means a massive stand-alone solar power generation system contributing to base load. In reality, commercial solar is 300 panels on the roof of a winery, or a large processing plant, or, in my case, a small commercial solar system consisting of 56 panels on my winery roof, with two inverters. That is all I need at present, but I know of other commercial solar installations on bigger wineries where 200 to 500 panel systems and on-site storage are included.
The best way to get up to speed on solar, is to invest in a system which suits your circumstances and requirements. People with good solar installations do not spend time on negative blogs, and they are usually very happy customers. People who sell and install the systems invariably have a lot of very happy customers, and they benefit from word of mouth referrals. The only people I read about who are not happy, are people arguing about imaginary problems. Well, there are virtually none, so go ahead and place an order.
Actually there is reason to doubt that at least some assets were 'sold' in that evidence of payment is impossible to find. I'm aware of two situations where privatization was reversed and compensation paid despite no recorded payment for the asset in the first place. Both of these issues occurred in transactions with EXTREMELY 'interesting' elected officials in the middle of the deals and one individual in a position to tip the bucket has received threatening phone calls advising them to 'drop it or else'. Unfortunately there are no possibilities of recourse in Queensland since we have no upper house, no opposition, a toothless watchdog and a totally compliant judiciary.
Actually Yes Minister, there have been multiple problems with the system. The first is the infiltration into both sides of government by societies and organisations that have agendas contrary to Australia's best interests- namely the Mont Pellerin Society and the Fabian Society.
In fact it's highly telling that for example you have an ALP Prime Minister making the national apology for what happened to the Stolen Generation and then his successor who is actually a part of the very organisation who were the legal impetus for what happened to the Stolen Generation (aka the Fabian Society). Additionally, the ALP policies regarding the NT intervention have been criticised for being rather paternalistic and the Gillard government's adoption of a QALY based health care system reeks of the proposals of Sir Julian Huxley in the 1936 Galton Eugenics lecture.
Conversely, in classic example of "voting for puppet A or puppet B" at the last election, due to Rudd's alleged affiliations (and the bail in moves behind the scenes certainly give credence to those allegations) we had both the ALP and Coalition being driven by Mont Pellerin Society interests.
The large bulk of this can be summed up by the sway the big banks globally have over both sides of parliament in this country.
In fact it's highly telling that Hawke got into power wanting to implement the findings of Campbell Report- proposals so economically radical that even the Coalition rejected them and when he got into power, commissioned a dummy report, the Martin Report to make it look like it was an ALP idea. When you hear Howard an Keating go at it over who is the most responsible for Australia's economic reforms over the past 30 years, that's why.
The second problem is the more visible one and in this regard, there is some crossover – namely the political donation system and the, at the very least suspicious, relationship between big problem and government in this country. I'm sure we all remember the trope that went around a few years back of "John Howard doesn't run this country; Kerry Packer does". Meanwhile the fact that key privatisations went through under the Carr and Kennett governments where Macquarie Bank was the chief beneficiary – only for senior members of both governments (including Carr himself) to wind up senior positions in Macquarie Bank after their terms in power, looks at the very least, incredibly suspicious.
The problem is that we are increasingly heading towards fascism- where the power of corporations have overthrown the power of governments. Detroit, where there's now a banking dictator in place over the elected officials, is where it all looks like it ends up- where those calling the shots don't even bother hiding the state of play anymore.
It's only when that nefarious link is broken and our politicians start working for us, instead of their financial overlords, that we'll finally be able to begin the task of getting this country back on track.
I'm quite aware of the issues you've noted and agree with your thoughts. If anything, I believe its even worse than you've suggested. Defeating that system is another issue again as its exceptionally well entrenched, not only politics but also banking & the il-legal circus, and not only in Australia but through the whole english-speaking world. A few folk of my acquaintance are doing their best although its often difficult to distinguish between genuine opponents of the con and plants appointed to collect info on dissidents.
A few things Colin. Firstly, Coal is now essentially a 500 year old technology which is antiquated, dirty and can be replaced with far more effective alternatives, even if that means some additional research. If you want to play the abundance card, the same argument could easily also be made for thorium, where we hold arguably the largest deposits of thorium on the planet.
As for baseload, others read, as I did, the article making the argument that this new technology was going to form a new backbone for baseload power. It's simply unfeasible unless you start talking about a massive solar energy collection array. If you think 300 panels on a winery is going to supply a something like 30,000 homes, then you need to revise your figures.
The fact is that no matter how much you talk about auxiliary sources, they will never form the backbone of you large scale grid – not unless you construct massive arrays out in the middle of the country- at which point you've ripped a stack of redundancy out of the system.Anyone with any electrical engineering training whatsoever would tell you that only a fool would advocate for ripping virtually all levels of redundancy out of the system.
Also, Imaginary problems"? You mean like issues with roof access and the flood of cheap dodgy panels and dodgy installers on the market? Wow way to prove my point about the dogmatic "magic bullet" attitude to solar.
Your response here is an example of precisely why the "the science is settled" crowd are every bit as bad as creationists with their anti-scientific approach.
The situation isn't quite as simple as some would have it. a common gripe has been that PV isn't suitable for baseload and while there may be at least some justification there, in Queensland during summer at least there is CONSIDERABLE load on the generation system during daytime, exactly when PV output is at its maximum production. Personally I don't use my PV output to run an airconditioner as the place was sufficiently well designed / energy efficient as to my need airconditioning. A lot of other houses in the general area however do use airconditioning and no doubt my excess is supplying those places with green electrons. OK maybe that doesn't constitute baseload in the sense applied by some, but it certainly does reduce reliance on dirty generation facilities. Another situation usually shoved under the carpet is the substantial incentive for householders to minimize the extent of rip-off electricity price. The argument has been raised multiple times that small (ie household) PV systems are relatively inefficient as compared with humungous solar farms. That may be correct in one sense, but even the most 'efficient' solar farm won't do diddley squat for individual home or business electricity bills, ergo 'efficiency' isn't by any means the only criteria that needs to be considered. As for the various nuclear technologies, I wouldn't want the task of flogging fission reactors. Whether or not reasoned arguments can be mounted in favour of them, its inconceivable that the sheeple would even consider their use in Australia. it remains to be seen if 'clean' nuclear (thorium or the like) can be developed to the point where its usable, and then there is the issue of convincing those of us thats its really what its purported to be and there won't be a repeat performance of Three Mile Island etc etc.That said, the bottom-feeding yankee media grub would try anything he thought would make him a few more billion.
An energy company I once worked for bought up a Geothermal outfit a few years previously, at great expense. They drilled the required 20 metre holes in the side of the hill uphill from a street full of new houses but they hit water. The water escaped with great enthusiasm and flooded out three of the properties at the bottom of the hill. It cost them millions in damages and to plug the leak – that was the really expensive bit, because they had to contract an oil well driller to re-drill and plug the hole. They lost all enthusiasm for geothermal after that. So, it would be great, but not if you live up-hill from other properties. Definitely a good thing, especially if you combine it with heat pump technology.
reverendhellfire says
Kermit my friend, you summed it up exactly.
SP Ausnet came out to the Redbox winery to program the smart meter at 1 pm today. 9 months after the paperwork was submitted and re-submitted twice more. No changes to the paperwork, all was in apple pie order. Seems like any excuse will do to discourage customers from generating power. in five hours since 1 pm, my system has drawn "0" kw from the grid, and sent over 400 kw back. Looking forward to seeing what a full sunny day can deliver. On the battery issue, a taxi operator said that they were going to use hybrid Camry cars after Falcon and Commodore are finished. The most important bit of information he had was that the battery pack replacement is down to $2400. That trend is putting the automotive battery pack into the zone for PV storage. Just need to get a pack out of a wreck now.
Solar PV is quite an exciting game, but only if you are playing. So, all those negative detractors, get a quote and go for it. You will enjoy reading your meter every evening for years to come.
From what I've been told by a number of cab operators, the Prius / Camry batteries are lasting extremely well. Interestingly they are some relatively old technology rather than supposedly state of the art lithium polymer. If indeed the replacement cost is around $2400, that would definitely make them more than competitive with lead acid deep cycle ones and consequently very attractive for household use. I wonder however if the $2400 is actually for a complete brand new battery pack or rather an exchange / refurbished one with only a few dead cells fitted ?? I'm particularly interested in getting a battery-electric car as fuel cost presently represents my most significant living expense. One of the options I've explored is the bigger (lithium) battery pack mit plugin conversion of a Prius although its only marginally cost-effective. If however the $2400 battery pack story is correct, a long range electric only Prius conversion should be much cheaper than the current $10,000 plus lithium conversions. I understand that three lithium packs give a 200k plus range at 80kmh & if two additional standard battery packs @ $4800 plus whatever is involved in the plugin bit result in the comparable performance, thats probably a much better proposition than the pig-ugly Leaf or the horrendously overpriced Volt.
The CEO of one of Melbourne's major Taxi groups told me personally that they were going over to Toyota Camry Hybrid cars and wagons for taxis in the not too distant future. He is the one who told me that the Camry battery pack is down to $2,400. Mind you, the Camry battery pack is not all that big, but I imagine the incentive for Toyota to install double packs in Camry taxi pack vehicles would be high. So, if the efficiency of lithium batteries improves remarkably over the next few years, then we could all be driving next gen cars made to the Camry recipe.
Poor old Jon, dead from the neck up. The future has so many surprises for us. I wish I was 18 again.
Jon says
All of you get a life, as you have demonstrated you have none. Sad 🙁
Jacob says
If only people could move past their illogical fear of nuclear power generation. Embracing it is the key to humanity's energy crisis, which will eventually escalate into a world war if we do not curb our use of fossil fuels – which are rapidly running out. Large scale investment and research into cold fusion is quite easily the best option for the world's future. It sees thousands of times more power generated than current methods, produces virtually zero waste and it is damn near impossible for a meltdown to occur, and even then, any radiation wouldn't go past the perimeter fence. Short sighted governments these days just want to keep polluting the atmosphere and not help preserve the planet as well as make all our lives better…
Given a few little 'incidents' involving nuclear plants, I personally don't believe there is anything illogical about fearing them. Who wants a repeat of Three Mile Island, Chernobyl or Fukushima in their backyards ?? If perchance the industry can manage to make a fusion reactor or a thorium reactor that works then it just might have a chance but fission reactors have proven to be their own worst enemy.
There have been 3 major problems with nuclear in over 40 years which in any energy company is small potatoes. Lets llook at the problems asocisted with Wind Turbines left to rust away because the maintenace is way beyond the economic viability of the power they produce. Millions of tons of Carbon Dioxide produced actually making them and now a great majority of them are useless. On a cost effective basis Nuclear is the way to go even at todays technology.
We can't assign anything like a true cost (whether in financial, ecological or in human terms) to the after-effects of Three Mile Island, Chernobyl or Fukushima because it will be many generations before it can be calculated. Certainly nobody within a few hundred kilometers of any of the sites would be supportive of any further rollouts of fission reactors.and I don't believe we have any right to create nightmares for future generations. Given that at least two relatively clean nuclear technologies are available or almost so, any new installations should involve those rather than something that produces toxic crap requiring safe storage for thousands of years..
Blind Freddy could see that hydro-power is THE way to go. Using one of several methods to turn gravity into electrical/mechanical power rings with the poetry of the universe.
How many turbines could be fed from the 3000-foot drop of the Murray on its way to the sea…or the 5000-foot fall of the Murrumbidgee on its way to the Murray? Or how about the 1.5 million cubic metres of water sloshing into and out of Port Philip Bay twice a day every day? And that doesn't even count Tasmania or the 40-foot tidal differences along parts of the north coast.
Output of power could be regulated minute to minute with simple stop-cocks and no storage would be needed.
" Who wants a repeat of Three Mile Island, Chernobyl or Fukushima in their backyards ?? "
Nobody. So don't build them in somebody's backyard. Just like we don't coal plants in people's backyards.
Nuclear power is orders of magnitude safer than coal. Nobody died at Fukushima. Nobody died at Three Mile Island. At Chernobyl, 237 people got radiation sickness, and 31 died. According to the World Health Organisation, the rates of cancer in the area are no higher than the general population. (Source: http://en.wikipedia.org/wiki/Chernobyl_disaster).
So that 31 deaths directly attributable to nuclear power generation in 50 years.
However, if we look at coal, "In the US alone, more than 100,000 coal miners were killed in accidents over the past century, with more than 3,200 dying in 1907 alone". "China, in particular, has the highest number of coal mining related deaths in the world, with official statistics claiming that 6,027 deaths occurred in 2004. To compare, 28 deaths were reported in the US in the same year.". "In some mining countries black lung is still common, with 4,000 new cases of black lung every year in the US (4 percent of workers annually) and 10,000 new cases every year in China (0.2 percent of workers).". All from http://en.wikipedia.org/wiki/Coal_mining
So, 31 deaths related to nuclear power in 50 years, compared to 6,000 deaths per year in China alone related to coal mining.
I wonder which is the safer technology?
Even then, compare rod-core, fast breeder, water cooled reactors, with high temperature pebble bed reactors. When things go bad with rod-core, water cooled reactors, what happens? 3-Mile Island, Chernobyl and Fukushima. They might be a small number of incidents, but when things go bad, they really go bad.
Compare that with pebble bed reactors – the reactor design that was always superior but only lost out because of the whims of the military industrial complex.
What happens when things go bad (ie the coolant fails) with a pebble bed reactor? In short order, the temperature of the reactor spikes from 800-1200 degrees, up to 1600 degrees. At that point due to doppler broadening and the geometric design of the pebbles, all nuclear chain reactions are stopped dead in their tracks, at which point the reactor starts to cool again, until it cools to a point where chain reactions can continue. Meanwhile the graphite casing around the pebbles, with its melting point of 2000 degrees has only gotten "a little warm" and was a good 400 degrees away from reaching its melting point.
Rod-core reactors come with massive risks and have a massive downside. Pebble bed reactors, once you go to thorium and perfect waste reprocessing techniques to make half lives negligible, essentially become problem free.
Two places I would never want to live remotely near are rod-core reactors (a ticking timebomb) and coal fired power stations (nasty smog factories). Conversely, while I'm not sure I'd want to live next door to a pebble bed reactor, I can honestly say that if I lived don the road from one, I wouldn't be too phased by it, given how safe the technology generally is.
Bosko says
Well rumour has it Ford is building a solar powered car. Their are new technologies that will be released in the not to distant future. They say that batteries will be the thing of the past.
From the information released, it appears the 'solar powered car' is merely a regular battery electric one with a solar panel on the roof to pump a few electrons into the batteries. Ford claims its used some kind of lens arrangement to boost output however its highly unlikely the output is sufficient to provide the kind of output to run the car directly off the PV panels. That said, anything that helps reduce support for middle-east terrorism is a VERY GOOD THING.
There is a place for both private enterprise & public sector entities in the power generation game. Private sector businesses are almost certainly the only ones capable of developing / manufacturing power generators, whether conventional or alternative, whereas the actual ownership and operation of the generators should always remain totally under public control. Its clear that the current crop of political animals has a pathological phobia of accountability, hence the headlong panic to flog off anything that could conceivably involve responsibllity. Mind you the same clowns promoting the sale of everything not bolted down are far from reticent about awarding themselves exorbitant salaries way beyond their level of ability. Even so, the operating cost of a government owned essential service (even after all the inefficiencies) must be infinitely less than that where at a bunch of ten-million dollar fatcats and a zillion assorted shareholders line up for their cut. The errors of privatizing essential services are obvious and hopefully no sentient being would support an extension of this fiasco.
Cannot agree with that. The cost of anyting remotely run by a Government usually ends up costing double or triple what it should. A great case in point is the buildings for schools that the previous Government was so keen on. Those schools that were allowed to get their own builders and tradesmen ended up with more bang for their buck than those who had to use Q Build. Buildings that would normally cost $20,000 each were costing the Government upwwards of $60,000 from Q Build so you arguement doesnt hold water. I have worked on Government jobs as a contractor and have always been ablwe to come in under budget and within time, something Q Build hasn't a clue how to do.
Investors in the power industry must come from private enterprise but and a big but there must be enough supplying power to force them to keep their prices low or lose to the opposition.
kimalice, you're only looking at half the picture there. The building for schools program had nothing to do with infrastructure at the time.
What most people don't know is that our banks are dangerously close to collapse (they currently have 20 trillion dollars in derivatives holdings – times their asset holdings) and in the GFC, they almost went under. What the school building project and the thousand dollar payouts were about, was pumping money back into the banks to prop them up. Think about it – if even only 10 million people got a thousand dollars each going into their bank accounts, that's still 10 billion dollars in stimulus going into the big banks. Same deal with the school building scheme where many who were principals and deputy principals were given the impression that it was more important that the money was spent than how it was spent.
However I agree with you that it speaks volumes of how unethical the current state of play is when politicians and bureaucrats feel no accountability or responsibility for the money they spend.
Half the picture, no thats the whole picture. We have seen time and time again different Government run and finaced projects costing way more than privately owned projects. The people will decide the price as if one supplier gets greddy then the people will swap, like the revolution in Home and cContents insurance going on now where the costs are being bought down by more private busineeses offering more for less.
The money was Tax Payer money, money that was squanderd on buildings that were overpriced, not suitable in some cases and built by a Government run enteprise that ripped off the Tax payer once again. IF iot had been done correctly and tenders allowed then we would have been able to build more for the samr money and that same money would have done the job in any case.
I would have preferred to see our money spent wisely not the way it was.
On the contrary, the irony is that not only were you wrong on the building for schools program (which had nothing to do with infrastructure and everything to do with bailing out the big banks), but your costing analysis is shortsighted and flawed.
You say private enterprise comes in under what governments do for building infrastructure, yet you neglect the long term costs to the people.
Suppose a major road costs NSW taxpayers, say $40million under private enterprise and $80 million under government and hypothetically say there are 4 million taxpayers in NSW. Sure the initial cost might be double, but what about the long term cost to taxpayers?
When a road is government owned and built, what do taxpayers generally pay to use it as a rule? Nothing, freeways and highways are just that – free to use.
Compare that with a motorway where taxpayers can easily be paying hundreds of dollars a year to use it through commuting to work. Even if $200 of their taxes has gone on the road in the government model and only $100 on the private enterprise model, then after the first year, they are already worse off.
Yet you want to claim that big business sucking the average taxpayer dry through economically exploiting crucial infrastructure is a better deal for them? Get real.
There are certainly a number of situations where government undertakings were horribly mis-managed and your example of schools is an obvious one, however despite the lower 'efficiency', every government run power company to date has proven to be infinitely more cost-effective than the likes of AGL & Origin. Even the gross stuffups typical of gubmunt muppets cost us less than the multi-million dollars salaries of avaricious CEOs, the operating profits and the shareholder dividends. Teflon Pete in Queensland started the rot by corporatizing Energex / Ergon so he could get his grubby claws into a few bucketloads of $$$$$, then fed the sheeple a blatant lie about privatized retail electricity being cheaper. Neither the situation with schools nor with power retailing is acceptable and in an ideal world, the perpetuators would be personally sued for blatant misuse of taxpayer funds. I was glad to see Beattie fail to get up in the seat of Forde during the last federal election, seems his porkies haven't yet been forgotten by the sheeple. Despite his admission that privatization was a dismal failure, I'd still love to see the bottom-feeding grub made personally responsible for the problem he created and exactly the same applied to the architects of every other scheme that squandered the sheeples hard-earned money.
From your posts, this one and previous its not really about Solar or saving the planet but a forum for you to denigrate those who take the chances and do the jobs and get paid the megabucks to do it. I have no qualms about paying people to run businesses successfully, I have no qualms about paying Politicians to run this country but you my friend take umbrage at them all. It reeks of jealousy and your own inability to make something of your own life.
Businesses pay mega bucks to CEO's to take the risks and if they fail they get shunted, the tax Payer pays the Ministers and all politicians to make the hard decisions based on real facts as they see it and if they get it wrong they are shunted at the next election.
We all know that there are Pollies and CEO's who aren't worth a damn but it all catches up with them in the end. we all know there are Pollies and CEO's who lie through their teeth to get a point across but as stated above they are found out and tossed out. That's the way countries are run unless of course you happen to live in a Communists country or a country run under strict sectarian laws and like it or lump it that's what we have here and either you accept that people are human and make mistakes whilst earning millions or you get so bitter that it runs your life.
There is a VAST difference between paying some expert a salary commensurate with his ability, and squandering tens of millions per annum on some ignoramus who couldn't possibly spend his salary in five lifetimes. Avarice is inexcusable regardless of who is doing the ripping-off. Same goes for politicians, too many of whom are failed lawyers & incapable of doing a real world job. Note that I don't have any issue with a self-made billionaire paying himself squillions (a la Big Clive), my beef is with public company scumbags who never did an honest days work in their entire lives and who produce absolutely nothing of consequence getting paid in a week sufficient to run a small country for years. When essential services were public sector controlled, the top level muppets were paid a mere fraction of what companies give CEO types, furthermore the public sector essential services didn't need to make a massive operating profit or to support a zillion shareholders. What household PV systems have done is allow Joe Average to thumb his nose at the parasites & regardless of whether a large scale solar farm or other alternative energy source is 'more efficient' according to whatever criteria, the fact remains that no other technology will help to address the imbalance between the she | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 5,875 |
\section{Introduction}
\label{sec:introduction}
Network medicine is a new paradigm of medicine that applies network science and systems biology approaches to study diseases as a consequence of pathobiological processes that interact in a complex network. Pieces of evidence in this field show that if a gene or molecule is involved in a disease, its direct interactors might also be suspected to play some role in the same pathological process. According to this hypothesis, proteins involved in the same disease show a high propensity to interact with each other, a property referred to as \textit{ ``disease module hypothesis''} \cite{networkmedicine, menche2015uncovering}. This hypothesis suggests that, if we identify a few disease components, the other disease-related components are likely to be located in their network-based ``neighbourhood'', called \textit{disease module}. Under a biological perspective, ``a disease module represents a group of
network components that together contribute to a cellular function whose disruption results
in a particular disease phenotype'' \cite{networkmedicine}.
Furthermore, subsequent studies have shown the tendency for biologically similar diseases to have their respective modules located in adjacent or overlapping areas of the interactome \cite{menche2015uncovering, goh2007human, booknetwork}.
According to Loscalzo et al. \cite{booknetwork} and Menche et al. \cite{menche2015uncovering}, ``proximity and degree of overlap of two disease modules (in the human interactome) has been found to be highly predictive of the pathobiological similarity of the corresponding diseases'' and ``network-based location of each disease module determines its pathobiological relationship to other diseases''. Indeed, different disease modules can overlap, so that perturbations caused by one disease can affect other disease modules that could lead to co-morbidity and pathogenetic mechanisms \cite{networkmedicine}. Analysing interconnections within disease modules can help reveal new disease genes, disease pathways, and identify possible drug targets or biomarkers for drug development and drug repurposing \cite{cheng2019network, networkmedicine}.
The tendency of phenotypically similar diseases to be close or to overlap in the interactome
suggests the possibility of \textit{inducing a hierarchical and possibly categorical structure of disease modules}, with specific and yet unexplored
relationships with existing disease classification taxonomies.
Disease taxonomies play a key role in defining the mechanisms of human diseases, potentially impacting both diagnosis and treatment. However, as remarked in \cite{networkmedicine, loscalzo2007human,zhou2018systems}, contemporary approaches to the classification of human diseases are mainly based on
anatomical pathological data and clinical knowledge.
Yet, modern molecular diagnostic tools have shown the shortcomings of this methodology, reflecting both a lack of sensitivity in identifying pre-clinical diseases and a lack of specificity in defining diseases unequivocally. On the other hand, inducing disease relationships solely from disease modules in the interactome is hindered by incomplete knowledge of disease-related genes \cite{networkmedicine, omim}.
In this study we propose a methodology to systematically compare categorical relationships automatically induced from proximity of disease modules in the human interactome network, with manually crafted categories in human-curated ontologies. Detected commonalities and differences may suggest latent and unknown molecular properties of diseases, help improve the current understanding of the disease mechanisms, and
facilitate precise clinical diagnosis consistent with molecular network properties \cite{Ghiassian2015, madeddu2020feature, cheng2019network, van2018gene}.
\vspace{-5pt}
\section{AIMS AND METHODS}
Network-based analyses of gene interaction data have helped to identify modules of disease-associated genes, hereafter referred to as disease modules (DMs), widely used to obtain both a systems level and a molecular understanding of disease mechanisms \cite{gustafsson2014modules}. Disease modules have been successfully used, for example, to prioritize diagnostic markers or therapeutic candidate genes, and in drug repurposing \cite{cheng2019network, networkmedicine, ay2007drug}.
However, according to Barabási et al. \cite{networkmedicine}, these results have marginally influenced the disease taxonomies and, conversely, to the best of our knowledge, disease taxonomies have not been used to analyse disease modules. In this study we aim for the first time to integrate taxonomic and network-based disease categorization principles, with the following innovative contributions:
\begin{enumerate}
\item to automatically induce a full-fledged hierarchical structure from proximity relations between DMs in the human interactome; \item to compare this structure with a human-defined disease taxonomy (such as the Disease Ontology\footnote{\url{https://disease-ontology.org}}));
\item to systematically identify categorical analogies and discrepancies between molecular and human-defined taxonomies.
\end{enumerate}
Our research hypothesis is that a study of the
relationships between molecular-based and human-curated disease taxonomies could help refine our knowledge on human diseases and
identify limitations and perspectives of current module-based computational approaches to the study of diseases.
As shown in the experimental Section \ref{results}, our study has some possibly relevant clinical implications:
\begin{enumerate}
\item To identify promising regions of the human interactome where new disease-gene relationships could be discovered\footnote{either exploiting data-driven methods or clinical experiments};
\item To identify unexplored molecular relationships among diseases;
\item To extend, correct and refine human-curated taxonomies.
\end{enumerate}
\noindent
Figure \ref{fig: workflow} shows the workflow of the proposed approach, described in detail in the next Sections. The main phases are the following: \\
\noindent
{\bf 1. Induction of a Taxonomy of Disease Modules:}
First, we automatically induce a hierarchical structure of diseases based on proximity relations of DMs in the human interactome. This taxonomic structure is hereafter referred to as the Interactome Taxonomy (I-T).\\
\noindent
{\bf 2. Taxonomy alignment and labeling:} Next, we align the I-T taxonomy with a human-curated \textit{reference ontology} (hereafter R-T), by creating a mapping between disease nodes in both taxonomies (red arrows in Box 2 of Figure \ref{fig: workflow}). Finally, a labeling algorithm finds the best map between categorical nodes in the R-T and the unlabeled inner nodes of the I-T (purple arrow in Box 2 of Figure \ref{fig: workflow}). \\
\noindent
{\bf 3. Systematic Comparative Analysis of I-T and R-T taxonomies:} The alignment between I-T and R-T supports a large-scale analysis of a vast collection of diseases jointly from an ontological and molecular perspective.
We provide insights to refine state of the art nosology and knowledge on disease interactions, by using our methodology to investigate the efficacy of the anatomical disease classification principle at the molecular level, identify nomenclature errors in disease-gene associations and discover unexplored molecular mechanisms among diseases.
\begin{figure}[ht!]
\centering
\includegraphics[width=1.\linewidth]{figures/workflow_velardi.pdf}
\caption{The work-flow of our study. Box $1$ shows the taxonomy induction phase, Box $2$ represents the phase of taxonomy alignment and labeling and Box $3$ summarizes the results of the analytic phase.}
\label{fig: workflow}
\end{figure}
\vspace{-15pt}
\section{Construction of the Interactome Taxonomy (I-T)}
\label{sec:induction of I-T}
We induce a disease taxonomy (named Interactome Taxonomy, I-T) by applying hierarchical agglomerative clustering to the human interactome network, exploiting proximity relations of disease modules.
Hierarchical agglomerative clustering (HAC) is a set of greedy approaches that create a hierarchy of clusters from unlabeled input data \cite{murtagh2017algorithms}.
Given a distance matrix of seed clusters, the HAC algorithm iteratively merges two clusters based on a selected inter-cluster distance measure. Common methods to merge clusters are Average and Complete linkage \cite{murtagh2017algorithms}.
In our context, clusters are DMs in the human interactome network.
However, due to the high incompleteness of the disease-gene associations modeled in the human interactome \cite{Venkatesan}, disease modules are not molecularly well-defined and devoid of a clearly dense network-structure \cite{menche2015uncovering}. To cope with this problem, we use two alternative definitions of modules adopted in network science, which have been commonly used in Network Medicine literature to physically identify disease modules \cite{menche2015uncovering, agrawal2018large}.\\
Given the human interactome network $G=(V, E)$ and a disease $d$ in a set of diseases $D_{it}$:
\begin{enumerate}
\item \textbf {Induced Module:} The Induced Module $I_{d} = (V_{d}, E_{d})$ is a subgraph of $G$, where $V_{d} \subseteq V$ is the set of genes-nodes associated with $d$ and $E_{d}$ is the set of gene-gene interactions $E_{d}=\{(u, v)|(u, v) \in E\;and\;u, v \in V_{d}\}$\cite{menche2015uncovering}. This definition includes in a DM all the disease genes but, due to the incompleteness of the network, it is usually a graph with many connected components lacking a strong local structure \cite{agrawal2018large}.
\item \textbf {Largest Connected Component (LCC) Module:} The $LCC_{d}$ module is the largest connected component of $I_{d}$ \cite{menche2015uncovering, agrawal2018large}. Unlike for the induced module $I_{d}$, $LCC_{d}$ usually has a denser local structure but may not include all the disease-related nodes $d$.
\end{enumerate}
Given the human interactome $G$, a set of diseases $D_{it}$ and their disease modules $DM_{it}$ in $G$, hierarchical clustering is performed using a distance matrix of disease modules (defined as previously explained), based on the following network-based distance measure (Eq.\eqref{eq:dist}) (used, e.g., in \cite{menche2015uncovering, booknetwork, cheng2018network}):
\begin{footnotesize}
\begin{equation}
dist(A,B) = \frac{\sum_{a \in A}min_{b \in B}SP(a,b) + \sum_{b \in B}min_{a \in A}SP(a,b)}{|A|+|B|}
\label{eq:dist}
\end{equation}
\end{footnotesize}
\noindent where A, B are respectively the set of nodes in modules $DM_A$ and $DM_B$ associated to diseases $d_{A}, d_{B} \in D_{it}$ and $SP$ is the shortest path length between two given nodes in $G$.
In our experiments, we used two DM definitions (Induced Module and LCC) and two cluster-merge methods (Average and Complete). The best solution among the four resulting I-Ts alternatives is identified using the methodology described in Section \ref{sec:selection}.
\section{Taxonomy Alignment and labeling}
\label{sec:alignmentlabelling}
The result of the hierarchical clustering algorithm is a binary tree taxonomy, hereafter referred to as Interactome Taxonomy (I-T). I-T is a connected directed acyclic graph $T(V_{T}, E_{T})$ in which nodes $V_{T}$ represent disease concepts and edges represent ``is-a'' semantic relationships\footnote{Edge $(v, u)$ with $\;u, v \in V_{T}$ means that $v$ \textit{is a} kind of $u$.}. In our context, leaf-nodes (i.e. nodes with out-degree equal to zero) are ``specific'' diseases $D_{it}$, physically represented by the corresponding modules $DM_{it}$, while inner nodes (i.e. non-leaf nodes) are disease categories $DC_{it}$.
Note that inner nodes $c \in DC_{it}$ are \textit{unlabeled}, and extensionally defined by the set of their subsumed disease nodes,
referred to as the \textit{clusters} $C_c$ of nodes $c$.
Similarly, given a ``reference'' human-crafted taxonomy, denoted as R-T, let $T(V_{R}, E_{R})$ be the set of its nodes and edges, $D_{rt}$ its disease (leaf) nodes, $DC_{rt}$ its categorical (inner) nodes and $C_{c'}$ the clusters associated with categorical nodes $c' \in DC_{rt}$. Contrary to the I-T, inner nodes in the R-T have also a human-defined label, the \textit{category name}.
\vspace{-9pt}
\subsection{Taxonomy Alignment}
\label{sec:alignment algorithms}
Whatever the choice of the R-T, the R-T and the I-T are expected to be defined on different sets of diseases nomenclatures, $D_{rt}$ and $D_{it}$. Furthermore, they are also expected to be structurally diverse. For example, R-T has usually a polyhierarchical structure, while I-T is by construction a binary tree.
To compare I-T and R-T we first need to create a mapping $M$ from
$D_{it}$ to $D_{rt}$ nomenclatures, and next, to prune the hierarchies so that they include the same set of leaf disease nodes, a process that we call \textit{taxonomy alignment}.
Let $M$ be an available mapping of disease nomenclatures (see Section \ref{data} for details). In Figure \ref{fig:merge}, mappings among nodes of the two taxonomies are highlighted using the same colours. As shown, $M$ is usually not one-to-one and we identify four cases:
\begin{enumerate}
\item Case 1: Some leaf nodes $D_{it}$ in I-T may map onto inner nodes in the R-T.
\item Case 2: Some $D_{it}$ nodes may map onto multiple nodes in the R-T.
\item Case 3: Some $D_{it}$ nodes may map onto the same node in the R-T.
\item Case 4: Some $D_{it}$ nodes may have no mappings in the R-T \textit{and vice-versa}. These nodes without mappings are depicted in Figure \ref{fig:merge} as white leaf nodes in both taxonomies.
\end{enumerate}
Our taxonomy alignment procedure consists of three algorithms: \textit{merge}, \textit{split}, and \textit{prune}. We apply \textit{merge} and \textit{split} to the R-T to solve cases 1, 2 and 3; instead, \textit{prune} is applied to both the R-T and the I-T, to solve case 4.
\begin{figure}[ht!]
\centering
\includegraphics[width=1.\linewidth]{figures/alignment/merge.pdf}
\caption{Visual example of the \textit{merge} algorithm.}
\label{fig:merge}
\end{figure}
\begin{algorithm}
\begin{footnotesize}
\SetAlgoLined
\SetKwFunction{FMg}{Merge}
\SetKwProg{Fn}{Function}{:}{}
\Fn{\FMg{rt, mapping}}{
diseases = keys(mapping)\;
rtmapped = {}
newMapping = Hashmap()
\For{diseaseId in diseases:}
{
rtmapped.union(mapping[diseaseId])\;
newMapping[diseaseId] = []\;
}
ancestors = rt.getColouredAncestors(rtmapped) \tcp*{Get the R\-T's coloured nodes with no R-T's coloured node among their ancestors}
\For{ancestor in ancestors:}
{
diseasesDesc = rt.getMappingDescendant(ancestors, mapping)\tcp*{Get the diseases linked to R\-T's nodes descendant of the coloured ancestors}
\For{diseaseId in diseasesDesc:}
{
newMapping[diseaseId].append(node)\;
}
}
\For{ancestor in ancestors:}
{
descs = rt.getDescendants(ancestor)\;
rt.removeNodes(descs)\tcp*{Turn every ancestor into a leaf}
}
mapping = newMapping\;
\KwRet rt, mapping\;
}
\label{algo:merge}
\end{footnotesize}
\caption{Merge}
\end{algorithm}
The \textit{merge} algorithm (see Algorithm
1) turns in leaves all the R-T coloured inner nodes. If the node has non-coloured descendants (that is, its descendands do not map onto any disease module in I-T), these descendants are removed. Else, the node and its coloured descendants are aggregated into a single multi-coloured node, as shown in Figure \ref{fig:merge} (right).
After the merge, the \textit{split} algorithm (see Algorithm 2) splits all the nodes with multiple colours (see Figure \ref{fig:split}). Note that these nodes inherit the ancestors of the splitted multi-coloured node. As a result of merge and split, all coloured R-T nodes are now leaf nodes, and every I-T node points to its correspondent R-T node. Furthermore, polyhierarchy in the R-T is preserved, as shown in Figure \ref{fig:merge-split}.
\begin{figure}[ht!]
\centering
\includegraphics[width=1.\linewidth]{figures/alignment/split.pdf}
\caption{Visual example of the \textit{split} algorithm.}
\label{fig:split}
\end{figure}
\begin{figure}[ht!]
\centering
\includegraphics[width=1.\linewidth]{figures/alignment/merge_poly.pdf}
\caption{Visual example of the \textit{merge} and \textit{split} algorithms for a polyhierarchical case.}
\label{fig:merge-split}
\end{figure}
\begin{algorithm}
\begin{footnotesize}
\SetAlgoLined
\SetKwFunction{FSp}{Split}
\SetKwProg{Fn}{Function}{:}{}
\Fn{\FSp{rt, mapping}}{
diseases = keys(mapping)\;
\For{diseaseId in diseases:}
{
nodes = mapping[diseaseId]\tcp*{The R\-T's nodes linked to diseaseId}
parents = rt.getParents(nodes)\tcp*{Get the set of parents of the given set of nodes}
rt.addNode(diseaseId, parents)\;
mapping[diseaseId] = diseaseId\;
}
\KwRet rt\;
}
\label{algo:split}
\end{footnotesize}
\caption{Split}
\end{algorithm}
Finally, the \textit{prune} algorithm (see Fig.
\ref{fig:pruning} and Algorithm
3) prunes both the R-T and the I-Ts by recursively removing survived leaf nodes not linked by any mapping relation in $M$. These are shown with a double circle in Figure \ref{fig:pruning}.
As a final result, the R-T and the I-T have as leaf nodes the same set of diseases, denoted as $D_{\cap}$.
\begin{figure}[ht!]
\centering
\includegraphics[width=1.\linewidth]{figures/alignment/pruning.pdf}
\caption{Visual example of the \textit{prune} algorithm.}
\label{fig:pruning}
\end{figure}
\begin{algorithm}
\begin{footnotesize}
\SetAlgoLined
\SetKwFunction{FPr}{Prune}
\SetKwProg{Fn}{Function}{:}{}
\Fn{\FPr{taxa, diseaseID}}{
drop = taxa.leaves() - diseaseID\;
\For{leaf in drop:}
{
taxa.remove(leaf)\tcp*{Remove the leaf from the taxonomy}
}
\For{leaf in taxa.leaves():}
{
\If{|rt.parents(leaf)| == 1 and rt.parents(leaf)[0].outDegree() == 1:}
{
taxa.replace(leaf)\tcp*{Recursively substitute the leaf with its parent until the leaf get a parent with out-degree > 1 or more than one parent}
}
}
\KwRet taxa\;
}
\label{algo:prune}
\end{footnotesize}
\caption{Prune}
\end{algorithm}
\vspace{-9pt}
\subsection{Selecting alternative Induced Taxonomies}
\label{sec:selection}
As remarked in Section \ref{sec:induction of I-T}, the I-T is built using different definitions of disease modules and different inter-cluster similarity functions during agglomerative clustering.
In this Section, we present a method to select the ``best'' I-T, among four I-Ts\footnote{Four aligned I-Ts resulting by the combination of the Induced and LCC disease module definitions with the Average and Complete clustering methods}, based on its structural and semantic similarity with the R-T. Note that a similarity function between two taxonomies can be computed only if they have been aligned. \\
Our method to compute the similarity between two taxonomies is based on the Lin semantic similarity \cite{lin1998information}:
\begin{footnotesize}
\begin{equation}
S_{T}(a, b):= \frac{2*IC_{T}(LCS_{T}(a, b))}{IC_{T}(a) + IC_{T}(b)}\label{eq:lin}
\end{equation}
\end{footnotesize}
\noindent
where $IC$ is:
\begin{footnotesize}
\begin{equation}
IC_{T}(x):= -log(\frac{|leaves_{T}(x)|+1}{MaxLeaves_{T} + 1})
\end{equation}
\end{footnotesize}
\noindent
where $a, b$ are two leaf nodes in a taxonomy $T$, and $LCS_{T}(a,b)$ is the least common subsumer of $a$ and $b$ in $T$; $leaves_{T}(x)$ is the set of leaves descendant of $x$ and $MaxLeaves_{T}$ is the number of leaves in $T$.\\
The Lin similarity increases when two nodes are structurally close in a taxonomy, and decreases otherwise. Furthermore, by construction, the distance between two nodes is normalized with respect of the maximum distance, a property that is particularly useful when extending this measure to compare taxonomies with different depths. This is a desirable property since the I-T is a binary tree and has a much higher depth than the R-T.
To compare each of the four induced I-Ts with a selected R-T, first, we calculate the pairwise Lin similarity $S_{T}(d_i, d_j)$
for each taxonomy $T$, where $\{(d_i, d_j)| d_i, d_j \in D_{\cap}\;and\;d_i \neq d_j \}$. Next, for each taxonomy $T$, we construct a vector $v_T$ of $S_{T}(d_i, d_j)$ similarity values. Finally, we calculate the cosine similarity between each of the induced taxonomies vectors $v_{IT_k} (k=1\dots 4)$ and $v_{RT}$. The intuition is that, if two taxonomies are similar, disease pairs that are ``close'' in one taxonomy should be ``close'' also in the other taxonomy, and those who are far apart in one taxonomy, should be far apart also in the other. The ``best'' I-T is selected according to:\\
\noindent
$argmax_{k}(cosSim(v_{IT_k},v_{RT}))$.
The experimental application of this methodology is described in Section \ref{results}.
\vspace{-9pt}
\subsection{Semantic Labeling of the Interactome Hierarchy (I-T)}
\label{sec:labelling}
As previously noted, the inner nodes of the aligned I-T have no semantic labels. To facilitate a comparative analysis of I-T and R-T, we defined an algorithm to label each inner node in the I-T with the most similar category label in the R-T. In order to find the most similar R-T category node, we exploit the notion of \textit{cluster} $C_c$ associated with a category node $c$ in a taxonomy, defined as the set of all its descendant disease nodes that are also in $D_{\cap}$. Then, a \textit{labeling} algorithm (see Algorithm
4) labels every I-T disease category $c$ with the name of the R-T category $c'$ with highest similarity score $sim(C_c,C_{c'})$ between the clusters of $c$ and $c'$\footnote{Note that the labeling method uses the full set of R-T categories to obtain more fine-grained labels
but the node clusters $C_c$ are defined on the common disease set $D_{\cap}$ of the aligned taxonomies.} . To compute the similarity between two clusters, we use the Jaccard coefficient, a popular measure of set similarity.
\begin{algorithm}
\begin{footnotesize}
\SetAlgoLined
\SetKwFunction{FMap}{labeling}
\SetKwProg{Fn}{Function}{:}{}
\Fn{\FMap{it, rt}}{
categories = it.nodes() - it.leaves()
labels = empty dictionary\;
\For{category in categories:}
{
clusterIT = getCluster(it, category)
catRT = getLabel(clusterIT, rt)\tcp*{Get the most similar R-T category}
labels[category] = catRT\;
}
\KwRet labels\;
}
\end{footnotesize}
\label{algo:label}
\caption{Labeling}
\end{algorithm}
\vspace{-15pt}
\section{Experimental set up}
\label{data}
This Section describes the data sources used in our experiments.
To conduct a disease module analysis, we considered the most recent release of the human protein-protein interaction network published by Barabasi et al. \cite{cheng2019network}, which is an extension of a highly cited and popular interactome used by Menche et al. \cite{menche2015uncovering}. The network has $|V| = 16\,677$ proteins and $|E| = 243\,603$ physical undirected protein interactions.
To construct disease modules, we collected disease-gene associations from DisGeNET \cite{pinero2020disgenet} with a GDA\footnote{GDA is a ``reliability'' score, for details see \url{www.disgenet.org/dbinfo\#section43}} score greater or equal of 0.3. Finally, we selected as disease modules the $948$ diseases with a set of disease genes of size at least $10$\footnote{smaller modules imply a limited knowledge of the related disease-gene associations to date, and may lead us to unreliable results.}.
We selected the Disease Ontology (DO) as Reference Taxonomy (R-T) \cite{schriml2012disease}. An alternative widely used reference ontology is ICD-9 (used, for example, in a work by Zhou et al. \cite{zhou2018systems}). However, ICD-9 was built to facilitate the statistical study of disease phenomena, and arranged according to epidemiological properties and anatomical site.
Hence, ICD-9 does not represent a good categorical framework for integrating network-based disease properties.
Instead, the Disease Ontology is a classification of human diseases organised by etiological agents such as infectious agents, clinical genetics and cellular processes. Therefore, even though the "localist" (i.e., anatomic and disciplinary classification) view of diseases is still a guiding principle, the DO also integrates the molecular insights of disease phenotypes.
By parsing the DO ``obo'' file\footnote{\url{http://www.obofoundry.org/ontology/doid.html}}, we generated a directed acyclic network hierarchy of $10012$ diseases and disease categories, $10061$ edges and $12 $ levels.
To create a mapping $M$ between the two different nomenclatures, we used partial mappings directly provided in DisGeNET and in the DO, that we further extended with the support of clinicians to cover all the 948 DMs.
To begin, we applied the method described in Section \ref{sec:labelling} to select the best induced I-T taxonomy, i.e., the one with the highest similarity with the selected R-T (namely, the Disease Ontology). Table \ref{tbl:rank} shows the result of this comparison. Note that similarity values are compared against those obtained by a random shuffling the disease nodes.
Based on the results of Table \ref{tbl:rank}, we select the I-T taxonomy obtained using Induced Modules to represent DMs, and the Average linkage method to merge clusters during hierarchical clustering. This induced taxonomic structure shows a higher similarity with the Disease Ontology and therefore represents a good basis for our study. Note however that all the compared methods produce taxonomies with a similarity value significantly higher than the random baseline. The observed differences are mainly due to some structural differences and to the positioning of outliers (isolated DMs in the interactome).
\begin{table}[h!]
\centering
\scalebox{0.8}{
\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|}
\hline
& \multicolumn{2}{c|}{{\bf Induced}} & \multicolumn{2}{c|}{\bf LCC}\\ \hline
Measure & Complete (RD) & { Average} (RD) & Complete (RD) & Average (RD)\\ \hline
Cos. Sim. (\%) & 43.59 (28.55) & {\bf 46.33} (29.84) & 39.94 (28.58) & 43.7 (29.71)\\
\hline
\end{tabular}%
}
\caption{\begin{footnotesize}Comparison of Lin-similarity vectors of the aligned R-T (the Disease Ontology) and I-T taxonomies obtained with four different variants of the proposed taxonomy induction method. The variants were obtained adopting two different network-based definitions of DMs (Induced and LCC) and two different techniques to merge clusters (complete and average). The value in the round brackets represents the average of values generated by ten random distributions of leaf nodes, leaving the taxonomy structure unchanged.\end{footnotesize}}
\label{tbl:rank}
\end{table}
\vspace{-20pt}
\section{Results}
\label{results}
Our research hypothesis in this work is that jointly analyzing the structural proximity of disease modules in the human interactome network and the semantic proximity of corresponding diseases in human-cured taxonomies could help both refine the classification of human diseases and
identify the limitations and perspectives of current module-based computational approaches to the study of diseases. In this Section, we summarize the major outcomes of a clinical analysis supported by the methodology presented in previous Sections. Our analysis is based both on the study of matching and unmatching pairs of R-T and I-T categories.
\vspace{-10pt}
\noindent
\subsection{Finding disease categories with a corresponding dense neighbourhood in the interactome. }
\label{dense neighbourhood}
First, we conducted an analysis to reveal in the human interactome large neighbourhoods of disease modules associated with disease categories in R-T. Dense neighborhoods of diseases in the interactome network are useful to identify promising disease categories for disease gene prediction, drug repurposing and comorbidities detection.
To find these large neighbourhoods, we verified the existence of topmost disease categories of the DO (our selected R-T) with a high overlapping with some inner (categorical) nodes in the I-T. A DO disease category $c'$ that is ``well-represented'' by an I-T category $c$ implies
a strong molecular proximity relationship among the diseases in cluster $C_c$. Symmetrically, this implies that there exists a molecular mechanism that strengthens the classification principle of the DO category.
We considered the 8 disease categories in the first level of the DO as the most general disease categories.
To evaluate the degree of similarity between these DO categories and their most similar correspondents in the I-T, we used the Jaccard similarity, i.e. the ``label score'' computed by the labeling algorithm of Section \ref{sec:labelling}. We also calculated the statistical significance of our results by computing the p-value over a random distribution.
Table \ref{tbl:macro} provides an overview of the topmost DO disease categories and their similarity degree with correspondent I-T categories induced from DM molecular network-proximity. In particular, we found that the DO disease categories that show a higher localization in a network neighborhood are ``disease of cellular proliferation'' and ``genetic disease''. This means that tumors and genetic diseases are highly localized in two neighbourhoods of the human interactome. From a biological network perspective, close DMs of ``disease of cellular proliferation'' are motivated by the fact that cancer diseases have similar genetic causes in differentiation and proliferation control genes such as the well-known $P53$ \cite{goh2007human, wood2007genomic,networkmedicine}.
The second best matching category is ``disease of anatomical entity'', i.e., disease grouped by human experts according to an anatomical localization principle. However, as shown in the Table \ref{tbl:macro}, the similarity value is high but not statistically significant. This is motivated by the fact that diseases belonging to this topmost category are grouped in diverse sub-categories scattered over the network rather than in a large ``anatomical'' neighbourhood.
To confirm this hypothesis, we performed a systematic automated pair-wise comparison among sub-categories of ``disease of anatomical entity''. We found that \textit{very rarely} category pairs belonging to different anatomical sub-systems have overlapping clusters in the I-T, with some obvious and well documented exception, like nervous and respiratory systems, gastrointestinal and integumentary systems, musculoskeletal and cardiovascular systems \cite{chhabra2005cardiovascular, huang2012skin, maron2013hypertrophic}. In other terms, our experiments show that the validity of the anatomical classification principle is not disproved by the DM localization hypothesis, at least, given our state-of-the-art knowledge of disease-gene associations. This observation leads us to consider one limitation of the study presented in this Section, which stems from the high incompleteness of the human interactome \cite{Venkatesan}. It follows that, while positive results (disease categories corresponding to highly overlapping disease modules) are useful pieces of evidence to identify interesting areas of the interactome to discover new disease-gene associations, the absence of such evidence could be either motivated by the non existence of a similarity relation, or by a lack of knowledge on gene interactions in specific areas of the interactome.\\
\begin{table}[h!]
\centering
\scalebox{1.0}{
\begin{tabular}{|c|c|c|c|}
\hline
R-T (Disease Ontology) & Induced I-T\\\hline
\textbf{Disease Category Name} (size) & \textbf{Best Label Score} (P-value)\\\hline
disease of cellular proliferation (255) & 54.77\% ($3.14\cdot10^{-20}$)\\\hline
disease of anatomical entity (434) & 50.05\% ($0.08$)\\\hline
genetic disease (12) & 41.66\% ($6.14\cdot10^{-10}$)\\\hline
disease by infectious agent (10) & 30\% ($1.92\cdot10^{-7}$)\\\hline
physical disorder (21) & 26.09\% ($1.51\cdot10^{-9}$)\\\hline
disease of mental health (76) & 21.51\% ($1.06\cdot10^{-13}$)\\\hline
syndrome (42) & 21.27 \% ($8.69\cdot10^{-11}$)\\\hline
disease of metabolism (55) & 16.36\% ($4.66\cdot10^{-11}$)\\\hline
\end{tabular}%
}
\caption{Correspondence among topmost DO categories and the induced taxonomy.
}
\label{tbl:macro}
\end{table}
\vspace{-15pt}
\subsection{Finding unexplored structural relations between disease categories. }
\label{sec:unexpected}
A more interesting result would be to identify ``unexpected'' and unexplored neighborhoods in the I-T, e.g., disease categories that are not presently connected in human-curated taxonomies but whose strong molecular similarities suggest that one such connection should be exploited to enrich the R-T ontology.
To help finding these relations we developed a visual tool to explore the I-T in a more systematic way. Supported by this tool, clinical experts have identified, among the others, the following interesting results:
there exist strong unexpected molecular relationships between glaucoma and pulmonary arterial hypertension,
cholestasis and chronic obstructive pulmonary diseases (COPD), peroxisomal diseases and ciliopathy-related syndromes. \textit{We remark that these categorical relationships can be detected in the I-T thanks to the labeling algorithm}.
By delving into these relationships, we were able to find confirmations in very recent clinical studies.
For example, Gupta et al. \cite{gupta2020secondary} and Lewczuk et al. \cite{lewczuk2019ocular} shed light on common molecular mechanisms and manifestations between pulmonary hypertension and glaucoma through multiple case reports. Instead, Tsechkovski et al. \cite{tsechkovski1997a1} observed that cholestasis and COPD patho-mechanisms are mediated by common molecular components like the Alpha 1-antitrypsin protein. However, the relationship between Alpha 1-antitrypsin mutations and liver disease is debated and yet to be elucidated \cite{schneider2020liver}. It is interesting to note that there is an emerging hypothesis connecting gut, liver and lung as playing a key role in the pathogenesis of COPD \cite{young2016gut}. Finally, Miyamoto et al. Zaki et al. \cite{zaki2016pex6} found biological mechanisms between peroxisomal diseases and ciliopathy related syndromes (e.g. Joubert syndrome, Bardet-Biedl syndrome, Jeune syndrome).
In conclusion, recent clinical evidence confirms that these detected relationships could be used to extend the DO.
Other unexplored strong relationships that we identified lack at the moment support from published studies\footnote{a clinical confirmation of our findings is clearly outside the scope of this research, although it represents a study hypothesis for further research by clinicians in the field.}, however the results reported above demonstrate the relevance and potentials of our proposed methodology.
\vspace{-9pt}
\subsection{Detection of nomenclature errors in disease-gene associations.}
\label{sec:nomenclature}
Finally, we tried to identify ``unconvincing'' strong matches between R-T and I-T categories.
An in-depth analysis by clinicians has led to the detection of a number of nomenclature errors in DisGeNET.
Disease modules in the interactome have been identified, as discussed in Section \ref{data}, using disease-gene associations in DisGeNET, one of the most widely used association databases. Publicly available disease-gene associations databases are manually or computationally curated and some of them integrate other disease-gene collections. However, especially for ambiguous diseases with similar names, all these mechanisms are prone to nomenclature errors resulting in wrong disease-gene associations. Although in our work we selected only associations with a high GDA score, errors might still survive.
The identification of wrong disease-gene associations is of primary importance both for disease gene discovery and clinical diagnoses. Indeed, on the one hand, disease gene discovery tools, using wrong disease-gene associations, would make wrong predictions. On the other hand, clinicians usually make and justify diagnoses using the disease-gene associations contained in public databases (as we said, DisGeNET is one among the most widely used resources) leading to wrong diagnoses or therapies for a patient.
Here, we demonstrate that our framework may facilitate the detection of wrong disease-gene associations in public databases, caused by nomenclature errors.
To this end, supported by clinicians, we identified a number of DO disease categories with an unconvincingly high overlapping with I-T inner nodes. Specifically, a clinical expert analyzed all DO/I-T categories pairs with a Jaccard similarity score greater or equal than $90\%$. Then, we manually verified the DisGeNET pieces of evidence supporting the related disease-gene associations.
Several nomenclature errors were found, among which we cite the following:
``hyper-IgM Immunodeficiency Syndrome'', ``obstructive lung disease'' and ``bone remodeling disease'' have several wrong disease-associations. For example, the ``hyper-IgM immunodeficiency syndrome'' is divided into five types by genetic association. In particular, ``hyper-IgM immunodeficiency syndrome'' type 2 is characterized by mutations of the \textit{AICDA} gene; type 3 by mutations of the \textit{CD40} gene, type 5 by mutations of the \textit{UNG} gene. However, DisGeNet links the three disease types to the same three genes\footnote{\url{https://www.disgenet.org/browser/0/1/0/C1720956/}}. This error is probably due to a wrong integration of the disease-gene associations of the CTD database that does not characterize the ``hyper-IgM immunodeficiency syndrome'' in types\footnote{\url{http://ctdbase.org/detail.go?type=disease&acc=MESH\%3aD053306\#descendants}}.
More in detail, in ``obstructive lung disease'' the pulmonary emphysema, focal emphysema, panacinar emphysema, centrilobular emphysema diseases have the same 12 disease-gene associations almost all supported by the same published study, but related only to the pulmonary emphysema or the generic category of emphysema. The same happens in ``bone remodeling disease'' for the following diseases: osteoporosis, age-related osteoporosis, post-traumatic osteoporosis, senile osteoporosis.
\vspace{-9pt}
\section{Discussion}
\label{discussion}
We believe that the biomedical understanding of diseases is on the edge of a radical change. The disease module hypothesis, with its relevant applications to disease-gene discovery and drug repurposing, is leading the revolution of bio-medical research of the future. For these reasons, we deem it fundamental to discover the degree of correspondence between disease similarity relations induced from the proximity of their related disease modules, and categorical similarity in human-curated disease taxonomies.
We developed a methodology to analyse relationships between diseases by leveraging, in a novel way, both taxonomic and molecular aspects.
The proposed methodology supported a systematic analysis of human-crafted disease categories and their relationships with the DM molecular network-proximity. In particular, we found that some disease in ``disease of cellular proliferation'' and ``genetic disease'' form promising large disease network-neighbourhoods that could be exploited by network analysis methods for disease-gene detection. Next, we evaluated the consistency of the ``disease anatomical entities'' at the molecular level and found that there is no strong evidence of a network-neighbourhood of anatomical entities but, contrarily, disease neighbourhoods related to anatomical systems are scattered. Furthermore, we used our methodology to find unexplored strong molecular relationships between ``specific'' disease categories, such as glaucoma and pulmonary hypertension, diseases that are distant in human-crafted taxonomies but appear to be related by co-morbidities and pathogenesis at the molecular level. Finally, we have been able to detect wrong disease-gene associations caused by nomenclature errors in public databases, that could potentially bias disease gene prediction methods and induce wrong clinical diagnoses.\\
\vspace{-9pt}
\section{Related Works}
\label{related works}
To the best of our knowledge, only one study has analysed in detail the molecular and categorical properties of DMs, as proposed in this project.
Zhou et al. \cite{zhou2018systems}, as a response to the limits of the contemporary disease taxonomies, demonstrate the inconsistency of the ICD-9 diagnostic classification system with the disease relationships in molecular networks. They propose a New Classification of Diseases (referred to as \textit{NCD}) to capture the molecular diversity of diseases and define clearer boundaries in terms of both phenotypical similarity and molecular associations.
The purpose of their study is to reform the ICD-9 by constructing a NCD in three steps. First, they create a network of diseases connected by molecular and phenotypic similarities. The disease nodes of the network define the low level of NCD, that is, the leaf nodes of the hierarchy. Then, the authors apply an overlapping community detection algorithm to the disease network to generate overlapping disease categories, representing the middle level of the NCD. Finally, they apply a non-overlapping community detection algorithm to the previously identifies network communities and generates disease categories for the top level of the NCD.
As highlighted by Zhou et al. \cite{zhou2018systems}, NCD is a simplified three-level hierarchical structure without explicit mappings with the reference classification system, the ICD-9. We build on \cite{zhou2018systems}, by proposing a method to create a full-fledged taxonomy with category labels, to favour a more systematic comparison between the automatically induced and manually created taxonomies.
Furthermore, as mentioned in Section \ref{data} the use of ICD-9 as a reference taxonomy has some drawbacks.
ICD-9 has been designed to promote international comparability in the classification and presentation of epidemiology and mortality statistics. Its hierarchical structure is not based on aetiology, but rather on anatomical and disciplinary principles,
to facilitate the statistical study of disease phenomena, and arranged according to epidemiological properties and anatomical site.
Hence, ICD-9 does not represent a good categorical framework for integrating network-based disease properties. Instead, the Disease Ontology (DO) has the purpose of identifying "commonalities of diseases located in a common molecular location, originating from a particular cell type or resulting from a common genetic mechanism" \cite{schriml2012disease}. Therefore, even though the "localist" view of diseases is still a guiding principle, the DO also exploits the molecular insights of disease phenotypes, thus representing a more appropriate baseline ontology. \\
\vspace{-15pt}
\section{Conclusions}
\label{conclusions}
We presented a novel disease module analytic strategy leveraging both a molecular and taxonomy perspective, providing new insights into the molecular mechanisms of diseases and a way to refine human-curated taxonomies. Our methodology has supported clinically relevant findings, such as promising areas of the interactome to discover new disease gene associations, unexplored disease molecular relationships, and nomenclature errors in disease-gene databases.
One limitation of our study arises from the highly incomplete state of the art knowledge on disease-related genes. This resulted in a limited mapping between human-crafted taxonomies and our induced hierarchy of disease modules (about 12\% of DO diseases), and furthermore prevented the interpretation of some evidence concerning unobserved molecular relationships, which could be either motivated by the non existence of such relations, or by the lack of knowledge on gene interactions in specific areas of the interactome.
\bibliographystyle{ieeetr}
\section{Introduction}
\label{sec:introduction}
Network medicine is a new paradigm of medicine that applies network science and systems biology approaches to study diseases as a consequence of pathobiological processes that interact in a complex network. Pieces of evidence in this field show that if a gene or molecule is involved in a disease, its direct interactors might also be suspected to play some role in the same pathological process. According to this hypothesis, proteins involved in the same disease show a high propensity to interact with each other, a property referred to as \textit{ ``disease module hypothesis''} \cite{networkmedicine, menche2015uncovering}. This hypothesis suggests that, if we identify a few disease components, the other disease-related components are likely to be located in their network-based ``neighbourhood'', called \textit{disease module}. Under a biological perspective, ``a disease module represents a group of
network components that together contribute to a cellular function whose disruption results
in a particular disease phenotype'' \cite{networkmedicine}.
Furthermore, subsequent studies have shown the tendency for biologically similar diseases to have their respective modules located in adjacent or overlapping areas of the interactome \cite{menche2015uncovering, goh2007human, booknetwork}.
According to Loscalzo et al. \cite{booknetwork} and Menche et al. \cite{menche2015uncovering}, ``proximity and degree of overlap of two disease modules (in the human interactome) has been found to be highly predictive of the pathobiological similarity of the corresponding diseases'' and ``network-based location of each disease module determines its pathobiological relationship to other diseases''. Indeed, different disease modules can overlap, so that perturbations caused by one disease can affect other disease modules that could lead to co-morbidity and pathogenetic mechanisms \cite{networkmedicine}. Analysing interconnections within disease modules can help reveal new disease genes, disease pathways, and identify possible drug targets or biomarkers for drug development and drug repurposing \cite{cheng2019network, networkmedicine}.
The tendency of phenotypically similar diseases to be close or to overlap in the interactome
suggests the possibility of \textit{inducing a hierarchical and possibly categorical structure of disease modules}, with specific and yet unexplored
relationships with existing disease classification taxonomies.
Disease taxonomies play a key role in defining the mechanisms of human diseases, potentially impacting both diagnosis and treatment. However, as remarked in \cite{networkmedicine, loscalzo2007human,zhou2018systems}, contemporary approaches to the classification of human diseases are mainly based on
anatomical pathological data and clinical knowledge.
Yet, modern molecular diagnostic tools have shown the shortcomings of this methodology, reflecting both a lack of sensitivity in identifying pre-clinical diseases and a lack of specificity in defining diseases unequivocally. On the other hand, inducing disease relationships solely from disease modules in the interactome is hindered by incomplete knowledge of disease-related genes \cite{networkmedicine, omim}.
In this study we propose a methodology to systematically compare categorical relationships automatically induced from proximity of disease modules in the human interactome network, with manually crafted categories in human-curated ontologies. Detected commonalities and differences may suggest latent and unknown molecular properties of diseases, help improve the current understanding of the disease mechanisms, and
facilitate precise clinical diagnosis consistent with molecular network properties \cite{Ghiassian2015, madeddu2020feature, cheng2019network, van2018gene}.
\vspace{-5pt}
\section{AIMS AND METHODS}
Network-based analyses of gene interaction data have helped to identify modules of disease-associated genes, hereafter referred to as disease modules (DMs), widely used to obtain both a systems level and a molecular understanding of disease mechanisms \cite{gustafsson2014modules}. Disease modules have been successfully used, for example, to prioritize diagnostic markers or therapeutic candidate genes, and in drug repurposing \cite{cheng2019network, networkmedicine, ay2007drug}.
However, according to Barabási et al. \cite{networkmedicine}, these results have marginally influenced the disease taxonomies and, conversely, to the best of our knowledge, disease taxonomies have not been used to analyse disease modules. In this study we aim for the first time to integrate taxonomic and network-based disease categorization principles, with the following innovative contributions:
\begin{enumerate}
\item to automatically induce a full-fledged hierarchical structure from proximity relations between DMs in the human interactome; \item to compare this structure with a human-defined disease taxonomy (such as the Disease Ontology\footnote{\url{https://disease-ontology.org}}));
\item to systematically identify categorical analogies and discrepancies between molecular and human-defined taxonomies.
\end{enumerate}
Our research hypothesis is that a study of the
relationships between molecular-based and human-curated disease taxonomies could help refine our knowledge on human diseases and
identify limitations and perspectives of current module-based computational approaches to the study of diseases.
As shown in the experimental Section \ref{results}, our study has some possibly relevant clinical implications:
\begin{enumerate}
\item To identify promising regions of the human interactome where new disease-gene relationships could be discovered\footnote{either exploiting data-driven methods or clinical experiments};
\item To identify unexplored molecular relationships among diseases;
\item To extend, correct and refine human-curated taxonomies.
\end{enumerate}
\noindent
Figure \ref{fig: workflow} shows the workflow of the proposed approach, described in detail in the next Sections. The main phases are the following: \\
\noindent
{\bf 1. Induction of a Taxonomy of Disease Modules:}
First, we automatically induce a hierarchical structure of diseases based on proximity relations of DMs in the human interactome. This taxonomic structure is hereafter referred to as the Interactome Taxonomy (I-T).\\
\noindent
{\bf 2. Taxonomy alignment and labeling:} Next, we align the I-T taxonomy with a human-curated \textit{reference ontology} (hereafter R-T), by creating a mapping between disease nodes in both taxonomies (red arrows in Box 2 of Figure \ref{fig: workflow}). Finally, a labeling algorithm finds the best map between categorical nodes in the R-T and the unlabeled inner nodes of the I-T (purple arrow in Box 2 of Figure \ref{fig: workflow}). \\
\noindent
{\bf 3. Systematic Comparative Analysis of I-T and R-T taxonomies:} The alignment between I-T and R-T supports a large-scale analysis of a vast collection of diseases jointly from an ontological and molecular perspective.
We provide insights to refine state of the art nosology and knowledge on disease interactions, by using our methodology to investigate the efficacy of the anatomical disease classification principle at the molecular level, identify nomenclature errors in disease-gene associations and discover unexplored molecular mechanisms among diseases.
\begin{figure}[ht!]
\centering
\includegraphics[width=1.\linewidth]{figures/workflow_velardi.pdf}
\caption{The work-flow of our study. Box $1$ shows the taxonomy induction phase, Box $2$ represents the phase of taxonomy alignment and labeling and Box $3$ summarizes the results of the analytic phase.}
\label{fig: workflow}
\end{figure}
\vspace{-15pt}
\section{Construction of the Interactome Taxonomy (I-T)}
\label{sec:induction of I-T}
We induce a disease taxonomy (named Interactome Taxonomy, I-T) by applying hierarchical agglomerative clustering to the human interactome network, exploiting proximity relations of disease modules.
Hierarchical agglomerative clustering (HAC) is a set of greedy approaches that create a hierarchy of clusters from unlabeled input data \cite{murtagh2017algorithms}.
Given a distance matrix of seed clusters, the HAC algorithm iteratively merges two clusters based on a selected inter-cluster distance measure. Common methods to merge clusters are Average and Complete linkage \cite{murtagh2017algorithms}.
In our context, clusters are DMs in the human interactome network.
However, due to the high incompleteness of the disease-gene associations modeled in the human interactome \cite{Venkatesan}, disease modules are not molecularly well-defined and devoid of a clearly dense network-structure \cite{menche2015uncovering}. To cope with this problem, we use two alternative definitions of modules adopted in network science, which have been commonly used in Network Medicine literature to physically identify disease modules \cite{menche2015uncovering, agrawal2018large}.\\
Given the human interactome network $G=(V, E)$ and a disease $d$ in a set of diseases $D_{it}$:
\begin{enumerate}
\item \textbf {Induced Module:} The Induced Module $I_{d} = (V_{d}, E_{d})$ is a subgraph of $G$, where $V_{d} \subseteq V$ is the set of genes-nodes associated with $d$ and $E_{d}$ is the set of gene-gene interactions $E_{d}=\{(u, v)|(u, v) \in E\;and\;u, v \in V_{d}\}$\cite{menche2015uncovering}. This definition includes in a DM all the disease genes but, due to the incompleteness of the network, it is usually a graph with many connected components lacking a strong local structure \cite{agrawal2018large}.
\item \textbf {Largest Connected Component (LCC) Module:} The $LCC_{d}$ module is the largest connected component of $I_{d}$ \cite{menche2015uncovering, agrawal2018large}. Unlike for the induced module $I_{d}$, $LCC_{d}$ usually has a denser local structure but may not include all the disease-related nodes $d$.
\end{enumerate}
Given the human interactome $G$, a set of diseases $D_{it}$ and their disease modules $DM_{it}$ in $G$, hierarchical clustering is performed using a distance matrix of disease modules (defined as previously explained), based on the following network-based distance measure (Eq.\eqref{eq:dist}) (used, e.g., in \cite{menche2015uncovering, booknetwork, cheng2018network}):
\begin{footnotesize}
\begin{equation}
dist(A,B) = \frac{\sum_{a \in A}min_{b \in B}SP(a,b) + \sum_{b \in B}min_{a \in A}SP(a,b)}{|A|+|B|}
\label{eq:dist}
\end{equation}
\end{footnotesize}
\noindent where A, B are respectively the set of nodes in modules $DM_A$ and $DM_B$ associated to diseases $d_{A}, d_{B} \in D_{it}$ and $SP$ is the shortest path length between two given nodes in $G$.
In our experiments, we used two DM definitions (Induced Module and LCC) and two cluster-merge methods (Average and Complete). The best solution among the four resulting I-Ts alternatives is identified using the methodology described in Section \ref{sec:selection}.
\section{Taxonomy Alignment and labeling}
\label{sec:alignmentlabelling}
The result of the hierarchical clustering algorithm is a binary tree taxonomy, hereafter referred to as Interactome Taxonomy (I-T). I-T is a connected directed acyclic graph $T(V_{T}, E_{T})$ in which nodes $V_{T}$ represent disease concepts and edges represent ``is-a'' semantic relationships\footnote{Edge $(v, u)$ with $\;u, v \in V_{T}$ means that $v$ \textit{is a} kind of $u$.}. In our context, leaf-nodes (i.e. nodes with out-degree equal to zero) are ``specific'' diseases $D_{it}$, physically represented by the corresponding modules $DM_{it}$, while inner nodes (i.e. non-leaf nodes) are disease categories $DC_{it}$.
Note that inner nodes $c \in DC_{it}$ are \textit{unlabeled}, and extensionally defined by the set of their subsumed disease nodes,
referred to as the \textit{clusters} $C_c$ of nodes $c$.
Similarly, given a ``reference'' human-crafted taxonomy, denoted as R-T, let $T(V_{R}, E_{R})$ be the set of its nodes and edges, $D_{rt}$ its disease (leaf) nodes, $DC_{rt}$ its categorical (inner) nodes and $C_{c'}$ the clusters associated with categorical nodes $c' \in DC_{rt}$. Contrary to the I-T, inner nodes in the R-T have also a human-defined label, the \textit{category name}.
\vspace{-9pt}
\subsection{Taxonomy Alignment}
\label{sec:alignment algorithms}
Whatever the choice of the R-T, the R-T and the I-T are expected to be defined on different sets of diseases nomenclatures, $D_{rt}$ and $D_{it}$. Furthermore, they are also expected to be structurally diverse. For example, R-T has usually a polyhierarchical structure, while I-T is by construction a binary tree.
To compare I-T and R-T we first need to create a mapping $M$ from
$D_{it}$ to $D_{rt}$ nomenclatures, and next, to prune the hierarchies so that they include the same set of leaf disease nodes, a process that we call \textit{taxonomy alignment}.
Let $M$ be an available mapping of disease nomenclatures (see Section \ref{data} for details). In Figure \ref{fig:merge}, mappings among nodes of the two taxonomies are highlighted using the same colours. As shown, $M$ is usually not one-to-one and we identify four cases:
\begin{enumerate}
\item Case 1: Some leaf nodes $D_{it}$ in I-T may map onto inner nodes in the R-T.
\item Case 2: Some $D_{it}$ nodes may map onto multiple nodes in the R-T.
\item Case 3: Some $D_{it}$ nodes may map onto the same node in the R-T.
\item Case 4: Some $D_{it}$ nodes may have no mappings in the R-T \textit{and vice-versa}. These nodes without mappings are depicted in Figure \ref{fig:merge} as white leaf nodes in both taxonomies.
\end{enumerate}
Our taxonomy alignment procedure consists of three algorithms: \textit{merge}, \textit{split}, and \textit{prune}. We apply \textit{merge} and \textit{split} to the R-T to solve cases 1, 2 and 3; instead, \textit{prune} is applied to both the R-T and the I-T, to solve case 4.
\begin{figure}[ht!]
\centering
\includegraphics[width=1.\linewidth]{figures/alignment/merge.pdf}
\caption{Visual example of the \textit{merge} algorithm.}
\label{fig:merge}
\end{figure}
\begin{algorithm}
\begin{footnotesize}
\SetAlgoLined
\SetKwFunction{FMg}{Merge}
\SetKwProg{Fn}{Function}{:}{}
\Fn{\FMg{rt, mapping}}{
diseases = keys(mapping)\;
rtmapped = {}
newMapping = Hashmap()
\For{diseaseId in diseases:}
{
rtmapped.union(mapping[diseaseId])\;
newMapping[diseaseId] = []\;
}
ancestors = rt.getColouredAncestors(rtmapped) \tcp*{Get the R\-T's coloured nodes with no R-T's coloured node among their ancestors}
\For{ancestor in ancestors:}
{
diseasesDesc = rt.getMappingDescendant(ancestors, mapping)\tcp*{Get the diseases linked to R\-T's nodes descendant of the coloured ancestors}
\For{diseaseId in diseasesDesc:}
{
newMapping[diseaseId].append(node)\;
}
}
\For{ancestor in ancestors:}
{
descs = rt.getDescendants(ancestor)\;
rt.removeNodes(descs)\tcp*{Turn every ancestor into a leaf}
}
mapping = newMapping\;
\KwRet rt, mapping\;
}
\label{algo:merge}
\end{footnotesize}
\caption{Merge}
\end{algorithm}
The \textit{merge} algorithm (see Algorithm
1) turns in leaves all the R-T coloured inner nodes. If the node has non-coloured descendants (that is, its descendands do not map onto any disease module in I-T), these descendants are removed. Else, the node and its coloured descendants are aggregated into a single multi-coloured node, as shown in Figure \ref{fig:merge} (right).
After the merge, the \textit{split} algorithm (see Algorithm 2) splits all the nodes with multiple colours (see Figure \ref{fig:split}). Note that these nodes inherit the ancestors of the splitted multi-coloured node. As a result of merge and split, all coloured R-T nodes are now leaf nodes, and every I-T node points to its correspondent R-T node. Furthermore, polyhierarchy in the R-T is preserved, as shown in Figure \ref{fig:merge-split}.
\begin{figure}[ht!]
\centering
\includegraphics[width=1.\linewidth]{figures/alignment/split.pdf}
\caption{Visual example of the \textit{split} algorithm.}
\label{fig:split}
\end{figure}
\begin{figure}[ht!]
\centering
\includegraphics[width=1.\linewidth]{figures/alignment/merge_poly.pdf}
\caption{Visual example of the \textit{merge} and \textit{split} algorithms for a polyhierarchical case.}
\label{fig:merge-split}
\end{figure}
\begin{algorithm}
\begin{footnotesize}
\SetAlgoLined
\SetKwFunction{FSp}{Split}
\SetKwProg{Fn}{Function}{:}{}
\Fn{\FSp{rt, mapping}}{
diseases = keys(mapping)\;
\For{diseaseId in diseases:}
{
nodes = mapping[diseaseId]\tcp*{The R\-T's nodes linked to diseaseId}
parents = rt.getParents(nodes)\tcp*{Get the set of parents of the given set of nodes}
rt.addNode(diseaseId, parents)\;
mapping[diseaseId] = diseaseId\;
}
\KwRet rt\;
}
\label{algo:split}
\end{footnotesize}
\caption{Split}
\end{algorithm}
Finally, the \textit{prune} algorithm (see Fig.
\ref{fig:pruning} and Algorithm
3) prunes both the R-T and the I-Ts by recursively removing survived leaf nodes not linked by any mapping relation in $M$. These are shown with a double circle in Figure \ref{fig:pruning}.
As a final result, the R-T and the I-T have as leaf nodes the same set of diseases, denoted as $D_{\cap}$.
\begin{figure}[ht!]
\centering
\includegraphics[width=1.\linewidth]{figures/alignment/pruning.pdf}
\caption{Visual example of the \textit{prune} algorithm.}
\label{fig:pruning}
\end{figure}
\begin{algorithm}
\begin{footnotesize}
\SetAlgoLined
\SetKwFunction{FPr}{Prune}
\SetKwProg{Fn}{Function}{:}{}
\Fn{\FPr{taxa, diseaseID}}{
drop = taxa.leaves() - diseaseID\;
\For{leaf in drop:}
{
taxa.remove(leaf)\tcp*{Remove the leaf from the taxonomy}
}
\For{leaf in taxa.leaves():}
{
\If{|rt.parents(leaf)| == 1 and rt.parents(leaf)[0].outDegree() == 1:}
{
taxa.replace(leaf)\tcp*{Recursively substitute the leaf with its parent until the leaf get a parent with out-degree > 1 or more than one parent}
}
}
\KwRet taxa\;
}
\label{algo:prune}
\end{footnotesize}
\caption{Prune}
\end{algorithm}
\vspace{-9pt}
\subsection{Selecting alternative Induced Taxonomies}
\label{sec:selection}
As remarked in Section \ref{sec:induction of I-T}, the I-T is built using different definitions of disease modules and different inter-cluster similarity functions during agglomerative clustering.
In this Section, we present a method to select the ``best'' I-T, among four I-Ts\footnote{Four aligned I-Ts resulting by the combination of the Induced and LCC disease module definitions with the Average and Complete clustering methods}, based on its structural and semantic similarity with the R-T. Note that a similarity function between two taxonomies can be computed only if they have been aligned. \\
Our method to compute the similarity between two taxonomies is based on the Lin semantic similarity \cite{lin1998information}:
\begin{footnotesize}
\begin{equation}
S_{T}(a, b):= \frac{2*IC_{T}(LCS_{T}(a, b))}{IC_{T}(a) + IC_{T}(b)}\label{eq:lin}
\end{equation}
\end{footnotesize}
\noindent
where $IC$ is:
\begin{footnotesize}
\begin{equation}
IC_{T}(x):= -log(\frac{|leaves_{T}(x)|+1}{MaxLeaves_{T} + 1})
\end{equation}
\end{footnotesize}
\noindent
where $a, b$ are two leaf nodes in a taxonomy $T$, and $LCS_{T}(a,b)$ is the least common subsumer of $a$ and $b$ in $T$; $leaves_{T}(x)$ is the set of leaves descendant of $x$ and $MaxLeaves_{T}$ is the number of leaves in $T$.\\
The Lin similarity increases when two nodes are structurally close in a taxonomy, and decreases otherwise. Furthermore, by construction, the distance between two nodes is normalized with respect of the maximum distance, a property that is particularly useful when extending this measure to compare taxonomies with different depths. This is a desirable property since the I-T is a binary tree and has a much higher depth than the R-T.
To compare each of the four induced I-Ts with a selected R-T, first, we calculate the pairwise Lin similarity $S_{T}(d_i, d_j)$
for each taxonomy $T$, where $\{(d_i, d_j)| d_i, d_j \in D_{\cap}\;and\;d_i \neq d_j \}$. Next, for each taxonomy $T$, we construct a vector $v_T$ of $S_{T}(d_i, d_j)$ similarity values. Finally, we calculate the cosine similarity between each of the induced taxonomies vectors $v_{IT_k} (k=1\dots 4)$ and $v_{RT}$. The intuition is that, if two taxonomies are similar, disease pairs that are ``close'' in one taxonomy should be ``close'' also in the other taxonomy, and those who are far apart in one taxonomy, should be far apart also in the other. The ``best'' I-T is selected according to:\\
\noindent
$argmax_{k}(cosSim(v_{IT_k},v_{RT}))$.
The experimental application of this methodology is described in Section \ref{results}.
\vspace{-9pt}
\subsection{Semantic Labeling of the Interactome Hierarchy (I-T)}
\label{sec:labelling}
As previously noted, the inner nodes of the aligned I-T have no semantic labels. To facilitate a comparative analysis of I-T and R-T, we defined an algorithm to label each inner node in the I-T with the most similar category label in the R-T. In order to find the most similar R-T category node, we exploit the notion of \textit{cluster} $C_c$ associated with a category node $c$ in a taxonomy, defined as the set of all its descendant disease nodes that are also in $D_{\cap}$. Then, a \textit{labeling} algorithm (see Algorithm
4) labels every I-T disease category $c$ with the name of the R-T category $c'$ with highest similarity score $sim(C_c,C_{c'})$ between the clusters of $c$ and $c'$\footnote{Note that the labeling method uses the full set of R-T categories to obtain more fine-grained labels
but the node clusters $C_c$ are defined on the common disease set $D_{\cap}$ of the aligned taxonomies.} . To compute the similarity between two clusters, we use the Jaccard coefficient, a popular measure of set similarity.
\begin{algorithm}
\begin{footnotesize}
\SetAlgoLined
\SetKwFunction{FMap}{labeling}
\SetKwProg{Fn}{Function}{:}{}
\Fn{\FMap{it, rt}}{
categories = it.nodes() - it.leaves()
labels = empty dictionary\;
\For{category in categories:}
{
clusterIT = getCluster(it, category)
catRT = getLabel(clusterIT, rt)\tcp*{Get the most similar R-T category}
labels[category] = catRT\;
}
\KwRet labels\;
}
\end{footnotesize}
\label{algo:label}
\caption{Labeling}
\end{algorithm}
\vspace{-15pt}
\section{Experimental set up}
\label{data}
This Section describes the data sources used in our experiments.
To conduct a disease module analysis, we considered the most recent release of the human protein-protein interaction network published by Barabasi et al. \cite{cheng2019network}, which is an extension of a highly cited and popular interactome used by Menche et al. \cite{menche2015uncovering}. The network has $|V| = 16\,677$ proteins and $|E| = 243\,603$ physical undirected protein interactions.
To construct disease modules, we collected disease-gene associations from DisGeNET \cite{pinero2020disgenet} with a GDA\footnote{GDA is a ``reliability'' score, for details see \url{www.disgenet.org/dbinfo\#section43}} score greater or equal of 0.3. Finally, we selected as disease modules the $948$ diseases with a set of disease genes of size at least $10$\footnote{smaller modules imply a limited knowledge of the related disease-gene associations to date, and may lead us to unreliable results.}.
We selected the Disease Ontology (DO) as Reference Taxonomy (R-T) \cite{schriml2012disease}. An alternative widely used reference ontology is ICD-9 (used, for example, in a work by Zhou et al. \cite{zhou2018systems}). However, ICD-9 was built to facilitate the statistical study of disease phenomena, and arranged according to epidemiological properties and anatomical site.
Hence, ICD-9 does not represent a good categorical framework for integrating network-based disease properties.
Instead, the Disease Ontology is a classification of human diseases organised by etiological agents such as infectious agents, clinical genetics and cellular processes. Therefore, even though the "localist" (i.e., anatomic and disciplinary classification) view of diseases is still a guiding principle, the DO also integrates the molecular insights of disease phenotypes.
By parsing the DO ``obo'' file\footnote{\url{http://www.obofoundry.org/ontology/doid.html}}, we generated a directed acyclic network hierarchy of $10012$ diseases and disease categories, $10061$ edges and $12 $ levels.
To create a mapping $M$ between the two different nomenclatures, we used partial mappings directly provided in DisGeNET and in the DO, that we further extended with the support of clinicians to cover all the 948 DMs.
To begin, we applied the method described in Section \ref{sec:labelling} to select the best induced I-T taxonomy, i.e., the one with the highest similarity with the selected R-T (namely, the Disease Ontology). Table \ref{tbl:rank} shows the result of this comparison. Note that similarity values are compared against those obtained by a random shuffling the disease nodes.
Based on the results of Table \ref{tbl:rank}, we select the I-T taxonomy obtained using Induced Modules to represent DMs, and the Average linkage method to merge clusters during hierarchical clustering. This induced taxonomic structure shows a higher similarity with the Disease Ontology and therefore represents a good basis for our study. Note however that all the compared methods produce taxonomies with a similarity value significantly higher than the random baseline. The observed differences are mainly due to some structural differences and to the positioning of outliers (isolated DMs in the interactome).
\begin{table}[h!]
\centering
\scalebox{0.8}{
\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|}
\hline
& \multicolumn{2}{c|}{{\bf Induced}} & \multicolumn{2}{c|}{\bf LCC}\\ \hline
Measure & Complete (RD) & { Average} (RD) & Complete (RD) & Average (RD)\\ \hline
Cos. Sim. (\%) & 43.59 (28.55) & {\bf 46.33} (29.84) & 39.94 (28.58) & 43.7 (29.71)\\
\hline
\end{tabular}%
}
\caption{\begin{footnotesize}Comparison of Lin-similarity vectors of the aligned R-T (the Disease Ontology) and I-T taxonomies obtained with four different variants of the proposed taxonomy induction method. The variants were obtained adopting two different network-based definitions of DMs (Induced and LCC) and two different techniques to merge clusters (complete and average). The value in the round brackets represents the average of values generated by ten random distributions of leaf nodes, leaving the taxonomy structure unchanged.\end{footnotesize}}
\label{tbl:rank}
\end{table}
\vspace{-20pt}
\section{Results}
\label{results}
Our research hypothesis in this work is that jointly analyzing the structural proximity of disease modules in the human interactome network and the semantic proximity of corresponding diseases in human-cured taxonomies could help both refine the classification of human diseases and
identify the limitations and perspectives of current module-based computational approaches to the study of diseases. In this Section, we summarize the major outcomes of a clinical analysis supported by the methodology presented in previous Sections. Our analysis is based both on the study of matching and unmatching pairs of R-T and I-T categories.
\vspace{-10pt}
\noindent
\subsection{Finding disease categories with a corresponding dense neighbourhood in the interactome. }
\label{dense neighbourhood}
First, we conducted an analysis to reveal in the human interactome large neighbourhoods of disease modules associated with disease categories in R-T. Dense neighborhoods of diseases in the interactome network are useful to identify promising disease categories for disease gene prediction, drug repurposing and comorbidities detection.
To find these large neighbourhoods, we verified the existence of topmost disease categories of the DO (our selected R-T) with a high overlapping with some inner (categorical) nodes in the I-T. A DO disease category $c'$ that is ``well-represented'' by an I-T category $c$ implies
a strong molecular proximity relationship among the diseases in cluster $C_c$. Symmetrically, this implies that there exists a molecular mechanism that strengthens the classification principle of the DO category.
We considered the 8 disease categories in the first level of the DO as the most general disease categories.
To evaluate the degree of similarity between these DO categories and their most similar correspondents in the I-T, we used the Jaccard similarity, i.e. the ``label score'' computed by the labeling algorithm of Section \ref{sec:labelling}. We also calculated the statistical significance of our results by computing the p-value over a random distribution.
Table \ref{tbl:macro} provides an overview of the topmost DO disease categories and their similarity degree with correspondent I-T categories induced from DM molecular network-proximity. In particular, we found that the DO disease categories that show a higher localization in a network neighborhood are ``disease of cellular proliferation'' and ``genetic disease''. This means that tumors and genetic diseases are highly localized in two neighbourhoods of the human interactome. From a biological network perspective, close DMs of ``disease of cellular proliferation'' are motivated by the fact that cancer diseases have similar genetic causes in differentiation and proliferation control genes such as the well-known $P53$ \cite{goh2007human, wood2007genomic,networkmedicine}.
The second best matching category is ``disease of anatomical entity'', i.e., disease grouped by human experts according to an anatomical localization principle. However, as shown in the Table \ref{tbl:macro}, the similarity value is high but not statistically significant. This is motivated by the fact that diseases belonging to this topmost category are grouped in diverse sub-categories scattered over the network rather than in a large ``anatomical'' neighbourhood.
To confirm this hypothesis, we performed a systematic automated pair-wise comparison among sub-categories of ``disease of anatomical entity''. We found that \textit{very rarely} category pairs belonging to different anatomical sub-systems have overlapping clusters in the I-T, with some obvious and well documented exception, like nervous and respiratory systems, gastrointestinal and integumentary systems, musculoskeletal and cardiovascular systems \cite{chhabra2005cardiovascular, huang2012skin, maron2013hypertrophic}. In other terms, our experiments show that the validity of the anatomical classification principle is not disproved by the DM localization hypothesis, at least, given our state-of-the-art knowledge of disease-gene associations. This observation leads us to consider one limitation of the study presented in this Section, which stems from the high incompleteness of the human interactome \cite{Venkatesan}. It follows that, while positive results (disease categories corresponding to highly overlapping disease modules) are useful pieces of evidence to identify interesting areas of the interactome to discover new disease-gene associations, the absence of such evidence could be either motivated by the non existence of a similarity relation, or by a lack of knowledge on gene interactions in specific areas of the interactome.\\
\begin{table}[h!]
\centering
\scalebox{1.0}{
\begin{tabular}{|c|c|c|c|}
\hline
R-T (Disease Ontology) & Induced I-T\\\hline
\textbf{Disease Category Name} (size) & \textbf{Best Label Score} (P-value)\\\hline
disease of cellular proliferation (255) & 54.77\% ($3.14\cdot10^{-20}$)\\\hline
disease of anatomical entity (434) & 50.05\% ($0.08$)\\\hline
genetic disease (12) & 41.66\% ($6.14\cdot10^{-10}$)\\\hline
disease by infectious agent (10) & 30\% ($1.92\cdot10^{-7}$)\\\hline
physical disorder (21) & 26.09\% ($1.51\cdot10^{-9}$)\\\hline
disease of mental health (76) & 21.51\% ($1.06\cdot10^{-13}$)\\\hline
syndrome (42) & 21.27 \% ($8.69\cdot10^{-11}$)\\\hline
disease of metabolism (55) & 16.36\% ($4.66\cdot10^{-11}$)\\\hline
\end{tabular}%
}
\caption{Correspondence among topmost DO categories and the induced taxonomy.
}
\label{tbl:macro}
\end{table}
\vspace{-15pt}
\subsection{Finding unexplored structural relations between disease categories. }
\label{sec:unexpected}
A more interesting result would be to identify ``unexpected'' and unexplored neighborhoods in the I-T, e.g., disease categories that are not presently connected in human-curated taxonomies but whose strong molecular similarities suggest that one such connection should be exploited to enrich the R-T ontology.
To help finding these relations we developed a visual tool to explore the I-T in a more systematic way. Supported by this tool, clinical experts have identified, among the others, the following interesting results:
there exist strong unexpected molecular relationships between glaucoma and pulmonary arterial hypertension,
cholestasis and chronic obstructive pulmonary diseases (COPD), peroxisomal diseases and ciliopathy-related syndromes. \textit{We remark that these categorical relationships can be detected in the I-T thanks to the labeling algorithm}.
By delving into these relationships, we were able to find confirmations in very recent clinical studies.
For example, Gupta et al. \cite{gupta2020secondary} and Lewczuk et al. \cite{lewczuk2019ocular} shed light on common molecular mechanisms and manifestations between pulmonary hypertension and glaucoma through multiple case reports. Instead, Tsechkovski et al. \cite{tsechkovski1997a1} observed that cholestasis and COPD patho-mechanisms are mediated by common molecular components like the Alpha 1-antitrypsin protein. However, the relationship between Alpha 1-antitrypsin mutations and liver disease is debated and yet to be elucidated \cite{schneider2020liver}. It is interesting to note that there is an emerging hypothesis connecting gut, liver and lung as playing a key role in the pathogenesis of COPD \cite{young2016gut}. Finally, Miyamoto et al. Zaki et al. \cite{zaki2016pex6} found biological mechanisms between peroxisomal diseases and ciliopathy related syndromes (e.g. Joubert syndrome, Bardet-Biedl syndrome, Jeune syndrome).
In conclusion, recent clinical evidence confirms that these detected relationships could be used to extend the DO.
Other unexplored strong relationships that we identified lack at the moment support from published studies\footnote{a clinical confirmation of our findings is clearly outside the scope of this research, although it represents a study hypothesis for further research by clinicians in the field.}, however the results reported above demonstrate the relevance and potentials of our proposed methodology.
\vspace{-9pt}
\subsection{Detection of nomenclature errors in disease-gene associations.}
\label{sec:nomenclature}
Finally, we tried to identify ``unconvincing'' strong matches between R-T and I-T categories.
An in-depth analysis by clinicians has led to the detection of a number of nomenclature errors in DisGeNET.
Disease modules in the interactome have been identified, as discussed in Section \ref{data}, using disease-gene associations in DisGeNET, one of the most widely used association databases. Publicly available disease-gene associations databases are manually or computationally curated and some of them integrate other disease-gene collections. However, especially for ambiguous diseases with similar names, all these mechanisms are prone to nomenclature errors resulting in wrong disease-gene associations. Although in our work we selected only associations with a high GDA score, errors might still survive.
The identification of wrong disease-gene associations is of primary importance both for disease gene discovery and clinical diagnoses. Indeed, on the one hand, disease gene discovery tools, using wrong disease-gene associations, would make wrong predictions. On the other hand, clinicians usually make and justify diagnoses using the disease-gene associations contained in public databases (as we said, DisGeNET is one among the most widely used resources) leading to wrong diagnoses or therapies for a patient.
Here, we demonstrate that our framework may facilitate the detection of wrong disease-gene associations in public databases, caused by nomenclature errors.
To this end, supported by clinicians, we identified a number of DO disease categories with an unconvincingly high overlapping with I-T inner nodes. Specifically, a clinical expert analyzed all DO/I-T categories pairs with a Jaccard similarity score greater or equal than $90\%$. Then, we manually verified the DisGeNET pieces of evidence supporting the related disease-gene associations.
Several nomenclature errors were found, among which we cite the following:
``hyper-IgM Immunodeficiency Syndrome'', ``obstructive lung disease'' and ``bone remodeling disease'' have several wrong disease-associations. For example, the ``hyper-IgM immunodeficiency syndrome'' is divided into five types by genetic association. In particular, ``hyper-IgM immunodeficiency syndrome'' type 2 is characterized by mutations of the \textit{AICDA} gene; type 3 by mutations of the \textit{CD40} gene, type 5 by mutations of the \textit{UNG} gene. However, DisGeNet links the three disease types to the same three genes\footnote{\url{https://www.disgenet.org/browser/0/1/0/C1720956/}}. This error is probably due to a wrong integration of the disease-gene associations of the CTD database that does not characterize the ``hyper-IgM immunodeficiency syndrome'' in types\footnote{\url{http://ctdbase.org/detail.go?type=disease&acc=MESH\%3aD053306\#descendants}}.
More in detail, in ``obstructive lung disease'' the pulmonary emphysema, focal emphysema, panacinar emphysema, centrilobular emphysema diseases have the same 12 disease-gene associations almost all supported by the same published study, but related only to the pulmonary emphysema or the generic category of emphysema. The same happens in ``bone remodeling disease'' for the following diseases: osteoporosis, age-related osteoporosis, post-traumatic osteoporosis, senile osteoporosis.
\vspace{-9pt}
\section{Discussion}
\label{discussion}
We believe that the biomedical understanding of diseases is on the edge of a radical change. The disease module hypothesis, with its relevant applications to disease-gene discovery and drug repurposing, is leading the revolution of bio-medical research of the future. For these reasons, we deem it fundamental to discover the degree of correspondence between disease similarity relations induced from the proximity of their related disease modules, and categorical similarity in human-curated disease taxonomies.
We developed a methodology to analyse relationships between diseases by leveraging, in a novel way, both taxonomic and molecular aspects.
The proposed methodology supported a systematic analysis of human-crafted disease categories and their relationships with the DM molecular network-proximity. In particular, we found that some disease in ``disease of cellular proliferation'' and ``genetic disease'' form promising large disease network-neighbourhoods that could be exploited by network analysis methods for disease-gene detection. Next, we evaluated the consistency of the ``disease anatomical entities'' at the molecular level and found that there is no strong evidence of a network-neighbourhood of anatomical entities but, contrarily, disease neighbourhoods related to anatomical systems are scattered. Furthermore, we used our methodology to find unexplored strong molecular relationships between ``specific'' disease categories, such as glaucoma and pulmonary hypertension, diseases that are distant in human-crafted taxonomies but appear to be related by co-morbidities and pathogenesis at the molecular level. Finally, we have been able to detect wrong disease-gene associations caused by nomenclature errors in public databases, that could potentially bias disease gene prediction methods and induce wrong clinical diagnoses.\\
\vspace{-9pt}
\section{Related Works}
\label{related works}
To the best of our knowledge, only one study has analysed in detail the molecular and categorical properties of DMs, as proposed in this project.
Zhou et al. \cite{zhou2018systems}, as a response to the limits of the contemporary disease taxonomies, demonstrate the inconsistency of the ICD-9 diagnostic classification system with the disease relationships in molecular networks. They propose a New Classification of Diseases (referred to as \textit{NCD}) to capture the molecular diversity of diseases and define clearer boundaries in terms of both phenotypical similarity and molecular associations.
The purpose of their study is to reform the ICD-9 by constructing a NCD in three steps. First, they create a network of diseases connected by molecular and phenotypic similarities. The disease nodes of the network define the low level of NCD, that is, the leaf nodes of the hierarchy. Then, the authors apply an overlapping community detection algorithm to the disease network to generate overlapping disease categories, representing the middle level of the NCD. Finally, they apply a non-overlapping community detection algorithm to the previously identifies network communities and generates disease categories for the top level of the NCD.
As highlighted by Zhou et al. \cite{zhou2018systems}, NCD is a simplified three-level hierarchical structure without explicit mappings with the reference classification system, the ICD-9. We build on \cite{zhou2018systems}, by proposing a method to create a full-fledged taxonomy with category labels, to favour a more systematic comparison between the automatically induced and manually created taxonomies.
Furthermore, as mentioned in Section \ref{data} the use of ICD-9 as a reference taxonomy has some drawbacks.
ICD-9 has been designed to promote international comparability in the classification and presentation of epidemiology and mortality statistics. Its hierarchical structure is not based on aetiology, but rather on anatomical and disciplinary principles,
to facilitate the statistical study of disease phenomena, and arranged according to epidemiological properties and anatomical site.
Hence, ICD-9 does not represent a good categorical framework for integrating network-based disease properties. Instead, the Disease Ontology (DO) has the purpose of identifying "commonalities of diseases located in a common molecular location, originating from a particular cell type or resulting from a common genetic mechanism" \cite{schriml2012disease}. Therefore, even though the "localist" view of diseases is still a guiding principle, the DO also exploits the molecular insights of disease phenotypes, thus representing a more appropriate baseline ontology. \\
\vspace{-15pt}
\section{Conclusions}
\label{conclusions}
We presented a novel disease module analytic strategy leveraging both a molecular and taxonomy perspective, providing new insights into the molecular mechanisms of diseases and a way to refine human-curated taxonomies. Our methodology has supported clinically relevant findings, such as promising areas of the interactome to discover new disease gene associations, unexplored disease molecular relationships, and nomenclature errors in disease-gene databases.
One limitation of our study arises from the highly incomplete state of the art knowledge on disease-related genes. This resulted in a limited mapping between human-crafted taxonomies and our induced hierarchy of disease modules (about 12\% of DO diseases), and furthermore prevented the interpretation of some evidence concerning unobserved molecular relationships, which could be either motivated by the non existence of such relations, or by the lack of knowledge on gene interactions in specific areas of the interactome.
\bibliographystyle{ieeetr}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 9,610 |
\section{Introduction}
\IEEEPARstart{F}{or} the past few years, vehicles have been getting smarter with the progress of technology by installing camera sensors, microcomputers, and communication devices \cite{zhou2014chaincluster} \cite{he2015full}. These vehicles are connected with themselves and other facilities to form a vehicular network. Due to its potential commercial value, the Internet of Vehicles (IoV) has become a hot topic that attracts the attention of academia and industry. The IoV provides a convenient platform for information exchange and sharing between users, such as traffic accidents and road conditions, which can improve the utilization of resources and traffic conditions effectively \cite{zhang2017security}. However, too many mobile and variable entities are involved in the vehicular network, they are usually strangers and do not trust each other. Because of that, information exchange in the IoV still face huge challenges about how to ensure information security and privacy protection in real applications.
The advent of blockchain technology makes it possible to change all of this. Blockchain is a public and distributed database which entered people's sight since Nakamoto published his white paper in 2008 \cite{nakamoto2008bitcoin}. Blockchain takes advantage of the knowledge of modern cryptography and distributed consensus protocol to achieve the purpose of security and privacy protection. Here, the digital signature is an effective means to achieve identity authentication and avoid information leakage, while the consensus protocol allows information to interact freely among users who do not trust each other without the need for a third platform. Thus, it can be used to construct a reliable information trading system because of its decentralization, security, and anonymity \cite{sharma2017software} \cite{li2018blockchain}. Despite this, how to design a reasonable blockchain structure based on the vehicle network, improve the efficiency of information exchange, and guarantee the truthfulness of pricing strategies is still a problem worthy of in-depth discussion.
In this paper, we consider such a scenario: In a smart city, there is a traffic administration (TA) that is responsible for monitoring real-time traffic conditions by collecting information of various road nodes in this city. The traditional approach is to install cameras at various road nodes, but doing so is costly and vulnerable to be damaged by natural and human activities. Especially in some remote corners, there is no need to install a separate camera. Driven by the IoV, the TA can crowdsource its tasks of traffic information collection to vehicles running on the road. Based on that, we need to study the traffic information exchange between TA and vehicles in a smart city. There are two challenges shown as follows: (1) how to construct a reliable and efficient traffic information trading framework implemented by blockchain?; and (2) how to build a fair and truthful mechanism that selects a subset of vehicles as information providers to maximize the TA's profit while preventing vicious competition?
To settle the first challenge, we propose a blockchain-based real-time traffic monitoring (BRTM) system to achieve a reliable and efficient information trading process between TA and vehicles. First, we use modern cryptography methods and digital signature techniques to protect the contents of communication from privacy leakage. In addition to this, the traditional proof-of-work (PoW) consensus mechanism cannot be applied to our resource-limited vehicle network because of its high computational cost and slow confirmation speed \cite{su2018secure}. Thus, we design a lightweight blockchain relied on the reputation-based delegated proof-of-stake (DPoS) consensus mechanism that is able to reduce confirmation time and improve throughput for this system. Here, All the TAs of different cities can be considered as the full nodes which are interconnected with each other to complete the consensus process. There is a reputation value associating with each TA in the BRTM system, which reflects its behaviors in the previous consensus rounds. A full node with a higher reputation value implies it has a higher voting weight and is more likely to become the leader in the future consensus round, thus ensuring the reliability and efficiency of the consensus process.
To settle the second challenge, we propose a budgeted auction mechanism so as to incentivize the vehicles in a city to take on the tasks issued by the TA actively. Here, the TA publishes a task set that contains a number of different tasks about traffic information on various locations. Each active vehicle in this city submits the tasks that it can accomplish and corresponding bid to the TA, then the TA selects a winner set from these active vehicles to undertake its tasks and pay them accordingly. We aim to maximize the TA's profit by selecting an optimal winner set, which can be categorized as a non-monotone submodular maximization problem with knapsack constraint. The simple greedy strategy can give us a valid solution, but it does not satisfy the truthfulness. If no truthfulness, a vehicle may increase its utility by offering a higher bid or colluding with other vehicles, which will damage the fairness and effectiveness of the auction mechanism. Thus, we design a truthful budgeted selection and pricing (TBSAP) algorithm that can guarantee the individual rationality, profitability, truthfulness, and computational efficiency for the budgeted auction mechanism.
Finally, the effectiveness of our proposed mechanisms is evaluated by numerical simulations. It is shown that our proposed mechanisms can enhance the reliability of the blockchain system by urging the nodes to behave rightfully and make sure that the information trading is fair and truthful. To our best knowledge, this is the first time to put forward a reliable blockchain-based traffic monitoring system in a vehicular network that is based on a budgeted auction mechanism to maximize the profit. The rest of this paper is organized as follows: In Sec. \uppercase\expandafter{\romannumeral2}, we discuss the-state-of-art work. In Sec. \uppercase\expandafter{\romannumeral3}, we introduce our traffic monitoring system and define the utility functions. In Sec. \uppercase\expandafter{\romannumeral4}, we present our design of lightweight blockchain elaborately. In Sec. \uppercase\expandafter{\romannumeral5}, we propose a truthful budgeted auction mechanism. Then we evaluate our proposed system and algorithms by numerical simulations in Sec.\uppercase\expandafter{\romannumeral6} and show the conclusions in Sec. \uppercase\expandafter{\romannumeral7}.
\section{Related Work}
With the development of Internet of Things (IoT), vehicles are no longer isolated individuals, but nodes in a connected network, which lead to the formation of the IoV \cite{kaiwartya2016internet}. Then, the IoV has been developed further due to the progress of computing power and modern communication devices. Kaiwartya \textit{et al.} \cite{kaiwartya2016internet} provided us with an IoV framework that focused on networking architecture mainly. Singh \textit{et al.} \cite{singh2019internet} presented an abstract network model for the IoV and related with different services relied on popular technologies. Ji \textit{et al.} \cite{ji2020survey} designed a novel network structure for the future IoV and gave a comprehensive review of the basic IoV information, which included several network architectures and representative applications of IoV.
In recent years, the rise of blockchain technology overturned the operating mode of the traditional IoT, thereby the blockchain-based IoT has promoted changes in trading methods. Firstly, in energy trading, Li \textit{et al.} \cite{li2017consortium} designed a secure energy trading system, energy blockchain, for the industrial IoT relied on consortium blockchain and credit-based payment scheme. Guo \textit{et al.} \cite{9165852} \cite{guo2020architecture} proposed a blockchain-based distributed multiple energies trading framework to address security and privacy protection. Xia \textit{et al.} \cite{xia2020bayesian} came up with a blockchain-enabled vehicle-to-vehicle electricity trading scheme that exploited Bayesian game pricing to deal with incomplete information sharing. Secondly, in computing resource trading, Yao \textit{et al.} \cite{yao2019resource} studies a resource management problem between the cloud server and miners since the computational power of industrial IoT was limited. Ding \textit{et al.} \cite{ding2020incentive} created a mechanism for the blockchain platform to attract lightweight devices to purchase more computational power from edge servers for participating in mining. Finally, in information trading, Wang \textit{et al.} \cite{wang2017blockchain} designed and realized a securer and more reliable government information sharing system by combining blockchain, network model, and consensus algorithm. Xu \textit{et al.} \cite{xu2018making} devised a blockchain-based big data sharing framework that was appropriate for the resource-limited devices. Chen \textit{et al.} \cite{chen2019secure} proposed a blockchain-based data trading framework that relied on consortium blockchain to achieve secure and truthful data trading for IoV. However, they did not really achieve reliability and ignored the high latency of the consensus process. In this paper, our trading model is different from either of the provious ones and attempt to design a secure and reliable system carefully.
The auction mechanism, as a technique of game theory, has been used to solve the allocation and pricing problems in a variety of applications, such as mobile crowdsensing \cite{zhang2015incentives} \cite{yang2015incentive}, edge computing \cite{kiani2017toward} \cite{jiao2019auction}, and spectrum trading \cite{zhu2014double} \cite{zheng2014strategy}. Zhang \textit{et al.} \cite{zhang2015incentives} surveyed the diverse incentive strategies that encouraged users to take part in mobile crowdsourcing. Yang \textit{et al.} \cite{yang2015incentive} designed two crowdsourcing models under the framework of the Stackelberg game and reverse auction theory respectively. Kaini \cite{kiani2017toward} put forward and solved an auction-based profit maximization problem under the background of the hierarchical model. Jiao \textit{et al.} \cite{jiao2019auction} proposed an auction-based market model for computing resource allocation between the edge server and miners. Zhu \textit{et al.} \cite{zhu2014double} devised a truthful double auction mechanism for cooperative sensing in radio networks. Zheng \textit{et al.} \cite{zheng2014strategy} achieved a social welfare maximization problem by re-distributing wireless channels, while they took the strategy-proof into consideration as well. In this paper, our proposed auction mechanism is similar to that under the mobile crowdsourcing, but there is a budgeted constraint in our model that constrains the range of the winner set. Therefore, both the theoretical analysis and applicable scope are different from the previous work.
\section{Traffic Monitoring System}
In this section, we introduce our traffic monitoring system including network model and utility functions for the entities.
\subsection{Network Model}
Consider a smart city, there is a traffic administration (TA) that is responsible for monitoring real-time traffic condition in this city. It can crowdsource its tasks of traffic information collection to vehicles on the road by paying them a certain amount of money. Therefore, the blockchain-based real-time traffic monitoring (BRTM) system consists of two important entities: TA and vehicle, which is shown in Fig. \ref{fig1}. In the BRTM system, the functionality of the entities in a smart city $S_a$, $a\in\mathbb{Z}^+$, can be shown as follows:
\begin{figure}[!t]
\centering
\includegraphics[width=\linewidth]{show.png}
\caption{An instance of BRTM system built on the United States, where the orange lines are active vehicles' requests to undertake the tasks and the black line are TA's acceptances for corresponding requests.}
\label{fig1}
\end{figure}
\textit{Traffic administration (TA): }The TA in the city $S_a$ can be denoted by $TA_a$, which collects the real-time traffic information from those vehicles running in this city. For instance, during peak time, traffic accidents often occur on some heavily trafficked roads. At this time, the $TA_a$ needs to analyze road conditions instantly according to the responses provided by those vehicles that run on the designated location. If $TA_a$ adopts the information provided by some vehicles, it must pay them with data coins. Here, data coin is a kind of digital currency considered as the payment for traffic information.
\textit{Vehicles: }The vehicles in this system are installed with camera sensors, wireless communication devices, and microcomputer systems, which are able to collect, process, and transmit data to other corresponding devices. The active vehicles in the city $S_a$ can be denoted by a set $V_a=\{v_{a1},v_{a2},\cdots,v_{ab},\cdots\}$, where active vehicles are those participating in information trading with $TA_a$ and idle vehicles do not want to share their traffic information. Once a transaction between $TA_a$ and $v_{ab}$ has been completed and validated, the vehicle $v_{ab}$ will receive a certain number of data coins from $TA_a$.
Based on that, a smart city in our BRTM system can be denoted by $S_a=(TA_a, V_a)$, and the whole BRTM system $\mathbb{S}$ can be denoted by $\mathbb{S}=\{S_1,S_2,\cdots,S_a,\cdots\}$. It is very easy to understand, for example, this system can be constructed in a country that is composed of a number of smart cities. Here, all TAs that serve under the cities in $\mathbb{S}$ are interconnected with each other to make up a peer-to-peer (P2P) wide-area network. We take Fig. \ref{fig1} as an instance to demonstrate it.
\begin{exmp}
Shown as the upper part in Fig. \ref{fig1}, there is a TA in the Dallas city that announces a number of traffic information collection tasks across the important intersections of the whole city. Some vehicles in this city request to undertake part of tasks at a certain price. For a vehicle, whether its request can be accepted is decided by the TA according to the TA's evaluation. Then, a BRTM system is built on the United States, shown as the lower part in Fig. \ref{fig1}. The four main cities, Los Angeles, Chicago, New York, and Dallas are interconnected with each other to form a large network.
\end{exmp}
The P2P network among the TAs in the BRTM system is used for constructing the blockchain network. Here, blockchain is an effective technique to record the transactions and guarantee the security. In our blockchain network, there are two types of nodes which are full node and lightweight node. For the full nodes, they not only executes the consensus process to validate the candidate block but also manages stores the blockchain that contains the whole transactions between TA and vehicles. For the lightweight nodes, they merely store the block headers that is convenient for them to check and verify. In our system $\mathbb{S}$, each $TA_a$ of $S_a\in\mathbb{S}$ is defaulted as a full node and each vehicle $v_{ab}\in V_a$ of $S_a\in\mathbb{S}$ is defaulted as a lightweight node because of lacking enough storage and computational power. Details of the blockchain design will be described in Sec. \uppercase\expandafter{\romannumeral4}.
\subsection{Definitions of Utility functions}
Consider a smart city $S=(TA,V)$ such that $S\in\mathbb{S}$ at some point, we neglect the subscripts and denote by $V=\{v_1,v_2,\cdots,v_n\}$ for convenience. This traffic administration $TA$ releases a task set $T=\{t_1,t_2,\cdots,t_m\}$ about traffic information for the active vehicles to undertake. For the $TA$, there is an appraisement $a_j$ for each task $t_j\in T$. For each vehicle $v_i\in V$, it can attempt to finish a subset of tasks $T_i\subseteq T$ based on its ability and willingness. The cost of $T_i$ for the $v_i$ can be defined as $c_i$, which is private and not known to the $TA$. Then, the vehicle $v_i$ determines a bid $b_i$ and respones the $TA$ with its bid-task pair $(T_i,b_i)$, where $b_i$ is $v_i$'s reserve price that is the lowest price it want to undertake the tasks $T_i$. Generally, we have $T_i\cap T_j\neq\emptyset$ for any vehicle $v_i$ and $v_j$. Here, for each task $t_i\in T$, we can quantify it as the traffic information at some position in this city, thereby an active vehicle is able to submit a subset of tasks based on its running path. After receiving the responses from all active vehicles, the $TA$ needs to select a winner (acceptance) set $W\subseteq V$ and give a payment $p_i$ for each $v_i\in W$. The utility for a vehicle $v_i\in V$ is
\begin{equation}
U_i=\left
\{\begin{IEEEeqnarraybox}[\relax][c]{l's}
p_i-c_i,&if $v_i\in W$\\
0,&if $v_i\notin W$
\end{IEEEeqnarraybox}
\right.
\end{equation}
The profit of the $TA$ is
\begin{equation}
P(W)=A(W)-\sum\nolimits_{v_i\in W}p_i
\end{equation}
where we denote by $A(W)=\sum_{t_j\in\cup_{v_i\in W}T_i}a_j$. Besides, in order to control cost, the $TA$ has a total budget $B$ such that $\sum_{v_i\in W}b_i\leq B$. Based on that, we want to design an incentive mechanism to execute this auction process.
\begin{figure}[!t]
\centering
\includegraphics[width=\linewidth]{trading.png}
\caption{The traffic information trading framework between TA and vehicles.}
\label{fig2}
\end{figure}
\section{Lightweight Blockchain Design}
In a smart city, the TA publishs a task set first, then those active vehicles in this city request to undertake part of tasks. If a vehicle's request is accepted by the TA, it will get a certain number of rewards. With the help of the blockchain technology, the TA can trade the traffic information with the active vehicles in a decentralized, secure, and verifiable manner. In the meantime, a budgeted auction mechanism is written in the smart contract. When a new round of trading begins, the smart contract in our BRTM system will be deployed and executed automatically in order to find the optimal profit for the $TA$ according to the vehicles' requests.
\subsection{System Initialization}
Consider a smart city $S=(TA,V)$, each vehicle $v_i\in V$ has to register with the certificate authority (CA) through correlating its license plate so as to acquire a unique identification $ID_i$. Then, each legitimate vehicle will be assigned with a private/public key pair $(SK_i,PK_i)$, where the private key is reserved by itself and the public key is known by all the legitimate nodes in the blockchain as a pseudonym. The asymmetric encryption are adopted widely in the current blockchain technology for the sake of data integrity. The data encrypted by the private (resp. public) key can be decrypted by the public (resp. private) key. After registering, the vehicle $v_i$ will obtain a certificate $Cer_i$ signed by CA's private key that can certify the authenticity of its identity. There is an account $A_i=\{ID_i,Cer_i,(SK_i,PK_i),B_i\}$ associated with the $v_i\in V$ where $B_i$ is its data coin balance. Similarly, the $TA$ has an account denoted by $A_*=\{ID',Cer',(SK',PK'),B',Rep'\}$ as well, where $Rep'$ is its reputation value which will be introduce later. If a round of trading is finished successfully, data coins will be transferred from $B_*$ to $B_i$.
\subsection{Information Trading Framework}
The elaborate process of traffic information trading in our BRTM system are drawn in Fig. \ref{fig2}, whose specific operation steps are summarized as follows:
\textbf{1) }The $TA$ publishs its task set $T$ across the active vehicles in this city. The published message can be denoted by $PubMsg=\{SK'(T),Cer',STime\}$, where is the task set is encrypted by the $TA$'s private key for security and $STime$ is the time stamp of this message generation.
\textbf{2) }After receiving the $PubMsg$ from the $TA$, each active vehicle $v_i\in V$ in this city has to verify the $TA$'s certification $Cer'$ by the CA's public key and then read the task set by the $TA$'s public key. Once verified, each $v_i$ will determine its task-bid pair $(T_i,b_i)$ and send its request message $ReqMsg$, denoted by $ReqMsg=\{PK'(T_i,b_i),Cer_i,STime\}$, back to the $TA$. Here, its task-bid pair is encrypted by the $TA$'s public key because it can only be read by the $TA$ for privacy.
\textbf{3) }The $TA$ waits to collect all the $ReqMsg$ from the active vehicles in this city, then determine the winner set $W$ and its corresponding payment $p_i$ for $v_i\in W$. This process is executed by the built-in smart contract, which adopts a budgeted auction mechanism explained in Sec. \uppercase\expandafter{\romannumeral5}.
\textbf{4) }The $TA$ sends the order message to each accepted vehicle $v_i\in W$, which can be denoted by $OrdMsg=\{PK_i(p_i),Cer',STime\}$. Here, the payment is encrypted by the $v_i$'s public key which can be read by the $v_i$ merely.
\textbf{5) }If receiving the $OrdMsg$ from the TA, it means that the $v_i$ has been selected as an information provider. Then, the $v_i$ can read it by its private key and send the response message that includes the traffic information associated with task $T_i$, denoted by $ResMsg=\{PK'(data),Cer_i,STime\}$, back to the $TA$. The data is encrypted by the $TA$'s public key due to the same reason as (2).
\textbf{6) }After the data transmission, the $TA$ will check and confirm whether the traffic information about task $T_i$ from the $v_i$ meets its requirement. If yes, the $TA$ pays the data coins $p_i$ to the $v_i$'s public wallet address.
\textbf{7) }Once receiving the payment from the $TA$, the $v_i$ will sends the confirm message, denoted by $ConMsg=\{PK'(Confirm),Cer_i,STime\}$, back to the $TA$. The $TA$ will sign it with a confirm message as well, then a transaction record is formulated until now.
\textbf{8) }The built-in smart contract in the $TA$ will record a series of transactions between $TA$ and vehicles in this city within a period of time, and package them into a new block. Before this block is added into the blockchain, it has to be reached a consensus among all the TAs in the BRTM system. The consensus process we adopt here is called as reputation-based delegated proof-of-work (DPoS) mechanism explained in Sec. \uppercase\expandafter{\romannumeral4}.C. After finishing the consensus process, this block will be appended into the blockchain in a linear and chronological order permanently.
\subsection{Reputation-based DPoS Mechanism}
A consensus process is essential to guarantee the consistency and security for the blockchain system. The classic PoW consensus mechanism is not suitable to our system because of lacking the necessary computational power in the vehicular networks. Therefore, we design a novel reputation-based DPoS mechanism that not only ensures reliability but also improves performance. Just as said before, all the TAs in the BRTM system $\mathbb{S}$ are considered as the full nodes, thereby the consensus process can be carried out among them. The operational steps are displayed as follows:
\textbf{1) Witness election: }Denote by the full node set $\mathbb{Z}=\{TA_1,TA_2,\cdots,TA_a,\cdots\}$, there is a reputation value $Rep_a$ associated with each full node $TA_a\in\mathbb{Z}$. This reputation $Rep_a$ can be considered as its stake that determines its voting weight directly. It implies that the nodes with higher reputation values can determine the results more than those with lower reputation values. At each witness election epoch, the voting result $R_a$ for each $TA_a\in\mathbb{Z}$ is defined as
\begin{equation}
R_a=\sum\nolimits_{TA_{a'}\in\mathbb{Z}\backslash\{TA_{a}\}}Rep_{a'}\cdot\mathbb{I}(a,a')
\end{equation}
where the $\mathbb{I}(a,a')$ is an indicator. Here, $\mathbb{I}(a,a')=1$ if the $TA_{a'}$ votes to support $TA_a$, otherwise $\mathbb{I}(a,a')=0$. All these reputation values and voting results are stored in the blockchain, thereby each node can check them by itself. We select a witness committee $\mathbb{M}\subseteq\mathbb{Z}$ that have the top $|\mathbb{M}|$ highest voting results. Then, it can be divided into two part such that $\mathbb{M}=\mathbb{D}\cup\mathbb{E}$ and $\mathbb{D}\cap\mathbb{E}=\emptyset$, where the full node in $\mathbb{D}$ is an active witness and in $\mathbb{E}$ is a standby witness. The active witnesses have the top $|\mathbb{D}|$ highest voting results, which are able to generate a new block like a leader. However, the standby witnesses can only verify and broadcast the block generated by an active witness.
\textbf{2) Block generation: }First, the active witnesses in the set $\mathbb{D}$ are sorted in a random sequence. Then, each $TA_a\in\mathbb{D}$ takes turn to be a leader round by round based on this sorting that is responsible for generating a new block. The leader has to verify and check all the transactions occurred recently and package those valid transactions into a new block. If a node in its turn does not produce a block over a given period of time successfully, it will be skipped and have no chance to be leader again in this election epoch. After passing $|\mathbb{D}|$ consensus rounds, namely an election epoch, we re-execute the witness election to elect a new witness committee $\mathbb{M}$ according to the new reputation values of the full nodes in $\mathbb{Z}$.
\textbf{3) Consensus process: }After producing a new block, the leader should broadcast it to all witnesses in $\mathbb{M}$. All witnesses should verify the leader's identity and check this block, then broadcast their verification results signed by their private key. Next, each witness $TA_a\in\mathbb{M}$ compares its verified outcome with those from other witnesses. If confirmed, it will send a confirmation message to the leader, which means that this witness agrees to accept the new block. For the leader, it will append the new block into the blockchain if the proportion of witnesses that agree to accept this block is more than two thirds. All the full nodes should synchronize their local blockchain storage according to the longest chain principle and all the lightweight node should update their blockchain headers based on the newest one.
\textbf{4) Reputation update: }When a consensus round is finished or interrupted, we need to update the reputation values of the full nodes in $\mathbb{Z}$ according to their behaviors during this consensus round. Generally, the positive behaviors contribute to the accumulation of reputation, but the negative behaviors had a bad effect. We denote by $Rep_a(i)$ the repuation value of the full node $TA_a\in\mathbb{Z}$ at the $i$-th consensus round. At the $i$-th consensus round, we define
\begin{equation}
\Delta_a(i)=A\cdot\alpha_a(i)+B\cdot\beta_a(i)+C\cdot\gamma_a(i)
\end{equation}
for each full node $TA_a\in\mathbb{Z}$. Here, if the $TA_a\in\mathbb{Z}$ participates the voting in witness election, we give $\alpha_a(i)=1$, otherwise $\alpha_a(i)=-1$. When the $TA_a$ is the leader at this consensus round, we give $\beta_a(i)=1$ if it generates a new block that is accepted by other witnesses eventually, otherwise $\beta_a(i)=-1$. If the $TA_a\in\mathbb{Z}\backslash\{\text{leader}\}$ is not the leader, we give $\beta_a(i)=0$. When the $TA_a\in\mathbb{M}\backslash\{\text{leader}\}$ is a member of witness committee but not the leader, we give $\gamma_a(i)=1$ if it verifies the block produced by the leader correctly, otherwise $\gamma_a(i)=-1$. If the $TA_a\in\mathbb{Z}\backslash\mathbb{M}$ is not a witness, we give $\gamma_a(i)=0$. Then, the $A$, $B$, and $C$ are three adjustable parameters that represent the rewards or punishments of voting, leader, and verification behaviors. Based on its behaviors $\Delta_a(i)$ at the $i$-th consensus round, we define the reputation value of the full node $TA_a\in\mathbb{Z}$ as
\begin{equation*}
Rep_a(i)=\left
\{\begin{IEEEeqnarraybox}[\relax][c]{l's}
\max\{1,Rep_a(i-1)+\Delta_a(i)\},&if $\Delta_a(i)\geq 0$\\
\min\{0,Rep_a(i-1)+\Delta_a(i)\},&if $\Delta_a(i)< 0$
\end{IEEEeqnarraybox}
\right.
\end{equation*}
where the $TA_a$'s voting is meaningless when its reputation down to zero according to the (3). Moveover, we initialize the reputation $Rep_a(0)=0.5$ for each $TA_a\in\mathbb{Z}$ and make $B>C>A>0$ because of their importance.
\subsection{Performance and Reliability}
Our BRTM system inherits the advantages of blockchain technology which helps to ensure the reliability of traffic information trading and privacy protection. Its main characteristics are summarized as follows: (1) Decentralization: the traffic information trading can be performed in a distributed manner without relying on the third trusted intermediaries, which avoids single point failure; (2) Reliability: when there is a node failing because of malicious attacks, the blockchain network can be guaranteed to work as usual; (3) Privacy protection: shown as Sec. \uppercase\expandafter{\romannumeral4}.B, asymmetric encryption is used to prevent the message from reading by others, which makes the private message remain confidential during the auction process; (4) Efficiency: our reputation-based DPos mechanism not only makes the consensus process more reliable but also improves efficiency by screening out the trustworthy nodes in advance; (5) Transaction authentication: all transaction must be checked and verified by the witness before appending into the blockchain, thereby it is extremely hard to dominate the majority of witnesses to create an unreal block. Based on that, our BRTM system provides us with a secure, reliable, and efficient traffic information trading platform.
\section{Budgeted Auction Incentive mechanism}
In this section, we consider how to model the trading process between $TA$ and $v_i\in V$ in a smart city $S=(TA,V)$. Auction mechanism is an execellent theoretical tool for this scenario. Here, the sellers are $V=\{v_1,v_2,\cdots,v_n\}$ and the buyer is $TA$. Each seller $v_i$ submits a task-bid pair $(T_i,b_i)$, and then the buyer determine whether to accept its request. If accept it, the buyer need to offer a payment. We call such an auction as ``reverse auction''. Thus, the single round auction mechanism can be formulated as Problem 1.
\begin{pro}
The active vehicles in $S$ given a task-bid pair vector $((T_1,b_1),(T_2,b_2),\cdots,(T_n,b_n))$, the $TA$ need to compute an allocation $W$ and payments $\{p_i\}_{v_i\in W}$ such that
\begin{equation}
\max_{W\subseteq V}P(W) \text{ s.t. } \sum\nolimits_{v_i\in W}b_i\leq B
\end{equation}
where it satisfies individual rationality, profitability, truthfulness, and computational efficiency.
\end{pro}
\noindent
The auction we use in this section is a single sealed-bid auction, thereby the task-bid pair given by each seller is private and not known to other sellers in order to avoid collaborating or forming an alliance. Once submitted, any seller can not change its task or bid during the auction. This is why we use asymmetric encryption in Sec. \uppercase\expandafter{\romannumeral4}.B.
\begin{defn}[Individual rationality]
A reverse auction is individual rational if there is no winning sellers getting less than its cost.
\end{defn}
For each vehicle $v_j\in V$, it must have an non-negative utility that is $p_i\geq c_i$ if $v_i\in W$.
\begin{defn}[Profitability]
The profit of an reverse auction is the difference between the value generated by winner set and the payment to the sellers, which is nonnegative.
\end{defn}
For the $TA$ in $S$, it has an allocation $W$ such that $\sum\nolimits_{t_j\in\cup_{v_i\in W}T_i}a_j\geq \sum\nolimits_{v_i\in W}p_i$.
\begin{defn}[Truthfulness]
A reverse auction is truthful if every seller's bid, which is the same as its truthful cost, is the dominant strategy that maximizes its utility.
\end{defn}
For each vehicle $v_i\in V$, it means that the $v_i$ cannot increase its utility by giving a bid $b_i$ that is different from its truthful cost $c_i$ no matter what others' bids are. Truthfulness is a very important property for an auction mechanism to avoid malicious price manipulation as well as ensure a fair and benign market competition environment. In our case, if a vehicle can obtain a better utility when offering an untruthful bid, then those malicious vehicles are able to cheat in the auction that benefit themselves but hurt the interests of others. By making all active vehicles bidding truthfully, the $TA$ can allocate its tasks to the most suitable vehicles. Therefore, truthfulness plays a very significant role in our auction design.
\begin{defn}[Computational efficiency]
A reverse auction is efficient if it can be done in ploynomial time.
\end{defn}
\subsection{Submodular Maximization}
Assume the $TA$ gives a payment $p_i$ with $p_i=b_i$ for each vehicle $v_i\in V$, the Problem 1 can be reduced to an optimization problem, called ``budgeted vehicle allocation problem'', that selects a winner set $W\subseteq V$ such that $\bar{P}(W)$ is maximized. We denote
\begin{equation}
\bar{P}(W)=A(W)-\sum\nolimits_{v_i\in W}b_i
\end{equation}
where $\sum_{v_i\in W}b_i\leq B$. To be meaningful, we assume $\bar{P}(\emptyset)=0$ and it exists at least one vehicle $v_k\in V$ such that $\bar{P}(\{v_k\})>0$ with $b_k\leq B$. However, the budgeted vehicle allocation problem can be reduced to the classic set cover problem in polynomial time, thereby it is NP-hard to find the optimal solution definitely. Based on that, we have to seek help from designing an approximation algorithm which will make use of submodularity of objective shown in (6).
\begin{defn}[Submodular function \cite{lovasz1983submodular}]
Given a set function $f:2^V\rightarrow\mathbb{R}$, it is submodular if
\begin{equation}
f(X\cup\{u\})-f(X)\leq f(Y\cup\{u\})-f(Y)
\end{equation}
for any $X\subseteq Y\subseteq V$ and $u\in V\backslash Y$.
\end{defn}
\begin{lem}
The objective function of budgeted vehicle allocation problem $\bar{P}$ is submodular.
\end{lem}
\begin{proof}
According to the (6), to show $\bar{P}(X\cup\{v_i\})-\bar{P}(X)\leq \bar{P}(Y\cup\{v_i\})-\bar{P}(Y)$ is equivalent to show $A(X\cup\{v_i\})-A(X)\leq A(Y\cup\{v_i\})-A(Y)$ for any $X\subseteq Y\subseteq V$ and $v_i\in V\backslash Y$. We have $A(X\cup\{v_i\})-A(X)=$
\begin{flalign}
&=\sum\nolimits_{t_i\in T_i\backslash\cup_{v_j\in X}T_j}a_i\geq\sum\nolimits_{t_i\in T_i\backslash\cup_{v_j\in Y}T_j}a_i\\
&=A(Y\cup\{v_i\})-A(Y)
\end{flalign}
Therefore, $\bar{P}$ is submodular.
\end{proof}
As we known, Buchbinder \textit{et al.} \cite{buchbinder2015tight} designed a double greedy algorithm for the unconstrained submodular maximization problem with a $(1/3)$-approximation under the deterministic setting and a $(1/2)$-approximation under the randomized setting. Back to our budgeted vehicle allocation problem, there is a constraint $\sum_{v_i\in W}b_i\leq B$ that is a knapsack constraint. This constraint affects the resulting profit obtained by the $TA$ and the number of vehicles that are selected as winners in the auction. Thus, a valid reverse auction mechanism design are required to ensure the truthfulness carefully. Based on the aforementioned analysis, this optimization problem can be catagorized to a non-monotone submodular maximization with knapsack constraint. Lee \textit{et al.} \cite{lee2009non} proposed a $(1/5-\epsilon)$-approximation algorithm to maximize any non-negative submodular function with knapsack constraint by means of fractional relaxation and local search method. Even though this algorithm can give us a constant approximation ratio, its process is complex and its performance is worse than the greedy-heuristic algorithm actually. The greedy-heuristic algorithm is shown in Algorithm \ref{a1}.
Here, we denote by $\bar{P}(v_i|W)=\bar{P}(W\cup\{v_i\})-\bar{P}(W)$ and $b^*$ is the bid offered by vehicle $v^*$. Shown as Algorithm \ref{a1}, we select a vehicle $v^*$ from the current constrained set $F$ with maximum unit marginal gain until $\bar{P}(v^*|W)<0$ or $F=\emptyset$. Despite the winner set returned by Algorithm \ref{a1} has no any theoretical bounds because of non-monotonicity and knapsack constraint, it is intuitive and has a good performance in the practical applications. Now, we have to explore whether the greedy-heuristic satisfies the aforementioned four properties in the reverse auction mechanism.
\begin{algorithm}[!t]
\caption{\text{greedy-heuristic}}\label{a1}
\begin{algorithmic}[1]
\renewcommand{\algorithmicrequire}{\textbf{Input:}}
\renewcommand{\algorithmicensure}{\textbf{Output:}}
\REQUIRE Function $\bar{P}$, bids $\{b_i\}_{v_i\in V}$, and budget $B$
\ENSURE Winner set $W$
\STATE Initialize: $W\leftarrow\emptyset$, $s\leftarrow 0$
\STATE Initialize: $F\leftarrow\{v_i:v_i\in V\backslash W \text{ and } b_i\leq B\}$
\WHILE {$F\neq\emptyset$}
\STATE Select $v^*$ such that $v^*\in\arg\max_{v_i\in F}\{\bar{P}(v_i|W)/b_i\}$
\IF {$\bar{P}(v^*|W)<0$}
\STATE Break
\ENDIF
\STATE $W\leftarrow W\cup\{v^*\}$
\STATE $s\leftarrow s+b^*$
\STATE $F\leftarrow\{v_i:v_i\in V\backslash W \text{ and } b_i\leq B-s\}$
\ENDWHILE
\RETURN $W$
\end{algorithmic}
\end{algorithm}
Next, let us look at whether the greedy-heuristic satisfies profitability, individual rationality, truthfulness, and computational efficiency one by one as follows:
\textbf{1) Individual rationality: }The $TA$ pay each vehicle in the winner set its bid, thus it is individually rational.
\textbf{2) Profitability: }Form line 5 in Algorithm \ref{a1}, the while loop is terminated when there is no vehicle having postive marginal gain, which guarantee $\bar{P}(W)>0$.
\textbf{3) Truthfulness: }Let us consider an example. There are five tasks issued by the $TA$, denoted by $T=\{t_1,t_2,t_3,t_4,t_5\}$, with appraisement $\{a_1=2,a_2=3,a_3=4,a_4=2,a_5=5\}$ and the budget $B=5$. There are three active vehicles denoted by $V=\{v_1,v_2,v_3\}$ in this city. They want to undertake the $TA$'s tasks as $T_1=\{t_1,t_3,t_5\}$, $T_2=\{t_1,t_2,t_5\}$, $T_3=\{t_3,t_4,t_5\}$, $c_1=2$, $c_2=2$, and $c_3=2$. When each vehicle offers a bid truthfully, we have $\bar{P}(\{v_1\}|\emptyset)/b_1=(A(\{v_1\})-b_1)/b_1=(11-2)/2=4.5$. Similarly, we have $\bar{P}(\{v_2\}|\emptyset)/b_2=4$ and $\bar{P}(\{v_3\}|\emptyset)/b_3=3.5$. Thus, vehicle $v_1$ is selected at the first iteration. At the second iteration, we have $\bar{P}(v_2|\{v_1\})/b_2=0.5$ and $\bar{P}(v_3|\{v_1\})/b_3=0$. Thus, vehicle $v_2$ is selected at the second iteration. Then, the greedy-heuristic terminates because the budget is exhausted. However, when vehicle $v_2$ offer an untruthful bid $b_2=c_2+\lambda$, we have $\bar{P}(v_2|\{v_1\})/b_2=3/(2+\lambda)-1$. If $\lambda\in(0,1)$, it will be selected as the winner at the second iteration. The algorithm terminates here and vehicle $v_2$ can get more payment by offering an untruthful bid, thus is does not satisfy truthfulness.
\textbf{4) Computational efficiency: }The running time of the greedy-heuristic is $O(Bnm/\min_{v_i\in V}\{b_i\})$ because it takes $O(nm)$, $|T|=m$ and $|V|=n$, to compute $\bar{P}$ and iterates at most $B/\min_{v_i\in V}\{b_i\}$ times, so computationally efficient.
\begin{algorithm}[!t]
\caption{\text{TBSAP Algorithm}}\label{a2}
\begin{algorithmic}[1]
\renewcommand{\algorithmicrequire}{\textbf{Input:}}
\renewcommand{\algorithmicensure}{\textbf{Output:}}
\REQUIRE Function $\bar{P}$, bids $\{b_i\}_{v_i\in V}$, and budget $B$
\ENSURE Winner set $W$
\STATE // Winner allocation stage
\STATE Initialize: $X\leftarrow\emptyset$, $s\leftarrow 0$
\WHILE {$X\neq V$}
\STATE Select $v^*$ such that $v^*\in\arg\max_{v\in V\backslash X}\{\hat{P}(v|X)\}$
\IF {$\hat{P}(v^*|X)<0$ or $s+b^*>B$}
\STATE Break
\ENDIF
\STATE $X\leftarrow X\cup\{v^*\}$
\STATE $s\leftarrow s+b^*$
\ENDWHILE
\STATE // Payment determination stage
\FOR {each $v_i\in X$}
\STATE Initialize: $Y_0\leftarrow\emptyset$, $s\leftarrow 0$, $j\leftarrow 0$
\STATE Initialize: $p_i\leftarrow -\infty$
\WHILE {$Y_j\neq V_{-i}$}
\STATE $v_{i_{j+1}}\leftarrow\arg\max_{v\in V_{-i}\backslash Y_j}\{\hat{P}(v|Y_j)\}$
\IF {$\hat{P}(v_{i_{j+1}}|Y_j)<0$ or $s+b_{i}>B$}
\STATE Break
\ENDIF
\STATE $Y_{j+1}\leftarrow Y_j\cup\{v_{i_{j+1}}\}$
\STATE $s\leftarrow s+b_{i_{j+1}}$
\STATE $p_i\leftarrow\max\left\{p_i,b_{i_{j+1}}\cdot\frac{A(v_i|Y_j)}{A(v_{i_{j+1}}|Y_j)}\right\}$
\STATE $j\leftarrow j+1$
\ENDWHILE
\IF {$s+b_i\leq B$}
\STATE $p_i\leftarrow\max\{p_i,A(v_i|Y_j)\}$
\ENDIF
\ENDFOR
\RETURN $X$ and $\{p_i\}_{v_i\in X}$
\end{algorithmic}
\end{algorithm}
\subsection{Truthful Auction Mechanism Design}
As mentioned above, the greedy-heuristic algorithm is not meaningful due to lacking truthfulness even though it simple to implement. Thus, we have to design a budgeted reverse auction mechanism that not only gets a good profit by encouraging vehicles to undertake the tasks, but also satisfies the four properties shown as before, especially for truthfulness, in order to protect from manipulating this system malignantly by offering a unreal bid. Therefore, a valid auction mechanism needs to be designed although it may lose some of its profits. We propose a truthful budgeted reverse auction mechanism based on Myerson's introduction \cite{nisan2007}.
\begin{thm}[\cite{nisan2007}]
An reverse auction mechanism is truthfully if and only if it satisfies as follows: (1) Monotonicity: If a vehicle (seller) $v_i\in V$ wins by its task-bid pair $(T_i,b_i)$, then it will win by any bid that is smaller than $b_i$ with the same task set $T_i$ as well. Namely, the $(T_i,b^\circ_i)$ will win by any bid $b^\circ_i<b_i$ when other sellers do not change their strategies; (2) Critical payment: The payment $p_i$ of a winner $v_i$ with its task-bid pair $(T_i,b_i)$ is the maximum bid with which the $v_i$ can win. Namely, the $(T_i,b^\circ_i)$ will not win by any bid $b^\circ_i>p_i$ when other sellers do not change their strategies.
\end{thm}
Based on the Theorem 1, we design our budgeted reverse auction mechanism consisted of the winner allocation stage and payment determination stage. From the bids $\{b_i\}_{v_i\in V}$, we denote by the unit marginal gain $\hat{P}$
\begin{equation}
\hat{P}(v_i|X)={\bar{P}(v_i|X)}/{b_i}=[{\bar{P}(X\cup\{v_i\})-\bar{P}(X)}]/{b_i}
\end{equation}
The winner allocation stage selects vehicles from $V$ in a greedy approach. All active vehicles in $V$ are sorted in a non-increasing sequence as
\begin{equation}
\hat{P}(v_1|X_0)\geq\cdots\geq\hat{P}(v_{i}|X_{i-1})\geq\cdots\geq\hat{P}(v_{n}|X_{n-1})
\end{equation}
where the $i$-th vehicle has the maximum unit marginal gain $\hat{P}(v_{i}|X_{i-1})$ over $V\backslash X_{i-1}$, $X_{i-1}=\{v_1,v_2,\cdots,v_{i-1}\}$, and $X_0=\emptyset$. From this sorting, we select the maximum $L$ with $L\leq n$ such that $\hat{P}(v_L|X_{L-1})\geq 0$ and $\sum_{v_i\in X_L}b_i\leq B$ where $X_L=\{v_1,v_2,\cdots,v_L\}$.
According to the winner set $X_L$, we have to determine the payment price $p_i$ for each vehicle $v_i\in X_L$. The reverse auction mechanism runs the winner allocation process repreatedly. Consider the vehicle $v_i\in V$, all active vehicles in $V_{-i}=V\backslash\{v_i\}$ are sorted in a non-increasing order as follows:
\begin{equation}
\hat{P}(v_{i_1}|Y_0)\geq\hat{P}(v_{i_2}|Y_{1})\geq\cdots\geq\hat{P}(v_{i_{n-1}}|Y_{n-2})
\end{equation}
where the $i_j$-th vehicle has the maximum unit marginal gain $\hat{P}(v_{i_j}|Y_{j-1})$ over $V\backslash Y_{j-1}$, $Y_{j-1}=\{v_{i_1},v_{i_2},\cdots,v_{i_{j-1}}\}$, and $Y_0=\emptyset$. From this sorting, we select the maximum $L_i$ with $L_i\leq n-1$ such that $\hat{P}(v_{i_{L_i}}|Y_{L_i-1})\geq 0$ and $\sum_{v_{i_j}\in Y_{L_i-1}}b_{i_j}+b_i\leq B$ where $Y_{L_i-1}=\{v_{i_1},v_{i_2},\cdots,v_{i_{L_i-1}}\}$. In short, there is a list $Y_{L_i}=\{v_{j_1},v_{j_2},\cdots,v_{i_{L_i}}\}$ associated with the vehicle $v_i$. For each position $i_{j+1}$ in this list $Y_{L_i}$, we can get the maximum bid $b_{i(j+1)}'$ that the vehicle $v_i$ should offer in order to replace $v_{i_{j+1}}$ with $v_i$ at the position $i_j$. To achieve it, we have $\hat{P}(v_i|Y_j)\geq\hat{P}(v_{i_{j+1}}|Y_j)$, which is equivalent to $[A(v_i|Y_j)-b_i]/b_i\geq[A(v_{i_{j+1}}|Y_j)-b_{i_{j+1}}]/b_{i_{j+1}}$. Thus, we have the following inequality:
\begin{equation}
b_{i(j+1)}'= b_{i_{j+1}}\cdot{A(v_i|Y_j)}/{A(v_{i_{j+1}}|Y_j)}
\end{equation}
From here, we can achieve a list $b'_i=\{b'_{i(1)},b'_{i(2)},\cdots,b'_{i(L_i)}\}$ where each $b'_{i(j)}$ is the maximum bid to replace the vehicle $v_{i_j}$ with $v_i$ in the list $Y_{L_i}$. The vehicle $v_i$ can replace any one in $Y_{L_i}$ without exceeding the budget $B$. Consider the $v_{i_{L_i+1}}$, it can be divided into the following three cases: (1) $\sum_{v_{i_j}\in Y_{L_i}}b_{i_j}+b_i> B$; (2) $\hat{P}(v_{i_{L_i+1}}|Y_{L_i})< 0$; and (3) $L_i=n-1$ where $v_{i_{L_i+1}}$ does not exist and can be considered as a virtual vehicle. For the case (1), the $v_{i_{L_i+1}}$ cannot be replaced by the $v_i$ because of the budget constraint, thereby we do not need to do anything. If not case (1), for the cases (2) and (3), the bid by the $v_i$ should be less than $A(v_i|Y_{L_i})$ so as to replace the $v_{i_{L_i+1}}$, thereby the maximum bid to replace the $v_{i_{L_i+1}}$ with $v_i$ is equal to $A(v_i|Y_{L_i})$. Therefore, for each winner $v_i\in X_L$, we have
\begin{equation}
p_i=\left
\{\begin{IEEEeqnarraybox}[\relax][c]{l's}
\max\{b'_i\},\text{ if } \sum\nolimits_{v_{i_j}\in Y_{L_i}}b_{i_j}+b_i>B\\
\max\{\max\{b'_i\},A(v_i|Y_{L_i})\},\text{ else}
\end{IEEEeqnarraybox}
\right.
\end{equation}
\noindent
Based on the (14), a truthful budgeted selection and pricing (TBSAP) algorithm is shown in Algorithm \ref{a2}.
\begin{lem}
The TBSAP is individually rational.
\end{lem}
\begin{proof}
Let $v_{i_i}$ be the vehicle $v_i$'s replacement which appears in the $i$-th position in the sorting (12) over $V_{-i}$. Because the vehicle $v_{i_i}$ cannot be in the $i$-th position when the winner $v_i$ joins in this sorting. Thus, if $i\leq L_i$, we have $\hat{P}(v_i|Y_{i-1})\geq\hat{P}(v_{i_i}|Y_{i-1})$ which results in $b_i\leq b_{i_i}\cdot A(v_i|Y_{i-1})/A(v_{i_i}|Y_{i-1})\leq p_i$. If $i>L_i$ or $i$ does not exist, we have $b_i\leq A(v_{i}|X_{i-1})$ since the $v_i$ is a winner, and $b_i\leq A(v_{i}|X_{i-1})=A(v_{i}|Y_{i-1})\leq A(v_i|Y_{L_i})\leq p_i$ because of the submodularity.
\end{proof}
\begin{lem}
The TBSAP is profitable.
\end{lem}
\begin{proof}
Recall that the vehicle $v_L$ is the last one that satisfies $A(v_L|X_{L-1})\geq b_L$ in the sorting (11), we have the profit $P(X_L)=\sum_{1\leq i\leq L}A(v_i|X_{i-1})-\sum_{1\leq i\leq L}p_i$ according to the (2), which is sufficient to show that $A(v_i|X_{i-1})\geq p_i$ for each $1\leq i\leq L$. For each vehicle $v_i\in X_L$, we consider the two sub-cases shown as follows:
\noindent
\textbf{Case 1: } Recall that the vehicle $v_{i_{L_i}}$ is the last one that satisfies $\hat{P}(v_{i_{L_i}}|Y_{L_i-1})\geq 0$ and $\sum_{v_{i_j}\in Y_{L_i-1}}b_{i_j}+b_i\leq B$ in the sorting (12), we have $p_i=\max\{b'_i\}$ if $\sum_{v_{i_j}\in Y_{L_i}}b_{i_j}+b_i>B$. Thus, we denote by
\begin{equation}
k=\arg\max_{1\leq j\leq L_i}\left\{b'_{i(1)},\cdots,b'_{i(j)},\cdots,b'_{i(L_i)}\right\}
\end{equation}
Based on that, we have
\begin{flalign}
p_i&=b_{i_k}\cdot{A(v_i|Y_{k-1})}/{A(v_{i_{k}}|Y_{k-1})}\leq A(v_i|Y_{k-1})\\
&\leq A(v_i|X_{i-1})
\end{flalign}
where the inequality (16) is because we have ${A(v_{i_{k}}|Y_{k-1})}\geq b_{i_k}$. From the Lemma 2, we have $b_i\leq p_i$. Consider a vehicle $v_i\in X_L$ with its bid $b_i$, it cannot be moved forward in the sorting (11) by increasing its bid. We can know that $i\leq k$ and $X_{i-1}\subseteq Y_{k-1}$ due to the fact that $X_j=Y_j$ when $j<i$. Therefore, we have $A(v_i|Y_{k-1})\leq A(v_i|X_{i-1})$ because of its submodularity, and the inequality (17) is established.
\noindent
\textbf{Case 2: }Otherwise, we have $p_i=\max\{\max\{b'_i\},A(v_i|Y_{L_i})\}$ if $\sum_{v_{i_j}\in Y_{L_i}}b_{i_j}+b_i\leq B$. Thus,
\begin{equation}
p_i\leq A(v_i|Y_{L_i})\leq A(v_i|X_{i-1})
\end{equation}
due to the similar analysis with the inequality (17). Combining the case 1 and case 2, this lemma can be proven.
\end{proof}
\begin{lem}
The TBSAP is truthful.
\end{lem}
\begin{proof}
According to the Theorem 1, it is sufficient to show that our budgeted reverse auction mechanism satisfies the monotonicity and critical payment. Let us look at the monotonicity first. Consider a vehicle $v_i\in X_L$ with its bid $b_i$, it cannot be moved backward in the sorting (11) by offer a lower bid $b^\circ_i$ with $b^\circ_i<b_i$ since $A(v_i|X_{i-1})/b^\circ_i>A(v_i|X_{i-1})/b_i$. Therefore, if $v_i$ is a winner by offering a bid $b_i$ in the winner allocation stage, it must be a winner by offering $b^\circ_i$.
Then, we show the payment $p_i$ is the critical payment for the vehicle $v_i$ where it cannot win this auction if giving a bid larger than $p_i$ definitely. Based on the (14), when $\sum_{v_{i_j}\in Y_{L_i}}b_{i_j}+b_i>B$, the $v_i$ must be able to replace one vehicle in $Y_{L_i}$ if it wants to be a winner. If the $v_i$ offers a bid $b_i^\circ$ larger than $p_i=\max\{b'_i\}$, we have
\begin{equation}
A(v_i|Y_{j-1})/b_i^\circ<A(v_{i_j}|Y_{j-1})/b_{i_j}\text{ for }1\leq j\leq L_i
\end{equation}
The $v_i$ cannot replace any one in $Y_{L_i}$ with bid $b_i^\circ$, thereby it cannot be a winner because of the budget constraint. Based on the (14), when $\sum_{v_{i_j}\in Y_{L_i}}b_{i_j}+b_i\leq B$, suppose the $v_i$ can not replace any vehicle in $Y_{L_i}$, it sill can be a winner if $A(v_i|Y_{L_i})\geq b_i$ since there is residual budget. If the $v_i$ offers a bid $b_i^\circ$ larger than $p_i=\max\{\max\{b'_i\},A(v_i|Y_{L_i})\}$, it not only fail to replace any one in $Y_{L_i}$ according to the (19), but also have $b_i^\circ>A(v_i|Y_{L_i})$, thereby it cannot be a winner.
\end{proof}
\begin{lem}
The TBSAP is computationally efficient.
\end{lem}
\begin{proof}
We have known that there are at most $B/\min_{v_i\in V}\{b_i\}$ winners and it takes $O(Bnm/\min_{v_i\in V}\{b_i\})$ to finish the winner allocation stage where $|T|=m$ and $|V|=n$. Then, for each winner $v_i\in X_L$, a process similar to the winner allocation stage needs to be executed that takes $O(Bnm/\min_{v_i\in V}\{b_i\})$ running time as well. Thus, the running time of the payment determination state is $O(B^2nm/(\min_{v_i\in V}\{b_i\})^2)$ which is the total time complexity as well. The TBSAP can be done in polynomial time.
\end{proof}
\begin{thm}
The TBSAP, shown as Algorithm \ref{a2}, is an effective budgeted reverse auction mechanism to solve Problem 1 that satisfies individual rationality, profitability, truthfulness, and computational efficiency.
\end{thm}
\begin{proof}
As indicated above, this theorem can be proved by putting from Lemma 2 to Lemma 5 together.
\end{proof}
\section{Numerical Simulations}
In this section, we first evaluate the performance of our reputation-based DPoS mechanism, then test the correctness and efficiency of our budgeted reverse auction algorithm. The simulation setup and results will be displayed.
\subsection{Simulation Setup}
To evaluate the reputation-based DPoS mechanism, we need to observe how different behaviors in a consensus round affects its reputation value. Here, we take two full nodes as an example to demonstrate it, where one is a normal node that behaves legitimately and the other is an abnormal node that sometimes makes some wrong behaviors, such as not voting in witness election, producing an invalid block as the leader, or verifying a block wrongly. Shown as the (4), we give the parameters $A=0.005$, $B=0.05$, and $C=0.01$. Then, we compare our reputation-based DPoS with the general DPoS mechanism whose each full node in $\mathbb{Z}$ is given by the same voting weight. In other words, we do not consider their reputation values in witness election of the general DPoS. In these two DPoS mechanism, each normal full node $TA_{a}$ votes to support $TA_{a'}\in\mathbb{Z}\backslash\{TA_a\}$ with $Rep_{a'}\geq\theta$ where $\theta=0.5$ is a threshold. Conversely, we consider the most extreme case where each abnormal full node $TA_{a}$ votes to support $TA_{a'}\in\mathbb{Z}\backslash\{TA_a\}$ with $Rep_{a'}<\theta$. In our BRTM system, we define the full node set with $|\mathbb{Z}|=100$ and the witness committee with $|\mathbb{M}|=70$. To simulate a real state, we give the reputation values of normal full nodes by sampling from $[0.5,1]$ uniformly and abnormal full nodes by sampling from $[0,0.5)$ uniformly. To evaluate the reliability of this system, we define the ratio of abnormal full nodes (RAFN) as ``$[\#\text{ abnormal full nodes}]/|\mathbb{Z}|$'' and the ratio of normal witnesses (RNW) as $[\#\text{ normal witnesses}/\mathbb{M}]$.
To simulate the budgeted reverse auction mechanism, we consider a smart city $S=(TA,V)$ with a $1000m\times1000m$ square area and the task set $T$ issued by the $TA$ are distributed over this area. Then, the active vehicles $V$ are distributed over this area arbitrarily as well. For each vehicle $v_i\in V$, its ability to detect is different, thereby we assume there is a detection distance $d_i$ that is distributed in $[10,30]$ uniformly. It means that the $v_i$'s task set $T_i$ contains all tasks whose distances from the $v_i$ are less than $d_i$. Finally, the TA's appraisement $a_j$ for each task $t_j\in T$ is distributed in $(0,10]$ uniformly and the cost of $T_i$ for the $v_i$ can be denoted by $c_i=\kappa\cdot|T_i|$ where the parameter $\kappa$ is distributed in $(0,5]$ uniformly.
\begin{figure}[!t]
\centering
\includegraphics[width=2.5in]{Reputation.png}
\caption{The reputation values change with different behaviors of the two full nodes in the consensus process.}
\label{fig3}
\end{figure}
\begin{figure}[!t]
\centering
\includegraphics[width=2.5in]{Ratio.png}
\caption{The ratio of normal witnesses (RNW) changes with the ratio of abnormal full nodes (RAFN).}
\label{fig4}
\end{figure}
\subsection{Simulation Results and analysis}
The simulation results about our reputation-based DPoS mechanism are shown in Fig. \ref{fig3} and Fig. \ref{fig4}.
\textbf{1) The impact of behavior on reputation: }Fig. \ref{fig3} draws the reputation values change with different behaviors of the two full nodes the consensus process. Shown as Fig. \ref{fig3}, we can see that the repuation of the normal node is increased gradually by its legitimate behaviors, but the reputation of the abnormal node is decreased by its wrong behaviors. Here, we assume there are $10$ consensus rounds for each election epoch, namely $|\mathbb{D}|=10$. To the normal node, it votes to elect witnesses at the first election epoch ($1$-th to $10$-th round), which adds $0.005$ reputation per round. At the second epoch ($11$-th to $20$-th round), it is selected as a witness member because of its good reputation. Thus, it votes and verifies the block correctly, which adds $0.015$ reputation per round. Especially, at the $15$-th consensus round, it becomes the leader that generates a block successfully, which adds $0.055$ reputation in this round. These legitimate behaviors increase its reputation until approaching $1$. To the abnormal node, it is selected as a witness member at the third epoch ($21$-th to $30$-th round). It does not vote and verify the block, which reduces $0.015$ reputation per round. Especially, at the $15$-th consensus round, it becomes the leader that generates a block successfully, which adds $0.055$ reputation in this round. Especially, at the $25$-th consensus round, it becomes the leader that generates an invalid block, which reduces $0.055$ reputation in this round.
\begin{figure}[!t]
\centering
\includegraphics[width=2.5in]{profit.png}
\caption{The performance obtained by greedy-heuristic and TBSAP algorithm under the different budgets and number of vehicles.}
\label{fig5}
\end{figure}
\begin{figure}[!t]
\centering
\includegraphics[width=2.5in]{payment.png}
\caption{The distributions of bid and payment for each vehicle under the different number of vehicles with budget $B=100$}
\label{fig6}
\end{figure}
\textbf{2) Reliability: }Fig. \ref{fig4} draws the ratio of normal witnesses changes with the ratio of abnormal full nodes, which describes the reliability of our BRTM system. The higher the ratio of normal witnesses is, the more reliable this system is. Shown as Fig. \ref{fig4}, the ideal line is the maximum RNW we can obtain theoretically. For instance, if RAFN is $0.6$, namely there are $60$ abnormal full nodes, the optimal RNW is equal to $100\cdot(1-0.6)/70$. The RNWs are all closed to the ideal value when the RAFN is less than $0.5$. This is because the number of abnormal nodes is less than normal nodes, thereby their voting hardly changes the outcome of witness election. However, when the RAFN is from $0.5$ to $0.75$, the RNW of our reputation-based DPoS is larger than that of general DPoS obviously since the normal nodes have larger voting weight even though their quantity is small in total. Therefore, the reliability of our system is improved by the reputation-based DPoS especially when the proportion of abnormal nodes is higher and the most extreme case happens where each abnormal node votes to support all abnormal nodes.
The simulation results about our budgeted reverse auction mechanism are shown in Fig. \ref{fig5} and Fig. \ref{fig6}.
\textbf{3) The TA's profit function: }Fig. \ref{fig5} draws the performance obtained by greedy-heuristic and TBSAP algorithm under the different budgets and number of vehicles in this city, where the number of vehicles $|V|$ is $500$ or $1000$. Shown as Fig. \ref{fig5}, we can observe that the TA's profit obtained by TBSAP is less than that obtained by greedy-heuristic under any budget in order to ensure the truthfulness. To the results obtained by greedy-heuristic, we can observe the TA's profit increases as the budget increases. When the budget is larger than $200$, the TA's profit keeps unchanged. There is a similar evolutive trend in the results obtained by TBSAP, but it declines slightly when the budget is larger than $200$. At this time, none of the optional vehicles has a positive unit marginal gain, thereby the operation step in line 25 of Algorithm \ref{a2} is possible to increase the payment and reduce the profit further.
\textbf{4) Bids and payments: }Fig. \ref{fig6} draws the distributions of bid and payment for each vehicle under the different number of vehicles with a budget $B=100$. Shown as Fig. \ref{fig6}, we can see that the points are more concentrated on the bottom left which have lower bids and payments when the number of vehicles is larger. This is because there are more active vehicles with lower bids that can be selected to undertake collection tasks. It explains why the TA's profit increases with the number of vehicles in this city.
\section{Conclusion}
In this paper, we designed and implemented a reliable and efficient traffic monitoring system based on blockchain technology and budgeted reverse auction mechanism. To enhance the security and reliability of this system, we gave a lightweight information trading framework by using asymmetric encryption. We devised a reputation-based DPoS consensus mechanism so as to improve the efficiency of recording and storing in blockchain. Then, to incentivize vehicles to undertake collection tasks, we developed a budgeted reverse auction algorithm that satisfies individual rationality, profitability, truthfulness, and computational efficiency. Finally, the results of numerical simulations indicated that our model is valid, and verify the correctness and efficiency of our algorithms.
\section*{Acknowledgment}
This work is partly supported by National Science Foundation under grant 1747818 and 1907472.
\ifCLASSOPTIONcaptionsoff
\newpage
\fi
\bibliographystyle{IEEEtran}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 1,662 |
Colbert's segment on his brush with the campaign finance laws is the first of its kind. As an entertainer, he means to be funny, but he is fairly serious at the same time; and of how many popular entertainers can be it said that they are skeptical of campaign finance reform, much less have given it any serious thought? Colbert, on his first try, professes to be baffled by the "lines" drawn by the law. He knows that merely to explain the difference between media and other corporations is sure to get a laugh. The split screen he used to make the point is about as good a jab at the inner contradictions and porous boundaries of the law as any found in standard anti-reform critiques.
It might end here, or it might go farther. It appears that Colbert will flirt with violating the law, or build a piece or two around the flirtation, but since he has hired Wiley Rein, he seems also prepared to keep to the legal side of the line—mostly. If he just walks the line from time to time—as visible as the line can be—regulators will have little appetite for challenging Colbert. His best bet is to avoid flagrancy, and this, Wiley Rein on the other end of the line, he (and even more, his corporate sponsors) may be committed to doing.
If Colbert does become a candidate and qualifies for the South Carolina ballot, then what will happen to his show as the voting nears and he wishes to make the most of his ploy?
Colbert's first-line of defense is to establish that his show is a news show, entitled to the protections of the "media exemption." Assuming that he is successful there—as he would be, most likely— then the question is whether his hosting of the show as a candidate presents any special issues, now and perhaps under the electioneering communication prohibition, effective within the 30 day period prior to the South Carolina primary.
2. That the content would refer—most definitely, since it is the heart of the joke—to his candidacy, and it would expressly advocate it.
3. The show will air before the voters of South Carolina.
If all these happen to be true, the Commission could be in a pickle: its prior Advisory Opinions could support a finding that Comedy Central will be making an illegal corporate contribution to candidate Colbert.
It is striking that when the Commission has considered the question in closer cases, it has asked, among other things, whether "the scheduling and duration of the [cable or TV] series, or the selection of individual topics" would be made "with reference to the timing of [the candidate's nomination or election to office.]" Advisory Opinion l994-15. Here it would: that is the framework for the jokes. But the Commission need not go so deeply into timing questions. For in the Colbert Report, the candidacy would be the central, explicit topic of discussion, inconsistent with the Commission's expectation that any show outside the reach of the campaign finance laws be "without references to the [candidate's] campaign or election to Federal office." Id.
The Commission also notes your representations that you do not intend to use the show to promote your candidacy or raise funds for your candidacy, and that no ads raising funds for or promoting your candidacy would be run during the show…. Based upon these conditions, the Commission concludes that you may continue to host your show during your candidacy without a prohibited contribution occurring.
If a corporate contribution may occur, then, what are the implications for the 30-day prohibition on electioneering communications—references to candidates, paid by a corporation, within this period? It would not apply to news show coverage, of course: but somebody could make trouble by arguing that if the corporation was already making contributions, illegal ones, to support Colbert, its host, then it was not functioning as a press entity in airing and promoting the show. The Commission has ruled that whether the press entity is acting as a press entity, in performing a particular "media activity," depends on a variety of factors. One such factor is whether "the candidate [having access to the broadcast facilities]…would have the ability to determine when or how…election advocacy messages are presented to the viewers…." Advisory Opinion 1996-48. See also Matter Under Review 3657 (Multimedia Cablevision), cited in Advisory Opinion 2004-07.
Colbert does have several escape routes here. He can wait out the agency, which may not have much taste for confronting Colbert on this issue. Or, he could file an Advisory Opinion request with the FEC, and determine whether the agency would look for a way out. Finally, he could arrange for a challenge to the law as applied in these circumstances. He is well represented, even if he would have preferred to hire Alberto Gonzalez; no doubt he will proceed wisely and with an eye to audience appeal.
All of this, from an election lawyer's point of view, would be highly entertaining. And perhaps good for more than just a laugh. | {
"redpajama_set_name": "RedPajamaC4"
} | 5,357 |
Kellogg's Closing Distribution Center In Cicero
By Dave Allen May 2, 2017
Another hit to the Central New York economy. Kellogg's has informed the state it will be closing it's distribution center in Cicero, putting 255 employees out of a job. Kellogg's say the plant on East Taft Road will be closed by the end of the year. Kellogg's says it's closing 38 other distribution centers around the country. | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 8,001 |
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Another solution is the textpos package which allows you to specify boxes at absolute positions on the page. \u03b20 is the value of y when x =0, and \u03b21 is the change in y when x increases by 1 unit. It\u2019s a little more complicated, but not much. If has degree , then it is well known that there are roots, once one takes into account multiplicity. Detexify is an attempt to simplify this search. The dashed line shows the absolute value function, j\u2020tj, for comparison. The concept of absolute value has many uses, but you probably won't see anything interesting for a few more classes yet. Thanks for reading! So typically when you decide on a frame\/bed, you still need to find a mattress (assuming you want to get rid of your current mattress). For some commands (e. With the rise in thin condoms, partners may be on the fence about trying the latest sensation. Negative values draw the element closer to its neighbors than it would be by default. This figure is rarely used in making treatment decisions. The dispersion is the difference between the actual value and the average value in a set. Multiple asterisks in a row are fine (**, ***), which are displayed as they are, but if you simply type * or \\*, nothing will be displayed in the compiled file. (Grab The Training Course and The Cheat Sheet for FREE) In this article, we will tackle the different ways to round numbers in MATLAB. I had already used up so many letters in both plain text and bold face that I needed more styles for English letters. Complimentary shipping and returns. Because symbolic variables are assumed to be complex by default, abs returns the complex modulus (magnitude) by default. The equations are numbered by LaTeX during the actual processing of the source file, so the number that LaTeX assigns to a given equation can change if we insert other equations before it. General Math Calculus Differential Equations Topology and Analysis Linear and Abstract Algebra Differential Geometry Set Theory, Logic, Probability, Statistics MATLAB, Maple, Mathematica, LaTeX Hot Threads. Print quality: KaTeX\u2019s layout is based on Donald Knuth\u2019s TeX, the gold standard for math typesetting. f (x) = {x if x > 0 0 if x = 0 \u2212 x if x < 0. This can be a negative amount. 1) - Solve equations containing absolute values. Welcome to The Cubes and Cube Roots (A) Math Worksheet from the Number Sense Worksheets Page at Math-Drills. ; Sum [f, {i, i min, i max}] can be entered as. 3 is a solution. f\u2032(x) < 0 at each point in an interval I, then the function is said to be decreasing on I. Press question mark to learn the rest of the keyboard shortcuts How difficult would this be to do in LaTeX? Current Unicode snakes I can find are: \ud80c\udd91, \ud80c\udd93, \ud80c\udd95, \ud80c\udd97, \ud80c\udd98, \ud80c\udd99, and \ud80c\udd9a. Set up two equations and solve them separately. LaTeX specific issues not fitting into one of the other forums of this category. 4, I find that I can simply type \\lvert and \\rvert into my display formula and Lyx \"does the right thing. tex) and Save the document. The absolute value symbol represents a number's distance from zero. The norm of a vector (or similar) can be denoted as \\lVert v\\rVert or, more generally, as \\left\\lVert \u2026 \\right\\rVert. Quantum yield. Instead of allowing for continuous values for the angular momentum, energy, and orbit radius, Bohr assumed that only discrete values for these could occur (actually, quantizing any one of these would imply that the other two are also. The$ 's around a command mean that it has to be used in maths mode, and they will temporarily put you into maths mode if you use them. Word-to-LaTeX in 4 steps. The $'s around a command mean that it has to be used in maths mode, and they will temporarily put you into maths mode if you use them. Takes the absolute value of x: log(x,base=y) Takes the logarithm of x with base y; if base is not specified, returns the natural logarithm: exp(x) Returns the exponential of x: sqrt(x) Returns the square root of x: factorial(x) Returns the factorial of x (x!) choose(x,y) Returns the number of possible combinations when drawing y elements at a. The advantage of this last expression over the first is that there are not so many negative signs in the answer. If we hadn\u2019t used them we would have gotten $$L = - \\frac{9}{2} < 1$$ which would have implied a convergent series! Now, let\u2019s take a look at a couple of examples to see what happens when we get$$L = 1$$. Substitute the value of h for x into the equation to find the y-coordinate of the vertex, k : f(2) = 2 2 - 4(2) + 8. Free absolute value equation calculator - solve absolute value equations with all the steps. This math worksheet was created on 2010-11-03 and has been viewed 303 times this week and 216 times this month. But for this we need some preliminaries, and we start with a discrete version of the derivative of a function f(x). ) g(x) = x2 + 9x2\/3 on [\u22127, 8]. Notice that we can get the \u201cturning point\u201d or \u201cboundary point\u201d by setting whatever is inside the absolute value to. f\u2032(x) < 0 at each point in an interval I, then the function is said to be decreasing on I. Read more \u00bb. An absolute value equation is an equation that contains an absolute value expression. Quantum yield. The array environment is basically equivalent to the table environment (see tutorial 4 to refresh your mind on table syntax. In the previous example the absolute value bars were required to get the correct answer. In this example, the value of the integral is (close to) one [*]; the discussion about the value of the integral being 0. ) in Microsoft Word. The norm of a vector (or similar) can be denoted as \\lVert v\\rVert or, more generally, as \\left\\lVert \u2026 \\right\\rVert. A value of 3 in cell A2 would return the result Positive, -9 the result Negative. It is skewed to the left because the computed value is negative, and is slightly, because the value is close to zero. , the virus response to AH should be. If value is equal to NegativeInfinity or PositiveInfinity, the return value is PositiveInfinity. To use one of these packages, just set the option citation_package to be natbib or biblatex, e. Finding Other Symbols. This website uses cookies to ensure you get the best experience. Default value is NULL. BA# basophil number absolute number BA%\/100 \u00d7 WBC count 103 cells\/\u00b5L *PDW \u2013 platelet distribution width and percent \u2013 platelet crit are NOT for diagnostic use and do not print. This will extend the definition of absolute value for real numbers, since the absolute value | x | of a real number x can be interpreted as the distance from. Whether to generate extra printing at method switches. For the kurtosis, we have 2. Not everyone is a strict stomach sleeper. L1 Loss function minimizes the absolute differences between the estimated values and the existing target values. Parameters : arr : [array_like] Input array or object whose elements, we need to test. 15 if you want to be more precise). ; Enter the table data into the table: copy (Ctrl+C) table data from a spreadsheet (e. In which case, you can use the arrow keys to help you navigate around the expression and type out what you want. to be identical in value. Mathematics printing\u2013Computer programs. Find the absolute maximum value and the absolute minimum value of the following functions in the given. Show Instructions In general, you can skip the multiplication sign. This polynomial is considered to have two roots, both equal to 3. I was working on a latex doc and was having this problem. since I am writing blog post that hosted by Github with Editor Atom , and use plugin markdown-preview-plus and mathjax-wrapper , and use mathjax Javascript display the math symbols on the web page. Fifty percent LRV is the common guideline for residential interiors. A value is said to be a root of a polynomial if. imgmath_latex\u00b6 The command name with which to invoke LaTeX. f'(x) = 0 at imaginary points i. In probability and statistics, the expectation or expected value, is the weighted average value of a random variable. Quantum yield calculation. As you are aware, there are commands to put a bar or a tilde over a symbol in math mode in LaTeX. ; Sum [f, {i, i min, i max}] can be entered as. An absolute value equation is an equation that contains an absolute value expression. ; The Comprehensive LaTeX Symbol List. ISBN 0-8176-3805-9 (acid-free paper) (pbk. A letter such as f, g or h is often used to stand for a function. (What happens if z= 0?) For example, the polar form of 1 + iis p 2(cos(\u02c7=4) + isin(\u02c7=4)). It is skewed to the left because the computed value is negative, and is slightly, because the value is close to zero. For the latest version, open it from the course disk space. String that specifies the document name of the LaTeX file\u2019s master document. 25\u2033DREAMPLUSH SUPPORTING MEMORY FOAM (6) 0. The simplest way on how to include |absolute value| bars in LaTeX is to use the this notation: \\left| and \\right|. The following is a table of all exact values for the sine and cosine of angles of multiples of 3\u00b0, up through 45\u00b0. Letters here stand as a placeholder for numbers, variables or complex expressions. CD4 Cell Count. \u201cdecelerating\u201d because we really assumed that the absolute value of the acceleration was that its maximum value on I is equal to its value at x = 0. Different possible applications are listed separately. Special cases are: Frexp(\u00b10) = \u00b10, 0 Frexp(\u00b1Inf) = \u00b1Inf, 0 Frexp(NaN) = NaN, 0 func Gamma \u00b6 func Gamma(x float64) float64. 23456 is displayed as 1. LaTeX doesn't have a specific matrix command to use. Option 3: Length Value. The absolute value of negative 7,346 is equal to 7,346. 67 \u00d7 10-8 J m-2 s-1 K-4 and T is absolute temperature. Systems of Equations. There are two basic ways to change font sizes in Latex, depending on whether you want to change the font size throughout your entire document, or just a portion of it. ) in Microsoft Word. Using a =. The minimum absolute step size allowed. The temperature in absolute units is T= 273+40 = 313 K. f\u2032(x) < 0 at each point in an interval I, then the function is said to be decreasing on I. or less) and is polymer fortified for added durability. The value of the integral is the volume times the average value of the function, the Monte Carlo computation estimates that average. Related MATLAB, Maple, Mathematica, LaTeX News on Phys. Following instructions on the website (there is a installation part) and set up IguanaTex properly. The same notion may also be used. 25\u2033DREAMPLUSH SUPPORTING MEMORY FOAM (6) 0. 1) - Solve equations containing absolute values. 3456 is displayed as 12. 723889 2020] [:error] [pid 476] failed to exec() latex for prismatic joints, latex error! exitcode was 2 (signal 0), transscript follows: [Sat Sep 05 11:44:22. 56 is displayed as 1234. LaTeX - bold vectors and arrow vectors Lately I'm writing a lot of papers in and every once and a while something comes up. 25\u2033DREAMPLUSH SUPPORTING MEMORY FOAM (6) 0. The absolute value of some expression can be denoted as \\lvert x\\rvert or, more generally, as \\left\\lvert \u2026 \\right\\rvert. The following problems range in difficulty from average to challenging. Water - Absolute or Dynamic Viscosity - Absolute or dynamic viscosity of water in centipoises for temperatures between 32 - 200 o F Water - Boiling Points at Vacuum Pressure - Online calculator, figures and tables giving the boiling temperatures of water in varying vacuum, SI and Imperial units. Math mode - Scaling absolute values - TeX - LaTeX Stack Tex. (This is all described on page 62 of the latex book). You can also apply the Sum Absolute Value formula of Kutools for Excel to solve the problem easily. As you see, the way the equations are displayed depends on the delimiter, in this case and . Essentially, the function will convert a numeric value into a text string. f(2) = 4 - 8 + 8. The absolute value of a number is the magnitude of a value, ignoring the sign. It renders as$\\lvert x\\rvert$. For complex input, a + ib, the absolute value is. LaTeX is the de facto standard for the communication and publication of scientific documents. The pipe in APL is the modulo or residue function between two operands and the absolute value function next to one operand. Word-to-LaTeX in 4 steps. The default font size depends on the specific operating system and locale. Absolute Value Equations. Note: We can use an absolute path from any location where as if you want to use relative path we should be present in a directory where we are going to specify relative to that present working directory. Strangely I cannot find a document online showing how to produce a single asterisk (*) in LaTeX, except the centered version (by \\ast in math environments). The definition of the decibel level L of a sound with intensity I relative to another intensity I 0 is L=10 log 10 (I\/I 0). You can have it show a graphical path, but getting just the text based path to a directory (for use in the Terminal for example) requires a couple of extra steps. On typesetting programs such as LaTeX, you may need to use a specialized representation. Lucid offers a wide range of memory foam, latex, and hybrid mattresses with \u2018Soft,\u2019 \u2018Medium\u2019, \u2018Medium Firm\u2019, and \u2018Firm\u2019 feels. The array environment is basically equivalent to the table environment (see tutorial 4 to refresh your mind on table syntax. CD4 Cell Count. For this example, plot y = x 2 sin (x) and draw a vertical line at x = 2. 0!!! Myeloma! DECIPHERING!MY!MYELOMALAB!RESULTS! Do!you!understand!your!myeloma!diagnosis!and! your!myeloma!lab!results?!Thisguideattempts!to! simplifythe. Geometrically, is the distance between and zero on the real number line. Variable or computed expression used in the column header. Note: We can use an absolute path from any location where as if you want to use relative path we should be present in a directory where we are going to specify relative to that present working directory. So the absolute value of negative 1 is 1. This action changed the latex statement in the legend field to Math mode. without worrying about it. Default value is \"bottom\". Browse our catalogue of tasks and access state-of-the-art solutions. LaTeX \u2013 bold vectors and arrow vectors Lately I\u2019m writing a lot of papers in and every once and a while something comes up. ; Exceptionally low prices and free delivery on all orders. Its value is represented by the Greek letter sigma (\u03c3), showing how much of the data is spread around the mean (also referred to as the average). I was wondering how would you put absolute value brackets around a fraction like the following: Thanks! Press J to jump to the feed. qreal qLn (qreal v) Returns the natural logarithm of v. As you see, the way the equations are displayed depends on the delimiter, in this case and . \u03b20 is the value of y when x =0, and \u03b21 is the change in y when x increases by 1 unit. 301051 implying that the distribution of the data is platykurtic, since the computed value is less than 3. latex_documents\u00b6 This value determines how to group the document tree into LaTeX source files. Equation Solver solves a system of equations with respect to a given set of variables. Back to top. And this is the Ceiling Function: The Ceiling Function. It is basically minimizing the sum of the absolute differences (S) between the target value ( Y i ) and the estimated values ( f(x i ) ):. You can type an absolute value symbol in LaTeX by typing \"\\mid\" and it will be replaced by the symbol when you generate your output. LaTeX is a powerful tool to typeset math; Embed formulas in your text by surrounding them with dollar signs$ The equation environment is used to typeset one formula; The align environment will align formulas at the ampersand & symbol; Single formulas must be seperated with two backslashes \\\\ Use the matrix environment to typeset matrices. So what about a Table Of Values?. It can be shown using either statistical software or a t -table that the critical value t 0. 5\u2033 SUPER DENSE SUPER SOFT MEMORY FOAM (7) 8\u2033 PATENT-PENDING\u201dBESTREST\u201d COILS (8) 1. Absolute Breadth Index - ABI: A market indicator used to determine volatility levels in the market without factoring in price direction. For PDF output, sometimes it is better to use LaTeX packages to process citations, such as natbib or biblatex. If left blank latex' will be used. Press question mark to learn the rest of the keyboard shortcuts How difficult would this be to do in LaTeX? Current Unicode snakes I can find are: \ud80c\udd91, \ud80c\udd93, \ud80c\udd95, \ud80c\udd97, \ud80c\udd98, \ud80c\udd99, and \ud80c\udd9a. ; Enter the table data into the table: copy (Ctrl+C) table data from a spreadsheet (e. \u03b20 is the value of y when x =0, and \u03b21 is the change in y when x increases by 1 unit. Detexify is an attempt to simplify this search. 4x - 2 = 3x + 1. 76 kg\/m3 \u00d79. For example, the absolute value of the number 3 and -3 is the same (3) because they are equally far from zero: From the above visual, you can figure out that:. The absolute value of a number is the magnitude of a value, ignoring the sign. , division, superscript, subscript), typing them out can move the cursor to the upper or lower area. Install Download the latest tarball here: latexcalc-1. Shop shoes, bags, cosmetics, fragrance, and jewelry for men and women. But another, I guess simpler way to think of it, it always results in the positive version of the number. Pretty cool. For PDF output, sometimes it is better to use LaTeX packages to process citations, such as natbib or biblatex. The absolute value of a Double is its numeric value without its sign. Through this course, you\u2019ll learn how to use algebra to solve everyday life problems, from calculating how much gasoline you\u2019ll need for your summer road trip to graphing college tuition costs. width is not NULL and type=\"latex\". In calculi of communicating processes (like pi-calculus), the vertical bar is used to indicate that processes execute in parallel. Just plug in the value you know to get the answer in the desired temperature scale using the appropriate conversion formula: Kelvin to Celsius : C = K - 273 (C = K - 273. Having done so, she is pleased to notice that Hello World is printed in the same font as the rest of her document (Computer Modern). LaTeX handles superscripted superscripts and all of that stuff in the natural way. LaTeX is available as free software. CD3+ Absolute Count. If the first argument is positive zero and the second argument is greater than zero, or. 23456 is displayed as 1. Absolute Value Symbol. The first one is used to write formulas that are part of a text. Welcome to The Cubes and Cube Roots (A) Math Worksheet from the Number Sense Worksheets Page at Math-Drills. For this example, plot y = x 2 sin (x) and draw a vertical line at x = 2. Defaults. The absolute value of some expression can be denoted as \\lvert x\\rvert or, more generally, as \\left\\lvert \u2026 \\right\\rvert. iperten Posts: 40 Joined: Thu Jul 12, 2007 11:53 am. It is differentiable everywhere except for x = 0. without worrying about it. latex_documents\u00b6 This value determines how to group the document tree into LaTeX source files. Useful Latex Equations used in R Markdown for Statistics - stats_equations. The main backbone is amsmath, so those unfamiliar with this required part of the L a T e X system will probably not find the packages very useful. In general, there is no guarantee of the existence of an absolute maximum or minimum value of f. 5-inch version that's more expensive, but it's more durable and made of natural resources. The dashed line shows the absolute value function, j\u2020tj, for comparison. I give up searching for now. Related MATLAB, Maple, Mathematica, LaTeX News on Phys. An antistreptolysin titer greater than 166 Todd units (or >200 IU) is considered a positive test in adults, while The normal value for adults is less than 166 Todd units, which indicates a negative test. String that specifies the document name of the LaTeX file\u2019s master document. 0!!! Myeloma! DECIPHERING!MY!MYELOMALAB!RESULTS! Do!you!understand!your!myeloma!diagnosis!and! your!myeloma!lab!results?!Thisguideattempts!to! simplifythe. Best Value Mattress Topper: If you prefer a latex mattress topper, Saatva has a 1. (+) V 2 < V 1 or V out < V in means damping. latexcalc is a \"LaTeX Calculator\" that calculates values inside your LaTeX files before typesetting them. There are 8 equal intervals (gaps) between the first and the last terms, so the value of each gap is = 6. 75 kg\/m3 The speci\ufb01cweightis \u03b3= \u03c1g =10. Simons \u2013 This document is updated continually. See full list on artofproblemsolving. For example, you can include mathematical expressions in text using LaTeX. You can play around with the commands shown here in the sandbox below and insert your equation into your LaTeX document. without worrying about it. A function may be thought of as a rule which takes each member x of a set and assigns, or maps it to the same value y known at its image. Here\u2019s an exploration: See the Pen Fixed Tables Solve Some Issues by Chris Coyier (@chriscoyier) on CodePen. o Absolute numbers greater than 1 are displayed with as many digits required to retain at least one decimal place and are displayed with a minimum of (# + 1) digits. It is calculated by taking the absolute value of the. Examples for the latter would be the conversion from Watts to dBm, the generation of noise circles in an ampli er 8. ANSWER Solved. The dashed line shows the absolute value function, j\u2020tj, for comparison. Absolute Value. %f Format as a floating point value. If z6= 0, then this product expression is unique. It indicates the ability to send an email. Its syntax is as follows:max(iterable[, default=obj, key=func]) -> value PARAMETER \u2026. Valeur Absolue, where the delicate art of high-end perfumery meets aromachology and neuro-cosmetics: we design each perfume, elixir of well-being, to enhance an essential emotion in womens\u2019 lives. How to use the Critical T-values Calculator. (+) V 2 < V 1 or V out < V in means damping. The * (\"star\") after the macro indicates to LaTeX that the delimiter symbols (here: vertical bars) should be scaled to the size of the macro's argument. To delete a value; right-click on the cell and click \"Delete Contents\" or \"Clear Contents\". adj For strings parallel to the axes, adj = 0 means left or bottom alignment, and adj = 1 means right or top alignment. Because symbolic variables are assumed to be complex by default, abs returns the complex modulus (magnitude) by default. This concept comes from Fermi-Dirac statistics. 4, I find that I can simply type \\lvert and \\rvert into my display formula and Lyx \"does the right thing. Solutions Graphing Practice;. So, the vertex is (h, k) = (2, 4) Step 3 : Find the axis of symmetry of the quadratic function. The Bottom Line. This can be a negative amount. There are two basic ways to change font sizes in Latex, depending on whether you want to change the font size throughout your entire document, or just a portion of it. I was working on a latex doc and was having this problem. A value is said to be a root of a polynomial if. In bounding |f\u2032\u2032(t+xi)| all we need is a bound for |f\u2032\u2032(x)| for xi < x < xi+1, which may be much smaller than the bound for f\u2032\u2032(x) for a < x < b. tex) and Save the document. Kutools for Excel- Includes more than 300 handy tools for Excel. To sum up, you can round down, up, to the nearest integer, and to X decimal places using the floor, ceil. Latex absolute value 14 December 2019, by Nadir Soualem; Search: Other keywords in this group. Absolute counts of both eosinophils and basophils did not change and were within the normal range following administration of. The physical damping value of the joint (latex error! exitcode was 2 (signal 0), transscript follows: [Sat Sep 05 11:44:22. 01 does seem applicable in this context. Text Math Macro Category Requirements Comments 000A5 \u00a5 U \\yen mathord amsfonts YEN SIGN 000AE \u00ae r \\circledR mathord amsfonts REGISTERED SIGN 02102 \u2102 C \\mathbb{C} mathalpha mathbb = \\mathds{C} (dsfont), open face C 0210C \u210c H \\mathfrak{H} mathalpha eufrak \/frak H, black-letter capital H. Latex mattresses are virtually silent, and ideal for discreet sexual activity. Absolute neutrophil count (ANC) \u00ee \u00ec \u00ec \u00ec\u2013 \u00ee \u00f1 \u00ec\/\u03bcL Acid phosphatase, serum Total \u00ec. Type the LaTeX code just as you do in LaTeX,. Mathematical modes. From this form, we can draw graphs. CD3+ Absolute Count. Return : An array with absolute value of each array. In calculi of communicating processes (like pi-calculus), the vertical bar is used to indicate that processes execute in parallel. Having done so, she is pleased to notice that Hello World is printed in the same font as the rest of her document (Computer Modern). To solve an equation such as $|2x - 6|=8$, we notice that the absolute value will be equal to 8 if the quantity inside the absolute value bars is $8$ or $-8$. Solution Ideal gas law \u03c1= p RT From Table A. ; Enter the table data into the table: copy (Ctrl+C) table data from a spreadsheet (e. Maximum number of (internally defined) steps allowed for each integration point in t. CodeCog's Equation Editor is great when you just need little snippets of code to insert here and there, but if you are creating a document that contains a lot of mathematical expressions, you will find it much easier and more efficient to create a complete. decreases as the distance between the true value and hypothesized value (H 1) increases. Need not be specified in the case of computed table columns. It is calculated by taking the absolute value of the. ABS() Number. SD can range from 0 to infinity. Z score requires historical data. Now, let\u2019s check $$x = - 5$$. I think I allocated reasonable personal time searching arbitrary posts on this board to find an example of tex coding that produces large absolute value symbols as the outermost grouping symbols. Example: The equation 2 x \u2013 5 = 9 is conditional because it is only true for x = 7. ixpr bool, optional. ONYX: L25500: Sihl_3529_SyntiSol_KissCut_ONYX_L25500 : Sihl_3515_ONYX_L25500 : Sihl_3516_ONYX_L25500 : Sihl_3566_Aurolux_ONYX_L25500 : Sihl_3629_ONYX_L25500. Select a blank cell you will place the sum at, and click Kutools > Formula Helper > Formula Helper. 2e03 and -1. More than just an online function properties finder. You can type it on most keyboards using the \"|\" symbol, located above the backslash. Tungsten isotope helps study how to armor future fusion reactors; First-ever mission to the Trojan asteroids passes NASA milestone. , the virus response to AH should be. The absolute value function exists among other contexts as well, including complex numbers. Strangely I cannot find a document online showing how to produce a single asterisk (*) in LaTeX, except the centered version (by \\ast in math environments). Boiling point: Temperature of saturated vapour or also of ebullient water under the same pressure. General Math Calculus Differential Equations Topology and Analysis Linear and Abstract Algebra Differential Geometry Set Theory, Logic, Probability, Statistics MATLAB, Maple, Mathematica, LaTeX Hot Threads. If value is equal to NaN, the return value is NaN. The first one is used to write formulas that are part of a text. 01 does seem applicable in this context. latexcalc is a \"LaTeX Calculator\" that calculates values inside your LaTeX files before typesetting them. Mean is 80, Standard Deviation is 11. Here's a screenshot to compare the look of the auto-sized fences (which happens to corresponds to \\bigg ) and of the look that results from choosing \\Big manually; personally, I have slight. BA# basophil number absolute number BA%\/100 \u00d7 WBC count 103 cells\/\u00b5L *PDW \u2013 platelet distribution width and percent \u2013 platelet crit are NOT for diagnostic use and do not print. Each value is a , a , or the keyword auto. GitHub Gist: instantly share code, notes, and snippets. You can also apply the Sum Absolute Value formula of Kutools for Excel to solve the problem easily. This polynomial is considered to have two roots, both equal to 3. First table is only 100 pixel width in any changes in browser window state, while other table will always stretch the full width of the window it is viewed in, that is the table automatically expands as the user changes the window size when you set width in %. An absolute value equation is an equation that contains an absolute value expression. Formula =Text(Value, format_text) Where: Value is the numerical value that we need to convert to text. Substituting that value of x into the expression for V(x) is the Stefan\u2013Boltzmann constant = 5. The absolute value of 3 is 3; The absolute value of 0 is 0; The absolute value of \u2212156 is 156; No Negatives! So in practice \"absolute value\" means to remove any negative sign in front of a number, and to think of all numbers as positive (or zero). Enjoy the videos and music you love, upload original content, and share it all with friends, family, and the world on YouTube. Next, we will learn how to solve an absolute value equation. The \"Int\" function (short for \"integer\") is like the \"Floor\" function, BUT some calculators and computer programs show different results when given negative numbers:. The norm of a vector (or similar) can be denoted as \\lVert v\\rVert or, more generally, as \\left\\lVert \u2026 \\right\\rVert. 2e-03 and -1. Here\u2019s an exploration: See the Pen Fixed Tables Solve Some Issues by Chris Coyier (@chriscoyier) on CodePen. Remember LRV runs on a scale of 0% to 100%, 50% would be a mid-value paint color. The bank of the river provides one side of the garden; along the other. The dB value is negative. Usually I 0 is chosen to be the intensity of the threshold of hearing 10-12 W\/m 2. In this inequality, they're asking me to find all the x -values that are less than three units away from zero in either direction , so the solution is going to be the. Vincent, who is a die-hard fan of the command line, recommends using the command-line. Sample size is 41 (1 for each value between 60-100, inclusive). More information about critical values for the t-distribution: First of all, critical values are points at the tail(s) of a specific distribution, with the property that the area under the curve for those critical points in the tails is equal to the given value of $$\\alpha$$ The distribution in this case is the T-Student distribution. Find Select the multiline text object you want to edit. The absolute value of a complex number is defined by the Euclidean distance of its corresponding point in the complex plane from the origin. But in the sense that \"absolute value\" means distance from the origin for a real number (on the one-dimensional number line), and \"modulus\" means distance from the origin for a complex number (on the 2-dimensional complex plane), I don't believe there is a big problem with the interchangeability of the terms. \" In my specific case I want absolute value bars around a fraction, so I used \\bigg\\lvert on the one side and \\bigg\\rvert on the other side. Quantum yield calculation. The first-degree equations that we consider in this chapter have at most one. LaTeX doesn't have a specific matrix command to use. If the absolute value of the t-value is greater than the absolute value of the critical t-value, then the null hypothesis is rejected. Measurement of fluorescence quantum yields. , division, superscript, subscript), typing them out can move the cursor to the upper or lower area. The following example shows the usage of abs() method. Sometimes the form of an answer can be changed. 1) - Solve equations containing absolute values. One-coat paint increases the possibility that you only need to use one coat but it is not an absolute since most one-coat paints come with a set of limitations. Recall that the absolute value |x| of a real number x is itself, if it's positive or zero, but if x is negative, then its absolute value |x| is its negation -x, that is, the corresponding positive value. Graphical illustration of the data is in Figure 1. First, the value of f\u2032\u2032(x) can vary from interval to interval. More accurately, it preprocesses files written in a superset of the LaTeX typesetting language and evaluates specified expressions in the text. This article reviews how to draw the graphs of absolute value functions. It is basically minimizing the sum of the absolute differences (S) between the target value ( Y i ) and the estimated values ( f(x i ) ):. 67 \u00d7 10-8 J m-2 s-1 K-4 and T is absolute temperature. The minimum absolute step size allowed. Text Math Macro Category Requirements Comments 000A5 \u00a5 U \\yen mathord amsfonts YEN SIGN 000AE \u00ae r \\circledR mathord amsfonts REGISTERED SIGN 02102 \u2102 C \\mathbb{C} mathalpha mathbb = \\mathds{C} (dsfont), open face C 0210C \u210c H \\mathfrak{H} mathalpha eufrak \/frak H, black-letter capital H. 6 LaTeX packages for citations. \u03c1= 106 N\/m2 297 J\/kgK \u00d7313 K =10. This happens in the case of quadratics because they all \u2026 Inverse of Quadratic Function Read More \u00bb. Ethanol | CH3CH2OH or C2H6O | CID 702 - structure, chemical names, physical and chemical properties, classification, patents, literature, biological activities. Valeur Absolue, where the delicate art of high-end perfumery meets aromachology and neuro-cosmetics: we design each perfume, elixir of well-being, to enhance an essential emotion in womens\u2019 lives. The definition of the decibel level L of a sound with intensity I relative to another intensity I 0 is L=10 log 10 (I\/I 0). Ordinary acrylic-latex paint usually requires two or more coats of paint. Manufacturer of narrow and large format digital printing media and paper supplies, including inkjet canvases, vinyl and electrostatic medias. The floor is the largest integer that is not greater than v. Ethanol | CH3CH2OH or C2H6O | CID 702 - structure, chemical names, physical and chemical properties, classification, patents, literature, biological activities. The equation for an absolute value is mentioned below. cd \/var\/log\/kernel. Related MATLAB, Maple, Mathematica, LaTeX News on Phys. The real absolute value function is continuous everywhere. Its value is represented by the Greek letter sigma (\u03c3), showing how much of the data is spread around the mean (also referred to as the average). If value is equal to NaN, the return value is NaN. Latex is designed to conform to one\u2019s figure and relieve pressure, often making sex on latex mattresses more comfortable. Next, we will learn how to solve an absolute value equation. The bank of the river provides one side of the garden; along the other. Manufacturer of narrow and large format digital printing media and paper supplies, including inkjet canvases, vinyl and electrostatic medias. LaTeX forum \u21d2 Graphics, Figures & Tables \u21d2 PSTricks | Absolute Value Inequality Shading Topic is solved Information and discussion about graphics, figures & tables in LaTeX documents. The General Steps to solve an absolute value equation are: Rewrite the absolute value equation as two separate equations, one positive and the other negative; Solve each equation separately; After solving, substitute your answers back into original equation to verify that you solutions are valid; Write out the final solution or graph it as needed. Follow these steps to solve an absolute value equality which contains one absolute value: Isolate the absolute value on one side of the equation. It is skewed to the left because the computed value is negative, and is slightly, because the value is close to zero. Useful Latex Equations used in R Markdown for Statistics - stats_equations. int qFloor (qreal v) Return the floor of the value v. L3 is the sum of cubes of individual elements, and so on and so forth. The equation $$\\left | x \\right |=a$$ Has two solutions x = a and x = -a because both numbers are at the distance a from 0. General Math Calculus Differential Equations Topology and Analysis Linear and Abstract Algebra Differential Geometry Set Theory, Logic, Probability, Statistics MATLAB, Maple, Mathematica, LaTeX Hot Threads. 4x - 2 = 3x + 1. The absolute value of a real number, denoted , is the unsigned portion of. Also note that using a higher text width will decrease the probability of encountering badly hyphenated word. (iii) Between 0x = and 4,x = the function is increasing. 8-4 package. The conjugate refers to the change in the sign in the middle of the binomials. LaTeX was first released in 1985 by Leslie Lamport as an extension of TeX. Latex how to insert a blank or empty page with or without numbering \\thispagestyle, ewpage,\\usepackage{afterpage} Latex arrows; Latex natural numbers; Latex real numbers; Latex binomial coefficient; Latex overset and underset ; LateX Derivatives, Limits, Sums, Products and Integrals; Latex absolute value; Latex piecewise function; Latex how to. Install Download the latest tarball here: latexcalc-1. ) Arrays are very flexible, and can be used for many purposes, but we shall focus on matrices. Font size, specified as a scalar value greater than zero in point units. A letter such as f, g or h is often used to stand for a function. The p-value is Answer the next three questions using the critical value approach. The equation $$y = 2x$$ expresses a relationship in which every y value is double the x value, and $$y = x + 1$$ expresses a relationship in which every y value is 1 greater than the x value. Then a ribbon with name IguanaTeX will appear in PowerPoint, How to use. WHAT IS LATEX? LaTeX is a programming language that can be used for writing and typesetting documents. The layout is fixed based on the first row. int qFloor (qreal v) Return the floor of the value v. The LaTeX Equation Editor below can be used to quickly generate mathematical expressions. press 'Ctrl+Alt+\\' or input \"Insert latex math symbol\" in vscode command panel, then input latex symbol name and choose symbol you want. Period: Period: Period: Find the phase shift using the. P(x) is the probability density function. To delete a value; right-click on the cell and click \"Delete Contents\" or \"Clear Contents\". The General Steps to solve an absolute value equation are: Rewrite the absolute value equation as two separate equations, one positive and the other negative; Solve each equation separately; After solving, substitute your answers back into original equation to verify that you solutions are valid; Write out the final solution or graph it as needed. This article reviews how to draw the graphs of absolute value functions. 12 - 2 = 9 + 1. The amsmath package provides commands \\lvert, \\rvert, \\lVert, \\rVert which change size dynamically. LaTeX forum \u21d2 General \u21d2 Latex symbol for vector magnitude. Absolute Value Fraction and Radical Templates () th Ctl+F Ctl+R 2 Full size fraction 3 Square Root n n root x x Subscript and Superscript Templates () 2 1 2 1 Ctl+H Ctl+L Ctl+J Superscript Subscript Super & Subscript x x x Summation Templates 1 Ctl+T, S Summation, no limits Summation w\/ limits k n k k x x = \u2211 \u2211 Integral Templates 4 1 Ctl+I. Entire document. Calculate the density and speci\ufb01c weight of nitrogen at an absolute pressure of 1 MPa and a temperature of 40oC. Insert LaTeX equation in PowerPoint Install IguanaTex. To solve an equation such as $|2x - 6|=8$, we notice that the absolute value will be equal to 8 if the quantity inside the absolute value bars is $8$ or $-8$. ) State Fermat's Theorem. Then a ribbon with name IguanaTeX will appear in PowerPoint, How to use. without worrying about it. x \u2192 Function \u2192 y. Python number method abs() returns absolute value of x - the (positive) distance between x and zero. An unnamed warrior and his army arrive in Norway and begin to kill entire Viking settlements, seers warn of a prophecy that bring about the final day of Ragnorak upon the arrival of the dark man known as 'The King without a name'. The General Steps to solve an absolute value equation are: Rewrite the absolute value equation as two separate equations, one positive and the other negative; Solve each equation separately; After solving, substitute your answers back into original equation to verify that you solutions are valid; Write out the final solution or graph it as needed. This represents the number of all T cells, which includes CD4 and CD8 cells. Thanks for reading! So typically when you decide on a frame\/bed, you still need to find a mattress (assuming you want to get rid of your current mattress). There are two basic ways to change font sizes in Latex, depending on whether you want to change the font size throughout your entire document, or just a portion of it. Absolute Value Equations. The default font size depends on the specific operating system and locale. This leads to two different equations we can solve independently. %f Format as a floating point value. Only in limited conditions can you use one coat of ordinary acrylic-latex paint. We're very responsive and we love hearing from folks who find our service useful. Get the latest machine learning methods with code. , the virus response to AH should be. It indicates the ability to send an email. It even does the right thing when something has both a subscript and a superscript. If f is continuous on a closed interval [a,b] (that is: on a closed and bounded interval), then the Extreme Value Theorem guarantees the existence of an absolute maximum or minimum value of f on the interval [a,b]. If z6= 0, then this product expression is unique. See full list on artofproblemsolving. If left blank latex' will be used as the default path. Copied to clipboard! Detail Value; Name: absolute value: Description: Function symbol. x \u2192 Function \u2192 y. When the value being rounded is negative, the definition is somewhat ambiguous. GitHub Gist: instantly share code, notes, and snippets. Notice that we can get the \u201cturning point\u201d or \u201cboundary point\u201d by setting whatever is inside the absolute value to. But another, I guess simpler way to think of it, it always results in the positive version of the number. LaTeX is very useful for doing maths assignments, preparing reports and thesis. Returns the absolute value of v as a qreal. This will look ugly when the formulas in the cases are complicated, such as fractions or integrals. The general form of an absolute value function is f(x)=a|x-h|+k. The real absolute value function is a piecewise linear. qreal qLn (qreal v) Returns the natural logarithm of v. The \"Int\" Function. Through this course, you\u2019ll learn how to use algebra to solve everyday life problems, from calculating how much gasoline you\u2019ll need for your summer road trip to graphing college tuition costs. 8-4 package. It is skewed to the left because the computed value is negative, and is slightly, because the value is close to zero. The absolute value of a complex number is defined by the Euclidean distance of its corresponding point in the complex plane from the origin. How this formula works. imgmath_font_size\u00b6 The font size (in pt) of the displayed math. There are two basic ways to change font sizes in Latex, depending on whether you want to change the font size throughout your entire document, or just a portion of it. Absolute Price Oscillator (APO) Aroon (AR) Aroon Oscillator (ARO) Average True Range (ATR) Volume on the Ask (AVOL) Volume on the Bid and Ask (BAVOL) Bollinger Band (BBANDS) Band Width (BW) Bar Value Area (BVA) Bid Volume (BVOL) Commodity Channel Index (CCI) Chande Momentum Oscillator (CMO) Double Exponential Moving Average (DEMA) Plus DI (DI+). The temperature 0 K is commonly referred to as \"absolute zero. Mathematical modes. But in the sense that \"absolute value\" means distance from the origin for a real number (on the one-dimensional number line), and \"modulus\" means distance from the origin for a complex number (on the 2-dimensional complex plane), I don't believe there is a big problem with the interchangeability of the terms. We've documented hundreds of LaTeX macros, packages, and configuration options, and we're adding more content every week! Please let us know if there's anything you'd particularly like to see added to our knowledge base. 3 posts \u2022 Page 1 of 1. 5 to -5, some round to -6. 5\u2033 SUPER DENSE SUPER SOFT MEMORY FOAM (7) 8\u2033 PATENT-PENDING\u201dBESTREST\u201d COILS (8) 1. For example, the absolute value of 5 is 5 and the absolute value of -4 is 4=-(-4). ) g(x) = x2 + 9x2\/3 on [\u22127, 8]. To delete a value; right-click on the cell and click \"Delete Contents\" or \"Clear Contents\". So what about a Table Of Values?. ; Exceptionally low prices and free delivery on all orders. Share this blog and spread the knowledge. where \u03b20 is called the y\u2013intercept and \u03b21 is called the slope. Back to top. The maximum absolute step size allowed. hmin float, (0: solver-determined), optional. f'(x) = 0 at imaginary points i. Given those examples, you can probably see that the general syntax of the ternary operator looks like this: result = testCondition ? trueValue : falseValue. Following instructions on the website (there is a installation part) and set up IguanaTex properly. Latex is designed to conform to one\u2019s figure and relieve pressure, often making sex on latex mattresses more comfortable. Example: The equation 2 x \u2013 5 = 9 is conditional because it is only true for x = 7. The absolute value symbol represents a number's distance from zero. For the kurtosis, we have 2. 5\u2033 SUPER DENSE SUPER SOFT MEMORY FOAM (7) 8\u2033 PATENT-PENDING\u201dBESTREST\u201d COILS (8) 1. LaTeX is available as free software. adj For strings parallel to the axes, adj = 0 means left or bottom alignment, and adj = 1 means right or top alignment. However, upon taking the absolute value we got the same number and so $$x = - \\frac{4}{3}$$ is a solution. CodeCog's Equation Editor is great when you just need little snippets of code to insert here and there, but if you are creating a document that contains a lot of mathematical expressions, you will find it much easier and more efficient to create a complete. 6 LaTeX packages for citations. Absolute values and norms. It instead has a slightly more generalised environment called array. LaTeX is one popular typesetting system. In the case the quantities inside the absolute value were the same number but opposite signs. General Math Calculus Differential Equations Topology and Analysis Linear and Abstract Algebra Differential Geometry Set Theory, Logic, Probability, Statistics MATLAB, Maple, Mathematica, LaTeX Hot Threads. Format_text is the format we want to apply. Sometimes, the output doesn\u2019t come out the way some of us might expect or want. The absolute value parent function, written as f (x) = | x |, is defined as. The absolute value of negative 7,346 is equal to 7,346. SD can range from 0 to infinity. cd \/var\/log\/kernel. Open an example in Overleaf. There is a local maximum at x = 0 and there are local (and absolute) minima at x = \u00a7 r 1 2. Determines if graph is drawn. 723889 2020] [:error] [pid 476] failed to exec() latex for prismatic joints, latex error! exitcode was 2 (signal 0), transscript follows: [Sat Sep 05 11:44:22. 5 Class 12 Maths Question 5. For example, if the format is a3 , 1. LaTeX handles superscripted superscripts and all of that stuff in the natural way. Sometimes the form of an answer can be changed. We've documented hundreds of LaTeX macros, packages, and configuration options, and we're adding more content every week! Please let us know if there's anything you'd particularly like to see added to our knowledge base. Given those examples, you can probably see that the general syntax of the ternary operator looks like this: result = testCondition ? trueValue : falseValue. A decibel (dB) is a relative measurement of sound loudness, not an absolute measure. Finding the Inverse Function of a Quadratic Function What we want here is to find the inverse function \u2013 which implies that the inverse MUST be a function itself. Strangely I cannot find a document online showing how to produce a single asterisk (*) in LaTeX, except the centered version (by \\ast in math environments). Latex how to insert a blank or empty page with or without numbering \\thispagestyle,\\newpage,\\usepackage{afterpage} Latex arrows; Latex natural numbers; Latex real numbers; Latex binomial coefficient; Latex overset and underset ; LateX Derivatives, Limits, Sums, Products and Integrals; Latex absolute value; Latex piecewise function; Latex how to. MATLAB For Beginners: 20-Minute Video Training Course. Gamma returns the Gamma function. An unnamed warrior and his army arrive in Norway and begin to kill entire Viking settlements, seers warn of a prophecy that bring about the final day of Ragnorak upon the arrival of the dark man known as 'The King without a name'. LaTeX - bold vectors and arrow vectors Lately I'm writing a lot of papers in and every once and a while something comes up. \u2013 Greg Hill Apr 17 '19 at 3:48. (ii) At 4,x = the value of the function is 1, and the slope of the graph of the function is 1. $\\begingroup$ @AmirBigdeli It is sometimes not written as $|a|$ to avoid confusion with the absolute value of a number. Show Instructions In general, you can skip the multiplication sign. I know next to nothing about Tex, LaTex, AMSTex, AMSLaTex, LaDeeDahTex or any other XTexes. To sum up, you can round down, up, to the nearest integer, and to X decimal places using the floor, ceil. Find the absolute maximum value and the absolute minimum value of the following functions in the given. The absolute number of a number a is written as $$\\left | a \\right |$$ And represents the distance between a and 0 on a number line. As you are aware, there are commands to put a bar or a tilde over a symbol in math mode in LaTeX. The absolute value of a Double is its numeric value without its sign. 4A65G69 1995 95-36881 688. Multiple asterisks in a row are fine (**, ***), which are displayed as they are, but if you simply type * or \\*, nothing will be displayed in the compiled file.","date":"2020-11-27 22:46:04","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 3, \"mathjax_display_tex\": 2, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.7837777137756348, \"perplexity\": 1458.1414294549163}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2020-50\/segments\/1606141194634.29\/warc\/CC-MAIN-20201127221446-20201128011446-00456.warc.gz\"}"} | null | null |
It's that time of the year again. The greatest time for most folks who are in love with sports. That's right. FOOTBALL SEASON!!!!!
This is the one time of the year when I may resort to physical violence if you so much as text me during a game. Calling will really get you in trouble. I'm only kidding…..or am I?
Anywho, this year I am participating in Jersey Girl Sunday sponsored by Design Her Label. It's a movement to show the world, women aren't just football wives and such. We are actually die-hard fans just as men are and in some cases, like myself, we root for our football teams harder than the men.
The start of the football season was not a comfortable one. At first the Eagles game nearly gave me a heart attack leading into the half. But once the third quarter got underway, my team began to wake up. The amount of yelling that went on in my house was startling, especially some of the choice words I had for our quarterback Nick Foles. I wanted him benched after the second quarter.
By the way, you guys may hear a lot more from me sports related as I am interviewing for a sports talk website. Wish me luck. | {
"redpajama_set_name": "RedPajamaC4"
} | 9,902 |
package jpath
import (
"errors"
"fmt"
)
// ErrorNoRoot means no rootDir was found in the parent directories
var ErrorNoRoot = errors.New(`unable to identify the project root.
Tried to find 'tkrc.yaml' or 'jsonnetfile.json' in the parent directories.
Please refer to https://tanka.dev/directory-structure for more information`)
// ErrorNoBase means no baseDir was found in the parent directories
type ErrorNoBase struct {
filename string
}
func (e ErrorNoBase) Error() string {
return fmt.Sprintf(`Unable to identify the environments base directory.
Tried to find '%s' in the parent directories.
Please refer to https://tanka.dev/directory-structure for more information`, e.filename)
}
// ErrorFileNotFound means that the searched file was not found
type ErrorFileNotFound struct {
filename string
}
func (e ErrorFileNotFound) Error() string {
return e.filename + " not found"
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 5,990 |
Q: How can I combine two queries with different WHERE / LIKE conditions? My two queries:
$compareTotals1 = mysqli_query($con,"
SELECT *, (SUM(rent_amount)+SUM(late_fees)-SUM(discount_amount)) AS total,
SUM(late_fees) AS latefees,
SUM(discount_amount) AS discounts
FROM transaction
WHERE paid_on LIKE '%2014%'
");
$compareTotals2 = mysqli_query($con,"
SELECT *, (SUM(rent_amount)+SUM(late_fees)-SUM(discount_amount)) AS total,
SUM(late_fees) AS latefees,
SUM(discount_amount) AS discounts
FROM transaction
WHERE paid_on LIKE '%2015%'
");
How I'm outputting results:
if ($row = mysqli_fetch_array($compareTotals1)) {
echo CURRENCY.number_format($row['total'],2);
echo CURRENCY.number_format($row['latefees'],2);
echo CURRENCY.number_format($row['discounts'],2);
} else {
echo "No Records.";
}
if ($row = mysqli_fetch_array($compareTotals2)) {
echo CURRENCY.number_format($row['total'],2);
echo CURRENCY.number_format($row['latefees'],2);
echo CURRENCY.number_format($row['discounts'],2);
} else {
echo "No Records.";
}
The paid_on LIKE '% %' is generated dynamically by a dropdown box and some javascript. That's the only part that changes.
How can I condense this into one query so I only need to use one mysqli_fetch_array?
A: Assuming you want multiple rows a union is likely the cleanest
$compareTotals1 = mysqli_query($con,"
SELECT *, (SUM(rent_amount)+SUM(late_fees)-SUM(discount_amount)) AS total,
SUM(late_fees) AS latefees,
SUM(discount_amount) AS discounts,
'2014' as Yr
FROM transaction
WHERE paid_on LIKE '%2014%'
UNION ALL
SELECT *, (SUM(rent_amount)+SUM(late_fees)-SUM(discount_amount)) AS total,
SUM(late_fees) AS latefees,
SUM(discount_amount) AS discounts,
'2015' as Yr
FROM transaction
WHERE paid_on LIKE '%2015%'
");
You may be able to combine the where's into an OR and be sure to spell out a group by or you will not know which is 2015 or 2014 unless * includes such details.
$compareTotals1 = mysqli_query($con,"
SELECT *, (SUM(rent_amount)+SUM(late_fees)-SUM(discount_amount)) AS total,
SUM(late_fees) AS latefees,
SUM(discount_amount) AS discounts,
case when paid_on like '%2014%' then '2014'
when paid_on like '%2015%' then '2015' end as yr
FROM transaction
WHERE paid_on LIKE '%2014%'
OR paid_on LIKE '%2015%'
--GROUP BY all fields from select relevant to group by... without structure and sample data from table can't figure out.
-- This might work though I'd be concerned all the * columns could be returning improper results.
GROUP BY case when paid_on like '%2014%' then '2014' when paid_on like '%2015%' then '2015' end
");
maybe... group by case when paid_on like '%2014%' then '2014' when paid_on like '%2015%' then '2015' end but this is very specific.
we might be able to group by paid_on, but it appears it's not just a year... so you may get multiple rows per year... so again without sample data for structure can't figure out what to do.
Or maybe you want a cross join more columns... not more rows...
$compareTotals1 = mysqli_query($con,"
Select * from (
SELECT *, (SUM(rent_amount)+SUM(late_fees)-SUM(discount_amount)) AS total,
SUM(late_fees) AS latefees,
SUM(discount_amount) AS discounts
FROM transaction
WHERE paid_on LIKE '%2014%') CROSS JOIN
(SELECT *, (SUM(rent_amount)+SUM(late_fees)-SUM(discount_amount)) AS total,
SUM(late_fees) AS latefees,
SUM(discount_amount) AS discounts
FROM transaction
WHERE paid_on LIKE '%2015%') B
");
A: Why not just use an OR in your WHERE?
$compareTotals1 = mysqli_query($con,"
SELECT *, (SUM(rent_amount)+SUM(late_fees)-SUM(discount_amount)) AS total,
SUM(late_fees) AS latefees,
SUM(discount_amount) AS discounts
FROM transaction
WHERE paid_on LIKE '%2014%'
OR paid_on LIKE '%2015%'
GROUP BY YEAR(paid_on) -- is `paid_on` a date?
");
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 8,892 |
SCRIPTURE
and
COSMOLOGY
Reading the Bible Between
the Ancient World and
Modern Science
KYLE GREENWOOD
www.IVPress.com/academic
For Stephen, Jessica and Michael
## CONTENTS
Preface
Acknowledgments
Abbreviations
> 1 Scripture in Context
**PART ONE: SCRIPTURE AND COSMOS IN CULTURAL CONTEXT**
> 2 Ancient Near Eastern Cosmologies
>
> 3 Cosmology in Scripture
>
> 4 Cosmology and Cosmogony in Scripture
**PART TWO: COSMOLOGY AND SCRIPTURE IN HISTORICAL CONTEXT**
> 5 Scripture and Aristotelian Cosmology
>
> 6 Scripture and Copernican Cosmology
**PART THREE: SCRIPTURE AND SCIENCE**
> 7 Cosmology and the Authority of Scripture
>
> 8 The Authority of Scripture and the Issue of Science
Notes
Bibliography
Image Credits
Author and Work Index
Subject Index
Scripture Index
Praise for _Scripture and Cosmology_
About the Author
More Titles from InterVarsity Press
Copyright
## PREFACE
The Bible has many authors, but one Author. It contains scores of books, but has one story. It was written in ancient times, but speaks to modern times. It is studied, parsed, dissected, analyzed and scrutinized by scholars, but is accessible, comprehensible and edifying to the layperson. The Bible is complex, yet simple; distant, yet near; foreign, yet familiar; and disturbing, yet comforting. The Bible is many things to many people, but for those whose faith is formed by its words, it is Scripture.
Scripture holds a special place in the lives of Christians. It contains God's revelation about himself and the world in which we live. What made Jesus' parables effective was, in part, that they touched the everyday life experiences of his audience, such as money, employment, agriculture and livestock. Likewise, we connect with Scripture on a personal level because its narratives deal with people like us in situations and circumstances with which we can readily identify. We can resonate with the jealousy of Cain, the hunger and thirst of the Israelites in the wilderness, the barrenness of Hannah, the love of Ruth and Boaz, the bond of friendship between David and Jonathan, the challenge of making ends meet and the frustration of living in a society ruled by those whose interests are not generally our own. The Bible takes place in reality, with historical figures in historical places participating in the thrills of life's victories and the agonies of life's defeats.
One of the first things I do each day is check the weather. I want to know how the meteorologists expect the day to shape up. Living in Colorado, this may entail a short-sleeved shirt and sunglasses on my way to work, and a coat and boots on my return. Nonetheless, I rely (somewhat reluctantly, at times) on the expertise of those who pay attention to things like barometric pressure, jet streams, water-vapor density and upper atmospheric conditions. This has not always been the case. When Jesus called his first disciples, they were fishing on the Sea of Galilee (Mk 1:16-20). Before Peter, James and John set to sea that morning, they didn't turn on the Weather Channel or check the Weather Bug app on their smartphones. They looked to the sky. "Red sky at night, sailor's delight; red sky at morning, sailors take warning" (see Mt 16:2-3). While you and I embrace weather reports with a healthy dose of skepticism, we recognize that those reports are generally reliable, based on decades of accumulating atmospheric data and mapping meteorological patterns. Peter, James and John simply looked to the skies.
The doctrine of the perspicuity of Scripture states that Scripture is clear and unambiguous on matters pertinent to salvation. It does not, however, apply to all matters. This should be an obvious conclusion, based on the overwhelming number of biblical commentaries and the voluminous sales of study Bibles. As someone who both studies and teaches the Old Testament professionally, I can attest that there are copious passages, topics and issues that require some explanation for students of the Bible.
One such issue is cosmology—that is, how the biblical authors and characters viewed the structure and nature of the known world. Why does the Bible refer to heaven as up there? How is it that birds, clouds, the sun, the moon and stars are located in heaven, God's home? What does Scripture mean when it refers to the "four corners," "ends" or "depths" of the earth? Why is Sheol at the opposite end of the cosmos from heaven? What does it mean for the cosmos to have an upper end and a lower end? Why does Elisha talk about "windows in the sky"? Is there really a firmament in the heavens that separates the waters above from the waters below? How could there be storehouses of snow in heaven? What are the "fountains of the deep"? These questions may not come to mind immediately to the casual reader of Scripture, but they are there for the asking.
A number of years ago, one of my college roommates told me about a man who had devoted his entire adult life to the study of the Bible. In his final days, he was asked to comment on his mastery of its contents. The man replied by running his finger back and forth across the worn leather binding, and said, "I've only scratched the surface." I can't attest to the authenticity of the story, but I can attest to the authenticity of its message. There is always more to be mined from the depths of its quarry. Having spent the last two decades studying the languages, history, geography and culture of ancient Israel and its neighbors, I am humbled by the vastness of my ignorance. It has been said that the more you know, the more you realize what you don't know. This has been true for me in my own study of the Bible, as I suspect it is for you as well.
I have learned some things, though, that I hope will benefit those who want to know more about the book they call Scripture. While I am dealing specifically with the issue of biblical cosmology and how the Bible has been interpreted differently in light of changes in our understanding of the cosmos, this book is really about reading the Bible faithfully, which I suspect is a goal for most, if not all, of those who have chosen to read _Scripture and Cosmology_. It is written for anyone who wants to be more engaged in the cultural context of ancient Israel. It is written for students of the Bible who are curious about what to do with biblical passages that seem out of date. It is written for Christians who want to get a sense of the history in which our Bible has been interpreted over the millennia. It is written for men and women who want their faith to be more engaged with the sciences. It is written for evangelicals who may be frustrated with interpretations of the Bible that don't seem to coincide with their own careful reading of the text. It is especially written for young believers who have begun to lose their faith for any of the reasons above.
#
## ACKNOWLEDGMENTS
The book before you represents my own thoughts and ideas, but those thoughts have been incubated through discussion, constructive criticism, and listening to the thoughts and ideas of others whose opinion I hold in highest esteem. Among them, I wish to thank my editor, Dan Reid, who has patiently worked with me from the earliest conception of the idea to the book's release. Bill Arnold, Peter Enns, Tremper Longman and John Walton were kind enough to offer important feedback on the initial proposal, helping me distinguish this book from others and providing helpful suggestions and bibliography. Seth Sanders helped me solidify some of my work dealing with Jewish commentaries by graciously sharing with me a bibliography on ancient Jewish sciences. Jeff Cooley was especially helpful in refining some of my arguments on the ancient Near Eastern and biblical material. Several of my colleagues (present and past) at Colorado Christian University have helped in various ways. Sid Buzzell, Megan DeVore, Johann Kim, Ryan Murphy, Aaron Smith and Kevin Turner either read portions of my manuscript or kept me abreast of books and articles pertaining to my thesis. Lene Jaqua offered essential feedback regarding the history of science. Bill Watson brought to my attention the types of discussions happening in seventeenth-century England. I am also most appreciative of the CCU library staff for their impeccable success in locating obscure books from around the planet. I owe most of the beautiful images in the book to Kim Walton, who not only took many of the photographs but also located many more, saving me the arduous task of procuring copyright permissions. My former student and TA, Alex Siemers, did much of the work on the indexes. I would also like to thank Rob Barrett, Jack Collins, Deborah Haarsma, Charles Halton, Randy Isaac and John Walton (again) for their kind reviews. Finally, I would be remiss not to thank my lovely wife, Karen, and our three children, Stephen, Jessica and Michael, for keeping my focus on the things that matter most in life.
#
## ABBREVIATIONS
AB | Anchor Bible
---|---
_ABD_ | _Anchor Bible Dictionary._ Edited by David Noel Freedman. 6 vols. New York: Doubleday, 1992.
ACW | Ancient Christian Writers
AfO | Archiv für Orientforschung
AnBib | Analecta Biblica
ANEM | Ancient Near East Monographs
_ANF_ | _The Ante-Nicene Fathers._ Edited by Alexander Roberts and James Donaldson. 1885–1887. 10 vols. Repr., Peabody, MA: Hendrickson, 1994.
ASOR | American Schools of Oriental Research
_BBR_ | _Bulletin for Biblical Research_
_CAD_ | _The Assyrian Dictionary of the Oriental Institute of the University of Chicago._ Chicago: The Oriental Institute of the University of Chicago, 1956–2006.
_CBQ_ | _Catholic Biblical Quarterly_
CBQMS | Catholic Biblical Quarterly Monograph Series
_ClQ_ | _Classical Quarterly_
_CTJ_ | _Calvin Theological Journal_
_DDD_ | _Dictionary of Deities and Demons in the Bible._ Edited by Karel van der Toorn, Bob Becking and Pieter W. van der Horst. Leiden: Brill, 1995. 2nd ed. Grand Rapids: Eerdmans, 1999.
_EvQ_ | _Evangelical Quarterly_
FAT | Forschungen zum Alten Testament
FC | Fathers of the Church
_HUCA_ | _Hebrew Union College Annual_
ICC | International Critical Commentary
_JANER_ | _Journal of Ancient Near Eastern Religions_
_JBL_ | _Journal of Biblical Literature_
_JBQ_ | _Jewish Biblical Quarterly_
_JCS_ | _Journal of Cuneiform Studies_
_JNSL_ | _Journal of Northwest Semitic Languages_
_JQR_ | _Jewish Quarterly Review_
LCC | Library of Christian Classics
LCL | Loeb Classical Library
NAC | New American Commentary
NCB | New Century Bible
NIBC | New International Biblical Commentary
NICNT | New International Commentary on the New Testament
NICOT | New International Commentary on the Old Testament
_NPNF1_ | _The Nicene and Post-Nicene Fathers._ Series 1. 14 vols. Edited by Philip Schaff. 1886–1894. Repr., Peabody, MA: Hendrickson, 1994.
_NPNF2_ | _The Nicene and Post-Nicene Fathers._ Series 2. 14 vols. Edited by Philip Schaff. 1886–1894. Repr., Peabody, MA: Hendrickson, 1994.
OIP | Oriental Institute Publications
OTL | Old Testament Library
OtSt | Oudtestamentische Studiën
SBLWAW | Society of Biblical Literature Writings from the Ancient World
_SJOT_ | _Scandinavian Journal of the Old Testament_
TOTC | Tyndale Old Testament Commentary
_VT_ | _Vetus Testamentum_
WBC | Word Biblical Commentary
_WTJ_ | _Westminster Theological Journal_
# 1
## SCRIPTURE IN CONTEXT
It was the best of times, it was the worst of times, it was the age of wisdom, it was the age of foolishness, it was the epoch of belief, it was the epoch of incredulity, it was the season of Light, it was the season of Darkness, it was the spring of hope, it was the winter of despair, we had everything before us, we had nothing before us, we were all going direct to Heaven, we were all going direct the other way—in short, the period was so far like the present period, that some of its noisiest authorities insisted on its being received, for good or for evil, in the superlative degree of comparison only.
Charles Dickens, _A Tale of Two Cities_
This unbearably long run-on sentence is perhaps among the most recognizable opening lines in English literature. Despite its setting "in the year of Our Lord one thousand seven hundred and seventy-five," attentive readers of Dickens's _A_ _Tale of Two Cities_ readily recognize the narrative as a work of fiction. They notice the metrical rhythm and cadence as a highly stylized literary device. They observe the polar opposite contrasts permeating the text. They appreciate the hyperbolic language of the superlatives. They note that even though the next line offers a description of the kings and queens of England and France, Dickens does not identify these pivotal characters. Beyond the literary clues, historians would tell us that _A Tale of Two Cities_ intentionally conjures imagery of the primary forces that led to the French Revolution. In other words, instead of reading the story as historical narrative, it is best to understand this literary masterpiece as historical commentary.
#### Text in Context
As any competent teacher of literature will tell you, one of the most important keys to understanding any literary work is context. The illustration from Dickens attests to this. Someone who reads _A Tale of Two Cities_ as historical narrative, rather than historical commentary, will miss the point. Dickens's concern was not with the historical accuracies of the period, however true they may be. Rather, his concern was more sociological. He wanted his readers to empathize with those who suffered because of the huge disparity between those for whom it was the best of times and those for whom it was the worst of times. Understanding the narrative within all the relevant contexts permits the reader to extract most accurately from the text the message and details Dickens intended.
If context clues are important for comprehending literature that is 150 years old, imagine how much more important they are for comprehending Scripture, written over two millennia ago. In any given passage, several contextual issues will surface. These include cultural, geographical, historical and literary, among others.
**_Cultural context._** Cultural context pertains to how people think and behave based on their environment. The book of Ruth is replete with examples of cultural norms and customs. The climax of the story relies on its audience getting the fact that Ruth's survival depended on a kinsman redeeming her. Another cultural issue is found in 3:7, "Now this was the custom in former times in Israel concerning the redemption and the exchange of land to confirm any matter: a man removed his sandal and gave it to another; and this was the manner of attestation in Israel." It is interesting to note that by the time of Ruth's composition, the sandal ceremony in 3:7 was not readily apparent. It had to be explained. The author did not want the audience to miss the significance of the act, so he provided a brief commentary on the relevance of the sandal ceremony.
Cultural context also relates to how people understand reality. For example, ancient Hebrews believed that people felt emotions with their kidneys and thought with their hearts. In Deuteronomy 6:5, the Lord commands Israel to "love the LORD your God with all your heart, and with all your soul, and with all your might." However, when the Synoptic Gospels cite this passage, they include both heart and mind (Mt 22:37; Mk 12:30; Lk 10:27). Unlike the Hebrews, the Greeks rightly identified the mind as the seat of the intellect. To avoid confusion, the Gospel writers explain the Hebrew concept of "heart" ( _lēb_ ) by translating it as "mind" ( _dianoia_ ).
**_Geographical context._** Geographical context is concerned with the location of events, particularly in relation to other locations in the narrative. Immediately after Solomon's death, the united monarchy of Israel dissolved into two separate nations. While Solomon's son Rehoboam ruled the kingdom of Judah, Jeroboam ruled the northern kingdom of Israel. Early in his reign, Jeroboam rebuilt Shechem as the new capital city and constructed altars in Dan and Bethel. These two cities were located at the northern and southern extremes of Jeroboam's kingdom, enabling every citizen of Israel to stay within the nation's borders to worship. Thus no one had an excuse to return to Jerusalem, where they might have been tempted to "revert to the house of David" (1 Kings 12:26). A sense of the geographical context of 1 Kings 12:25-33 helps the reader infer the significance of Jeroboam's choice of sites.
**_Historical context._** Historical context relates to the sequence of events, not only in the immediate narrative context, but also in the broader history of the world. As an example, consider the short prophetic book Haggai. This book is set "in the second year of Darius the king, on the first day of the sixth month." This date formula, along with other information taken from ancient Near Eastern texts, allows us to date the book of Haggai very precisely to the year 520 B.C. In fact, the New Living Translation is so confident of the historical data that it has translated Haggai 1:1 as follows: "On August 29 of the second year of King Darius's reign . . ." However, knowing the date is only significant as it relates to other events in Israelite history. So the fact that the book of Haggai took place in 520 B.C. indicates to the reader that the events in the book occurred after the Babylonian exile, which ended with the decree of Cyrus in 539 B.C. Thus the concerns of Haggai are different from the concerns of preexilic prophets like Amos and Hosea. Moreover, the historical context sheds important light on one of the main issues of the book, namely, the reconstruction of the temple, which had been destroyed by the Babylonians sixty-six years prior to Haggai's prophetic message.
_**Literary context.**_ Literary context pertains to how a book is structured and how the individual passages and literary units fit within the whole. Literary analysis is an imprecise art. As a case in point, Thomas Krüger's commentary on Ecclesiastes summarizes eight separate scholarly attempts to outline the literary structure of the book of Ecclesiastes. However, the fact that scholars have invested considerable time in the endeavor demonstrates its importance for understanding the book.
A less complicated book in terms of its literary structure is the aforementioned prophetic book Haggai. Although there remains room for discussion, the following outline represents a basic understanding of its literary structure.
> I. First Word from the Lord (1:1–1:15)
>
> A. Question 1 (1:3)
>
> B. Consider (1:5, 7)
>
> II. Second Word from the Lord (2:1-9)
>
> A. Question 2 (2:3)
>
> B. The Lord Will Shake the Heavens (2:6)
>
> C. The Lord Will Shake the Nations (2:7)
>
> D. The Lord Will Fill the Temple (2:9)
>
> III. Third Word from the Lord (2:10-19)
>
> A. Question 3 (2:12-13)
>
> B. Consider (2:15, 18)
>
> IV. Fourth Word from the Lord (2:20-23)
>
> A. The Lord Will Shake the Heavens (2:21)
>
> B. The Lord Will Overthrow the Nations (2:22)
>
> C. The Messiah Will Rule the Earth (2:23)
One quickly notices that the climax of the book comes in the final section. The imperative "consider" (literally "please set your heart," _śîmû_ [ _na_ ʾ] _lĕbabkem_ ) forms an inclusion, or bracket, around sections 1-3. Whereas the first three sections raised questions, the final section supplies the answer. The answer rests not in any earthly kingdom but in the messianic kingdom whose power lies not in horse and chariot but in the strength of the Lord of Hosts.
A subcategory of literary context is genre. Genre analysis is concerned with _how_ a particular type of literature is to be understood. Some examples of genre include proverb, lament, military annals, genealogy, itinerary, prophetic oracle and hymn. When Nathan confronts David about his affair with Bathsheba, he tells David a story. In fact, he tells him a parable, but David misunderstands the genre. David thinks Nathan is recounting a tragic injustice in the kingdom that requires royal intervention. Instead, Nathan uses a short fictitious tale to confront the king about his abuse of power. It is not until Nathan reveals the genre by declaring "You are the man" (2 Sam 12:7) that David understands the gravity of the situation. Having a proper understanding of the intended genre of a text is imperative for proper biblical exegesis.
_**Example from 2 Kings.**_ A contextual analysis of 2 Kings 7:1-2 illustrates the importance of attending to the various contextual issues of a text.
But Elisha said, "Hear the word of the LORD: thus says the LORD, Tomorrow about this time a measure of choice meal shall be sold for a shekel, and two measures of barley for a shekel, at the gate of Samaria." Then the captain on whose hand the king leaned said to the man of God, "Even if the LORD were to make windows in the sky, could such a thing happen?" But he said, "You shall see it with your own eyes, but you shall not eat from it."
Even though many readers may not be able to immediately locate this text in its historical, literary and geographical contexts, a quick glance at the narrative surrounding the text would resolve those issues. The narrative is set in the ninth century B.C., in the midst of an Aramean siege on Samaria. Samaria was Israel's capital city, while Aram was Israel's hostile neighbor to the north. The siege had left Samaria in such dire straits that four Israelite lepers determined it was better to risk defecting to Aram, where there was food, than to starve to death in Samaria. As a prophetic narrative, the main point is to demonstrate not only Elisha's validity as a true prophet but also the Lord's power over both Israel and Aram.
The passage also raises an important question about the cultural context. What is the meaning of the clause "Even if the Lord were to make windows in the sky"? Note how several modern translations render it.
ESV: "If the LORD himself should make windows in heaven"
NRSV: "Even if the LORD were to make windows in the sky"
NIV: "even if the LORD should open the floodgates of the heavens"
NLT: "even if the LORD opened the windows of heaven"
Taken literally, the text would suggest that God would install panes of glass in the sky. Common sense would lead most modern readers to realize that this expression is a reflection of human observation rather than scientific analysis. It would be preposterous to posit that on the basis of carefully constructed scientific experiments the ancient Hebrews had determined that there were sheets of glass that required divine latching and unlatching. Most people would implicitly deduce that the phrase used here in 2 Kings 7:2, and again in 7:19, explains how the ancients perceived the atmosphere.
Imagine living in rural or semi-urban ancient Israel, in which you have no Internet access, no television, no radio or even _Encyclopedia Britannica_. Columbus had not sailed to the New World, Magellan had not circumnavigated the globe, Sputnik had not yet orbited the earth, Neil Armstrong had not walked on the moon and the Hubble Telescope had yet to capture one image of the galaxies of the universe. If you're an ancient Israelite, what do you know about the world? How big do you imagine it to be? What shape is it? Where does the sun go at night? Where does the moon come from? Where have the stars been hiding? What's on the other side of the sea, or the mountains? How far down does the earth go, and what's beneath it? How deep are the lakes and seas? Where does spring water come from? Where do rain and snow come from? The answers to these questions would be as obvious to you as they were to any ancient observer. Which is to say, it wouldn't be obvious at all.
#### A New Yorker's Geography
In 1976 _, The New Yorker_ published on its cover Saul Steinberg's famous illustration of a New Yorker's view of the world. Looking west from the Lower East Side of Manhattan, the New Yorker shows great familiarity with his immediate surroundings. As his mind moves west, his grasp of the details diminishes rapidly. "Jersey" lies immediately beyond the Hudson River, but there is no concern for any landmarks. Beyond "Jersey" lies the rest of the United States and North America, with only vague reference to geographical landmarks, such as the Rocky Mountains and Las Vegas. The Pacific Ocean, barely larger than the Hudson River, separates the United States from the rest of the known world, which consists solely of China, Japan and Russia, with Japan being only slightly smaller than its transpacific neighbors.
Steinberg's point was not that New Yorkers are ignorant of world geography. Rather, the brilliance of the drawing is that it captures the geographical cultural worldview not only of New Yorkers but also of humans in general. By nature, we create our perceptions of reality based on observational experience. One of the reasons universities have general education requirements is to expand those experiences, thus broadening one's understanding of reality. When a New Yorker leaves the five boroughs and begins to see the land beyond the Hudson, then she can appreciate its spacious skies, amber waves of grain, purple mountains' majesty and fruited plain. Until then, the names, places and geological formations remain vague ideas in the Great Unknown.
The cover art of the March 29, 1976, edition of _The New Yorker_ demonstrates the natural tendency to view the world through one's own cultural lens. According to Steinberg's depiction, the New Yorker does not consciously ignore the rest of the world. The rest of the world simply is not part of his reality. He has not hiked the Appalachian Trail; bought pecans in Macon, Georgia; bartered for a used lawnmower in Christopher, Illinois; chewed on barbeque ribs in St. Louis; gasped for air in Rocky Mountain National Park; or surfed the waves off the coast of San Diego. He only knows what he has seen, which is very limited. He has a faint notion of the West and the rest of the world, but that notion is limited to what others have told him about it, what he imagines it must be like. In a similar manner, the ancient Hebrews' only knowledge of the world around them was limited to what their parents told them, what they had seen for themselves and what they imagined it must be like.
#### Worldview
The term _Weltanschauung_ , or "worldview," was coined by Immanuel Kant in his _Critique of Judgment_. Kant defines _Weltanschauung_ as one's "intuition of the world." For Kant, _Weltanschauung_ was a philosophical notion related to issues of epistemology—that is, how we know what we know. In this classical sense, worldview entails the implicit and explicit presuppositions with which one processes information. Where my daughter might see a bent bicycle rim as a useless piece of junk, a girl in the slums of Kibera, Kenya, would relish it as a luxurious toy to be propelled by a wooden stick, eliciting laughter and providing a sense of escape from dreadful living conditions. Both children see the same object, but their worldviews tint the way they see that object.
Everyone is guilty, if such an indictment is appropriate, of basic assumptions about how the world around him or her operates, or should operate. The 1981 movie _The Gods Must Be Crazy_ provides a comical description of the clash of worldviews. In this film, a careless passenger aboard a small plane discards his empty Coke bottle, which plummets to earth and lands at the feet of an African Bushman. Since the foreign object fell from the sky, the Bushman and his fellow villagers assume it was a gift from the gods. While at first it's seen as a divine blessing, the internal strife caused by the Coke bottle's presence leads them to conclude that the gods were, in fact, crazy for introducing such a divisive device into their camp.
The point is not that the Bushmen were wrong about the origins of the Coke bottle. Rather, it is how they perceived reality. From their experience, the only things that ever descended from the sky were rain, snow, hail and lightning. Since these phenomena derived from the heavens, the abode of the gods, it only stood to reason that the Coke bottle also derived from the heavens. Although the audience knows differently, the Bushmen's _Weltanschauung_ precluded them from perceiving these events in any other way.
Another way of thinking about worldview is "cognitive environment." As John Walton explains, "There is a great difference between explicit borrowing from a specific piece of literature and creating a literary work that resonates with the larger culture that has itself been influenced by its literatures." These cultural influences were not factors that ancient Israel adopted as their own. Rather, this cognitive environment constituted part of their essence as residents of the ancient Near East. The authors of the Hebrew Scriptures communicated their message within a particular milieu. Its authors wrote in Hebrew and Aramaic, the languages that were in use at that time in their region of the world. Their texts represented the cultural norms, business practices, laws, forms of worship, modes of travel, living arrangements and diet of people who lived in a world far different from twenty-first-century Western civilization. The ancient Israelites viewed the world in a way that is, in many respects, nonsense to the modern reader. Thus, for the purposes of this book, "worldview" refers to this same cognitive environment that saturated ancient Israel.
**_Cosmological worldview of ancient Israel._** Although it's a fallacy to say there was one, and only one, ancient worldview, it is not too reckless to assert that certain philosophical assumptions guided human behavior. The ideas and concepts prevalent in ancient Israel were, generally speaking, the very same ideas and concepts prevalent throughout the ancient Near East. As Walton states,
The Israelites received no revelation to update or modify their "scientific" understanding of the cosmos. They did not know that stars were suns; they did not know that the earth was spherical and moving through space; they did not know that the sun was much further away than the moon, or even further than the birds flying in the air. They believed that the sky was material (not vaporous), solid enough to support the residence of deity as well as to hold back waters.
One of those assumptions is the cosmological worldview, which Richard J. Clifford calls "the biblical three-tiered universe of the heavens, the earth and the sea." Consequently, the ancient Israelite concept of the cosmos looks something like what Sandra Richter depicts in her book _The Epic of Eden_ (see figure 1.1). In fact, this view of the cosmos was not unique to ancient Israel. It was the accepted view of reality throughout the ancient Near East.
**Figure 1.1.** Biblical view of the cosmos
The first tier comprised the heavens, the dwelling place of the sun, moon, stars and planets. Since the sun and moon appeared to track across the sky in an arc only to hide during "off hours," it was assumed that they disappeared beneath the earth. Other heavenly luminaries, such as planets and stars, entered through small pin-sized holes in a heavenly canopy.
The middle tier in the ancient cosmological worldview was the earth. The flat earth served as the focal point of human reality. Like the Lower East Side of Manhattan, the earth was the viewpoint from which cosmological observations were made. On either side of terra firma, the ancient Israelites knew of mountains and seas that essentially limited the scope of travel. No mortal could know what lay beyond them. The earth was held in place by pillars, which functioned as the earth's foundation. When people died, they were buried in the ground, and their bodies remained in Sheol, the abode of the dead.
The heavenly canopy not only served as the earth's roof but also functioned as a floodgate for the upper seas. The upper seas explain how water fell from heaven. Thus the canopy controlled the amount of precipitation that could descend to earth at any given time. As these waters encircled the earth, the waters that lay beneath the earth were called the abyss, or watery deep. The bottomless bodies of water, such as the oceans, seas and large lakes, pooled beneath the earth's surface. From these pools, springs bubbled and well water was captured.
**_Proverbs 8:22-31._** I will address the biblical evidence concerning the three-tiered cosmological structure throughout chapters three and four. However, it might be helpful at this early stage to set the ideas of the previous section into a biblical context. This passage from Proverb 8 is known as the Hymn of Wisdom. Although its main purpose is to demonstrate that God's wisdom is eternal, the passage's relevance to this discussion should be readily apparent.
> The LORD created me at the beginning of his work,
>
> the first of his acts of long ago.
>
> Ages ago I was set up,
>
> at the first, before the beginning of the earth.
>
> When there were no depths I was brought forth,
>
> when there were no springs abounding with water.
>
> Before the mountains had been shaped,
>
> before the hills, I was brought forth—
>
> when he had not yet made earth and fields,
>
> or the world's first bits of soil.
>
> When he established the heavens, I was there,
>
> when he drew a circle on the face of the deep,
>
> when he made firm the skies above,
>
> when he established the fountains of the deep,
>
> when he assigned to the sea its limit,
>
> so that the waters might not transgress his command,
>
> when he marked out the foundations of the earth,
>
> then I was beside him, like a master worker;
>
> and I was daily his delight,
>
> rejoicing before him always,
>
> rejoicing in his inhabited world
>
> and delighting in the human race. (Prov 8:22-31)
This poem is structured loosely according to the three-tiered system of the universe. Proverbs 8:23-26 pertains to the earth, including the mountains, hills, fields and dust. The second section, Proverbs 8:27-28, is concerned with the heavens, including the canopy (circle on the face of the deep) and the skies. The final section, Proverbs 8:29, describes boundaries of the sea. The waters, which appear above the heavens and below the earth, are mentioned in all three sections because without the divinely appointed boundaries, the whole earth would flood.
#### Scripture and Cosmology
Over forty years ago Luis Stadelmann was the first to argue systematically that one realm in which the ancient Near Eastern cognitive environment manifested itself in the biblical text was cosmology. Stadelmann argued that the "three-leveled structure of the world has its roots not only in the basic human experience of the external world from whose impressions man conceived such an imaginative depiction, but also in the mythological traditions so cherished among Israel's neighbors. It is also natural that the Hebrews be influenced by the cultural achievements and thought patterns of the peoples with whom they came into contact." Thus, according to Stadelmann, one of the most profound cultural influences on the Old Testament was cosmology. Stadelmann's argument was not particularly provocative. He merely demonstrated that the ancient Hebrews, like every society before and after, were influenced by their cultural context. Among scholars of the world of ancient Israel today, there is no significant disagreement over how the ancients viewed the structure of the cosmos.
It is my contention, then, that a high view of Scripture employs a hermeneutic that accommodates the biblical writers' immersion in their ancient, pre-Enlightenment cultural context. Therefore, as with other cultural matters, such as social customs and language, the biblical texts reflect that worldview in their written communication. This will be demonstrated in three parts. First, I will establish the diverse ways in which the ancient Near Eastern concept of the three-tiered cosmos projects itself onto the biblical text. Second, I will show that as astronomical advances were made concerning the structure of the universe, interpreters had to accommodate their views of Scripture in light of that new information. Finally, I will draw conclusions regarding an appropriate posture toward biblical interpretation in light of other points of contact between science and Scripture.
# _Part One_
## SCRIPTURE _and_ COSMOS
## _in_ CULTURAL CONTEXT
# 2
## ANCIENT NEAR EASTERN COSMOLOGIES
The ancient residents of the geographical region in and around Israel did not call their homelands "the ancient Near East." Historians and Bible scholars use the term to make generalizations about a cluster of civilizations in the distant past. As is often the case with such generalities, modern uses of this label are primarily dependent on the interests of those making the designation. So, as we begin our investigation of ancient Israel's cultural context, it would be wise to begin by defining the parameters of that context.
#### What Is the Ancient Near East?
Generally speaking, the ancient Near East was composed of the lands that would today include Kuwait, Iraq, Syria, Lebanon, Israel, Palestine, and portions of Iran, Turkey and Egypt. Millennia ago, these lands were occupied by the major world powers of Assyria, Babylon, Egypt and Hatti, as well as smaller states like Ammon, Aram, Edom, Israel, Judah and Moab. From a geographical perspective, the ancient Near East encompassed the mass of land from the Mediterranean Sea in the west, to the Persian Gulf and Zagros Mountains in the east; from the Taurus Mountains in the north, to the Red Sea in the south.
However, geography is but one factor. The other factor to consider is chronology. Although there is some dispute over the logical conclusion to the period, the two most logical end dates for the period are 539 B.C., with the rise of the Persians, and 332 B.C., with their subsequent fall to Alexander the Great. The main argument for 539 B.C. is that the Persian Empire marked a change in the cultural landscape of the region. By contrast, the rationale for 332 B.C. is that Alexander's reign introduced not only a new empire but a hoard of classical literature that opened up new avenues for studying myth and history in the ancient world. Although both options are valid, it is necessary for this volume to consider that significant portions of the Old Testament were written between the fall of Babylon in 539 B.C. and the fall of Persia in 332 B.C. For the purposes of this book, then, the ancient Near East concludes with the latter date.
#### Why It Matters
The world of the ancient Near East was a mystery for centuries. Of course, Bible scholars knew these worlds existed, but they were irrelevant for biblical interpretation in their view. After all, how could texts from foreign lands have anything valuable to say about Jesus? These were pagan lands, hosts of the people who took Israel captive, prayed to false gods and instigated idolatry. The only interest biblical interpreters had in these barbarous peoples was in contrast to God's people, first the Israelites, then the Christians. Even though the contextual world of the Bible garnered little attention from exegetes, the ancient voices of Israel's neighbors would not be silenced forever.
Egyptian hieroglyphics fell out of use in the fourth century A.D., leaving the language of the pharaohs in a linguistic dark age for nearly a millennium and a half. During Napoleon Bonaparte's military expedition into the Nile delta in the year 1799, one of his soldiers came across a large black basalt slab inscribed in three separate languages: Greek, Demotic and hieroglyphics. The inscribed rock became known as the Rosetta Stone and proved to be the key to deciphering the lost language of hieroglyphic Egyptian. When Napoleon learned of its discovery, he assembled an entourage of scholars to scour the land in search for other important cultural artifacts. Two years later, though, the British defeated the French and collected the Rosetta Stone as spoils of war. Two decades later, in his _Lettre à M. Dacier_ , the French scholar Jean-François Champollion articulated the essence of the language, effectively demonstrating that hieroglyphics had been deciphered. It would not be long before Egyptologists flocked to Egypt's ancient ruins, translating them for the first time into modern languages, and discovering the wealth of cultural, political and religious information contained therein.
Discovery and decipherment of the Mesopotamian material would shortly follow suit. These ancient texts lay buried in the sands of the Arabian desert until the early nineteenth century, when the French explorer A. H. Layard unearthed thousands of clay tablets written in cuneiform script. The decipherment of the text was confirmed in 1857 when the Royal Asiatic Society set before a few scholars a yet untranslated text from the Assyrian king Tiglath-pileser I (1114–1076 B.C.). Although a few scholars were able to translate lengthy texts, it had not garnered widespread interest in the guild until December 3, 1872. On that date George Smith presented a paper to the Society of Biblical Archaeology on what is now known as the _Epic of Atrahasis_ , a Babylonian flood story with many similarities to the biblical flood account. In 1876, Smith published _The Chaldean Account of Genesis_. Suddenly, the texts from the land between the rivers took on a whole new level of significance.
Excavations throughout the ancient Near East ensued in the following decades, and continue to this day. Beginning in 1907 archaeological digs in Boghazköy, Turkey, yielded important inscriptions from the ancient kingdom of Hatti. Although these Hittites are clearly distinct from the Hittites mentioned in the Old Testament Historical Books, the excavations produced myriads of historical, administrative, legal, lexical, mythological and religious texts. A little over two decades later, thousands of texts were discovered in the coastal city of Ugarit, located on the northeastern shore of the Mediterranean Sea, near Mount Zaphon. Among the most fascinating and significant texts were those related to Canaanite religion, whose mythological characters had close parallels to biblical concepts and deities. As new cites were found—such as Mari (1933), Alalakh (1937) and Emar (1971), to name a few—more texts surfaced that continued to shed light on the life and culture of the ancient Near East.
When these vast caches of Mesopotamian, Anatolian, Canaanite and Egyptian texts were first discovered and translated in the nineteenth and early twentieth centuries, scholars immediately became enamored of the vast similarities between these texts and the Hebrew Bible. These important texts were welcomed with the same unrestrained, sensationalist vigor as today with the latest archaeological "find." As my two former teachers Bill Arnold and David Weisberg observe, "The last half of the nineteenth century had witnessed an explosion of knowledge and information from Mesopotamia, and many uncritical comparisons had been made with the more familiar biblical materials." Specifically, Arnold and Weisberg were commenting on Friedrich Delitzsch's famous "Babel und Bibel" lectures of 1902, which heightened public awareness to the profundity of the Mesopotamian tablets.
Now, at a stroke, the walls that have shut off the remoter portion of the Old Testament scene of action fall, and a cool quickening breeze from the East, accompanied by a flood of light, breathes through and illuminates the whole of the time-honoured Book—all the more intensely because Hebrew antiquity from beginning to end is closely linked with this same Babylonia and Assyria.
Delitzsch, and the academy in general, saw in all of these finds the keys to unlocking the secrets of the Bible.
In time, scholars naturally began to temper their enthusiasm. Realizing that these amazing finds were not as earth-shattering as originally thought, scholars began to exercise more caution in drawing parallels between ancient Near Eastern texts and the Bible. But that transition has not come easily. K. Lawson Younger Jr. succinctly describes that process as follows:
Over the last one hundred and fifty years, questions of how to handle the "parallels" between the biblical text and the ancient Near Eastern materials have received different answers. On the one hand, some scholars have been guilty of overstressing the parallels, a type of "parallelomania," while others—often in reaction to the excesses of the former—have downplayed the parallels to the point of ignoring clear, informative correlations, producing a type of "parallelophobia."
As Younger rightly notes, two extreme positions emerged. Those of one position interpreted the Bible through the lens of the ancient Near Eastern texts at every turn. Those of the other position discounted the comparative material as having any relevance for biblical interpretation.
From these extremes, a more moderate position emerged, known as the "contextual method." Advocates of the contextual method acknowledge that the biblical authors were not necessarily in direct contact with these sources. Rather than assume a direct borrowing from source A to source B, the contextual method recognizes that ancient Near Eastern texts arrive from a variety of cultural conditions: social, historical, linguistic, geographical and chronological. Nonetheless, the peoples of the ancient Near East shared many cultural concepts, such as language and superstitions, as well as ideas of family, life, death, kingship, labor and war, to name a few.
Naturally, ancient Israel and Judah were part of this ancient cultural milieu. We know from the biblical text, as well as from extrabiblical data, that Israel had contact with their surrounding nations. They lived at times in Egypt, Babylon and the Persian Empire. Their kings made marriage alliances with Phoenicia (1 Kings 16:31) and Egypt (2 Kings 3). They engaged in battle with numerous nations and kings. They welcomed foreigners into their community (Lev 19:34; Josh 6:22-25; Ruth 4:13-15). They even participated in many of the same cultic practices as their neighbors, such as building idols (1 Kings 16:25-33), offering child sacrifices (2 Kings 16:3) and practicing sorcery (2 Kings 21:6). As John Walton states,
It is to be expected that the Israelites held many concepts and perspectives in common with the rest of the ancient world. This is far different from suggesting literature was borrowed or copied. This is not even a case of Israel being influenced by the peoples around them. Rather we simply recognize the common conceptual worldview that existed in ancient times. We should therefore not speak of Israel being influenced by that world—they were part of that world.
In light of these cultural connections, considering the texts of the ancient Near East is not optional. Although we cannot defer to these texts as the definitive commentary on the biblical texts, they provide necessary contextual insight into the world of ancient Israel. In some cases where the biblical text is opaque, these texts often provide clarity. However, more often than not, these texts provide a context in which to read the Bible that is often missing for modern readers.
In light of these considerations, the logical starting point in our study of the biblical cosmology would be to assess the cosmologies of ancient Israel's neighbors. Whereas the biblical authors assumed the ancient audience would comprehend their conceptual world, we are far removed, often missing analogies and direct allusions to a world that was ingrained in their worldview. This is where a contextual analysis will prove most useful, since many of the ancient Near Eastern texts provide more descriptive details than the biblical text, using a vast array of representations: technical, mythological, iconographic and textual.
#### Ancient Near Eastern Cosmography
When we think of the cosmos, we think in terms of planets, moons, comets, asteroid belts, orbits, solar systems, galaxies, light years, black holes and dark energy. Our understanding of the cosmos has been informed by centuries of atmospheric observation with the naked eye, telescopes, moon landings, space stations and satellite imagery. Thanks to the Hubble Telescope, we have images of faraway galaxies, nebulae, star clusters and galactic "debris." Our cosmography, or map of the universe, then, takes all of these data into consideration. The vastness of the universe really is beyond comprehension.
The ancients were no less intrigued by the complexities and perplexities of their own cosmography. Land travel was limited to the reliability and durability of transportation. In fact, it has been estimated that a donkey carrying about 150 pounds could only travel about fifteen to twenty miles per day. Sea travel was considered perilous; thus mariners generally maintained visual contact with land, although some vessels ventured out far enough to discover islands such as Crete and Cyprus. In fact, the vast majority of ancient people probably never wandered more than a few miles from their homeland. In other words, the capacity to learn about the cosmos was restricted to a relatively small parcel of land and water we call the ancient Near East. What lay beyond the mountains and seas, above the clouds and beneath the earth, remained a mystery. Indeed, the vastness of their universe was equally beyond comprehension.
Despite the limits to their observational evidence, the ancients were not deterred from drawing some rather confident conclusions about the structure of the cosmos. In light of the evidence, modern scholars of the ancient Near East have been able to deduce a fairly consistent picture of how the ancients viewed their universe. They perceived the cosmos as consisting of three parts: the earth, the heavens and the sea. The earth was the plot of land on which they lived, traveled, traded, toiled and suffered. It was terra firma, that on which they carried out their existence and in which their bodies would be placed at their expiration. It was also the point of view from which they experienced the heavens and sea. From where they stood, the earth remained still, while the sun rose in the east and set in the west. The stars came out at dusk and faded at dawn. The day was illumined by the sun, while the night was illumined by the moon. The heavens were the realm of birds and clouds and were "up there." The ancients also observed that life-sustaining water was all around them. When they traveled to the edges of their world, they encountered it. It came from above in the form of rain, snow and hail. It came from below in the form of dew, springs, wells, streams and rivers. It was only logical, then, that the entire cosmos was surrounded by it.
This tripartite division is evident in a variety of places but appears prominently in creation epics. In the Babylonian creation epic _Enuma Elish_ there existed only two waters: fresh water of the deep (Apsu) and salt water of the sea (Tiamat). Eventually, the chief Babylonian deity Marduk defeats Tiamat, splaying her body like a shellfish in two, with one half serving as the firmament, the other half becoming earth. Similarly, _Atrahasis_ , a Mesopotamian creation account famous for its similarities with the flood account in Genesis 6–9, opens with Anu, Enlil and Ea casting lots for possession of the heavens, the earth and the sea. We also see this tripartite construction in the Egyptian _Memphite Theology_ :
> Hail to you—by all flocks,
>
> Jubilation to you—by all foreign lands,
>
> To the heights of _heaven_ , to the breadth of the _earth_ ,
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> To the depths of the _ocean_ ,
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> The gods bowing to Your Majesty.
These texts and others, as well as various images (especially from Egypt), depict a consistent picture in the ancient Near East. From Mesopotamia to Egypt, and all points in between, the ancients viewed the earth as consisting of three structural parts: the heavens, the earth and the sea.
#### Forms of Ancient Near Eastern Writings
As with any collection of literature, the ancient Near Eastern material comes in various forms. These include genres such as military annals, mythology, etiology, royal propaganda, construction narratives, prayers, hymns, omens and astronomic texts, to name a few. Just as we must get a sense of how the biblical text is to be understood, so we must establish how the ancient Near Eastern texts are to be received. For example, the storm god was often depicted as one who holds lightning or rides on a cloud. This does not mean that the ancients believed that if they looked to the skies on a stormy evening they would catch a glimpse of a man-like creature poised to unleash his electric arsenal. However, these depictions and characterizations do point to a worldview in which the storm god is accountable for all facets of weather. The authors of these texts were not myopic and dense in their understanding of the cosmos or the natural world. They were creative enough to communicate their multifaceted views of reality in a myriad of literary conventions. While some of the details may vary from one author to another, from one region to another, or one era to another, the authors shared a common cognitive environment that colored their view of the cosmos.
**_Earth._** First of all, the earth was not seen as a globe. Nor was it considered to encompass all of the land mass that we now know constitutes planet Earth. Instead, the Semitic word "earth" (ʾ _r_ ṣ) might better be understood by its alternate meaning, "land."
**Figure 2.1.** _Babylonian Map of the World_
It could refer to a geopolitical territory, as in the land of Egypt. Or it could refer to a parcel of farmland. It could also indicate the underground land to which one returns upon death. In any case, the earth of the ancients was defined by the territory on which humans spent their existence.
_Earth's dimensions._ In both Egypt and Mesopotamia the earth was thought to be a flat disk. The horizon constituted the ends of the earth. Where the earth ended, the cosmic seas began. This is evident in both visual representations and textual descriptions.
One of the visual representations of Mesopotamian geography is found on the so-called _Babylonian Map of the World_. A clay tablet discovered in southern Iraq, the map provides a graphic depiction of the Babylonian view of the earth, along with corresponding text that describes the artwork (see figure 2.1).
As is typical of all ancient cultures, the Babylonians thought of themselves as being near the center of the earth, which is surrounded by an oceanic ring. The circular shape of the earth can also be seen in the _Etana Epic_ from Mesopotamia, which recounts two separate attempts by Etana, the king of Kish, to reach the heavens on the back of an eagle. In their first ascent, the eagle makes note of the changing geography below.
> When he bore him aloft one league,
>
> The eagle said to him, to Etana,
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> "Look, my friend, how the land is now!
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> Examine the sea, look for its boundaries.
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> The land is hills.
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> The sea has become a stream."
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> When he had borne him aloft a second league,
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> The eagle said to him, to Etana,
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> "Look, my friend, how the land is now!
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> The land is a hill."
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> When he had borne him aloft a third league,
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> The eagle said to him, to Etana,
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> "Look, my friend, how the land is now!
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> The sea has become a gardener's ditch."
From a literal bird's-eye view, the seas appeared as a ditch, encircling the earth.
The flat-disk shape of the earth was also the predominant view in Egypt. According to John Wilson, "The Egyptian conceived of the earth as a flat platter with a corrugated rim. The inside of the platter was the flat alluvial plain of Egypt, and the corrugated rim was the rim of mountain countries which were foreign lands." We can see this quite clearly in the image from a fourth-century-B.C. Egyptian sarcophagus (see figure 2.2).
**Figure 2.2.** Egyptian image of three-tiered cosmos
Although certain aspects of the image are vague, we may draw some fairly firm conclusions regarding Egyptian cosmology from it. First, the outer circle represents a surrounding ocean, like in Mesopotamia. Second, the Egyptian signs on the innermost circle indicate that this region represents the land of Egypt, while the iconography inside the circle represents the world beneath Egypt. Finally, the region between the inner and outer circles represents Egypt's distant lands. As with the Mesopotamians, the Egyptians' world revolved around them and extended radially until it reached the cosmic seas.
According to the _Babylonian Map of the World_ , at the very outskirts of the earth lay nine regions, only five of which remain visible on the fragmentary map. These regions may represent islands or unspecified distant provenances or have some cosmic connotation. In any case, they bring to our attention the fact that the ancients did not necessarily have a precise concept of the size of their earth.
One way of designating earth's parameters was with respect to the four winds, or four compass points. This becomes more apparent when we consider a small fragment from the Babylonian city Uruk. Although fragmentary, Wayne Horowitz's reconstruction shows how the artist conceived of the earth as a flat disk oriented according to the seasonal winds with respect to the compass points. This directional demarcation of earth's dimensions is also evident in numerous royal inscriptions in which the king refers to himself as the "king of the four quarters." This designation was not intended to convey the idea of a square earth, but to demonstrate the extent of the king's rule. He ruled the entirety of the cosmos, from north to south and east to west.
In the _Epic of Gilgamesh_ the hero is lauded for his expedition to the outer limits of the earth.
> He is Gilgamesh, perfect in splendor,
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> Who opened up passes in the mountains,
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> Who could dig pits even in the mountainside,
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> Who crossed the ocean, the broad seas, as far as the sunrise.
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> Who inspected the edges of the world, kept searching for eternal life,
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> Who reached Ut-napishtim the far-distant, by force.
What is particularly fascinating about the description is the lack of detail. The author does not know what lies beyond the edges of the world, except that that is where one must go to find eternal life. What he does know, however, is that once he reaches the sea, he has left the land of mortals. Moreover, the sea indicates the end of the earth.
Similarly, the Egyptian _Report of Wenamun_ narrates the hero's maritime adventures. Although he does not reach the end of the earth, the mere thought of Wenamun attempting to sail the seas to the Mediterranean coastal city of Byblos struck fear in the harbor master for daring to test the earth's limits.
The harbor master said to Wenamun, "Indeed, Amun has founded all the lands. He founded them after having first founded the land of Egypt from which you have come. . . . What are these foolish travels they made you do?" I said to him: "Wrong! These are not foolish travels that I am doing. There is no ship on the river that does not belong to Amun."
Wenamun successfully landed in Byblos. However, it shows how uncertain the Egyptians were about the length of the earth. While Wenamun was confident the creator god Amun would assure his safety, the harbor master was not. The ends of the earth were a great unknown.
The Egyptians' fascination with the sun gives them a slightly different perspective on the earth's dimensions. Since the sun traverses the sky, rising in the east and setting in the west, they could at least measure earth's parameters according to the sun's daily course.
> To him belongs the Southlands as well as the North,
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> for he took them, alone, for his own, in his strength;
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> His boundaries were set while he was still upon the earth,
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> wider than all the earth, higher than heaven.
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> From him the gods request their necessities—
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> and it is he who supplies from his stores.
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> Owner of arable fields, riverbanks, and new land—
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> to him belongs each title-deed in his registry;
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> From beginning to end of the stretched cord
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> he measures all earth with his gleaming countenance.
From the Egyptian's perspective the sun would ascend from the eastern horizon and then descend below the western horizon. Living in the flat plains of the Nile, it would have appeared to them that the place of the sun's rising and setting entailed the extremities of their geography.
_Earth's foundations._ Since the earth was surrounded by water, one of the mysteries of the ancient world was how it stayed afloat. Anyone from the shoreline could see that the land extended below the surface of the water. If they dropped a clod of dirt into the water, they could see that the dirt sank. If a small amount of earth sinks, how did the whole mass of earth not sink? This problem was not resolved univocally; there was no broad ancient Near Eastern consensus on how this occurred. Two main possibilities emerged. One solution was that the earth was supported by pillars. Another solution was that the earth actually floated on the waters.
The view found most prominently in Mesopotamian sources was based on a construction analogy. Just as houses, palaces and temples needed foundations, the ancients surmised that the divinely constructed cosmos also needed a foundation to support it. Thus it seemed necessary that the earth would have been supported by subterranean pillars. Two metaphors were used to illustrate earth's structural support. One was that mountains, which supported the heavens, had roots in the netherworld. For example, in 714 B.C., the Assyrian king Sargon campaigned into the Zagros Mountains on his way to Urartu. Encountering Mount Simirria, he recounted the following: "Mount Simirria, a mighty mountain-peak, which spikes upward like the cutting-edge of a spear, on top of the mountain-range, the dwelling of Belet-Ili, rears its head. Above, its peak leans on the heavens, below its roots reach into the underworld." Gilgamesh, the only mortal to have survived the great flood and who lives at the edge of the earth, offers a similar description in his quest for eternal life from Utnapishtim.
> When he reached Mount Mashu,
>
> which daily guards the rising and setting of the Sun,
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> above which only the dome of the heavens reaches,
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> and whose flank reaches as far as the Netherworld below . . .
Likewise, Hammurabi wrote in the prologue of his famous Law Code, "When they [Anu and Bel] made it [Babylon] famous among the four quarters of the world and its midst was established an everlasting kingdom whose foundations were firm as heaven and earth." Hammurabi's unwavering juridical control was predicated on the fact that heaven and earth were equally steady, fixed and firm.
Mountains figured prominently in their landscape and offered a visual metaphor for what must have provided the basis for earth's foundation. They are sturdy and impenetrable. Moreover, their bases could not be reached. Regardless of the depths to which one dug, their roots would not be found. It only made sense that they continued into the netherworld, providing the necessary structure to and foundation of earth's surface.
Perhaps the most illustrative evidence, however, comes from a Kassite-period _kudurru_ , or boundary marker (see figure 2.3). Depicted on this stone is a visual representation of a tripartite cosmos. In terms of the earth's foundation, one should take note of the three visible foundation pillars—the fourth would be visible on the reverse side. These pillars arise from the chaotic cosmic sea, represented by the sea serpent, and are affixed to the terrestrial disk. Since every house, palace or temple required foundation stones to provide stability to the structure, the ancient Mesopotamians likewise conceived of the earth itself as requiring a foundation for its stability.
**Figure 2.3.** Babylonian _kudurru_
While the concept of the foundational pillars provided the understanding of the earth's physical foundations, the so-called Tree of Life offered a metaphysical explanation for the unified integration of the cosmos. In his volume on Genesis and ancient Near Eastern cosmology, Walton notes that the Tree of Life, which is commonly found at the center of the cosmos, has roots that "are fed by the great subterranean ocean, and its top merges with the clouds, thus binding together the heavens, the earth, and the netherworld." He further points to the _Epic of Erra and Ishum_ as evidence that this _mesu_ tree provides support for the earth.
> Where is the _mesu_ -wood, flesh of the gods,
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> The proper insignia of the King of the World,
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> The pure timber, tall youth, who is made into a lord,
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> Whose roots reach down into the vast ocean
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> Through a hundred miles of water, to the base of Arallu,
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> Whose topknot above rests on the heaven of Anu?
While the foundational pillars provided the physical support, the roots of the Tree of Life provided the cosmic synergy necessary to hold all things together.
In Egypt we find another solution to the problem of the floating earth. It is based on the concept of the once visible, but now invisible, primordial ocean. According to this view, the cosmic sea is found directly beneath earth's surface.
**Figure 2.4.** Upper and lower seas of Egypt
What keeps earth afloat is its own buoyant qualities.
According to Egyptian cosmogony, "a hillock suddenly appeared out of the dark, windy, surging wateriness of Chaos (Egyptian 'Nun')." The support of this hillock, or primordial mound, also needed accounting. As we will see in some detail in the sections that follow, one of the fundamental concepts in Egyptian thought was that of the sun god traversing the sky and netherworld on his bark. Naturally, this maritime voyage required cosmic waters above and below the earth (see figures 2.4 and 2.5). The first image crudely represents the idea of the upper and lower waters. The second image depicts the sun bark in its predawn position. Having passed through the netherworld during the night, the sun is ready to emerge from the cosmic waters to introduce a new day.
**Figure 2.5.** Emergence of Re from the netherworld
In the barque, the sun, in the form of a soaring scarab beetle, is embraced by Isis and Nephthys, while the beetle pushes the sun disk toward the sky goddess Nut, who receives the god Re. Her upside down position designates the inversion of the sun's course, which will now once again run in the opposite direction from its course through the netherworld, here embodied Osiris, who surrounds the netherworld with his curved body.
Since the terrestrial hillock was seen as being surrounded by water, the earth must have floated, so the ancient Egyptians thought. In a land surrounded by reeds, the obvious structural support for an island mass was a reed mat. According to one text, at the beginning of creation a single reed grew into a thicket, which floated from Elephantine to its final resting place in Hermopolis. The Egyptian texts as a whole do not supply an abundance of evidence to support this theory. However, given their perception of a watery underworld and the pervasive presence of reeds, it is not difficult to imagine this idea infiltrating Egyptian thought.
Although we find the concept of a floating earth primarily in the Egyptian material, we also see traces in Mesopotamia. The text "The Founding of Eridu" outlines the process by which Marduk, the chief deity in the Babylonian pantheon, created the earth and then filled the earth with humans, animals, plants, rivers and other essential elements. The climax of the text is the construction of Marduk's temple Ekur. What is of interest to Mesopotamian cosmography, however, is how the earth was set on the waters.
> A pure temple, a temple of the gods, for them to dwell in, had not been made,
>
> But all the lands were sea,
>
> And the spring in the sea was a water-pipe.
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> Then Eridu was made, Esagil was created,
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> Esagil, which Lugaldukuga founded in the Apsȗ.
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> Babylon was made, Esagil was completed.
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> He made the Anunnaki gods, all of them,
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> And they gave an exalted name to the pure city in which they were pleased to dwell.
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> Marduk constructed a raft on the surface of the waters,
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> He made earth and heaped it up on the raft.
According to this account, then, earth was seen as a reed-constructed raft that floated on the omnipresent seas. Although this particular view is not found elsewhere, it demonstrates yet another way in which the ancients comprehended the interface of land and sea.
_Earth's depths._ The concept of an underworld (or netherworld) was shared by all ancient Near Easterners. As its name implies, it was located beneath earth's surface. In some respects, it was a place of terror and dread. At other times it was perceived as a place of peace, where the trials of life were no more. In Egypt, it was simply the beginning of a new existence. In all cases, it was the inevitable destination of all living things.
The fullest descriptions of the netherworld in Mesopotamia are found in the Akkadian myths the _Descent of Ishtar_ (and its Sumerian counterpart, _Descent of Inanna_ ), _Nergal and Ereshkigal_ and _Epic of Gilgamesh_ , tablet 12 (and its Sumerian recension). Although each has its own distinctive features, these myths share a common theme of a deity descending into the realm of the dead.
The most prominent of these myths is the _Descent of Ishtar/Inanna_. Ishtar was the goddess of sexuality and war. When she elected to descend into the nether region, all sexual activity on earth ceased. Upon her ascent, she is reunited with her lover Tammuz, presumably renewing sexuality and fertility on earth. While the myth is a fascinating tale for mythological and religious reasons, our concern here is its characterization of the netherworld.
> To Kurnugi, land of no return,
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> Ishtar daughter of Sin was determined to go;
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> The daughter of Sin was determined to go
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> To the dark house where those who enter cannot leave,
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> On the road where travelling is one-way only,
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> To the house where those who enter are deprived of light,
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> Where dust is their food, clay their bread.
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> They see no light, they dwell in darkness,
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> They are clothed like birds, with feathers.
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> Over the door and the bolt, dust has settled.
Although far from complete, this excerpt provides a general sense of the Mesopotamian view of the netherworld. It was a realm of darkness, guarded by gates, prohibiting the return of the deceased to the land of the living.
In the ancient Mesopotamian worldview, the "land of no return" was synonymous with the grave. There was no hope for a resurrection, nor was there any reason to entertain the concept. The best one could hope for was to rest in peace, the responsibility of which lies in the survivors of the deceased, as seen in this prayer to family ghosts:
> You, the ghosts of my family, progenitors in the grave,
>
> (The ghosts of) my father, my grandfather, my mother, my grandmother, my brother, my sister,
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> (The ghosts of) my family, my kin, (and) my clan,
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> As many as are sleeping in the netherworld, I make a funerary offering to you.
For Mesopotamians, descent to the grave was the inevitable fate of all humans and was personified in Canaanite literature as Môt, the Semitic name for Death. There they could expect to eat dust and contend with demons. However, their torturous existence in the netherworld could be lessened with the help of the living, who could provide proper burial practices and offerings. In turn it was thought that the dead could provide favors for the living from their land down under.
Such dire notions of the grave were the rule for the common person. However, "important deceased humans, such as Gilgamesh, Etana, and Dumuzi, resided with the gods in the underworld and even became underworld gods themselves." Rather than lying in graves, they resided in temples or palaces in a great underworld city (see figure 2.3). In any event, the netherworld was inescapable for the nondivine.
Death itself was a hostile venture. While divine beings such as gods and demons could ascend and descend along the "Stairway of Heaven," the deceased entered via the "Road of No Return." In this passage from the _Epic of Gilgamesh_ , the road is a one-way street, leading to the house of darkness.
> He seized me, drove me down to the dark house, dwelling of Erkalla's god,
>
> To the house which those who enter cannot leave,
>
> On the road where travelling is one way only,
>
> To the house where those who stay are deprived of light,
>
> Where dust is their food, and clay their bread.
Due to the uncertainty of the netherworld itself, different traditions emerged regarding the terminus of this road. In some cases, the road led directly to the netherworld. Elsewhere, it terminated at the Hubur River, which ferried the deceased for the remainder of their journey.
> Our fathers in fact give up and go the way of death.
>
> It is an old saying that they cross the river Hubur.
Whether by road or river, or both, the Mesopotamians believed one does not simply arrive in the netherworld. The deceased had to be transported there physically.
Egyptian thought also conceived of the transition from life to death as a dangerous enterprise. As John Taylor notes, "Many concerns were that the offerings should be supplied in perpetuity, and that the deceased should not fall victim to the many dangers which threatened the unwary or ill-prepared." However precarious the journey was envisioned, the destination was not seen as such. Rather than thinking of the netherworld as the "Land of No Return," Egyptians referred to it as "the land that loves silence" and "the beautiful West."
In time ideas about the eternal destination changed. In the Pyramid Texts from the Old Kingdom (ca. 2650–2150 B.C.), the dead kings ascended to the heavens, where they dwelled among the deities.
**Figure 2.6.** Egyptian map of the underworld
Throughout the majority of Egyptian history, though, the abode of the dead lay beneath earth's surface. It was the passageway of the sun god's nightly journey and "contains everything that has ever existed."
According to the _Book of Two Ways_ , the netherworld could be reached by one of two pathways: earth or water (see figure 2.6). This "map" was literally placed in the tomb of the deceased and was thought to have provided the deceased a guide for safe travel from the realm of the living to the afterlife. The journey was treacherous, involving meandering paths, dangerous demons, fiery lakes and other obstacles. However, along with the map, the coffins held important travel aids such as amulets and spells to assist the deceased along their way.
**Figure 2.7.** Egyptian geography of the netherworld
The geography of the Egyptian netherworld is depicted in a number of ways. In some cases, it is simply the inverse of earth (see figure 2.2). Elsewhere it resembles life in Egypt, complete with rivers, flora, fauna and manual labor (see figure 2.7). Mostly, though, the netherworld is the underworld pathway of the nocturnal sun, whose rays give life to the previously comatose souls of the deceased.
The sun's twelve-hour voyage to the underworld is described in the Amduat text _Books of the Netherworld_ from the New Kingdom period. In the first hour, the sun god passes over the horizon on his night bark, beginning his descent to the netherworld. In the second and third hour, the sun god continues to float on abundant waters, passing grain-carrying peasants. The water turns to sand in the fourth hour, requiring the sun god's bark to be towed by four tow men. Additional towers are needed in the fifth hour, as the sun god descends to the depths of the netherworld, where he dies in the sixth hour. Upon his resurrection in the seventh hour, the deceased comes to life. His cries of joy are heard by the living as ordinary sounds of everyday life during the eighth hour. In the ninth hour, the tow men give way to oarsmen, as the sun god prepares for sailing into dawn. During the tenth and eleventh hours, the bark is prepared for the sun god's rebirth on the eastern horizon. Finally, at the twelfth hour, the sun god emerges from the netherworld and the deceased returns to a state of unconsciousness.
Mesopotamians and Egyptians alike had some inhibitions regarding the netherworld. Even the Egyptians, who believed in a form of resurrection, were wary of this realm of the unknown. Throughout the ancient Near East, the netherworld was a physical abode of the dead in the heart of the earth. Tributaries of the primeval depths meandered through its caverns. It was inhabited by demons and chthonic entities. Above all, the netherworld was the ultimate destination for all humanity, with no expectation of returning to life on earth.
**_Heavens._** The ancients did not have just one view of the heavens, or sky. The sky could be a solid dome or a tent. There could be one level, three levels or seven. In Mesopotamia, it was the habitat of the gods, a mirror image of life on earth. This was not exactly the case in Egypt. Despite variant traditions of the heavenly realm, there are some common themes, indicating a shared general cosmography of the heavens.
It was a nearly universal truth that the sky was a solid structure. In Egypt, it was a flat roof, whereas in Mesopotamia it was dome-shaped. The solidity of the sky was necessary for several reasons. First, as we will see in our discussion on the sea, it served as a barrier for the upper waters. Second, it provided a floor for the heavenly deities and their abodes. Third, it was the ceiling to which the celestial bodies were fixed. In any case, it is best to think of the sky as a firmament, a firm barrier between the sky and heaven.
As Horowitz has argued, in Mesopotamia it was thought that the firmament was made of a blue stone, giving it its blue hue. Its stone composition may well have been confirmed by the physical evidence of meteors having chipped off its underside. Of course, the ancients could only speculate on the firmament's material composition based on their observations and analogy to materials with which they were familiar. The Egyptians did not seem to show a preference to the firmament's material structure, other than that it had some watery consistency to it, allowing the sun god a surface on which to sail. It seems likely, then, that the Egyptians may have considered the firmament to be like a plane of glass, firm enough to withhold upper waters but clear enough to see the bluish tint of the cosmic sea.
Since the firmament was a physical structure, it required a physical support system. In Egypt, it was "either supported by pillars, staves, or scepters, or is set on top of the mountains at the extreme ends of the earth." In mythological terms, the sky goddess Nut was upheld by the air god Shu (see figure 2.8). Mesopotamians held two separate views on heaven's support system. One idea, similar to Egypt, was that the heavens were supported by the mountains. Of course, Mesopotamia's topography contributed to this perception, since its terrain was especially flat, but within view of the lofty Zagros Mountains. Ziggurats, the mountain-shaped confines of cultic sanctuaries, dotted the landscape as the Mesopotamians replicated the dual function of the mountains as both heavenly supports and vertical stairways to heaven (see figure 2.9). Their shape was meant to resemble the actual mountains on which the gods ascended and descended from their heavenly dwelling places.
**Figure 2.8.** God Shu supporting Nut, goddess of the sky
Another idea is that the firmament was more like a tent, which requires a supporting pole and guide lines. The most graphic depiction we have of this concept is found in _Enuma Elish_ , when Marduk takes Tiamat's corpse and sets her body as a canopy over earth.
**Figure 2.9.** Mesopotamian ziggurat
> He set down her head and piled [ ] upon it,
>
> He opened underground springs, a flood was let flow.
>
> From her eyes he undammed the Euphrates and Tigris,
>
> He stopped up her nostrils, he left . . .
>
> He heaped up high-peaked mountains from her dugs.
>
> He drilled through her waterholes to carry off the catchwater.
>
> He coiled up her tail and tied it as "The Great Bond."
>
> [ ] Apsu beneath, at his feet.
>
> He set her crotch as the brace of heaven,
>
> He set [half of] her as a roof, he established the netherworld.
>
> [ t]ask, he caused the oceans to surge within her.
>
> [He spre]ad his net, let all (within) escape,
>
> He formed the . . . [ ] of heaven and netherworld,
>
> Tightening their bond.
What is less than clear in translation is that Marduk secures the bonds of heaven and earth, fastens the lead-ropes and then tethers them above and below, thus keeping Tiamat's skin firmly in place as heaven's firmament. Regardless of the variations of descriptive language, the common motif is that of a canopy overhead supported by physical structures.
Our most lucid sketches of heaven's details derive from Mesopotamian sources. Without going into great detail concerning the assorted views on the number of layers above the firmament, it is fair to divide the heavens into two parts: the lower heavens and the upper heavens. The lower part pertains to the visible heavens, in which earthbound observers could take sight of the astral bodies. The upper layer consists of all that lies above the firmament. Nevertheless, in the ancients' minds both the abode of the deities and the air overhead were considered "heaven," and there was no linguistic or conceptual difference between the two.
_Lower heavens._ By definition, the visible heavens refer to the observable skies. Its inhabitants include stars, planets and constellations, all of which were called stars. However, the ancient distinction between planet and star is somewhat different from our own, and it is not always consistent. The term _star_ may refer to stars, constellations or the five principal planets, Mercury, Venus, Mars, Jupiter and Saturn. While the five principal planets were sometimes identified as stars, elsewhere the term _planets_ refers to these five plus the sun and moon. Each of these was thought be a separate source of light.
They recognized that planets and stars behaved differently in their patterns, so they developed a science related to the observation of these patterns and recorded them in charts known as the astrolabes, MUL.APIN and other texts. It was surmised that the celestial bodies followed various "paths" in the sky, as they related to the horizon. These were known as the paths of Anu, Enlil and Ea, named for the Mesopotamian triad of supreme deities. In the Babylonian astrolabe texts, both stars and planets are indicated by the determinative MUL, which indicates a star or celestial luminary. However, it was also noted that the five visible planets did not behave exactly like the stars. The Babylonians noted that the planets' position in relation to the fixed stars deviated over time. While the stars appeared to remain stationary, planets appeared to move in retrograde due to the variable rates at which they orbit the sun. So in Akkadian stars were called _kakkabu_ , "star, meteor, falling star, star-shaped object or formation," while planets were called _bibbu_ , "wild sheep; planet, star, comet (?)." The fixed stars maintained their positions with respect to each other, but together they were seen to have rotated on a disk. Based on these observational models, it appears the ancients believed the stars were inscribed on the underside of a rotating firmament.
One of the mysteries the ancients pondered was the location of these luminaries during their off hours. To where did the sun descend, and how did it rise on the opposite horizon each morning? Where did the moon and constellations hide during the day? Why was Venus periodically invisible? The solutions were not always consistent, so we find a couple of explanations.
At the end of each day, the sun would retire to its chamber, as seen in _Prayer to the Gods of the Night_ :
> The judge of truth, father of the impoverished girl,
>
> Shamash has entered his cella.
While in its chamber, the sun would rest from shedding light. As the god of justice, it would also cease from rendering judgments, which was the concern of the supplicant in the _Prayer to the Gods of the Night_. The location of the cella, however, is unclear.
One view coincides with the Egyptian concept of the sun's journey through the netherworld as it traveled from the western horizon to the eastern horizon. We can see evidence of this in numerous prayers to the sun god Shamash, in which he is given such epithets as "king of heaven and earth, judge above and below, lord of the dead, guide of the living" and "judge of heaven and earth." While in the underworld, the sun would bring light and offer judgments on behalf of its residents. However, as we have seen earlier, the netherworld was considered an abode devoid of any light. Addressing this discrepancy, Wolfgang Heimpel states, "The Babylonians may have resigned themselves to conceptual discontinuity: they found it natural that the sun god knew the world below, they saw in their sun god a judge of the living and the dead, and they believed that the dead would not see sunlight in their worldly existence." In other words, as judge over the netherworld, it was not necessarily the case that the Mesopotamians thought the sun traveled through the netherworld, as was the case in Egypt. However, according to MUL.APIN, the sun follows the same path as the moon and the other planets. Since the _Descent of Ishtar/Inanna_ undoubtedly places Venus (Inanna/Ishtar) in the netherworld, it may be the case that all planets were thought to have traversed the nether region during their periods of invisibility.
The more likely scenario, for which there is greater evidence, is that the sun's nocturnal chamber was above the firmament, in the upper heavens. In fact it was widely thought that all the "divine celestial bodies (sun, moon, and stars) pass through doors or gates as they become visible in the sky." We can see a broad example of this idea in the aforementioned _Prayer to the Gods of the Night_.
> The princes are closely guarded
>
> The locking-bolts lowered, the locking rings placed,
>
> (Though previously) noisy, the people are silent,
>
> (Though previously) open, the doors are locked.
>
> The gods of the land (and) the goddesses of the land,
>
> Shamash, Sin, Adad, and Ishtar
>
> Have entered into the lap of heaven.
Jeffrey Cooley rightly notes that this "lap of heaven" refers to the upper heavens, the portion "that is not visible to humanity but in which the gods reside." Access through the firmament for the sun (Shamash), the moon (Sin), Venus (Inanna/Ishtar), storms (Adad) and the constellations (the "gods of the night") was obtained through the portals variously called bolts, bars, doors and gates. The celestial bodies entered and exited through these openings as they moved from the upper heavens to the lower heavens, and vice versa.
_Upper heavens._ As Cooley pointed out, the upper heavens were reserved for the deities, although some deities took up residence in the underworld or the abyss. One clear depiction of the upper heavens is found on a _kudurru_ of the Kassite king Nabu-apla-iddina (see figure 2.10). Although the purpose of the text and its corresponding relief is "to commemorate (Nabu-apla-iddina's) restoration of the temple of Shamash at Nippur," it provides an ancient perspective on the upper heavens. J. Edward Wright offers a concise summary of the imagery as it pertains to the heavenly sphere:
The depiction on this tablet shows Shamash enthroned as king in heaven. Shamash is the large figure on the right seated on a throne that has some zoomorphic characteristics. Above his head are the symbols of the celestial gods Sin (moon), Shamash (sun), and Ishtar (star). The wavy lines at the bottom of this scene indicate water, and beneath the waters is a solid base in which four stars are inscribed. These waters, then, are the celestial waters above the sky. This tablet depicts the god Shamash enthroned as king in the heavenly realm above the stars and the celestial ocean.
The Mesopotamians thought of the upper heavens as a physical realm above the upper waters. Its floor was solid, enabling its residents to stand, sit or otherwise conduct their affairs. Matters in the upper heavens paralleled matters on earth, such that when a king presented himself before the altar of Shamash in that god's temple, it was as if he were standing before the throne of the god above the firmament.
**_Sea._** When we think of water, we have numerous categories for its various locations and sources. The salty oceans encompass the globe as one mass of water, wrapping the continents in its embrace.
**Figure 2.10.** Sun disk tablet of Nabu-apla-iddina
Both the saline seas and the freshwater lakes are surrounded by land. Evaporation carries moisture from these bodies of water into the atmosphere, where it gathers into clouds and falls once again to earth, forming streams and brooks before joining other tributaries in creeks and rivers, as they make their way to sea level. We are also aware that groundwater can be accessed by wells or emerge from springs.
While we see boundaries and distinctions in types and sources of waters, the ancients thought of water in only two forms: fresh and salt. In Mesopotamia, these two sources of water were personified as Apsu and Tiamat, respectively. Tiamat, the sea goddess, derives from the Akkadian word _tâmtû_ , "sea." Apsu is the god of the deep. In both Mesopotamia and Egypt, the entirety of the world was thought to have been encircled by water, but not in the sense that we think of oceans covering over 70 percent of the globe. Rather, earth's disk was surrounded by a mass of water: above, below and all around (see figure 1.1 above). In fact this idea was not unique to the peoples of the ancient Near East; it was ubiquitous in primitive cultures.
_Cosmic ocean._ We saw earlier in this chapter that the ancients conceived of the earth arising out of primordial waters, called the cosmic ocean. Whether floating like a reed mat or supported by subterranean pillars, the earth was thought to be surrounded by these cosmic waters. At its inception, a barrier, or firmament, was placed over the earth to protect it from the upper waters. If not for these cosmic barriers, the cosmic ocean's destructive torrent would bring deluge to the earth by breaking through the firmament, bursting through springs of the deep or crashing over the shores.
In both Egypt and Mesopotamian sources, we find evidence of the cosmic ocean surrounding earth like a moat. We saw this in the _Etana Epic_ and in the _Babylonian Map of the World_ (see figure 2.1 above), in which the earth, depicted as a disk, was at the epicenter of two concentric rings. Likewise, in Gilgamesh's quest to find Utnapishtim, the hero "eventually comes to the shore of the sea that encircles the earth." Several Egyptian pharaohs, such as Thutmose III, Hatshepsut, Amenhotep II and Rameses III, referred to the inhabited world as all that the ocean encircles. In mythological terms, Nun was both the waters of the underworld and "the waters encircling the world, the Okeanos which formed the outermost boundary." Since fresh water flowed into salt water, there is some ambiguity regarding the lines of distinction between the two types of water. In all likelihood, the ancients viewed the salty waters as constituting the top layers of the ocean, while the freshwater Deep lay below the surface.
The cosmic waters were considered the source of chaos, represented by its chief protagonist, the great sea serpent. In the Ugaritic _Epic of Baal_ , this serpent was personified by the seven-headed Litan ( _ltn_ ), who surrounds the earth. The sea serpent representing the cosmic forces of the abyss is also evident in the previously mentioned Babylonian _kudurru_ (see figure 2.3 above). Note the presence of two serpents: one in the depths of the earth and one in the upper heavens, indicating that the cosmic oceans inhabited both the lower and upper heavens. We see this in Egypt as well (see figure 2.4 above). In the first, one serpent encircles the whole earth, while in the second, two separate serpents distinguish between the cosmic waters above and those below, as we saw in the _kudurru_.
_The deep._ The waters of the deep were primarily known as a great mystery, prompting a fear of deep water masses. All land waters were connected to the deep: "waters of the water table just beneath the earth's surface, waters in marshes and swamps, waters in rivers, waters in the sea, and distant cosmic waters." This is not to say that rivers and lakes were bottomless, but that all bodies were connected to the deep, either at their source or their terminal. The connectivity of these waters to the cosmic seas perpetuated a fear that played prominently in a number of Mesopotamian law codes in which accused parties could be subjected to the river ordeal. See, for example, this text from the Law Code of Hammurabi:
If a man charges another man with practicing witchcraft but cannot bring proof against him, he who is charged with witchcraft shall go to the River Ordeal, he shall indeed submit to the divine River Ordeal; if the divine River Ordeal should overwhelm him, his accuser shall take full legal possession of his estate; if the divine River Ordeal should clear that man and should he survive, he who made the charge of witchcraft against him shall be killed; he who submitted to the divine River Ordeal shall take full possession of his accuser's estate.
Since it was assumed that the accused could not swim, his guilt or innocence relied on the divine use of the watery deep.
The fear of the deep is also related to its association with the grave. In the _Epic of Gilgamesh_ , the seas are called "the lethal waters." As Horowitz observes, "Although no text explicitly places dead human beings in the Apsu, there is evidence that the Apsu and underworld were either confused with one another or that the Apsu was thought to be a netherworld inhabited by malevolent spirits." See, for example, this Sumerian-Akkadian bilingual incantation text:
> A black tragacanth grew up in Eridu,
>
> it was created in a pure place.
>
> Its appearance was pure blue, stretching out to the depths.
>
> The way of Ea in Eridu is full of plenty,
>
> His dwelling is at the netherworld,
>
> His sleeping place is the watery deep.
Ea (also known as Enki) was "god of the subterranean freshwater ocean," the Apsu. As god of the Apsu, it is natural that Ea's temple was also located there (see figure 2.11).
**Figure 2.11.** Ea, Mesopotamian god of the deep
_Weather and the waters above the firmament._ In addition to being the abode of divine beings, the heavens were also seen as the most prominent source of precipitation. Clearly this arose from the observation that rain, snow and hail fell from the heavens. If the firmament served to hold back these heavenly waters, then there must have been gates or windows through which these forms of precipitation fell. Storm gods are often depicted in iconography riding on the Bull of Heaven because the sound of a running bull resembled the sound of thunder. They carried lighting as arrows for their divine bows. In Mesopotamia the storm god was Ishkur/Adad. This god was known as the one who rides on the clouds and inspects the canals of heaven and earth. In _Enki and the World Order_ , Ishkur is responsible for opening "the holy bar which blocks the entrance to the interior of heaven." In some texts, the gates are described more graphically as the "teats of heaven." In the Ugaritic _Epic of Baal_ , rain is called "heaven's dew," "the rain of the Rider on the Clouds," "dew that the heavens pour" and that "stars pour out." For the rain to pour from heaven, it was evident to the ancients that there were storehouses of snow and reservoirs of water above the firmament.
**Figure 2.12.** Celestial cow
Although Egypt was not without rainfall, it was certainly less accustomed to seeing precipitation than the civilizations in the Fertile Crescent. Seasonal rains fell, but these showers were insufficient for maintaining civilization. From an observational perspective, then, the waters above the firmament on which the sun bark sailed may have leaked on occasion, as depicted in the image of the celestial cow (see figure 2.12). However, the "teats of heaven" in Egypt did not provide the same level of sustenance as those in Mesopotamia. For the Egyptians, water did not fall from heaven as much as it flowed from the Nile, "which provided irrigation, transportation, communication, drinking water, water for washing, a disposal system, and plentiful fish, fowl, and game." The Egyptians relied on its seasonal flooding for their survival.
This mighty river, whose headwaters trickled four thousand miles south of the Nile delta, obtained divine status in Egypt. Its waters were not merely the result of rainfall on faraway slopes. Instead, the river itself seemed to be the source of all water. According to Mark Smith, "The stones of the mountains grow and flourish because they are watered by the Nile inundation, which is itself said to be the emanation of the Primaeval Ocean." This ocean not only renews the hills and mountains but is also the source of the Mediterranean. In fact in many Coffin Texts, the primeval ocean was a close collaborator in the origins of the entire cosmos. Given that they thought the earth was surrounded by the cosmic seas, it should not surprise us that their chief water source was a percolation of the deep. While the Egyptians thought, like the Mesopotamians and Canaanites, that a ceiling in the sky held back the upper waters, they did not necessarily consider it to be their primary source of water.
_Contrasting Egypt and Mesopotamia._ The contrast between Mesopotamia and Egypt on this particular cosmological feature serves to remind us of two important facts. First, the impetus for the ancient sciences was observational analogy. The inexplicable became explicable through analogies with the ordinary. While the residents of the Fertile Crescent could more readily observe the heavenly origins of precipitation, those in Egypt were less inclined to do so. Moreover, Egypt's northern neighbors were much more inclined to see other types of weather features, such as hail and snow, and figure them into their normative cosmology. Second, due to variations in geography, topography, climate, language, cultural phenomenon and other variables, it is not surprising to learn that not all ancient Near Eastern cosmologies were identical. Of course, there were many parallels throughout the ancient world, but it is too simple to conclude that each region, let alone each person, observed the cosmos similarly. We should not conclude that we cannot speak of ancient Near Eastern cosmological commonalities; however, we must be cognizant of nuances, recognizing that various texts and images demonstrate different perspectives.
#### Summary and Conclusion
Although a thorough examination of all the evidence for ancient Near Eastern cosmologies is beyond the scope of a single chapter, we have seen, nonetheless, certain consistencies among the Egyptian, Canaanite and Mesopotamian sources. Operating from an analogical posture, the ancients concluded that the cosmos consisted of three tiers. Their viewpoint derived from the earth on which they lived and worked. The center of their world was the locus of their residence. For the Egyptians, the center was the Nile, while the Babylonians viewed Babylon as the epicenter. The earth itself was a flat disk, either floating on the cosmic seas or upheld by foundational pillars. Beneath the earth were caverns and catacombs, the dark realm of the dead, as well as the abyss, subterranean rivers and chthonic deities and demons. Suspended over the earth was a ceiling (best described as a firmament), supported by pillars, tent poles and lead ropes, or divine power. It separated the heavens below from the heavens above, both of which constituted the second tier. The lower heavens were occupied by the celestial bodies, while the upper heavens belonged to the divine. In Egypt, the firmament also contained the pathway for the sun god Re as he traversed the sky. Besides separating the lower and upper heavens, the firmament also had the crucial role of controlling precipitation. Its gates and windows regulated the flow of rain, hail and snow from the watery reservoirs above. These cosmic waters constituted the third tier. They surrounded the earth, bubbling up from the deep through springs, rivers and streams or falling from the heavens through windows. These three tiers, the heavens, the earth and the seas, provided the basic structural models necessary for explaining the entire cosmos.
It might be argued that the language used by the ancients is purely phenomenological and did not necessarily represent how they actually thought of the cosmos. That is to say, was this model in reality merely a metaphor for a deeper, more sophisticated understanding of the real nature of the universe? After all, we often use similar language when we speak of the sunset, the depths of the sea, the sky opening up and rain falling from heaven.
There are several reasons we must reject this notion. First, wherever we find physical descriptions of the cosmos, it is described as three-tiered. Second, wherever we find iconographic images or drawings of the cosmos, they are three-tiered. Third, nowhere in the ancient world do we find the authors explaining their cosmology in any other terms besides the three-tiered system. Finally, we know that ancients thought of the cosmos in terms of the heavens, earth and seas because eventually these ideas were challenged by Aristotle and Ptolemy, whose ideas were later challenged by Copernicus, Galileo and Kepler. If the ancients were already thinking in terms of a heliocentric cosmos, in which the spherical earth orbited the sun, there would have been no need for opposition when these cosmological innovations were introduced. In fact, the ancients very much adhered to the concept of a three-tiered cosmos.
# 3
## COSMOLOGY IN SCRIPTURE
During the Aramean siege of Samaria in the ninth century B.C., the king of Israel's chief officer asked the prophet Elisha how a severe famine could conclude abruptly. It was such a preposterous notion that the officer asked, "Even if the LORD were to make windows in the sky, could such a thing happen?" (2 Kings 7:2). Was the officer speaking figuratively or literally? Did he believe water fell from heaven through openings in a firmament, or did he have a workable understanding of the hydraulic cycle? Did he rely on divine intervention for each and every raindrop, or did he recognize the chemical reaction of two parts hydrogen and one part oxygen forming the water molecule? As we look at cosmology in the Bible, it is necessary to keep in mind these types of questions. In short, did the ancient Hebrews think along the same lines as their geographical and cognitive counterparts, or did they think in the same types of terms and categories as modern people?
I have made the case that the ancients conceived of the cosmological structure as it appeared to them observationally and analogically. Although their views were not necessarily in full agreement on every point, there was a general consensus that the cosmos consisted of three tiers: heavens, earth and sea. According to the evidence, therefore, this viewpoint was held throughout the ancient Near East, from Egypt to Anatolia, from the Mediterranean Sea to the Persian Gulf. It is found in mythological texts, military annals, historiography, prayers and hymns, coffin texts, incantations and spells, and iconography. In short, this three-tiered cosmology permeated the ancient world.
Although the mythological constructs of various societies operated within this worldview, these two conceptual realities—mythology and cosmology—did not necessarily overlap. One's view of the cosmos was not inseparably intertwined with one's view of the deities. We need only look at the mythological systems of Egypt and Mesopotamia to illustrate this point, with their different pantheons, temple structures and concepts of the afterlife. In other words, there is no need to dismiss the three-tiered cosmos as "pagan" any more than we should dismiss the Pythagorean Theorem (a2 \+ b2 = c2) simply because it is taught in public schools and secular universities. We accept the validity of the Pythagorean Theorem not on metaphysical grounds but on the repeatable observation that the square of two sides of any right triangle is equal to the square of its hypotenuse.
Since the ancient concept of the three-tiered cosmos was based on observational analysis rather than theological or philosophical grounds, it should not surprise us that the biblical authors also adhered to this cosmological construct. While the purpose of this chapter is to tease out the particulars, there are few instances in which it is stated explicitly. In the first recording of the Decalogue, or Ten Commandments, the creation week is given as the rationale for keeping the Sabbath. "For in six days the Lord made _heaven_ and _earth_ , the _sea_ , and all that is in them, but rested the seventh day; therefore the LORD blessed the sabbath day and consecrated it" (Ex 20:11). Ezra also speaks about the three-tiered cosmos in his prayer of covenant renewal after reading from the book of the law. "You are the LORD, you alone; you have made _heaven_ , the heaven of heavens, with all their host, the _earth_ and all that is on it, the _seas_ and all that is in them" (Neh 9:6). The book of Proverbs refers to it in the father's instructions to his son regarding how the Lord in his wisdom created the cosmos.
> The LORD by wisdom founded the _earth_ ;
>
> by understanding he established the _heavens_ ;
>
> by his knowledge the _deeps_ broke open,
>
> and the clouds drop down the dew. (Prov 3:19-20)
In Revelation, while one angel proclaims the fall of the metaphorical Babylon, another angel shouts, "Fear God and give him glory, for the hour of his judgment has come; and worship him who made _heaven_ and _earth_ , the _sea_ and the springs of water" (Rev 14:7).
These four texts are not sufficient to declare confidently that the whole of Scripture speaks of a three-tiered cosmos. However, they do indicate that at least four different authors along the chronological spectrum in the history of Israel and the church spoke of the cosmos in terms of these three tiers.
As we look through the whole of Scripture, we will note that whenever the biblical authors reference the structure of the cosmos, they do so using the same terminology and conceptual framework as their ancient counterparts. To demonstrate the parallels between the biblical and ancient Near Eastern worldviews, this chapter will follow the outline of the previous chapter. We will first look at the earth's dimensions, foundations and depths. Next, we will investigate the biblical view of the heaven's firmament, its lower heavens and its upper heavens. Finally, we will track the Bible's view of the sea as cosmic ocean, the sea as the deep and the origins of meteorological phenomena.
#### Earth
The ancient Hebrews did not think their planet was a round globe. For that matter, they did not even consider it to be a planet, since planets were in the heavens. Like their surrounding neighbors, the ancient Hebrews believed the earth was a small, round disk supported by pillars. The disk was relatively small by our standards, but its ends could not be reached. Beneath the surface lay the underworld, the final resting place of the deceased.
**_Earth's dimensions._** In the first chapter of Job, the Lord inquires of the Satan's whereabouts, to which the Satan replies, "From going to and fro on the earth, and from walking up and down on it" (Job 1:7). The picture presented here is "like an emperor's spy looking for any secret disloyalty to the crown." Beyond that, the text assumes an earth that the Satan can cover completely by foot, as evidenced by the Hebrew words _šû_ ṭ, "to roam," and _hithalēk_ , "to walk about." These verbs connote wandering around a parcel of land, such as in Numbers 11:8 and Genesis 13:17. In the former, the Israelites roam around ( _šû_ ṭ), picking up manna from the ground. In the latter, the Lord commands Abram to "walk through [ _hithalēk_ ] the length and breadth of the land" because that is the land the Lord would give him. So when the Satan roams about the earth in Job 1 (and again in 2:2), the idea is that the ground he covers encompasses the entirety of the earth.
For the biblical authors the usual way to describe the size of earth was with the phrases "ends of the earth" or "from the rising of the sun to its setting." Of course, we may use similar phrases today for the same purpose. However, when we do, we recognize the immensity of the globe (approximately twenty-five thousand miles in circumference), while also realizing that the farthest we can get from our current location is the opposite side of the globe. This was not the case for the ancients, however. For them, the "end of the earth" pertained to the lateral distance from the eastern horizon to the western horizon. Of the two phrases, "end(s) of the earth" is far more prominent in the Bible, occurring forty-four times. It is found in both poetry and prose, in the Old Testament as well as the New Testament.
In several passages, the phrase "end(s) of the earth" refers to the vastness of God's sovereign reign (e.g., 1 Sam 2:10; Ps 48:10; 72:8; Is 52:10). Elsewhere the phrase indicates the remotest locations of the earth (e.g., Deut 28:49; Is 45:22; Jer 25:31-33; Acts 1:8). Perhaps the most enlightening passage, though, comes from the book of Daniel, when the Babylonian king Nebuchadnezzar recounts this dream to Daniel:
> Upon my bed this is what I saw;
>
> there was a tree at the center of the earth,
>
> and its height was great.
>
> The tree grew great and strong,
>
> its top reached to heaven,
>
> and it was visible to the ends of the whole earth. (Dan 4:10-11)
In Daniel's interpretation, we also learn that the tree provided shade for all the animals of the earth, and shelter for all the birds of the sky. Daniel 4 assumes one of two realities about the biblical view of the earth. One option is that the earth was considered flat. No matter how tall a structure may be, for it to be visible across the earth, the earth must not have a convex surface. More specifically, it cannot be a sphere since the horizon would interfere with one's view of the tree. A second option is that all the inhabitants of a spherical earth dwell on a relatively small land mass in the vicinity of Babylon. The dimensions of the earth must have been extremely constricted, especially in light of modern conceptions. Its dimensions must have been small enough for the massive tree to be seen by those living at its extremities. In East Africa, Mount Kilimanjaro rises approximately seventeen thousand feet above the Serengeti plain and can be seen nearly three hundred miles away. For perspective, it is about two thousand miles from the Persian Gulf to the Mediterranean Sea. This, then, leads us to a third option. Since the Old Testament authors refrained from spherical language regarding the earth, it is almost certain that Daniel also held the view of a small, flat earth.
One might object to the use of a dream for making declarations about a biblical view of the cosmos. It is perhaps even more objectionable that we would look to a dream of a Babylonian king! After all, just because the Bible describes various human perspectives, it does not mean that the divine Author endorses those positions. However, we should note first of all that Daniel himself is not put off by Nebuchadnezzar's views. He sees no reason to clarify the king's misunderstanding of the earth's shape. Second, as Paul Seely rightly notes, "The universal visibility of the tree is predicated upon its height, not upon it being seen in a dream." Even in a dream, the sun is not visible at night because it is on the opposite side of the globe.
Nebuchadnezzar's dream—and Daniel's interpretation of it—relies on a small, flat earth. Finally, the main thrust of this volume is to demonstrate that much of the Bible is, in fact, largely descriptive of the human perspective. Without commending slavery, misogyny, war, monarchies and incest, the Bible nonetheless depicts these customs as legitimate cultural norms. So it should not surprise us that the Bible, through the prophet Daniel, would validate Nebuchadnezzar's vision of a flat earth.
It is sometimes argued that certain biblical passages clearly describe a spherical earth. The arguments stem from the translation of the Hebrew word ḥ _ûg_ as "circle" in Job 22:14; 26:10; Proverbs 8:27 and Isaiah 40:22. Unfortunately, ḥ _ûg_ only occurs four times in the Old Testament, so there is not much lexical evidence on which to base a definitive translation. Even the Aramaic and Syriac cognate _ḥ_ _ugtā_ offers little assistance, since its primary use is in translations of the biblical texts.
What, then, does it mean for the earth to have a circle? First, each of the passages in which we find this description is in a cosmological context. In Job 22:14 Eliphaz states that Job is accusing God of being distant, aloof and blind to Job's situation. God is so distant, in fact, that he "walks on the dome [ḥ _ûg_ ] of heaven." Most Bible translations render ḥ _ûg_ as "vault," because they recognize the cosmological imagery evoked here. John Hartley rightly notes, "From the ancient perspective, when God created the universe, he drew a circle to hold back the heavenly waters from covering the earth (Prov 8:27). His abode is located above this circle." This also seems to be the case in Isaiah 40:22, although both R. N. Whybray and John Oswalt recognize the possibility that the circle may instead refer to the horizon. In both Job 26:10 and Proverbs 8:27, the circle has been inscribed on the face of the waters. In each case the Hebrew root ḥ _q_ is used to define the "limits" of this circle as a boundary line. In terms of ancient Near Eastern cosmography, it is the line that separates the waters above from the waters below, also known as the firmament.
Besides the evidence from the immediate context, we can find other linguistic evidence to rule out the possibility of ḥ _ûg_ referring to a spherical earth. First, Isaiah 44:13 uses another form of the word as the instrument for drawing circles—namely, a compass. Describing how a craftsman makes an idol, the prophet says:
The ironsmith fashions it and works it over the coals, shaping it with hammers, and forging it with his strong arm; he becomes hungry and his strength fails, he drinks no water and is faint. The carpenter stretches a line, marks it out with a stylus, fashions it with planes, and marks it with a compass [ _mĕ_ ḥ _ûgâ_ ]; he makes it in human form, with human beauty, to be set up in a shrine. (Is 44:12-13)
In the ancient world as in the modern world, the compass is an instrument used for inscribing arcs and circles on a level surface, not for shaping balls. Moreover, the Septuagint could have clarified the matter by using the Greek word _sphaira_ ("sphere"), a word available to Aristotle at least a century before the Septuagint was written. However, this is not the case. In three instances, the Septuagint utilizes a form of the word _gyros_ ("ring" or "circle," from which we get our word _gyroscope_ ) in its earthly description. Whereas _sphaira_ is explicitly an orb, _gyros_ most commonly refers to a two-dimensional ring, such as an earring, bracelet or moat. In short, we have no lexical grounds for treating the circle of the earth as anything other than a two-dimensional ring. The biblical authors did not portray the earth as a globe or sphere.
One final point concerning the shape of the earth in the biblical world deserves brief mention. Due to the mention of its four corners, it is sometimes suggested that the ancients thought of the earth as a table, with four square edges. This is not a common feature in the Bible, but we do find the expression "four corners of the earth" in Isaiah 11:12; Ezekiel 7:2 and Revelation 7:1; 20:8. Rather than thinking of these corners in terms of a squared edge, it is best to think in terms of the four compass points, as we saw in the previous chapter. In other words, the phrase "four corners of the earth" seems to have been an idiom related to the four cardinal directions, which encompassed the totality of earth's surface.
**_Earth's foundations._** The biblical record is clear and consistent that the earth is supported by pillars or foundations. The evidence comes to us from both prose and poetry from various books throughout the Bible. In the Old Testament various forms of the Hebrew root _ysd_ are used in the authors' descriptions of building constructions. The foundation itself is called either a _yĕsôd_ or _môsādâ_ , while the act of laying that foundation is _yāsad_. The same words that are used to describe the foundations of a house, temple or palace are the same words used to describe the foundations of the earth. Similarly, in the Septuagint and in the New Testament, the Greek word _themelion_ is used for both the common and the cosmic sense of "foundation." The consistent use of these words for both a building and the earth demonstrates that the biblical authors viewed the construction of the earth on the analogy of a house, temple or palace.
**Table 3.1**
All these were made of costly stones, cut according to measure, sawed with saws, back and front, from the foundation to the coping, and from outside to the great court. The foundation was of costly stones, huge stones, stones of eight and ten cubits. There were costly stones above, cut to measure, and cedarwood. (1 Kings 7:9-11) |
Where were you when I laid the foundation of the earth?
Tell me, if you have understanding.
Who determined its measurements—surely you know!
Or who stretched the line upon it?
On what were its bases sunk,
or who laid its cornerstone? (Job 38:4-6)
---|---
To illustrate the concept of the earth's foundations, let us look at two building texts side by side (see table 3.1). The column on the left describes Solomon's construction of the temple. The column on the right recounts God's construction of the earth. Just as Solomon measured and cut massive stones for the temple's foundation, by analogy, God measured and crafted foundation stones for the earth.
According to the biblical authors, these foundations provide the structural support for the entire earth. The prophet Isaiah provides a clear example of this concept.
> Whoever flees at the sound of the terror
>
> shall fall into the pit;
>
> and whoever climbs out of the pit
>
> shall be caught in the snare.
>
> For the windows of heaven are opened,
>
> and the foundations of the earth tremble.
>
> The earth is utterly broken,
>
> the earth is torn asunder,
>
> the earth is violently shaken.
>
> The earth staggers like a drunkard,
>
> it sways like a hut;
>
> its transgression lies heavy upon it,
>
> and it falls, and will not rise again. (Is 24:18-20)
Isaiah envisions a world upheld by pillars (see 1 Sam 2:8). Like a building in an earthquake, when the earth's foundation shakes, the whole earth trembles.
Unlike Israel's ancient neighbors, there is no indication that the Hebrews had a notion of the earth floating on the cosmic sea. The one possible hint of that idea is found in Job 26:7.
> He stretches out Zaphon over the void,
>
> and hangs the earth upon nothing.
In fact, N. H. Tur-Sinai argues ṣ _āpôn_ ("Zaphon") derives from the Hebrew verb ṣ _ûp_ , "to float," suggesting the void refers "to the miraculous fact that the earth, despite its heaviness, floats on the water." His view has not been adopted by other scholars, and Marvin Pope simply calls the interpretation "bizarre." Although Hartley does not follow Tur-Sinai's reading of ṣ _āpôn_ , he does surmise that the earth "is being pictured as a disk or a plate floating on the deep." Some modern interpreters, wishing to impose modern scientific views onto the biblical text, understand this verse as an indication that the ancients believed the earth was suspended in outer space. Given that elsewhere the author of Job speaks about a God who shakes the pillars of earth (9:6) and heaven (26:11), and who built the earth on foundation stones (38:4-6), this view cannot be sustained. In light of the immediate context, it is clear that Job 26:7 articulates the extent of God's sovereignty—from the top of God's celestial Mount Zaphon to the depths of Sheol, the land of nothingness.
**_Earth's depths._** Beneath the disk-shaped earth was the abode of the dead, sometimes called the "depths of the earth." In the Old Testament, these depths are known as Sheol, Abaddon, the grave, the pit or simply the earth. New Testament references to the abode of the dead are much less prominent, primarily owed to the theological reality of death's defeat through Jesus' accomplished work on the cross (1 Cor 15:50-57). Nonetheless, Hades entails the same concept, and we find allusions to Sheol with the single mention of Abraham's bosom (Lk 16:23). These terms, and the idea they represent, demonstrate a biblical view of the netherworld on par with Israel's ancient neighbors.
As we saw from Job 26:7, God's domain extends from the heights above to the depths below, thus establishing the limits of God's cosmos. It is natural, then, for the Bible to speak of the depths of the earth, or Sheol, as the polar opposite of the world's upper extremity. Job 11 makes use of this cosmological understanding to demonstrate the unfathomable nature of God.
> Can you find out the deep things of God?
>
> Can you find out the limit of the Almighty?
>
> It is higher than heaven—what can you do?
>
> It is deeper than Sheol—what can you know?
>
> Its measure is longer than the earth,
>
> and broader than the sea. (Job 11:7-9)
>
> The psalmist uses the same idea to communicate God's sovereignty.
>
> For the LORD is a great God,
>
> and a great King above all gods.
>
> In his hand are the depths of the earth;
>
> the heights of the mountains are his also.
>
> The sea is his, for he made it,
>
> and the dry land, which his hands have formed. (Ps 95:3-5)
For the biblical authors, Sheol and heaven were opposite sides of the same coin. It was unnecessary, even impossible, to be transported from this world to another world.
> Though they dig into Sheol,
>
> from there shall my hand take them;
>
> though they climb up to heaven,
>
> from there I will bring them down. (Amos 9:2)
Sheol could be reached by descending, whereas heaven could be attained by ascending.
The nature of Sheol in the Old Testament corresponds quite closely with the Mesopotamian view of the KUR.NU.GI.A, "the land of no return," transliterated as Kurnugi in the _Descent of Ishtar/Inanna_. This is especially prominent in the book of Job, whose main character would prefer to cease existence by going to Sheol over continuing his life of misery. The idea that Sheol was the eternal abode of the dead permeates the book but is most clearly indicated in Job's first response to Eliphaz.
> Remember that my life is a breath;
>
> my eye will never again see good.
>
> The eye that beholds me will see me no more;
>
> while your eyes are upon me, I shall be gone.
>
> As the cloud fades and vanishes,
>
> so those who go down to Sheol do not come up;
>
> they return no more to their houses,
>
> nor do their places know them anymore. (Job 7:7-10)
For Job, and the rest of ancient Israel, the grave was literally the final resting place for the dead, as indicated by the parallel word "Abaddon," which means "place of destruction."
As we would expect, the biblical concept of the netherworld coincides closely with the ancient Near Eastern concept. Besides being located in the lowest regions of the earth, entrance to Sheol is accessed by "gates" (Ps 107:18; Is 38:10) or "bars" (Job 17:16). One may return from the gates of the netherworld, but once one has passed through the gates into the netherworld, there is no return (see Jon 2:6-7). We also see in the biblical view of the netherworld a close connection to the ancient Near Eastern concept of passing through water to reach it (Ps 69:1-2; Is 43:2). Yet another characteristic of the biblical netherworld is that it is a place of deep darkness (Job 17:13; Lam 3:6). Finally, the path to Sheol may have been a treacherous one, lined with demons or chthonic deities. This possibility arises from Job 5:7, in which the _bĕnê rešep_ ("sparks") probably refers to the underworld plague demons. While theological clarity would come later with respect to the nature of death and the grave, the ancient Israelites thought no differently about it than did their contemporaries from other nations.
#### Heavens
From the vantage point of earth, the heavens consisted of everything overhead, including the birds, clouds, sun, moon, stars, God and angels. The highest part of heaven belonged to the realm of the divine, while the lower parts of heaven belonged to everything else. It was the upper extreme of the cosmos, at the opposite end of Sheol.
_**Firmament.**_ As was the case in the ancient Near East, biblical authors portrayed the sky as having a solid ceiling, which also served as the floor of God's throne room. Two separate, but related, metaphors were used to describe this ceiling. One appealed to their nomadic past, using tent imagery. The other employs the imagery of a more temporary structure. Of course, both imagine the heavens and earth as a cosmic temple complete with a floor, walls and a roof.
The ancient Hebrews referred to this roof in various ways. One of those ways was by drawing on the parallels of the heavenly canopy with a tent. When we think of tents today, often our first impression is a fully enclosed nylon dome used on brief camping experiences to "get away from it all." It must be kept in mind, though, that in Israel's early days tents served as long-term residences. While we do not have any archaeological evidence of these structures, based on the biblical descriptions of their uses as well as the very detailed description of the tabernacle, we know they must have been constructed of sturdy materials and large enough to shelter families. The canopies of these tents were held upright by strong poles and taut lines. These are the tents to which the ancient Hebrews would have made analogy to the cosmos, and so we see these analogies in Scripture.
We see this most clearly in Psalm 104 and Isaiah 40, texts that will be discussed more fully in chapter four. However, they are necessary here to understand the connection between the cosmos and a tent.
You stretch out the heavens like a tent. (Ps 104:2)
> It is he . . . who stretches out the heavens like a curtain,
>
> and spreads them like a tent to live in. (Is 40:22)
In at least eleven separate places in the Old Testament, we find this idea of God stretching out the heavens. In light of Psalm 104 and Isaiah 40, we should understand this stretching in relation to a tent. As Hartley notes on Job 9:8, "The physical universe is obviously being described on the analogy of a physical building, with the earth as its base and the heavens a canopy above." God has spread the tent canopy of the heavens over the earth, such that it is taut and will not sag or be blown off its support poles by a gust of wind. In other words, the canopy is firmly fixed in place.
In addition to the tent analogy, the ancient Hebrews employed a metaphor more closely resembling a domed structure. The Hebrew word most commonly used for this type of celestial barrier is _raqia_ ʿ. The term is used sparingly in the Old Testament, occurring a mere fifteen times, and has been translated in English Bibles as "dome," "expanse," "firmament," "sky" and "vault." Both the Greek Septuagint and the Latin Vulgate treat the word as referring to a hard dome. At its core, the Hebrew root _rq_ ʿ refers to something that has been spread out, in general, or hammered out, specifically. For example, in Exodus 39:3 gold leaf is hammered ( _rq_ ʿ) for the construction of the priestly ephod. In Numbers 16:38 bronze censers are shaped by hammering ( _rq_ ʿ), and Jeremiah 10:9 describes how silver was hammered ( _rq_ ʿ) to fashion idols. Luis Stadelmann concludes, "The impression most likely left on the modern mind by a survey of these ancient ideas about the shape of the firmament is that of a solid bowl put over the earth, like a vault or heavenly dome." So we see from these examples that the firmament ( _raqia_ ʿ) was compared to hammered metal, like the tin roof on a home.
That the firmament was considered a solid structure is evident in several passages in the Old Testament. The heavens have foundations (2 Sam 22:8), as well as pillars (Job 26:11), are capable of shaking (Is 13:13; Hag 2:6) and can be measured (Job 38:5; Ps 19:4). In Exodus 24:10 the firmament is seen from below as "something like a pavement of sapphire stone, like the very heaven for clearness." The prophet Ezekiel has a similar vision of the firmament, describing it "like a sapphire" (Ezek 1:26; 10:1). Sapphire, of course, is a deep blue gemstone, the color of a cloudless sky. In fact, to illustrate the idea behind it, James Bruckner translates this phrase from Exodus 24 as "clear as the deep blue sky." These physical properties of the firmament are only possible if the heavens were considered a solid surface.
Being a fixed, solid structure, the firmament required support, which was provided by pillars (ʿ _ammûdîm_ ) or foundations ( _môsĕdôt_ ). The former is used with reference to tent poles (Ex 26:32) or columns to a temple or house (Judg 16:25; 1 Kings 7:6). The latter pertains to footers (2 Sam 22:18), such as those found under a building (Ezek 41:8). Both terms have also been used to describe the foundations of the earth (Ps 75:3; Is 40:21). These terms were metaphorical, but in reality the ancient Hebrews thought it was the mountains that provided the firmament's support structure (Job 26:11). With a solid roof and firm foundations, the heavens are just as likely to tremble as a house would during an earthquake (Is 13:13; Hag 2:6).
**_Lower heavens._** The firmament served two purposes. It separated the waters above from the waters below, and it separated the upper heavens from the lower heavens. While the upper heavens were reserved for God and his emissaries, the lower heavens were the realm of planets, constellations, birds and clouds. We would call these lower heavens "sky," or that which can be seen from the earth. In fact, the NRSV often translates _šāmayim_ ("heavens") as "air" or "sky" when referring to overhead objects.
From earth's plane, birds are the closest heavenly bodies. Of course, they occupy both the land and the skies, but when they are high aloft, they are untouchable. For the ancients, who lacked access to the skies, this was especially true. Eagles and hawks could be seen soaring tirelessly above the treetops. Flocks of ducks and other migratory birds passed through the clouds. Even from the peaks of mountains or the heights of plateaus, humans would see these aeronautical wonders achieving great elevations.
The phrase "birds of the air" appears in the NRSV thirty-eight times. In each case, "air" corresponds to Hebrew _šāmayim_ or Aramaic _šĕmayyā_ ʾ _._ In several cases the phrase carries implications of doom and demise, for the most inglorious of deaths is not to be buried with one's ancestors, and to have the birds of the air feed on your corpse (e.g., 1 Sam 17:44; 1 Kings 21:24; Jer 19:7). Elsewhere, however, the phrase is used for showing extremes. For example, in Ezekiel 38:20 "birds of the air" is part of a hendiadys. The list intends to portray everything from one end to the other and everything in between. In other words, all of creation will recognize and fear the Lord. Another instance of hendiadys is found in Zephaniah 1:3, which says,
> I will sweep away humans and animals;
>
> I will sweep away the birds of the air
>
> and the fish of the sea.
>
> I will make the wicked stumble.
>
> I will cut off humanity
>
> from the face of the earth, says the LORD.
Here we see the tripartite structure of the cosmos, with heavens, sea and earth, accompanied by the creatures who occupy each of the three parts: birds, fish and humans.
Just above the birds in the lower heavens (on a typical day) are the clouds. Although clouds should more naturally be thought of in terms of the cosmic sea, their presence in the atmosphere helps us see the relationship between the sky and the heavens. In several poetic passages, clouds are synonymous with the heavens.
> LORD, when you went out from Seir,
>
> when you marched from the region of Edom,
>
> the earth trembled,
>
> and the heavens poured,
>
> the clouds indeed poured water. (Judg 5:4)
> Look at the heavens and see;
>
> observe the clouds, which are higher than you. (Job 35:5)
> Your steadfast love, O LORD, extends to the heavens,
>
> your faithfulness to the clouds. (Ps 36:5)
In these verses the authors use synonyms to convey similar ideas. When you look up as far as you can see, what you see are the heavens, filled with clouds. In fact, in a few places biblical authors write about the clouds being in the heavens, rather than being synonymous with the heavens. For example, after Elijah's infamous showdown with the 450 prophets of Baal on Mount Carmel, the Lord brings an end to the three-year drought. Shortly after Elijah has noticed a small cloud forming in the distance, "the heavens grew black with clouds and wind; there was a heavy rain" (1 Kings 18:45). Similarly, Psalm 147:8 says,
> He covers the heavens with clouds,
>
> prepares rain for the earth,
>
> makes grass grow on the hills.
We see in these passages the idea that the Israelites viewed the clouds as part of the heavens. Since they are visible from earth, they are in the lower heavens.
In the highest level of the lower heavens the ancients would have observed the sun, moon, stars and planets. These celestial bodies could be seen from earth, but even though their view was unaided by telescopes, the ancients intuitively recognized that they must have been very far away (Job 22:12). Clouds could obstruct their view, and birds passed between them and the earth. The occasional eclipse, likewise, would have shown the sun to be more distant than the moon. But they had to be beneath the firmament to be visible at all. Since the cosmos was geocentric, if these bodies fell, they would fall to earth, rather than burn up in outer space (Is 14:12; Dan 8:10; Obad 4).
Sometimes, however, the celestial bodies were not visible, which elicited a couple of explanations. In the case of the sun and moon, one could deduce from their arced paths across the sky that these bodies continued their paths under the earth, arising from the opposite horizon the next day (Ps 50:1; 113:3; Eccles 1:5; Mal 1:11), unless of course their tracks were stopped by divine intervention (Josh 10:12-14). For stars and planets, however, there had to be another explanation. With the emergence of the sun's light each dawn, numerous constellations seemingly vanished into the firmament, and at dusk reappeared in their previous locations. This observation led to two competing explanations. One view was that these nocturnal bodies simply lost their luster in comparison to the brightness of the much larger diurnal luminary, the sun. In this view, the astral bodies were merely "lesser lights" to govern the night (Gen 1:16; Jer 31:35). The alternate view was that the stars must have retreated into celestial chambers where they retired during the daylight hours (Neh 4:21; Job 9:7). While both views were compatible with Yahwistic monotheism, the latter view became somewhat problematic for monotheism, as we will soon discover in our discussion of the upper heavens.
There is little evidence that the ancient Israelites had any notion of the planets as separate from other celestial bodies. There is also little to suggest that they had any notions different from the Babylonians. The only two possible mentions of planets in the Old Testament are Isaiah 14:12 and Amos 5:26. In Isaiah 14 it is fairly certain that "Day Star, Son of Dawn" refers to Venus, the so-called morning star. In Amos 5:26, the Hebrew _kiyyun_ is often translated as "Saturn," but this is highly problematic. In this latter case, the celestial body is not even a planet. In the case of the former, the celestial body is a planet but is identified as a star, the morning star to be precise. In fact the word "planet" never appears in the Old Testament, at least in reference to a celestial body. This is not surprising, since our word "planet" is derived from the Greek _planētēs_ , meaning "wanderer." In the Septuagint the word is only attested in Hosea 9:17 as a translation of the Hebrew _nōdĕdîm_ , referring to those who "flee, escape, wander about." In the New Testament (Jude 13), as with all other early Christian literature, _planētēs_ is used only in conjunction with _asteres_ , "star." So, in the pre-Copernican cosmological systems, planets were viewed as wandering stars, whose heavenly paths were irregular. Incidentally, we will see in the coming chapters that the wandering nature of the planets is what became the most perplexing feature of the Aristotelian and Ptolemaic systems.
While we know that the sun is the source of the moon's light, it is not clear whether the ancients had the same understanding. On the one hand, the Old Testament clearly speaks of the moon's light, often in parallelism with the sun's light. For example, Isaiah 13:10 says,
> the sun will be dark at its rising,
>
> and the moon will not shed its light.
On the other hand, it is likely they would have recognized phases of the moon in relation to the sun's position, or a darkened moon during a solar eclipse. It seems likely that they would have deduced from these astral events that the moon is not its own source of light. Nonetheless, the biblical texts do not offer any confirmation to this effect.
Upper heavens. Popular representations of God have his voice booming from the skies, or an aura radiating from above the clouds. Children learn songs about how to get to heaven . . . and it is not by roller skates or rocking chair! Parents sing hymns about heaven coming down and glory filling their souls. That God dwells in heaven is, perhaps, one of the most commonly held beliefs of people of all faiths. This is no less true in Christianity, historically speaking. When Jesus taught his followers how to pray, he began, "Our Father which art in heaven" (Mt 6:9 KJV). This idea that God is in heaven (and we are not) permeates the biblical record.
As we have already seen, the earth was considered to be covered by a roof. This roof, or firmament, separated the lower heavens from the upper heavens and served as a barrier to the celestial ocean. In Exodus 24:10 Moses, Aaron and his sons see God standing on top of the firmament. In Ezekiel 1:26, God is seated on his throne, which is resting on the firmament. These brief but vivid portrayals of the upper heavens help us see how the ancient Israelites conceived of the realm above what could be seen by typical mortals. The upper heavens, the region above the firmament, was space reserved for the deity.
Twice in Genesis 24 Abraham refers to God as "the LORD, the God of heaven" (Gen 24:3, 7). In an additional twenty verses, we find the phrase "God of heaven." Although the Bible is clear that the entire universe is under God's domain, and that no singular place can contain his presence, heaven is God's supreme abode from where he rules the cosmos. In Job 22, Eliphaz continues his confrontation of the protagonist's wayward theology.
> Is not God high in the heavens?
>
> See the highest stars, how lofty they are!
>
> Therefore you say, "What does God know?
>
> Can he judge through the deep darkness?
>
> Thick clouds enwrap him, so that he does not see,
>
> and he walks on the dome of heaven." (Job 22:12-14)
Eliphaz accuses Job of thinking God is not omniscient, that God is blind to Job's sin. He is not, however, challenging the notion that God dwelled above the firmament. This was a given. The contention was on the perception of what God did from that abode. According to conventional wisdom and orthodox theology, God ruled from that abode, aware of all human thoughts, words and deeds.
From his cosmic temple in the upper heavens, God rules all of creation. His throne is in heaven (Ps 11:4). In the well-known passage of Isaiah's call (Is 6), the prophet sees the Lord sitting on his high and lofty throne, with the hem of his robe filling the temple in Jerusalem. Behind this vision are significant cosmological concepts. The word translated as "hem" (Hebrew _šûl_ ; "train" in some translations) refers to the very edges of the garment, the part of the priestly vestment from which tassels hung. That the temple was filled by this hem conjures the image of a deity who cannot be confined in the temple. Of course, this is in contrast to the commonly held belief that the purpose of a temple was to house the deity and provide a point of intersection between the human and the divine. Isaiah's vision, though, depicts God as uncontainable. If the edge of God's robe filled the temple, and his glory filled the earth (Is 6:3), then God's high and lofty place was in the heavens. This is the image we get in the last chapter of Isaiah.
> Thus says the LORD:
>
> Heaven is my throne
>
> and the earth is my footstool;
>
> what is the house that you would build for me,
>
> and what is my resting place? (Is 66:1)
In anthropomorphic terms, God is so big that as he rests on his throne in the upper heavens he props his feet on the earth. In so doing his robe would extend along the surface of the earth, filling the temple with only its hem.
Ezekiel provides us with another view of God's heavenly throne.
And above the dome over their heads there was something like a throne, in appearance like sapphire; and seated above the likeness of a throne was something that seemed like a human form. Upward from what appeared like the loins I saw something like gleaming amber, something that looked like fire enclosed all around; and downward from what looked like the loins I saw something that looked like fire, and there was a splendor all around. Like the bow in a cloud on a rainy day, such was the appearance of the splendor all around. This was the appearance of the likeness of the glory of the LORD.
When I saw it, I fell on my face, and I heard the voice of someone speaking. (Ezek 1:26-28)
In this account we notice several descriptors relating to God's throne in the upper heavens. First, God's throne is above the firmament. Ezekiel 1:22 describes the firmament as "like a dome, shining like crystal, spread out above their heads." Second, the throne only resembles a throne. The prophet can only describe it in terms with which he is familiar, but the description cannot be precise. Third, the throne room is awesome in appearance, requiring multiple metaphors to describe it, such as amber, fire and rainbows. Together with Isaiah 6 and Isaiah 66, Ezekiel shows that God's heavens are not the same as the heavens in which the birds fly, the clouds float or the stars hang.
As we saw in the previous chapter, in the ancient Near East the upper heavens were the realm of all deities. Although in the Hebrew Bible the Lord is the chief deity of the upper heavens and he is the God of heaven, there is room for other divine or semidivine beings. These beings go by various names in the Old Testament, but collectively they are commonly referred to as the divine council. According to Samuel Meier, "God's council was composed of numerous supernatural creatures associated with the stars and planets and the rule of the cosmos: 'all the host of heaven' (1 Kings 22:19), the 'sons of God' (Job 1:6; 2:1), and 'seraphs were in attendance above him' (Is 6:2)." To this list we could also add divine messenger-warriors who travel from the divine to the earthly realms (Gen 19:1; 28:12; 2 Sam 24:10-17; 2 Kings 19:35; Ps 148:1-4), named angels like Gabriel (Dan 8:16; 9:21) and Michael (Dan 12:1), cherubim who guard God's sanctuary (Gen 3:24; Ex 25) and carry his throne (Ezek 10), and the Satan (Job 1:6-12; 2:1-7; Zech 3:2). In the case of the Satan, it is interesting to note that in the book of Job, this chief adversary is not only free to roam the earth (Job 1:7; 2:2) but also has access to the upper heavens (Job 1:6; 2:1). On rare occasions, humans would have access to the upper heavens. However, physical access to the upper heavens for humans was especially rare. The only two who did make the journey were Enoch (Gen 5:21) and Elijah (2 Kings 2:11), and these men ascended _prior_ to dying. As in the ancient Near East, the upper heavens described in the Old Testament were reserved for the divine. In the Bible, then, the "King of heaven" (Dan 4:37) was the sole arbiter of those who had the pleasure of serving in his court and standing in his presence.
In the discussion of the lower heavens I noted that one of the views concerning the celestial bodies posed challenges to Israel's monotheistic religion. Under the influence of the ancient Near Eastern worldview, in which natural and celestial phenomena were deified, the Old Testament authors and prophets found themselves battling astral worship. The biblical prohibitions against such practices demonstrate clear evidence of its practice.
Since you saw no form when the LORD spoke to you at Horeb out of the fire, take care and watch yourselves closely, so that you do not act corruptly by making an idol for yourselves, in the form of any figure—the likeness of male or female, the likeness of any animal that is on the earth, the likeness of any winged bird that flies in the air, the likeness of anything that creeps on the ground, the likeness of any fish that is in the water under the earth. And when you look up to the heavens and see the sun, the moon, and the stars, all the host of heaven, do not be led astray and bow down to them and serve them, things that the LORD your God has allotted to all the peoples everywhere under heaven. (Deut 4:15-19)
The temptation was all too strong to view these bodies as more than just luminaries in the sky "to rule over the day and over the night" (Gen 1:18). "The ancients were led to worship the celestial bodies because their livelihood depended on nature, and these objects (i.e., their size, movements, etc.) are related to seasonal changes. Moreover, it is clear that the people thought that the stars were manifestations of gods or heavenly beings." In this view they were not just in the firmament but also above it, in the abode of the divine (2 Kings 21:3; 23:4; Jer 7:18; 44:17-25). In Israelite monotheism the problem was not that personified stars might be deemed angelic but that they would be worshiped. It was acceptable for stars to be part of God's divine council (Judg 5:20; Job 38:7). It was not acceptable for stars to be worshiped as equal to or superior to Israel's God.
#### Sea
The third tier of biblical cosmology is the sea. As was the case with ancient Israel's neighbors, the land mass they called earth was thought to be surrounded by water—east and west, above and below. The ends of the earth were sometimes demarcated by the seas on either side. Weather came from the storehouses in the heavens, while springs from the deep fed the rivers and watered the earth. Although water was necessary for life, the cosmic sea held the potential for disaster, unless its Creator placed it under his control.
**_From sea to sea._** Earlier in the chapter we looked at the earth's dimensions with respect to the phrases "ends of the earth" and "from the rising of the sun to its setting." We use this kind of language for measuring various sorts of objects. So we may speak of the length of a football field as "end zone to end zone," or its width as "sideline to sideline." We often hear about "bumper-to-bumper" warranties, "wall-to-wall" carpet or being drenched "head to toe." Sometimes, though, it is useful to provide the parameters of something based on what lies just beyond the scope of the thing being measured, especially when what lies beyond is especially noteworthy. The United States could be described as stretching from the Atlantic to the Pacific (from sea to shining sea), or from Canada to Mexico. So it is in the Old Testament that three biblical authors refer to the whole extent of earth as _miyyām ad yām_ , "from sea to sea" (Ps 72:8; Amos 8:12; Zech 9:10). Another idiom that may apply is the twice-used idea that the earth extends from the eastern sea to the western sea (Joel 2:20; Zech 14:8). In both places the idiom seems to imply the outermost boundaries of the earth, although commentators are not in agreement. While the eastern and western seas may simply be references to the Mediterranean and Dead Seas, their use in these two passages suggests a broader geographical boundary. In fact, these seas are not mere geographical markers but cosmological markers that encompass the breadth of Yahweh's reign. In other words the full extent of God's sovereignty is from one cosmic sea to the other.
**_Weather and water above the firmament._** The firmament served two functions. It separated the realm of the divine from the realm of mortals, and it separated the waters above from the waters below (Gen 1:6-8; Ps 148:4). It is well attested in the Old Testament that rain, dew, snow, hail and lightning come from heaven.
Then Moses stretched out his staff toward heaven, and the LORD sent thunder and hail, and fire came down on the earth. And the LORD rained hail on the land of Egypt. (Ex 9:23)
> For as the rain and the snow come down from heaven,
>
> and do not return there until they have watered the earth,
>
> making it bring forth and sprout,
>
> giving seed to the sower and bread to the eater. (Is 55:10)
>
> When he utters his voice there is a tumult of waters in the heavens,
>
> and he makes the mist rise from the ends of the earth.
>
> He makes lightnings for the rain,
>
> and he brings out the wind from his storehouses. (Jer 51:16)
The ancient Israelites believed that above the firmament were heavenly reservoirs where precipitation was stored for the proper time (Deut 28:12; Job 38:22; Ps 137:7; Jer 10:13; Amos 9:6).
Exactly where these reservoirs were thought to be located is uncertain. Modern depictions of biblical cosmology tend to situate them between the firmament and the upper heavens (Ps 29:10). In these representations the heavenly waters are seen as occupying a convex planar tube. This may in fact be how the ancient Israelites viewed the heavenly waters. However, we might also consider the possibility that these reservoirs were in the upper heavens, in the divine realm, since weather is one of many weapons in God's arsenal (e.g., Ex 9:22-34; Job 37:1-6; Ps 147:16-18). It makes sense that they would be available to him in the upper heavens, to be at his ready disposal (Job 38:22-24). Moreover, the motif of rivers flowing from God's sanctuary is common in the Bible (Gen 2; Ezek 47; Rev 22), so it seems there was a view that the source of all water was God's throne room. On the other hand, given the boundless limits of God's power in the Bible, it really does not matter where the weapons are stored. In anthropomorphic terms, they may have been issued just as easily by his voice as by his hands.
Since the firmament was considered to be a hard, nonporous surface whose function was to hold back the heavenly waters, there had to be sluice gates or retractable windows to allow the heavenly waters to leak to earth. We find textual evidence for these windows (ʾ _ӑ_ _rubbôt_ ) in only six Old Testament verses (Gen 7:11; 8:2; 2 Kings 7:2, 19; Is 24:18; Mal 3:10), but related Hebrew words indicate holes in a roof (Hos 13:3), in a house (Jer 9:21) or in a person's head as eyes (Eccles 12:3). Moreover, if we read these passages in light of their ancient Near Eastern context, it is clear that these are the slits in the firmament by which precipitation exited the upper heavens.
Two of the instances of ʾ _ӑ_ _rubbôt_ occur in 2 Kings 7, the passage with which we began this book and to which we returned at the opening of this chapter. In response to Elisha's prediction that by the next day crop prices would dramatically drop (see 2 Kings 6:25), the king's chief officer says, "Even if the LORD were to make windows in the sky, could such a thing happen?" (7:2, 19). What Elisha was promising was not possible, even if it started to rain immediately. In the ancient Near East, "metaphors such as locks, bolts, bars, nets, and so on were used to express how the sea was kept in its place." The metaphor is also at work here. The royal official appeals to the common understanding of his day that for rain to fall the heavenly reservoirs would need to be accessed. The most logical access was through sluice gates in the firmament.
Water beneath the earth. I noted in the last chapter that Mesopotamians thought of the cosmic waters in two parts: fresh water of the deep (Apsu) and salt water of the sea (Tiamat). In ancient Israelite cosmology the sea ( _yām_ ) referred to the cosmic ocean, the third part of the tripartite structure of the cosmos. The deep ( _tĕhôm_ ) "normally refers to the subterranean waters, . . . though it can also refer to the 'flood' caused by an overflow of the underground water (cf. ʾ _ēd_ in Gen 2:6) as well as to a huge mass of waters, such as _tĕhôm_ in Gen 1:2." Although they go by different names, the concepts are quite similar.
Beneath the earth lay the source of streams and rivers (Deut 8:7; Job 38:16; Prov 8:24), lakes and ponds (Ps 33:7; Is 41:18), aquifers and freshwater wells (Gen 26:19; Ps 78:15). In an evocative prophecy against Assyria, Ezekiel utilizes the cosmological concept of the deep to describe her luxury.
> Consider Assyria, a cedar of Lebanon,
>
> with fair branches and forest shade,
>
> and of great height,
>
> its top among the clouds.
>
> The waters nourished it,
>
> the deep [ _tĕhôm_ ] made it grow tall,
>
> making its rivers flow
>
> around the place it was planted,
>
> sending forth its streams
>
> to all the trees of the field.
>
> So it towered high
>
> above all the trees of the field;
>
> its boughs grew large
>
> and its branches long,
>
> from abundant water in its shoots. (Ezek 31:3-5)
According to this view it is the _tĕhôm_ , not mountain runoff, that is the source of the Tigris and Euphrates Rivers.
In biblical cosmography the deep is at the opposite end of the cosmos from heaven (Gen 49:25; Deut 33:13; Hab 3:10), at the remotest end of the cosmos (Ps 68:22; Mic 7:19). As such it was also viewed at times as synonymous with Sheol (Job 26:5; Ps 69:14-15; Jon 2:3-5). So it was the deep that covered Pharaoh's army (Ex 15:5; Neh 9:11; Is 51:10; 63:3) and required the Lord's strength to protect his own from it (Is 51:10).
**_God's control over the cosmic sea._** Since the earth was deemed to be encapsulated in water, human existence was quite perilous. Should the windows of heaven fail to open, drought would ensue, resulting in famine, starvation and death. If those windows remained open too long, or if the fountains of the deep burst open, or if the rivers and oceans encroached too far onto land, the waters would engulf the living, wash away crops and destroy habitat. Due to this precarious balance between not enough water and too much water, the ancient Israelites were very aware of the need for God to control the cosmic sea.
While driving in the western United States, it is not uncommon to cross a bridge with a sign naming the river over which the bridge passes, only to discover that the so-called river is but a sandy ditch. In Hebrew, such a dried river bed is called a _nā_ ḥ _al_ , or wadi (e.g., Num 6:23), which contains water only during the rainy season. In a semiarid climate like the southwest United States or Syria-Palestine, where the rainy season lasts only a few months, fresh water is not taken for granted. Precipitation of any sort is a welcome necessity. When it fails to come, wells dry and rivers become wadis. In the Bible, God controls the weather by either shutting up the heavens (1 Kings 8:35; Job 12:15) or opening its windows (Gen 27:28; 1 Sam 12:17; 1 Kings 18:1; 2 Chron 6:27). There was a direct correlation between precipitation and obedience to God (Deut 28:12, 23). In the absence of God's beneficence, all Israel would be like one of those wadis—an unproductive, uninhabitable, sandy wasteland (Is 45:18).
It is not only precipitation that God regulates. He controls all the waters encircling the cosmos (Ps 77:14; 135:6; Amos 7:4; Hab 3:10). One of the more prominent themes throughout the Old Testament is God's redemption of Israel through the miraculous event of crossing the Red Sea as they made their exodus from Egyptian bondage.
And you divided the sea before them, so that they passed through the sea on dry land, but you threw their pursuers into the depths like a stone into mighty waters. (Neh 9:11)
> Was it not you who dried up the sea,
>
> the waters of the great deep;
>
> who made the depths of the sea a way
>
> for the redeemed to cross over? (Is 51:10)
In their escape, God controlled the waters of the depths so the Israelites could cross safely, while the Egyptians drowned.
The flood narrative of Genesis 6–9 most poignantly expresses God's sovereignty over the cosmic seas.
For my part, I am going to bring a flood of waters on the earth. (Gen 6:17)
On that day all the fountains of the great deep burst forth, and the windows of the heavens were opened. The rain fell on the earth forty days and forty nights. (Gen 7:11-12)
As John Walton says, "In all of these texts it is the cosmic waters of every sort that are involved in the flood. The act of creation had involved setting boundaries for the cosmic waters. In the flood the restraints were removed, thus bringing destruction." In Genesis 6–7 God has reversed the creation of Genesis 1, in which God separated the waters above from the waters below, and the land from the sea. Now all the waters above and below converge on land, burying it under a heap of cosmic waters. This did not happen as a result of a monsoon or tsunami. The catastrophic flood of Genesis 6–7 only happened because God removed the boundaries of the deep and threw open the heavenly sluice gates.
In several places in the Old Testament God's sovereignty over the seas is represented in mythological terms, borrowing from terminology known to the ancient Israelites from their neighbors. These are Leviathan, Rahab, Tannin and Yam. In Canaanite literature from Ugarit, Leviathan is known as _ltn_ ( _lītānu_ ), a "primeval sea-serpent thought to surround the earth." In the Old Testament, Leviathan represents the chaos of the cosmic sea that only God can subdue (Job 41:1; Is 27:1). Rahab recalls the ancient times when Yahweh defeated and subdued the sea at the time of creation, as in Psalm 89:8-10:
> O LORD God of hosts,
>
> who is as mighty as you, O LORD?
>
> Your faithfulness surrounds you.
>
> You rule the raging of the sea;
>
> when its waves rise, you still them.
>
> You crushed Rahab like a carcass;
>
> you scattered your enemies with your mighty arm.
Yet another of Yahweh's subjugated foes of the sea is the Tannin, "a sea monster (or dragon) who served in various texts as a personification of chaos or those evil, historical forces opposed to Yahweh and his people." In cosmological contexts the Tannin represents the sea, over which God has control (Gen 1:21; Job 7:12). The last of the terms with which we are concerned is _yām_ , the Semitic word for "sea." In most cases in the Hebrew Bible, _yām_ simply refers to a large watery mass, or to the cosmic ocean. However, in some cases the authors personifies these waters, as in Psalm 89:9, or in Nahum 1:4, where Yahweh "rebukes the sea," or Habakkuk 3:8, where the prophet wonders if Yahweh's rage is "against the sea." While scholars disagree on how exactly these characters function in the Old Testament, what is clear is that the Scriptures portray the seas as being under God's command. While Israel's neighbors deemed it a chaotic abyss teeming with divine torment, the sea posed no threat to the Creator of the heavens, earth and seas.
#### Summary and Conclusion
Given that the ancient Israelites breathed the same cultural air as their geographical neighbors, it is no wonder that the biblical view of the cosmos has much in common with the broader ancient Near Eastern worldview. In the Bible and in ancient Near Eastern literature and iconography, the earth was considered a flat disk, not a sphere, supported by foundational pillars. It was a relatively small plot of land, whose four compass points indicate the ends of the earth. Sheol, or the abode of the dead, lay beneath the earth. This "land of no return" was situated at the opposite end of the cosmos as the heavens. The heavens were divided into the lower and upper heavens by a dome or tent-like structure known as the firmament. In the lower heavens were the birds, planets and stars. The upper heavens were reserved for deities and angels. Surrounding the entire cosmos were the cosmic seas. The seas above were suspended by the firmament, which had windows through which precipitation fell. The seas below, also known as the deep, were the source of springs, wells, rivers and lakes. The seas were also the source of chaos, or at least potential chaos, whose powers needed to be constrained. Although some of the specifics vary between Egypt, Mesopotamia, Syria and Israel, this general cosmological viewpoint was held throughout the ancient Near East.
Due to the lack of complete uniformity among the various ancient cultures, there are some subtle differences between the ancient Hebrews' view of the cosmos and those of their neighbors. First, we do not find any evidence in the Bible of the notion that the earth floats on the cosmic ocean. Second, while the Bible makes several references to a Tree of Life, which is commonly found at the center of God's sanctuary (Gen 2:9; 3:22-24; Rev 22:2), its function is not to bind the three tiers of the cosmos, as is the case in the ancient Near Eastern literature. Third, while astral worship was prominent in the ancient Near East, it is systematically denounced in the Bible. Finally, in the ancient Near East celestial bodies retired to heavenly chambers at the conclusion of their shift. In the Bible, there is no evidence of this.
These similarities, and even the dissimilarities, indicate that the biblical authors were not engaged in a systematic correction of the pagan worldviews. We do not see these authors writing apologetical treatises against the scientifically naive viewpoints of their uninspired neighbors. They do not speak of atmospheric pressure systems affecting weather. We do not read about the gravitational pull of the planets, the solar orbit of the earth or the earth's rotation on its axis. The texts do not inform us of faraway galaxies, supernova, comets or black holes. In short, the biblical authors wrote according to the best scientific evidence of their time, an observational viewpoint that was best expressed through analogy and phenomenological language.
# 4
## COSMOLOGY AND COSMOGONY IN SCRIPTURE
The New Testament begins in a peculiar fashion. Rather than giving us one authorized version of the life of Jesus, it provides four separate accounts of his life and ministry. Sometimes the variety of perspectives gives the modern reader fits, leading to the so-called Synoptic problem. In short, the Synoptic problem "is the attempt to explain how Matthew, Mark, and Luke agree, yet disagree, in these three areas: content, wording, and order." Evidence for the problems is well attested, but a few examples here will be helpful for the point I will soon be making.
1. Who approached Jesus about the sick slave of the centurion, the centurion himself (Mt 8:6) or his friends (Lk 7:6)?
2. When Jesus calmed the sea, did his disciples call him Lord (Mt 8:25), Teacher (Mk 4:38) or Master (Lk 8:24)?
3. Who gave the Great Commandment, Jesus (Mt 22:34-40; Mk 12:28-34) or a teacher of the law (Lk 10:25-28)?
4. How many donkeys did Jesus use in his triumphal entry, one (Mk 11:1-11; Lk 19:28-40) or two (Mt 21:1-11)?
For some, these discrepancies provide all the proof they need to discredit the Bible's reliability as a source of history, and by extension, theology. For others, these issues pose no problems, but represent various human perspectives on the same events. What is without dispute is that the Synoptic problem demonstrates the multitextured nature of the biblical record. Even though the presence of four Gospels, rather than just one, presents us with a few interpretive challenges, we are grateful for the more comprehensive portrait of Christ.
The Old Testament seemingly begins with less confusing messages. The first chapter is a narrative of the beginning of the cosmos, in a book that emphasizes beginnings: humanity, sin, murder, nations and Israel. Genesis 1 is systematic. It is laid out in a sequential framework and has a certain orderliness and simplicity to it that suggests it carries the lone authoritative word on creation. But such a view fails to take into consideration the many other creation accounts in the Old Testament, including the very next chapter of the book.
Although creation is referenced and alluded to throughout the Hebrew Bible, God's creative activity is specifically recounted in at least thirteen separate passages: Genesis 1, Genesis 2, Exodus 20:8-11, Nehemiah 9:6, Job 38:2-11, Psalm 8:3-8, Psalm 19:1-6, Psalm 74:12-17, Psalm 95:1-7, Psalm 104:1-17, Psalm 136:1-9, Proverbs 8:22-36 and Isaiah 40:12. Several generalizations may be made regarding the various creation accounts. First, with the exception of Genesis 1, the days of creation are irrelevant. Second, the order of creation varies. Third, creation is always recounted in poetic language, or highly stylized prose. Fourth, the general act of creation is consistent throughout the biblical witnesses. Fifth, the theology of creation is consistent throughout the biblical witnesses. Finally, the cosmological perspective is consistent with the three-tiered cosmological worldview of the ancient Near East.
In the previous chapter we looked at how the three-tiered cosmological framework was evident throughout the Old Testament. In this chapter we will focus our attention on the creation passages just mentioned. There are two reasons for doing this. First, it highlights the diversity of creation accounts in the Old Testament so we can appreciate the broader Old Testament testimony to God's creative activity. Second, it allows us to see highly concentrated cosmological language employed by an array of biblical authors. Whereas in the last chapter I predominantly cited isolated verses to demonstrate cosmological features in the Hebrew Bible, in this chapter we will be able to see entire literary units utilizing imagery and metaphors that assume the ancient Near Eastern cosmological worldview.
In the last two chapters I have been making the case for a three-tiered cosmological structure, first in the ancient Near East, then in the Old Testament. As such, the chapters were organized according to the structural features of the cosmos: earth, heaven, sea. In this chapter, however, I look at the cosmological features within a given creation account. As a result this chapter resembles a series of commentaries. Due to the theological, historical and cultural interests contained within each account, these passages have been well treated in commentaries, monographs and journals. It is not my objective to rehash all the arguments made in the history of scholarship. Rather, my objectives for this chapter are (1) to provide a basic understanding of the consensus of scholarship, and (2) to help readers of the Bible become more aware of the cosmological worldview assumed by the biblical authors and their original audiences.
#### Genesis 1
The literary structure of Genesis 1 has been well documented, dating back at least as far as Thomas Aquinas in the thirteenth century A.D. He calls the first three days "the work of creation," in which God created a formless heaven and earth. The last three days of creation he calls "the work of distinction," in which "heaven and earth were perfected, either by adding substantial form to formless matter, as Augustine holds, or by giving them the order and beauty due to them." The heavens were adorned with luminaries, the waters were adorned with fish and birds (Aquinas says that air and water were considered the same thing in Gen 1), and the earth was adorned with animals and humans. In the middle of the last century, W. H. Griffith Thomas formalized the observation such that his chart is replicated in numerous study Bibles and commentaries.
**Table 4.1**
**Forming** | **Filling**
---|---
Day 1: light and dark | Day 4: lights of day and night
Day 2: sea and sky | Day 5: creatures of water and air
Day 3: fertile earth | Day 6: creatures of the land
Genesis 1, then, presents the creation in a neat literary package, with the first three days of forming the space that would be filled by the creatures of days four through six. The stylistic beauty of Genesis 1 does not stop there, though. Each day has a recurring, formulaic structure:
> Then God said . . . let there be/let _x_ do . . . and it was so
>
> Then God saw that it was (very) good
>
> There was evening and there was morning, day _n_.
While it is a stretch to call Genesis 1 "poetry," it is clear that it is highly stylized prose. The style of Genesis 1 is unlike any other prose in the Hebrew Bible. This is not simply due to the orderliness of God's creative act, since as we will see there were certainly other ways to present the creation event. Instead the account of Genesis 1 should indicate to the reader that the interests of its author lie in the theological message of its contents, not necessarily in scientific precision, especially given that in all of Scripture "there is not a single instance in which God revealed to Israel a science beyond their own culture."
**_Day one._** On day one of creation in Genesis 1, there are three vivid parallels to ancient cosmology. The first is the use of the merism "heavens and earth." The pairing of the heavens and the earth is a reference to "the totality of cosmic phenomena." Next, we see a preordered cosmos, as expressed by the phrase _tōhû wābōhû_ , "formless void." Although some modern commentators like to view this as chaos, it is better to understand it as "unproductive and empty, uninhabited," or "nonproductive, nonfunctional, and of no purpose." The earth is incapable of being productive, as its present condition is engulfed in the cosmic ocean, "the deep" ( _tĕhôm_ ). The vision of the cosmos in these first verses of Genesis is one in which the entirety of an uninhabitable earth is submerged in a dark abyss, one only God can make hospitable to life and productivity.
_**A second day.**_ On a second day, God began the process of making earth habitable and functional by separating "the waters from the waters" (1:6). By placing a firmament ( _rāqîa_ ʾ) in the heavens, God placed a roof over the earth to hold back "the waters that were above the dome" (1:7). Since God's wind "swept over the face of the waters" in 1:2, the waters seem to have originally been a massively deep, dark abyss. When God set the firmament in place, then, some of the waters must have been pushed upward, to form the waters above. Umberto Cassuto imagines the scene of day two as follows:
Thus as soon as the firmament was established in the midst of the layer of water, it began to rise in the middle, arching like a vault, and in the course of its upper expansion it lifted at the same time the upper waters resting on top of it. . . . Above now stands the vault of heaven surmounted by the upper waters; beneath stretches the expanse of lower waters, that is, the waters of the vast sea, which still covers all the heavy, solid matter below.
The firmament is then given the name "heaven" ( _šāmayim_ ).
**_A third day._** The process of productivity continued on a third day with God separating water from land so that earth could bring forth vegetation. Here we see the waters gathering into "one place," rather than many oceans, seas, lakes and ponds. That the waters below the firmament were gathered "into one place" only makes sense in an ancient cultural context, in which "one place" stands "in contrast to an implied 'every place' when the waters covered the whole earth." This "one place" probably refers to the cosmic ocean that encircles the earth and flows beneath it, and is the source for all bodies of water. Theologically it is important to recognize that for the ancient audience it was God who assigned these waters to designated spaces (Job 38:8; Jer 5:22). It was only with divine approval that they could breach their barriers (Gen 6–9).
**_A fourth day._** Although undefined light has already been present in the cosmos, the luminaries are finally placed "in the firmament." In the previous chapter, we saw how the ancient Hebrews had different views on the locus of the luminaries, whether they belonged in the upper heavens or the lower heavens. Here, though, they are "fixed in a solid dome," like glow-in-the-dark stickers on a child's bedroom ceiling. In a direct assault against astral worship, the sun and moon are not identified by name but are simply called the greater light and the lesser light. Although only one of these two celestial bodies actually emits its own rays, they are both called lights ( _mĕ_ ʾ _ōrōt_ ), a thought that is consistent with ancient cosmology. Incidentally, the word translated as "lights" ( _mĕ_ ʾ _ōrōt_ ) is identical to the term that refers to the lamps used in the tabernacle (e.g., Ex 25:8; 27:20; 35:8; Lev 24:2; Num 4:1-49). Almost as an afterthought, the author also mentions the stars, which probably included the five visible planets, Mercury, Venus, Mars, Jupiter and Saturn.
**_A fifth day._** On a fifth day, God makes sea creatures and sky creatures. Birds "fly above the earth across the dome of the sky" (1:20). Similar to the luminaries in the firmament, from the perspective of an earthbound observer the birds appear to move "on the face of" it, skirting the bottom of the heavenly firmament. In the opposite region of the cosmos, the seas brought forth "living creatures." There is no distinction between fresh water and salt water, only seas, an allusion to the cosmological view that all waters were connected to the cosmic seas. Within the seas reside the _tannînīm_ (plural of _tannîn_ ), "the great sea monsters." We have already seen that the _tannîn_ often represents a cosmic foe of Yahweh. In Genesis 1:21, though, these sea monsters are just one of God's creations, along with "every living creature that moves, of every kind, with which the waters swarm," affirming once again that Genesis 1 is antimyth.
**_The sixth day._** For the first time in this creation account, the definite article is used in conjunction with one of the days of creation. The first five days have merely been "a day," but on day six it is "the day." The conclusion of the creative event is the land creatures, corresponding with the land and vegetation of day three, culminating with the creation of humanity, both male and female. From a cosmological perspective, the day highlights the unity of the three tiers. Humanity's dominion would encompass creatures from the entire cosmos: fish of the sea, birds of the heavens and living creatures of the earth.
**_The seventh day._** The seventh day begins the same way the first day did, with the merism "the heavens and the earth." It is also worth noting that unlike days one through six, day seven has no "morning and evening," leading many early Jewish and Christian commentators to interpret the seventh day as the messianic age or "the Day of the Lord," and the first six days as eras. While establishing the Jewish custom of Sabbath, it is of greater significance that God is established as the sovereign ruler who "rests" over all his creation.
#### Genesis 2
Even the most casual reader recognizes that Genesis 2 has a different feel from Genesis 1. Beginning with Genesis 2:4, the dissimilarities are more obvious than the similarities (see table 4.2).
**Table 4.2**
| **Genesis 1** | **Genesis 2**
---|---|---
**Narrative Focus** | creation of cosmos | creation of man and woman
**Setting** | cosmos | Garden of Eden
**Divine** **Name** | God (Elohim) | Lord God (Yahweh Elohim)
**Characters** | God | God, the man, the woman
**Length of Creation** | seven days | "on the day"
**Means of Creation** | divine speech:
"God said" | divine activity:
God planted, took, spoke directly to the man,
formed, took one of the man's ribs, brought
the woman to the man
**Creation Type** | general:
God; earth; waters; plants; "greater light and
lesser light"; birds of the sky; swimming
creatures; living creatures; humanity | specific: four named rivers; three named regions;
three named gems; two named humans;
two named trees; one named deity
Order of Creation | vegetation (day 3)
birds and fish (day 4)
land animals (day 5)
humans (day 6) | man (2:7)
vegetation (2:8-9)
land animals and birds (2:18-20)
woman (2:21-25)
Not only does Genesis 2 look different from Genesis 1, but it also has a different function in the broader narrative of the Bible. Genesis 1 can stand alone as a story. While Genesis 2 could stand alone, it serves as the background for Genesis 3 and the rest of the Old Testament narrative.
Genesis 2:4 is structured as a chiasm, a literary structure that emphasizes the central element. "These are the generations [ _tôlĕdôt_ ] of
> A the heavens
>
> B and the earth
>
> C when they were created.
>
> Cʹ In the day the LORD God made
>
> Bʹ the earth
>
> Aʹ and the heavens."
The central elements, "created" and "made," draw attention to the function of this particular genealogy. In Genesis there are thirteen sections introduced by the _tôlĕdôt_ formula. In most cases, the formula precedes a genealogical record, but here and in Genesis 25:19 and Genesis 37:2 it is used idiomatically to refer to a "record of events." In each case it serves as an introductory statement to the following narrative material. In this case it introduces the creation of the cosmos, as indicated by the phrase "heavens and earth" and its chiastic counterpart, "earth and heavens."
As such, the delineation of the cosmos in Genesis 2:5-24 is much more narrowly focused than what was outlined in Genesis 1:1–2:3. In Genesis 2 our view of the cosmos is restricted to its center, the Garden of Eden, depicted here as a type of temple, which was viewed in the ancient world as the center of the cosmos. As Gordon Wenham notes, "The garden of Eden is not viewed by the author of Genesis simply as a piece of Mesopotamian farmland, but as an archetypal sanctuary, that is a place where God dwells and where man should worship him." That Eden represents God's temple, the intersection of heaven and earth, is evident from tabernacle and temple descriptions elsewhere in the Bible (e.g., Ex 25–40; 1 Kings 6; Ezek 47; Rev 21–22). More specifically, Eden closely resembles the holy of holies. Both are populated with fruit trees (Gen 2:9; 1 Kings 6:29-35), with the Tree of Life occupying the center (Gen 2:9; 1 Kings 6:29-35; Rev 22:2). Rivers flow _out of_ Eden as they flow _out of_ the temple (Gen 2:10; Ezek 47:1; Rev 22:1), an especially relevant concept since the Tigris and Euphrates flow _into_ the Persian Gulf rather than _out of_ a common source. Both Eden and the temples were adorned with precious metals (Gen 2:11-12; Ex 25:10-31; 1 Kings 6:20; Rev 21:18-21). Angels guard the entrance (Gen 3:24; Ex 25:17-22; Ezek 1:5-11; Rev 21:12). All these factors point to the conclusion that Eden was not simply paradise for Adam and Eve; it was the intersection of heaven on earth. Eden was God's sanctuary. It was the center of the cosmos.
#### Exodus 20:8-11
In the first issue of the Decalogue the incentive given for the fourth commandment is based on creation. "For in six days the LORD made heaven and earth, the sea, and all that is in them, but rested on the seventh day; therefore the LORD blessed the sabbath day and consecrated it" (Ex 20:11). Although the force of the command derives from God's rest on the seventh day, the summary of God's creative act is ordered according to the three-tiered cosmos: heaven, earth and sea.
#### Nehemiah 9:6
In the year 539 B.C., the Persians defeated the Babylonians and became the newest world empire. In that same year King Cyrus of Persia issued a decree whereby all who had been held captive by the Babylonians were released to their homeland to rebuild their homes and restore their cultures (Ezra 1:1-4). The Israelites faced many obstacles from within (Ezra 4; Hag 1) and without (Neh 4–5). Finally, by the year 445 B.C., the exiles had rebuilt the temple (Ezra 6) and the protective walls around Jerusalem (Neh 6). A month-long celebration ensued, in which the people celebrated the Feast of Booths while Ezra read from the Law (Neh 8). Following a period of confession and repentance, Ezra delivered an elaborate prayer, in which he recalled God's faithfulness to his people from creation through the exile (Neh 9:6-31).
Ezra's summary of creation is neither lengthy nor extravagant. He makes no mention of the days of creation, the greater and lesser lights, or the making of humanity in the image of God. Instead he recounts the creation of the cosmos in one simple sentence. "You have made heaven, the heaven of heavens, with all their host, the earth and all that is on it, the seas and all that is in them" (Neh 9:6). In so doing, Ezra was able to declare succinctly that the Lord created everything—the heavens, earth and seas, and everything contained within each of the three tiers of the cosmos.
#### Job 38:2-38
The book of Job deals with one of the more profound theological issues facing humans on a regular basis. Job wants to know where God is in his suffering. Having lost his children, his home and his wealth, he demands a hearing before the Almighty.
> I will say to God, Do not condemn me;
>
> let me know why you contend against me.
>
> Does it seem good to you to oppress,
>
> to despise the work of your hands
>
> and favor the schemes of the wicked? (Job 10:2-3)
Job contends that if he could just be heard, God would side with him and relieve him of his suffering. Ultimately, though, the reader of Job's saga discovers that the question, why do bad things happen to good people? is the wrong question. The more pertinent question is, who is God? When God finally responds to Job "out of the whirlwind," he speaks in cosmological language. He asks Job rhetorically, were you there when I created the cosmos? If not, perhaps you should take more care in how you characterize me. In the opening thirty-seven verses of God's monologue, God poetically describes the cosmos in terms of its three tiers and their principal parts (see table 4.3).
**Table 4.3**
**Earth** | **Heavens** | **Seas**
---|---|---
dimensions (Job 38:5, 18)
building construction (Job 38:4, 6)
netherworld (Job 38:17) | stars and
constellations (Job 38:7, 31-32)
dwelling place of light and
darkness (Job 38:19, 24) | boundaries of the seas (Job 38:8, 10-11)
the deep (Job 38:16, 30)
terrestrial waters (Job 38:25)
heavenly weather
(Job 38:9, 22, 24-26, 28-29, 34, 37)
In this magnificent chapter, God declares his sovereignty over all creation. Unlike Job, God knows the dimensions of the earth, on what it is built and what lies beneath it. He controls the constellations, knows the heavenly residence of light and darkness, and existed when the stars shed their first light. God not only controls the weather and set boundaries for the oceans and rivers, but he has also been to their sources. In Job 38, God declares his control over all three tiers of creation—earth, heavens and seas.
#### Psalm 8
This hymn to the creator stirs within the psalmist the unfathomable mystery that God would think so highly of humanity. The psalmist looks to the heavens and sees the moon and stars (Ps 8:3-4), with no mention of the planets, suggesting that the psalmist thought of the planets as stars. He marvels that God would give humans dominion over all three tiers of the cosmos, from the beasts of the field (i.e., earth), to the birds of the heavens and the creatures of the seas.
#### Psalm 19
For most of the last century, Bible scholars saw in Psalm 19 two separate poems that had been joined together in the final compilation of the Psalter. However, recent studies have not only questioned that assessment but also convincingly demonstrated the unity of the psalm. Regardless of its compositional history, the structure of Psalm 19 is readily apparent, with the first six verses describing how the heavens profess God's glory and the last eight verses attesting to the beauty and worth of God's law. From a theological perspective, the two parts are necessarily unified as relating to the two means by which God has revealed himself to humanity: general revelation (Ps 19:1-6) and special revelation (Ps 19:7-14); that is, through his creation and through his word.
As Daniel Ashburn has aptly stated, "The psalmist does not find the beauty and expanse of the cosmos as mere passive clues of a Creator. Rather, Creation is actively proclaiming the glory of God; it is speaking aloud in words that must be spoken and must be heard." Unlike the other creation psalms, Psalm 19 attends only to the highest tier of the cosmos. It would be naive to assume from this psalm that God only reveals himself through the heavenly creation. We can just as easily recognize God's wonder and majesty in the flight of the bumblebee, the towering redwood forests or the changing tides. This psalm, though, focuses on that aspect of God's creation which is visible throughout the entire earth and is on constant display (Ps 19:2).
We also see in this psalm evidence of an ancient Near Eastern understanding of the cosmos. Both the earth (Ps 19:4) and the heavens (Ps 19:6) have ends, or points of termination, implying a closed universe. Each morning the sun emerges from the tent where it had lodged for the night. The sun rises and completes a circuit of the heavens (Ps 19:6), indicating a geocentric cosmos. A flat earth is assumed by the fact that the earth has ends, and that when the sun is not in its tent its rays heat the entirety of earth's surface.
#### Psalm 74:12-17
According to Hermann Gunkel's classification system, Psalm 74 is considered a communal lament or complaint. After calling on God to complain about the abominations committed by his enemies on the Lord's sanctuary, the psalmist recalls God's mighty acts of creation. As the God who created and subdued creation, he is more than capable of overthrowing his adversaries.
In six short verses the psalmist declares the power of God, the King from of old. God showed his sovereignty by establishing earth's boundaries ( _gĕbûlôt_ ; "bounds" in NRSV; Ps 74:17). He demonstrated his dominion over the heavens by placing the luminaries in their proper place. Most emphatically, God portrayed his power over the cosmic and chaotic seas by dividing them into the upper and lower seas, breaking the heads of _tannînīm_ , crushing the head of Leviathan, opening springs and closing streams. According to the psalmist, since God has authority over the earth, heavens and seas, God could more than capably handle the desecration of the sanctuary.
#### Psalm 95:1-7
In this call to worship, the congregation is invited to bring thanksgiving and praise to the "great King above all gods" (Ps 95:3).
> In his hand are the depths of the earth;
>
> the heights of the mountains are his also.
>
> The sea is his, for he made it,
>
> and the dry land, which his hands have formed. (Ps 95:4-5)
Contrary to other psalms that describe the Creator's acts, this psalm focuses only on the lower two tiers of the cosmos, the earth and the seas. However, as King of the cosmos, God's power extends throughout the entire known universe: "above all gods" in heaven, the highest heights, deepest depths, dry land and sea.
#### Psalm 104
Psalm 104 provides the most extensive account of creation outside of Genesis 1. Patrick D. Miller notes how the psalm is structured according to the three-tiered cosmos.
1. Creation of Heaven (2-4)
2. Creation of Earth (5-23)
1. Creation of Earth and Water (5-9)
2. Provision of Water for Fertility and Life (10-13)
3. Provision of Home and Food (14-18)
4. Provision of Time for the Creatures (19-23)
5. Interlude (24)
3. Creation of Sea (25-26)
4. Concluding Coda (27-35)
According to this analysis, the heavens of Psalm 104 refer to God's residence, which lies in the upper roof chambers (ʿ _ălîyyāh_ ; see also Judg 3:20; 2 Sam 18:33; 1 Kings 17:19; 2 Kings 23:12). These chambers rested above the waters, a reference to the upper seas held back by the firmament. In this psalm the elements serve as God's heavenly attendants. Normally the deep and the terrestrial waterways would be associated with the seas. Moreover, the birds would be associated with the heavens. Here, however, the earth has a much broader scope, including everything that has been separated from the cosmic sea. It includes the mountains and valleys, springs and streams. It contains land animals, waterfowl, nesting birds and vegetation. Even the moon and sun, though set in the heavens, function for the benefit of earthly creatures. Whereas in Psalm 74 God's power was demonstrated through the subjugation of the sea, in Psalm 104 God's greatness is exhibited by the sea's friendly creatures, including Leviathan, who plays in it. Here Leviathan is not a sea monster needing to be tamed, but just another of the sea's inhabitants.
#### Psalm 136:1-9
In Herman Gunkel's opinion, Psalm 136 was likely used in ancient Israel as a responsive reading. It was a liturgical reminder that since God had been faithful in the past, he would continue to be faithful in the future. The psalm moves through the history of Israel, from creation to their return to the Promised Land. As God of gods and Lord of lords, he made the earth and heavens (including the "great lights"), and divided the seas so the Israelites could make their exodus from Egypt.
#### Proverbs 8:22-31
The book of Proverbs contrasts two character qualities—wisdom and folly. The wise person is characterized by righteousness, justice and discipline. The fool displays unrighteousness, injustice and sloth. In Proverbs 7–8, these qualities are personified as Lady Wisdom and Dame Folly. Dame Folly is seductive, constantly attempting to lure young men from the righteous path (Prov 7). Lady Wisdom takes her stand at the city gates, giving wisdom and wealth to those who will heed her call (Prov 8).
In Proverbs 8:22-31 Lady Wisdom is said to have been the first of God's creations. As Wisdom literature these verses are not deifying wisdom. They are reiterating a common wisdom theme, namely, that since God is the source of all wisdom, he has created everything with order and purpose. In describing the origin of wisdom, Proverbs 8 roughly follows the outline of the three-tiered cosmos: earth (8:23-26), heavens (8:27-28) and sea (8:29). The earth is set on foundations (8:29), contains mountains and hills (8:25), and is inhabited by humanity (8:31). The heavens are above the solid sky (8:28), which holds back the upper seas (8:27). The seas, whose shores are assigned by God, consist of deep springs (8:24) and fountains (8:28). Although the purpose of the passage is to explain the origin of wisdom, it provides another vantage point of the ancient Israelite view of the cosmos.
#### Isaiah 40:12
As the prophet comforts the exiled Israelites, he reminds them of the God who is able to provide that comfort. He comes with might, he is strong, he is a shepherd and he is the creator of the cosmos. The universe was not created haphazardly or randomly. It was made with deliberate precision. Each of the three parts of the cosmos was carefully apportioned according to his specifications. The waters (seas) were measured by the handful. The heavens were sized according to the span of his hands. The earth was weighed on scales, and its dust calculated with a gauge.
#### Summary and Conclusion
Israel's recollection of God's creative act was an integral part of their worship. It reminded them that God was able to do all things, since he was the one who brought the cosmos into existence. It also reminded them that the God who had been faithful in the past would be faithful to them in the present and future.
In reviewing the creation accounts, several observations can be made. First, a seven-day creation week is only present in Genesis 1, although an allusion to the week is also found in Exodus 20:11. Second, aside from Genesis 1 the order of creation is more closely related to the ancient cosmological structure than it is to the structure of a week. Third, the various biblical creation accounts are poetic in nature, using metaphors, anthropomorphic language and other literary devices to convey concepts that would otherwise be foreign to human understanding. Fourth, the various creation accounts conform to the notion that God is the author of all aspects of the created order. Fifth, each of the creation accounts emphasizes God's sovereign power over the cosmos. God is not locked in an epic battle with the forces of nature, but has subdued them and commands them to submit to their assigned purpose. Finally, the general guiding principle for the authors of these creation accounts is the three-tiered cosmological structure. God is the maker of the heavens, the earth and the seas.
# Part Two
## COSMOLOGY _and_ SCRIPTURE
## _in_ HISTORICAL CONTEXT
# 5
## SCRIPTURE AND ARISTOTELIAN COSMOLOGY
On a second day of creation God created a firmament to separate the waters above from the waters below. This makes sense if the firmament acts as a roof over a flat earth. What would happen, though, if some mathematically minded people determined that the earth was round?
Could heaven still be "up there" on a global earth? Would it still be feasible to think of waters above a firmament that has both an above and a below? What if these same mathematical minds calculated that the five principal planets were actually farther from the earth than the sun and moon and that the stars were farther still? How far away must the firmament be to separate the upper heavens from the lower heavens? Are the stars below the firmament, within the firmament or above the firmament? As humans became more acutely aware of their cosmic surroundings, it became readily apparent that certain biblical texts would need to be rethought.
#### Spherical Cosmology
It is unclear exactly when it was first deduced that the earth was a sphere. In the early to mid-fifth century B.C., the Greek philosopher Parmenides proposed a spherical cosmos with earth at its center. His reasons were not mathematical or even cosmological, but philosophical. For Parmenides, the definition of being was uniformity, and the most uniform geometric shape is the sphere, "which is indicative of there being no gaps or empty places. Rather it is identical throughout, consisting of like bordering on like." Shortly after Parmenides, another Greek philosopher by the name of Philolaus introduced the concept of the spheres. According to this model, the sun, moon and planets orbited a central sphere of fire, called the hearth. While Philolaus moved the center of the cosmos away from the earth, he did not have the foresight to suggest the sun as the center of the cosmos, or even of the solar system.
In the first half of the fourth century, Eudoxus of Cnidus took the first steps in bridging the gap between Platonic philosophy and empirical science. His ideas are known to us primarily through Aristotle's _Metaphysics_ and Euclid's _Elements_ , as none of his works have survived. According to Aristotle, Eudoxus proposed twenty-seven spheres: three for both the sun and moon, four for each of the five planets and one for the fixed stars. Although Eudoxus is credited with articulating the shape of the cosmos on mathematical grounds, he was operating on the rather universal assumption that the earth and its celestial satellites were spherical in form. It seems, then, that by 400 B.C., the Greek philosophers had fairly well established the concept of a spherical earth and cosmos.
**_Aristotle._** Other than Jesus, Aristotle is perhaps the most influential thinker in history. Born in northern Greece in 384 B.C., he had an illustrious academic pedigree. Starting at the age of seventeen, Aristotle studied with Plato for twenty years at the Academy in Athens. Four years after the death of Plato, Aristotle was beckoned by Philip II of Macedon to tutor the king's son Alexander, the future monarch of the Greek Empire. About a decade later, Aristotle founded the Lyceum, a rival Athenian institution to Plato's Academy.
Building on the ideas of the Greek philosophers who preceded him, especially Eudoxus, Aristotle accepted the spherical nature of the earth as well as the cosmos. Whereas Eudoxus postulated twenty-seven spheres, Aristotle required fifty-five spheres, due to the need for spheres within spheres.
But it is necessary, if all the spheres combined are to explain the observed facts, that for each of the planets there should be other spheres (one fewer than those hitherto assigned) which counteract those already mentioned and bring back to the same position the outermost sphere of the star which in each case is situated below the star in question; for only thus can all the forces at work produce the observed motion of the planets.
In contrast to Eudoxus, Aristotle's spheres were interconnected, meaning that one Unmoved Mover was all that was required to move the entire system of spheres. Despite the drastic increase in the number of spheres required, Aristotle agreed with the general premise that the cosmos required one sphere for each of the heavenly bodies, for a total of seven cosmic spheres (see figure 5.1).
**Figure 5.1.** Aristotle's spheres
For Aristotle the cosmos could be divided into two sections: sublunary and superlunary. The former referred to everything contained within the sphere of the moon, while the latter pertained to the spheres beyond the moon. The superlunary region was considered perfect and unchanging. Thus comets, asteroids and other celestial irregularities naturally must have occurred within the sublunary realm. The Aristotelian cosmos was composed of five elements: earth, water, wind, fire and ether. These were arranged in the cosmos according to their density. The first four elements were found in the sublunary sphere, while the superlunary realm was composed of the fifth element, ether. As Harry Lee Poe and Jimmy Davis nicely summarize, "Objects moved until they reached their natural place. Rocks (being composed of mostly the element earth) move downward, while flames (being lighter) move upward." Naturally, being composed of the heaviest element, earth resided at the center of the cosmos. By contrast, the stars in the Milky Way congregate at the outermost sphere of the cosmos due to the "permanent accumulation of ignited vapor" released from comets as ether. Those distant stars, Aristotle deduced, were fixed in the firmament, beyond which only God existed.
From centuries of observations of the heavens, viewers had long noted the rotations of the heavenly bodies. Since Aristotle and his predecessors believed the earth to be stationary, the apparent movements of the planets and stars were due to their orbit of the earth. Although Aristotle's contemporary Heraclides, another of Plato's students, had proposed that this phenomenological effect was due to the earth spinning on its axis, Aristotle rejected this notion on metaphysical grounds. Circular movement was a property only of the superlunary realm; therefore, the earth could not rotate. Unable to find a cause for their rotation elsewhere, Aristotle argued that the consistent and constant celestial movements were the result of rotating spheres put in motion by an Unmoved Mover, "a spiritual something at the outermost part of the universe which he conceived as the ultimate source of all celestial movement." Thus, for Aristotle, the cosmos was a single, eternal entity, bound by concentric, solid spheres centered around the earth, whose predictable movements could be accounted for by an Unmoved Mover.
The spheres' solidity is an important vestige of the ancient Near Eastern concept of a solid firmament. Like the pre-Platonic view of the stars being fixed in the firmament, Aristotle concluded "that the circles move and that the stars stay still and are carried along because fixed in the circles." Although he situated the stars in a solid sphere, Aristotle was less clear on the planetary spheres, which he considered to be composed of immaterial ether. However, this movement of the entire cosmic system required the physical connection of one sphere to another, and the movement of planets required a physical connection of the planets to their respective spheres. Even though Aristotle was not particularly dogmatic about the nature of the spheres, the idea of physical spheres around which the planets rotated quickly became vogue. Whether Aristotle actually believed this is uncertain; nevertheless, it is the view that was adopted by biblical interpreters for the next two thousand years.
**_Ptolemy._** The genius of Aristotle's cosmology was its simplicity. Spheres within rotating spheres seemed to account for nearly every astronomical phenomenon observed. That is, _nearly_ every astronomical phenomenon. Despite its aesthetic beauty, the Aristotelian cosmology was unable to account for the apparent retrograde motion of planets, as well as the changes evident in their brightness. Four hundred years later an Alexandrian attempted to resolve these conflicts by refining the concept of the epicycle, first introduced by Apollonius.
In A.D. 85 Claudius of Ptolemais, more commonly known as Ptolemy, was born along the Nile River. Unlike his Platonic predecessors, Ptolemy staked his livelihood on the exactitude of mathematics rather than on metaphysical assertions. It is not that he was uninterested in philosophical inquiry; rather he preferred to draw philosophical conclusions from his quantitative analysis of the natural world. His impeccable scholarship was appreciated by the Ptolemaic Dynasty, which funded his astronomical research in Alexandria. Ptolemy's most famous work is known by its Arabic title, _The_ _Almagest_ , which translates as "the greatest," but was originally titled _Mathematical Syntaxis_.
**_Figure 5.2._** Ptolemy's epicycles
For the most part Ptolemy agreed with Aristotle's conception of the cosmos. Like Aristotle, Ptolemy considered earth to be the center of the universe. It was surrounded by the seven planets—Moon, Mercury, Venus, Sun, Mars, Jupiter, Saturn—all of which were carried through the cosmos on their respective spheres. Furthermore, the fixed stars established the outer perimeter of the cosmos. Unlike Aristotle, though, Ptolemy was not metaphysically bound to a geocentric earth in the strict sense that the earth was not at the precise center of the spheres. Furthermore, planets were not fixed precisely on their spherical plane, but orbited an epicycle that moved with the sphere. These small variations to Aristotle's cosmos allowed Ptolemy to predict the position of any planet with an accuracy of one degree (see figure 5.2). As a planet orbited its epicycle, it gave the appearance from a fixed earth that it repeatedly reversed its course. Moreover, this model of epicycles resolved the problem of the planets' change of brightness by accounting for a means by which their distance from earth varied.
Size of the universe. Nearly three centuries before Ptolemy, a librarian by the name of Eratosthenes calculated the circumference of the earth to be approximately 250,000 stadia. If we take a stade to be about 157.5 meters, as is often assumed, Eratosthenes's circumference of the earth would be equal to about 39,375 km. Following the mathematical methods employed by the Greek astronomer Hipparchus (190–120 B.C.), Ptolemy arrived at a mean distance of 59 earth radii for the moon's distance to the earth (208,860 km) and 1,210 earth radii for the sun's distance (4.28 million km). While Eratosthenes' figure for the earth's circumference is staggeringly close to its actual circumference of 40,075 km, Ptolemy's calculations for more distant bodies, such as the moon, sun and stars were less accurate. In fact, he concluded that the distance to the fixed stars was approximately 20,000 earth radii (125,340,000 km), which is less than the actual distance of 14,591 earth radii to the nearest star, the sun (92,960,000 km). However, since a geocentric universe requires each of the heavenly bodies to orbit the earth in twenty-four hours, these astronomical numbers breached believability. Even with a universe as small as Ptolemy's it required the fixed stars to orbit the earth at over 600,000 times the speed of light! As if this weren't fast enough, Ptolemy recognized that to posit a larger universe would require impossibly high rates of speed for the fixed stars.
**_Summary and implications._** Ancient Greek astronomers changed the way the heavens were viewed. While the Babylonians had been careful charters of the skies, the Greeks formed mathematical theories to explain the cosmos. The Babylonians were vigilant and meticulous observers; the Greeks systematized astronomical research. By positing a series of concentric spheres within an eternal, geocentric cosmos, they were able to situate the planets in the cosmos, calculate the diameter of the earth and the distances to the heavenly bodies, and predict planetary motion.
In addition to the mathematical advances of the Greeks in astronomy, it is necessary to keep in mind that their cosmography was initially founded on principles devised by the philosopher Plato, particularly his theory of forms. According to Platonic thought, "The world that appears to our senses is in some way defective and filled with error, but there is a more real and perfect realm, populated by entities (called 'forms' or 'ideas') that are eternal, changeless, and in some sense paradigmatic for the structure and character of the world presented to our senses." Thus for Plato and his students the sphere represented the perfect geometrical form, the ideal shape for the perfect cosmos.
As is well attested, Platonic thought eventually made its way into theological discussions. The two most prominent features of Platonism are (1) the division of body and soul, and (2) the incorruptible and immutable nature of heaven in contrast to the corruptible and decaying nature of earth. Both of these views formed the core of the heretical movement called Gnosticism. Aristotle's idea of the Unmoved Mover, which provided philosophical rationale for the existence of God, was especially appealing to monotheistic religions. In time Aristotelian cosmology and biblical faith became inseparable, not because Aristotle was a Christian, but because his system was easily reconciled with biblical anthropology and monotheism. As the pinnacle of God's creation, it was only natural that humans would dwell at the center of the cosmos. To suggest that some other celestial body occupied this honored position in the universe was to contradict Scripture. Likewise, situating the Unmoved Mover beyond the firmament of the fixed stars correlated nicely with the biblical view of God above all creation and outside of creation. Given Christianity's strong theological dependence on Aristotelian cosmology, it is not surprising that it took three exceptional thinkers, two millennia and one new invention to shake it from this flawed cosmology.
**Table 5.1.** Biblical interpreters from Aristotle to Copernicus
**Biblical Interpreters**
---
Philo of Alexandria (20 B.C.–A.D. 50)
Josephus (A.D. 37–after 100)
Theophilus of Antioch (A.D. 120–190 [?])
Irenaeus (A.D. 130–202)
Lactantius (A.D. 260–330)
Ephraim of Syria (A.D. 306/337–373)
Basil of Caesarea (A.D. 329–379)
Gregory of Nyssa (A.D. 335–394) | Ambrose (A.D. 340 [?]–397)
John Chrysostom (A.D. 340/350–407)
Augustine of Hippo (A.D. 354–430)
Maimonides (Rambam) (A.D. 1135–1204)
Thomas Aquinas (A.D. 1225–1274)
Dante Alighieri (A.D. 1265–1321)
Martin Luther (A.D. 1483–1546)
John Calvin (A.D. 1509–1564)
**Collections of Works**
**Old Testament Pseudepigrapha**
Song of the Three (2nd c. B.C.)
1 Enoch (2nd c. B.C.–1st c. A.D.)
2 Enoch (1st c. A.D.) | Testament of Abraham (1st–2nd c. A.D.)
3 Baruch (2nd c. A.D.)
Testament of Adam (2nd–5th c. A.D.)
**Old Testament Apocrypha**
2 Esdras (2nd c. A.D.)
New Testament (1st–2nd c. A.D.)
Apostles' Creed (4th c. A.D.) | Genesis Rabbah (5th c. A.D.)
Babylonian Talmud (3rd–6th c. A.D.)
#### Spheres and Scripture
The responses to Aristotelian cosmology took many forms. Biblical interpreters were both Jew and Gentile, hailed from regions from Alexandria to Zurich, wrote in languages as diverse as Greek and German, and spanned two millennia (see table 5.1). Although their knowledge of the cosmos increased slightly over time—in particular the size and shape of earth's landmasses—their deeply held beliefs about the theological structure of the cosmos remained as immovable as Aristotle's Unmoved Mover.
As we review a sampling of the cosmological interpretations from around 400 B.C. to A.D. 1550, we will notice the emergence of a few common themes—not expressed by all, but representative of views across a wide interpretive spectrum. First, the three-tiered model of the cosmos as heaven, earth and sea remains acceptable. Second, the earth remains the center of the cosmos, around which the heavenly spheres revolve. Third, interpreters have accepted that the universe is larger than originally thought, but is still considered much smaller than is known today. Fourth, the views of the Greek philosophers such as Aristotle and Ptolemy are common knowledge. There is some discussion about the degree to which faithful interpreters should adhere to their views, but there is a general consensus that the "astronomers are the experts" on matters of cosmic sciences. Finally, and perhaps most significantly, it is widely recognized that some portions of Scripture have to be reinterpreted in light of Aristotelian cosmology. On occasion, Aristotelian cosmology is rejected in favor of a "biblical" view of the cosmos, even though Aristotle's explanation comports better with the scientific evidence available at the time.
**_Earth._** In the ancient Near East, the earth was thought to be small and flat. Thanks to the mathematical calculations and metaphysical assertions of the Greeks, such a model would be placed under a certain strain. However, with the exception of the rare exegete who insisted on a flat earth, biblical interpreters generally found uncomplicated ways of harmonizing the "biblical view" of the cosmos with the innovative Aristotelian approach.
_Earth's elements._ As I noted at the beginning of this chapter, Aristotle's universe was composed of five elements, with the sublunary region being made of earth, wind, fire and water. This simple explanation was readily endorsed. In his _Life of Moses_ , the first-century Hellenistic Jewish philosopher Philo explains the significance of the priestly garments in light of these four elements.
Thus is the high priest arrayed when he sets forth to his holy duties, in order that when he enters to offer the ancestral prayers and sacrifices there may enter with him the whole universe, as signified in the types of it which he brings upon his person, the long robe a copy of the air, the pomegranate of water, the flower trimming of earth, the scarlet of fire, the ephod of heaven, the circular emeralds on the shoulder-tops with the six engravings in each of the two hemispheres which they resemble in form, the twelve stones on the breast in four rows of threes of the zodiac, the reason-seat of that Reason which holds together and administers all things.
Of course, only three of the elements are inhabitable, since humans cannot survive in fire. The medieval Jewish commentator Maimonides (also known as Rambam) employed his audience's knowledge of the four sublunary elements to define the earth of Genesis 1:1 as everything below the heavens consisting of _ere_ ṣ ("earth"), _rua_ ḥ ("spirit" = "air"), _mayim_ ("water") and ḥ _ōšek_ ("darkness" = "fire"). Even Martin Luther, in the sixteenth century, casually asserts, in agreement with the Greek philosophers, that the earth is made of these four elements. So we see a general acceptance of this particular aspect of Aristotelian cosmology.
_Earth's dimensions._ Although the Greek word _sphaira_ ("sphere") was available to the New Testament authors and earliest biblical interpreters, we find no evidence of any discussion concerning the spherical nature of the earth. However, where the concept of a spherical earth is mentioned in later Christian thought, there does not seem to be any debate about it. Basil of Caesarea said with respect to the sun's light, "It is diffused through the air in the light of its course over the hemisphere." The Jewish commentary _Genesis Rabbah_ (ca. fifth century A.D.) states that when God created the earth he "took two balls, one of fire, the other of snow, and he worked them together and from the mixture of the two the world was created." The nature of Jewish commentary was quite different from how we might go about finding the intent of the text. Sometimes the rabbis looked for creative ways to tie one passage of the Bible to another through plays on words. At other times they would dissect Hebrew words to extract all possible meanings of a text. Whatever the particular method a commentator used, it is clear from this text that the world was assumed to be ball-shaped. No explanation was needed to defend the view. While these two texts do not provide overwhelming evidence for the spherical nature of the earth, they do indicate that it was accepted by the prominent Christian exegete Basil and the widely accepted Jewish commentary _Genesis Rabbah_.
However, not everyone believed in a spherical earth. There were a few prominent flat-earthers as late as the medieval period. The most conspicuous of these was Lactantius, a third-century Christian author who served as an advisor to Constantine. He thought it ridiculous that there could be people living on the underside of the earth. These so-called antipodes would have to be standing upside down if that were the case.
How is it with those who imagine that there are antipodes opposite to our footsteps? Do they say anything to the purpose? Or is there any one so senseless as to believe that there are men whose footsteps are higher than their heads? or that the things which with us are in a recumbent position, with them hang in an inverted direction? that the crops and trees grow downwards? that the rains, and snows, and hail fall upwards to the earth?
The only way the earth could be a sphere in Lactantius's mind was for the same principle to apply to the heavens. If earth was round, the heavens must encompass the earth in a circular fashion. Using a wheel as analogy, earth would be the hub, and the heavens the rim. Those arguments were unconvincing to Lactantius, though, since "it is impossible for the heaven to be lower than the earth."
Augustine was also skeptical of the antipodes, thinking it fanciful to imagine people living on the opposite side of the globe.
As to the fable that there are Antipodes, that is to say, men on the opposite side of the earth, where the sun rises when it sets on us, men who walk with their feet opposite ours, there is no reason for believing it. Those who affirm it do not claim to possess any actual information; they merely conjecture that, since the earth is suspended within the concavity of the heavens, and there is as much room on the one side of it as on the other, therefore the part which is beneath cannot be void of human inhabitants. They fail to notice that, even should it be believed or demonstrated that the world is round or spherical in form, it does not follow that the part of the earth opposite to us is not completely covered with water, or that any conjectured dry land there should be inhabited by men. For Scripture, which confirms the truth of its historical statements by the accomplishment of its prophecies, teaches not falsehood; and it is too absurd to say that some men might have set sail from this side and, traversing the immense expanse of ocean, have propagated there a race of human beings descended from that one first man.
There is a significant difference between the approach taken by Lactantius and the one articulated by Augustine. For Augustine it was "scientific conjecture" rather than a proven fact. It conformed neither to common sense nor with Scripture, which teaches that the earth is flat. However, he is willing to concede a spherical earth if it can be proven. Since Scriptures "confirm the truth," if it is proven that the earth is round, and that there are, in fact, antipodes, then Augustine was more than willing to accept the scientific position against his own sensible and biblically based position.
The size and shape of the earth do not garner much attention, but where it is mentioned it provides some helpful insights into biblical interpreters' conception of its dimensions. According to the _Babylonian Talmud_ , the circumference of the earth was 6,000 _parasang_ , 1 _parasang_ being equivalent to 30 stadia, and 1 stade being approximately 157.5 meters. According to this system of measurement, the earth's circumference would have been about 28,350 km, significantly smaller than its actual size of 40,075 km. Other descriptions are less precise. Philo describes the earth as being three-quarters land and one-quarter sea, while the apocryphal book _2 Esdras_ depicts the third day of creation as dividing the earth into seven parts, six of which would remain sea, while only one part would become dry land (6:42-43).
New Testament authors referred to the earth according to its parameters rather than its size. In Matthew 12:42 (// Lk 11:31) Jesus predicts the coming of the queen of the South "from the ends of the earth" to rise in judgment. In Acts the disciples are commissioned with the gospel message to go out "to the ends of the earth" (Acts 1:8) in order to bring salvation to the Gentiles (Acts 13:47). Paul cites Psalm 19:4 as scriptural evidence that the gospel is intended for all, even to those at "the ends of the earth" (Rom 10:18). Twice in Revelation (Rev 7:1; 20:8) the phrase "four corners of the earth" is employed to denote the extremities of the earth.
It's also clear on a few occasions that the entire inhabited surface of the earth could be visible from one extraterrestrial vantage point. The Gospel of Mark describes the coming of the Son of Man with the clouds as an event that will be visible to everyone, at which time angels will "gather his elect from the four winds, from the ends of the earth to the ends of heaven" (Mk 13:27). Likewise, Matthew 4:8 and Revelation 1:7 depict the entire populated world as an observable plane, when viewed from the heights.
Again, the devil took him to a very high mountain and showed him all the kingdoms of the world and their splendor; and he said to him, "All these I will give you, if you will fall down and worship me." Jesus said to him, "Away with you, Satan! for it is written,
> 'Worship the Lord your God,
>
> and serve only him.'"
Then the devil left him, and suddenly angels came and waited on him. (Mt 4:8-11)
> Look! He is coming with the clouds;
>
> every eye will see him,
>
> even those who pierced him;
>
> and on his account all the tribes of the earth will wail.
So it is to be. Amen. (Rev 1:7)
Along with Daniel 4:10-12, which was discussed in chapter three, the biblical text of Matthew 4 and Revelation 1 operates under the assumption that all the inhabitants of earth live in a region small enough to be seen from a fixed elevation. It also precludes the possibility of people living on the opposite side of a sphere.
As we saw in part one, the ancient Near Eastern view of the earth's dimensions was that of a small, circular disk. The earth was literally conceived as having longitudinal and latitudinal limits. By the time of the New Testament authors, however, that notion had been dispelled. They knew the earth was spherical, but the land itself still had borders. Whether inhabitable land was one-fourth or one-seventh of the surface area of the earth, there was a limit to how far one could travel on the globe.
_Earth's foundations._ Despite consenting to a ball-shaped earth, some interpreters had theological misgivings about relenting on the nature of its foundations. The earth does not move (1 Chron 16:30) because it is set firm on its foundations (Job 38:4; Ps 102:25; 104:5; Is 48:13). In fact, the Aristotelian model did not allow for a movable earth either, making it easy for biblical interpreters to maintain the old idea of the earth fixed on its footers. Of course, "earth" had two distinctive meanings. It could refer to the spherical planet situated at the center of the cosmos, or to the habitable land that made up just one portion of that planet. It is not difficult to imagine the latter with pillars or foundations. After all, something must keep the landmass from sinking into the seas. Such is the case in _2 Enoch_ , in which God calls earth the "solid structure" that he set "above the waters" (28:4). Likewise, Theophilus of Antioch (A.D. 180s) explains the meaning of "earth" in Genesis 1 as "the ground and foundation." Two centuries later, John Chrysostom uses similar language in his homily on Genesis 1:1.
Notice how the divine nature shines out of the very manner of creation, how he executes his creation in a way contrary to human procedures, first stretching out the heavens and then laying out the earth beneath, first the roof and then the foundation. Who has ever seen the like? Who has ever heard of it? No matter what human beings produce, this could never have happened—whereas when God decides, everything yields to his will and becomes possible. So don't pry too closely with human reasoning into the works of God; instead, let the works lead you to marvel at their maker.
There still existed, then, in a post-Aristotelian world, the idea that at some level the earth was built like a house, requiring some sort of foundation to keep it in place.
If, however, one considers the entire globe as resting on pillars, that becomes more challenging to comprehend, even for the ancients. Commenting on Psalm 104:5, John Calvin wonders, "Since it is suspended in the midst of the air, and is supported only by pillars of water, how does it keep its place so steadfastly that it cannot be moved?" Luther avoids the issue in this case by treating "earth" allegorically as a reference to the church. Similarly, at Isaiah 48:13, Luther takes a metaphorical approach. Where Isaiah reads, "My hand laid the foundation of the earth, and my right hand spread out the heavens," Luther takes it to mean, "I have heaven in my hand and enclosed it in my hand. I have closed my fingers around it." So he reconciles the cosmological conundrum by appealing to allegorical language. Calvin wrestles with the issue at Isaiah 48:13 by resorting to an alternate reading of the Hebrew _tippe_ ḥ _â_ , translated as "spread out" in the NRSV. Ultimately he decides it does not matter which translation is preferred. Whether it means "measured" or "upheld," it is God's wisdom that supports "the huge mass of the heavens in continual motion, so that it neither totters nor leans more to one side than to another." Both Luther and Calvin found it necessary to interpret their understanding of the earth's foundation in light of their understanding of the cosmos as presented to them by the Aristotelian system, despite the fact that this model was founded not on biblical principles but on Platonic philosophy.
The phrase "foundations of the world" occurs ten times in the New Testament. In each case, the phrase is used idiomatically to refer to the beginning of creation. Behind the idiom, though, is the ancient notion that the earth had a literal foundation which was laid at the beginning of time. Since none of the New Testament authors comment on their use of this phrase, it is unclear whether they had in mind an earth with pillars and footings or simply recognized that, like any other created thing, it had a physical beginning.
_Earth's depths._ During the so-called intertestamental period, from the close of the Hebrew canon to the inception of the Christian era, the idea of Sheol—the grave—underwent a major modification. In the Old Testament world, Sheol was seen in similar fashion to the rest of the ancient Near Eastern world. It was the abode of the dead, the final resting place beneath the earth for all who once lived. It was no respecter of one's relationship with God—both the just and the unjust were destined for the grave. During the intertestamental period, though, the doctrine of resurrection was formulated and became a heated point of controversy between the Sadducees and the Pharisees. The location of the cosmic grave had not changed—it remained at the center of the earth, which in Jewish tradition was created on the second day in Genesis 1 ( _2 Enoch_ 28). In _Genesis Rabbah_ 1.6.1.b, the abyss and Gehenna are one and the same. However, it became a temporary resting place for the righteous until God would create the new heavens and new earth ( _2 Esdras_ 7:74-75).
Despite the modifications from the Old Testament concept of the grave, Aristotelian cosmology provided no reason to abandon the idea of a region beneath the surface of the earth. It shows up most conspicuously in the Apostles' Creed. After confessing that Jesus was crucified, dead and buried, the creed alludes to Ephesians 4:9, affirming that Jesus descended into hell. That is, Jesus died like anyone else, confirming that his death was an actual expiration of life. In fact, Dante in the fourteenth century capitalized on the acceptance of a subterranean hell in the _Divine Comedy_ , which he wrote in three parts: _Inferno_ , _Purgatorio_ and _Paradiso_. In the _Inferno_ , Dante leads his readers on a journey through the nine circles of hell, which of course correspond to Aristotle's spherical cosmos. According to Dante's doctrine of hell, the deceased are sentenced to a particular circle based on the degree of their sin.
> First circle: Virtuous heathen
>
> Second circle: Lust
>
> Third circle: Gluttony
>
> Fourth circle: Greed
>
> Fifth circle: Wrath
>
> Sixth circle: Heresy
>
> Seventh circle: Violence
>
> Eighth circle: Fraud
>
> Ninth circle: Treachery
It is in the ninth circle, the deepest in earth's core, where Judas and Satan dwell, along with Brutus and Cassius.
The word _Gehenna_ derives from the Hebrew _gê_ ʾ ḥ _innōm_ , "the valley of Hinnom," known by the prophet Jeremiah as "the valley of slaughter" (Jer 7:30-33) because it was there that child sacrifices were offered to the Canaanite god Molech (2 Kings 23:10). In the intertestamental period, Gehenna became synonymous with judgment ( _1 Enoch_ 27:2; 90:26; _2 Esdras_ 7:36). This view carried over into New Testament times as well. Among the twelve occurrences of Gehenna ( _geenna_ ), all but one come from the lips of Jesus. For Jesus, Gehenna was a place of unquenchable fire.
The Old Testament location of the Valley of Hinnom is well known, but that is not the case for the New Testament's Gehenna. All we know is that it was a place in which the reprobate would be thrown. However, there are three other places of judgment in the New Testament that have an unmistakable cosmic connotation. The first is Hades, "the Greek name for the underworld and its ruler." In Greek mythology, Hades was one of three brothers born to Kronos and Rhea, with each given one of the three tiers of the cosmos. Zeus was given the sky, Poseidon was granted the sea and Hades received the underworld (earth). His House of Hades was carefully guarded, not to prevent entrance but to prevent escape. In the New Testament Hades can refer either to the abode of the dead or to death personified. One of the clearest examples of Hades as the abode of the dead is found in the story of the rich man and Lazarus (Lk 16:19-31). In this parable contrasting a rich man and a poor man, the rich man is buried. After his death, he experiences unspeakable torment in Hades. His counterpart, Lazarus, does not descend to Hades but descends to Abraham's bosom, the second cosmic locus of death in the New Testament. For Lazarus, death was not an experience of torment but one of comfort. According to the second-century-A.D. pseudepigraphal _Testament of Abraham_ , Abraham's bosom is a place where "there is no toil, no grief, no moaning, but peace, exultation and endless life." Considering the rich man must look up to see Lazarus, it appears Hades is deeper in the earth than Abraham's bosom, or at least is a separate part of Abraham's bosom. The third cosmic realm of the underworld in the New Testament is _tartaroō_ , found only in 2 Peter 2:4. Translated simply as "hell" in the NRSV, _tartaroō_ finds its origins in the Greek mythological character Tartaros, whose chief function was to hold defeated immortals, who by definition could not be killed and descend to Hades. In 2 Peter 2:4, _tartaroō_ is described as a place of chains, deep darkness and judgment. The New Testament's consistent witness on the location of judgment, then, is that it lies in the underworld and is best characterized by torment, darkness and unquenchable fire.
**_Heavens._** Aristotle's contribution to cosmology is most significant as it relates to the heavens. He articulated the notion of concentric spheres and spheres within spheres, each of which related to the seven celestial bodies we call the sun, moon and planets. Fixed within the outermost sphere were the stars. Above the stellar sphere was nothing, except the Unmoved Mover, who or which put the spheres in motion. Since both Judaism and Christianity have something to say about heaven, it is expected that biblical interpreters intersected with Aristotelian cosmology rather frequently.
_Nature and number of the spheres._ One of the questions with which interpreters wrestled was the number of heavens, arising primarily from a close reading of Genesis 1:1 and Genesis 1:8. In his homilies on Genesis known as the _Hexaemeron_ , Basil comments, "We must enquire furthermore whether there is another heaven in addition to the one that was created first, or whether it is the same that was called firmament, and whether there are two heavens." The question for Basil was whether there could be one, two, three or many heavens. From a scientific perspective, Basil mocks the Greeks for not being able to agree among themselves. From a theological perspective, Basil is unconcerned with the number of heavens, only that we find our basis from Scripture, not the philosophers, for "it is possible for us to believe that God made two heavens." In fact, if there were two heavens, Basil says, it would only confirm Paul's account of being caught up in the third heaven (2 Cor 12:2). Although the Greeks say "that for the seven stars there are seven circles, in which they move around," Basil is unconvinced by their so-called wisdom. Ultimately he determines that the two heavens in Genesis 1 are separate accounts of the same creation.
While Basil's homilies repeatedly disparage the "pagans with their fabrications," the more common approach was to accept the Aristotelian structure of the heavens with its seven solid spheres. _Second Enoch_ recounts the fourth day of creation as follows:
> And on the fourth day I commanded: "Let there be great lamps on the heavenly circles."
>
> On the first, the highest circle, I placed Kronos [Saturn];
>
> on the 2nd <lower down, I placed> Afridit [Venus];
>
> on the 3rd Arris [Mars];
>
> on the 4th the sun;
>
> on the 5th Zeous [Jupiter];
>
> on the 6th Ermis [Mercury];
>
> and on the 7th, the lowest, the moon. ( _2 Enoch_ 30:2-3)
The order is somewhat interesting in that it deviates from Ptolemy's arrangement of the planets: Moon, Mercury, Venus, Sun, Mars, Jupiter, Saturn. This in turn differs from the order given in _Genesis Rabbah_ : Sun, Jupiter, Moon, Saturn, Mercury, Venus, Mars.
Regardless of the arrangement, the nature and number of spheres was fairly settled. Philo agrees that heaven contained seven spheres, stating that the planets and the fixed stars "are marshaled in seven ranks, and manifest large sympathy with air and earth." The medieval Jewish commentator Maimonides noted that "the stars, the sun, and the moon are not, as people believe, on the surface of the spheres, but they are fixed in the spheres," which he based on Genesis 1:8, which says, "in the firmament" rather than "upon the firmament." Unlike Basil, Maimonides concludes that the heavens of Genesis 1:1 are different from the heavens in Genesis 1:6, and these are in fact two different heavens.
Luther, in his _Lectures on Genesis_ , goes to great lengths to explain the number of spheres in both theological and scientific terms. Noting that the philosophers are in agreement on the seven planetary orbits, he comments that "there are four spheres of productive and destructible materials, then also eight others of unproductive and indestructible materials." After giving some attention to what both philosophers and theologians have said on the nature and number of spheres, Luther admits that the philosophers are the ones thinking more logically about the matter. In fact, he commends Jerome for staying silent on the issue and confesses his own ignorance on what Scripture actually means in reference to the firmament in the heavens.
_Heaven's firmament._ Some of the most fascinating and invigorating conversations among post-Aristotelian biblical interpreters concern the nature of the firmament. We have just seen that the number of heavens was a point of discussion, but other issues arose as well. From what material was the firmament constructed? Was it a solid or liquid? How high was it? What was above it? The answers to these questions were not unanimous, but together they demonstrate how biblical interpreters wrestled with fitting their pre-Aristotelian concepts into a post-Aristotelian world.
It was common for readers attempting to interpret the Bible as literally as possible to view the firmament as some type of barrier separating the upper heavens from the lower heavens. In the Aristotelian model, it was no longer viable for the dome in the sky to be at the same altitude as the sun, moon and stars. Since each of the seven planets was assigned to its own sphere, the firmament had to have been that on which the fixed stars were attached. Such, at least, is the impression we get from the widest range of commentators, as nicely summarized by Thomas Aquinas: "For the starry heaven divides the lower transparent bodies from the higher, and the cloudy region divides that higher part of the air, where the rain and similar things are generated, from the lower part, which is connected with the water and included under that name." For Aquinas, the outermost sphere—the sphere of the fixed stars—constitutes the firmament, which separates the waters above from the waters below (Gen 1:6).
In his commentary on Genesis 1:6, Ambrose (fourth century A.D.) also calls the outer sphere "the specific solidity of this exterior firmament." This view is echoed by many others, as we will see in our discussion of the cosmic sea. As a means of contrast, it is interesting to note that the _Babylonian Talmud_ maintains the pre-Aristotelian view that the firmament "is that in which sun and moon, stars and constellations are set."
In describing the firmament's shape, interpreters preferred analogies to a roof or dome. The apocryphal book _Song of the Three_ refers to it as the "dome of heaven" (v. 34). Theophilus (second century A.D.) also adopted this language, calling the firmament a "dome-shaped covering." Chrysostom describes the illogical way in which God created the cosmos, by first creating the roof before laying the foundation. According to _Genesis Rabbah_ , God "made a roof over his world only with water." Even for these post-Aristotelian interpreters, it seemed logical that a barrier of some sort separated outer space from God's heavenly abode.
The firmament was real to these early interpreters, meaning it must have been made of some real substance. It was not simply an air bubble ( _Genesis Rabbah_ 4:3a; _2 Baruch_ 21:4). According to _3 Baruch_ 3:7, when humans built a tower to the heavens (Gen 11:1-9), "they attempted to pierce the heaven, saying, 'Let us see whether the heaven is (made) of clay or copper or iron.'" This comes from the biblical presentation that the _raqia_ ʿ is something that is beaten or hammered like bronze (Ex 39:3; Num 16:38; Jer 10:9). Origen is less certain about the specific material that makes up the firmament, but he is certain that it is "without doubt firm and solid." Chrysostom likewise calls the firmament "some sort of barrier." Although Basil is also uncertain about the precise material constituting the firmament, he offers a few suggestions, such as crystal and mica. These seem reasonable to him because they "resemble air and clear and pure water."
_Heaven's luminaries._ In Genesis 1:16, God makes two lamps. The larger lamp, which we call the sun, ruled the day, and the smaller lamp, which we call the moon, ruled the night. From an Aristotelian perspective these were only two of the seven planets. From our current perspective, both the Bible and Aristotle are imprecise. Before Copernicus shifted our view of the cosmos from the earth (geocentrism) to the sun (heliocentrism), observers of the heavens had come to recognize that the moon was not its own source of light. This posed a challenge to Genesis 1:16, which clearly states the opposite. We might see the passages in the New Testament that refer to the light of the moon (Mt 24:29; Mk 13:24; Rev 8:12; 21:23) as figures of speech, in the same vein as we use the phrase today. And this may be the case. However, a look at two discussions on the topic should give us reason not to jump too quickly to this conclusion.
Centuries before Copernicus, Rabbi Yohanan said, "Only the orb of the sun was created for the purpose of giving light. If so, why was the moon created? It was for the signification of the seasons, specifically so that, through [regular sightings of the moon, Israelites would] sanctify new months and years." Rabbi Azariah also said, "Only the orb of the sun was created for the purpose of giving light. If so, why was the moon created at all? The Holy One, blessed be he, foresaw that the nations of the world were going to make [the heavenly bodies] into gods." However, the issue was not altogether settled among the rabbis. Despite the scientific evidence to the contrary, Rabbi Berekhiah affirms the biblical text, saying, "Both of them were created in order to give light, as it is said, 'And they shall serve for light.'"
The disagreement between Luther and Calvin is typical of the interpretive dances made by exegetes attempting to reconcile Scripture and cosmology. For Luther, both the moon and the stars receive their light from the sun.
They also say the moon derives its light from the sun. This is really well proved at an eclipse of the moon, when the earth, intervening in a direct line between the sun and the moon, does not permit the light of the sun to pass to the moon. I do not deny or condemn these claims, but I declare it is by divine might that such power has been given to the sun that through its own light it also lights up the moon and the stars; likewise, that the moon and the stars were so created that they are receptive to the light which is sent out by the sun.
While Luther sees the moon as borrowing light from the sun, Calvin maintains that the moon was in fact its own source of light, albeit a much less significant source. Observing that the moon is much larger than the sun, the moon must be a "lesser light" not because of its size but because of the amount of light it emits in comparison to the sun. Noting that Moses was aware that the moon had to borrow a portion of light from the sun, Calvin states that Moses was not "ignorant of the fact, that the moon had not sufficient brightness to enlighten the earth, unless it borrowed from the sun; but he deemed it enough to declare what we all may plainly perceive, that the moon is a dispenser of light to us." Some may argue that Calvin is more biblical in his interpretation, upholding the authority of Scripture, while Luther is conforming to human secular ideas. However, if the moon is not its own source of light, as Luther suggests, then perhaps his way of interpreting the Bible in light of scientific discovery is not only appropriate but preferred.
_Upper heavens._ The idea that God dwells above the firmament was not lost with the adoption of a spherical cosmic system. His abode was moved further from earth, as mathematical calculations had greatly expanded humans' understanding of the distances to the sun, moon and the other planets. But the highest heaven was still thought of being "up there."
The New Testament is replete with allusions to God's heavenly abode being above the heavenly dome.
And when Jesus had been baptized, just as he came up from the water, suddenly the heavens were opened to him and he saw the Spirit of God descending like a dove and alighting on him. (Mt 3:16 // Mk 1:10)
But I say to you, Do not swear at all, either by heaven, for it is the throne of God, or by the earth, for it is his footstool. (Mt 5:34-35)
So whoever swears by the altar, swears by it and by everything on it; and whoever swears by the sanctuary, swears by it and by the one who dwells in it; and whoever swears by heaven, swears by the throne of God and by the one who is seated upon it. (Mt 23:20-22)
"Look," he said, "I see the heavens opened and the Son of Man standing at the right hand of God!" (Acts 7:56)
He who descended is the same one who ascended far above all the heavens, so that he might fill all things. (Eph 4:10)
Since, then, we have a great high priest who has passed through the heavens, Jesus, the Son of God, let us hold fast to our confession. (Heb 4:14)
For it was fitting that we should have such a high priest, holy, blameless, undefiled, separated from sinners, and exalted above the heavens. (Heb 7:26)
Now the main point in what we are saying is this: we have such a high priest, one who is seated at the right hand of the throne of the Majesty in the heavens, a minister in the sanctuary and the true tent that the Lord, and not any mortal, has set up. (Heb 8:1-2)
At once I was in the spirit, and there in heaven stood a throne, with one seated on the throne! (Rev 4:2)
Then I heard every creature in heaven and on earth and under the earth and in the sea, and all that is in them, singing,
> "To the one seated on the throne and to the Lamb
>
> be blessing and honor and glory and might
>
> forever and ever!" (Rev 5:13)
Then I saw a great white throne and the one who sat on it; the earth and the heaven fled from his presence, and no place was found for them. (Rev 20:11)
This particular view of God's cosmic abode is consistent with that of the Old Testament. God's throne is in heaven above, and his footstool is on earth below. The heavens must be opened for God to descend from them or for Jesus to ascend to them.
However, that is not the only view of heaven given to us in the New Testament. On the one hand, the locus of God's reign lies above. On the other hand, it is present with the coming reign of God in Christ. The phrase "the kingdom of heaven has come near" occurs three times in the Gospel of Matthew. In the first instance, John the Baptist is predicting the coming of Jesus (Mt 3:2). The second occurrence comes when Matthew tells us that this had become the message Jesus preached (Mt 4:17). Finally, Jesus tells his disciples to preach the same message as they go (Mt 10:7). When Jesus taught his disciples to pray, he prayed,
> Your kingdom come.
>
> Your will be done,
>
> on earth as it is in heaven. (Mt 6:10)
According to New Testament theology, heaven is not the place where one goes after death. It is the place of God's reign, which has come to earth. For this reason, the resurrection of the body is central to Christian theology. The dead do not fly away to the sweet by and by above the firmament, but await the resurrection to live in the new Jerusalem on earth (Rev 21–22).
The multivalent views in the New Testament resulted in divergent interpretations of the upper heavens. One view was dominated by Aristotelian/Platonic dualism, in which earth and its mortal inhabitants are imperfect shadows of the perfect forms that are the heavens and eternal souls. This is found most prominently in Dante's _Paradiso_ , in which the immortal soul leaves the body to ascend to God's abode in the Empyrean, the tenth sphere. It is also seen in the apocryphal book of _2 Enoch_. The angels dwell in the seventh heaven, corresponding to the sphere of the fixed stars, while God resides in the tenth heaven ( _2 Enoch_ 20). The other view is the more orthodox position, in which heaven is not a cosmic location but is representative of God's sovereign rule. Even while operating in an Aristotelian cosmology, Calvin understood the theological significance of heaven not as a place above the firmament, but believed "that the majesty of God fills all things, and is everywhere diffused; and that he is so far from being shut up in the temple, that he is not shut up or confined within any place whatever."
**_Seas._** Aristotle's cosmos had little, if anything, to say about the third tier of the ancient cosmological system. The nature of the cosmic abyss, if there even was such a thing, was of no consequence to the heavenly spheres. This is not to say that interpreters were completely unconcerned with this tier, but their primary concern was attempting to reconcile Genesis 1:6 with a spherical earth surrounded by solid planetary spheres. They spent considerable rhetorical energy demonstrating how there could be water above the firmament without it falling down, especially in light of the nature of the five elements. Since water is heavier than ether, it defied physics for it to be in the heavens.
Deuterocanonical books waver very little from the ancient Hebrew view of a firmament separating waters above from waters below. In _Song of the Three_ , the three men in the fiery furnace praise all aspects of God's creation, including all the waters above the heavens ( _Song of the Three_ 38). The _Testament of Adam_ , written in the first few centuries A.D., opens with a type of hymn describing the liturgical purposes of the eight hours of the night. Of particular interest is the fifth hour, in which "is the praise of the waters that are above the heaven" (1:5). These waters are an ocean with mighty waves, not simply a metaphor for precipitation. Precipitation is to be praised in the sixth hour of the night. Clouds were certainly near the firmament, but not above the firmament.
About the taking away of Enoch; how the angels took him up to the first heaven. And it came about, when I had spoken to my sons, those men called me. And they took me up onto their wings, and carried me up to the first heaven, and placed me on the clouds. And, behold, they were moving. And there I perceived the air higher up, and higher still I saw the ether. And they placed me on the first heaven. And they showed me a vast ocean, much bigger than the earthly ocean. ( _2 Enoch_ 3:1-3)
Enoch is first taken up to the first heaven, where he stands on clouds. Then he is placed on the sphere of the first heaven, from where he can see the cosmic ocean below his feet. Elsewhere, it is only with the aid of an angel of the Lord that Baruch is able to cross waters above the heaven, which form an impassable river for all other creatures ( _3 Baruch_ 2:1).
Early Jewish interpreters had similar views of the cosmic seas. In the _Babylonian Talmud_ 's account of the Tower of Babel, the rabbis express the view that the solid firmament held back the waters above. In their schemes to build the tower, the nations said, "Let us build a tower, ascend to heaven, and cleave it with axes, that its waters might gush forth." Some rabbis disagreed about the origin of the earth's water supply, however. Rabbi Eliezer claimed that they came from the ocean, based on Genesis 2:6. This seemed problematic to others, though, since the ocean is salty. Rabbi Joshua offered a more thorough explanation:
The whole world drinks from the upper waters, as it is said, "And drinketh water as the rain of heaven cometh down" (Deut 11:11). If so, what is the force of the verse, "But there went up a mist from the earth" (Gen 2:6)? This teaches that the clouds grow in strength as they rise towards the firmament and open their mouth as a flask and catch the rain water, as it is said, "Which distil rain from His vapour" (Job 36:27).
Both Eliezer and Joshua appeal to Scripture for their solutions, but Joshua's response takes into account the waters above the firmament, not just the waters below the earth. Rabbi Joshua's interpretation is quite similar to that of Josephus, who interpreted the firmament as a crystalline dome through which precipitation would pour and irrigate the earth. Like those who wrote the deuterocanonical books, Rabbi Ben Pazzi thought there was more water above the firmament than below it.
The church fathers also weighed in on this issue from time to time. For Theophilus of Antioch there was equal water above the firmament as below it. Half of the water "was taken up that it might serve for rains, and showers, and dews for mankind. And half the water was left on earth for rivers, and fountains, and seas." Others were not quite sure what to make of the waters above the firmament. Chrysostom struggles to find adequate answers to this dilemma.
Now, what would you say this means, the firmament? Water that has congealed, or some air that has been compressed, or some other substance? No sensible person would be rash enough to make a decision on it. Instead, it is better to be quite grateful and ready to accept what is told us and not reach beyond the limits of our own nature by meddling in matters beyond us, but rather to know only the simple fact and keep it within us—namely, that by the Lord's command the firmament was produced, causing division of the waters, keeping some below and being able to carry the rest elevated on top of it.
Ultimately Chrysostom concludes that it is best not to question these things. The Lord has established it in his Word; therefore waters lie above the firmament. Basil, however, is a little more creative in his solution.
They question us: If the body of heaven is like the form of a sphere, as its appearance indicates, how do the fluid waters that have a slippery nature remain on the dome of heaven at a great height in its orbit, their station being firm on it? But we say to them that not as it appears to us from within to bear the shape of a vault and the figure of an orb is in fact its outer appearance and that of the exterior form. For its upper height does not have the form of a sphere, nor is it constructed in the likeness of a wheel. But there is a level place constructed above it—just as we see that baths rise up on the inside in domes on all sides, but the roof of their ceiling from outside is flat and in a stable position.
On the one hand, the Bible says God placed a firmament in the heavens, separating the heavens above from the waters below. On the other hand, Aristotelian cosmology had established spherical heavens. Basil is trying to imagine any scenario in which water could stay atop a concave bowl. The only way this could happen is if the bowl were concave from below, but flat above, like the arches in Roman architecture (see figure 5.3).
**Figure 5.3.** Roman arches
Augustine is so befuddled by this matter that he resorts to allegory, understanding the water above the heavens to be "the very matter of the world," that is, the material from which the land would be created. The church fathers, then, were reluctant to dismiss the rational observations about the physical world, but they were more reluctant to dismiss Scripture as a reliable witness of the cosmic structure.
Among medieval interpreters, Maimonides and Aquinas find another way of dealing with the issue. For Maimonides, the idea of waters above the firmament becomes too incredible to reconcile with reality.
But the account of the firmament, with that which is above it and is called water, is, as you see, of a very mysterious character. For if taken literally the firmament would appear at first thought to be merely an imaginary thing, as there is no other substance but the elements between us and the lowest of the heavenly spheres, and there is no water above the air; and if the firmament, with that which is over it, be supposed to be above the heavens, it would _a fortiori_ seem to be unreal and uncomprehensible.
Rather than dismiss Scripture or abandon common sense, Maimonides opts to reinterpret this passage so that the waters above the firmament are "water by name only, not in reality." Aquinas in his _Summa Theologica_ adopts the views of the church fathers who preceded him. In response to the question, "Whether there are waters above the firmament?" Aquinas poses three objections. First, it does not look like there are waters up there (Maimonides). Second, water cannot rest on a sphere (Basil). Third, water would be useless up there. In response to these challenges to Genesis 1:6-7, Aquinas affirms the biblical view that there are waters above the firmament, but "their exact nature will be differently defined according as opinions on the firmament differ," whether it is the starry heavens or the atmosphere in which the clouds gather. Both Maimonides and Aquinas are aware of the problems of a literalistic reading of Genesis 1:6-7, but arrive at different conclusions on how best to reconcile those problems with the biblical text.
The problem has not gone away by the time of Luther and Calvin. Luther's approach is similar to that of Chrysostom.
But what is most remarkable is that Moses clearly makes three divisions. He places the firmament in the middle, between the waters. I might readily imagine that the firmament is the uppermost mass of all and that the waters which are in suspension, not over but under the heaven, are the clouds which we observe, so that the waters separated from the waters would be understood as the clouds which are separated from our waters on the earth. But Moses says in plain words that the waters were above and below the firmament. Here I, therefore, take my reason captive and subscribe to the Word even though I do not understand it.
Like Aquinas, Luther would like to imagine that the firmament is just a metaphor for the cloud layer, but his insistence on attending to the letter of Scripture prohibits him from doing so in this case. Even though it does not make sense, his priority is to submit to the authority of God's Word. Calvin is likewise troubled by this contradiction to the senses.
Moses describes the special use of this expanse, "to divide the waters from the waters," from which words arise a great difficulty. For it appears opposed to common sense, and quite incredible, that there should be waters above the heaven. Hence some resort to allegory, and philosophize concerning angels; but quite beside the purpose.
Whereas Luther wished to think of the firmament as clouds, Calvin actually attempts to demonstrate as much by appealing to Scripture and science. He says, "We know, indeed, that the rain is naturally produced; but the deluge sufficiently shows how speedily we might be overwhelmed by the bursting of the clouds, unless the cataracts of heaven were closed by the hand of God." Since the hand of God is figurative language for God's power, the firmament is also figurative language for the clouds, the so-called heavenly chambers (Ps 104:3; 148:4).
Biblical interpreters in the post-Aristotelian era treated the issue of the waters above the firmament in various ways. For early interpreters it was quite easy to maintain the ancient Hebrew view of a celestial sea above the firmament. For later interpreters this view became strained in light of the apparent discrepancies with the nature of the heavens and the scientific understanding that water does not come from the firmament, but from the water cycle. In spite of these contradictions to reality, some maintained their method of biblical interpretation, even at times against their better judgment.
#### Geocentrism, Anthropocentrism
The heavens, earth and sea of Hebrew cosmology were tiny compared to modern standards. Though the extent of God's creation was enormous from their point of view, the ancients simply had no way of conceiving of an earth with a circumference of nearly twenty-five thousand miles. Nor could they have ever imagined planets beyond Saturn, let alone stars and galaxies billions of light years away. In the Aristotelian era, significant changes were made to the ancient perception of reality. For one, it was no longer sustainable to hold to a flat earth. Even though this facet of cosmology gave way to a more enlightened view of the shape of the earth, interpreters tended to assume that the rest of creation revolved around their home.
At the beginning of this chapter I noted how Aristotelian cosmology was especially appealing to Christian theology because it emphasized humanity as the pinnacle of God's creation. Since humans were made in the image of God (Gen 1:26-27) and a little lower than God himself (Ps 8:5), it was only fitting that all of God's creation would revolve around humanity. The idea that the sun, moon and planets orbit the earth is often called geocentrism, but a better term might be anthropocentrism. The theological concern was not that the earth was the center, but with the Homo sapiens who inhabit it and rule over it (Gen 1:26).
Neither geocentrism nor anthropocentrism appears in the writings of the interpreters from this period. Instead, they discussed how the heavens moved or revolved around the earth. In his commentary titled _On the Creation of the World_ , Philo of Alexandria speaks of the artistic, even musical, quality of these revolutions.
Again, when on soaring wing it has contemplated the atmosphere and all its phases, it is borne yet higher to the ether and the circuit of heaven, and is whirled round with the dances of planets and fixed stars, in accordance with the laws of perfect music, following that love of wisdom which guides its steps.
In his _Allegorical Interpretation of Genesis_ , he notes that it is too simplistic to think of the six days of creation as being actual days, since the designation of days is only meaningful with respect to the sun as it "goes over and under the earth," which was not created until day four. Basil disagrees with Philo's conclusion, but agrees that a day constitutes the time it takes for the sun to circle the earth. Even Aquinas concurs that "night and day are brought about by the circular movement of a luminous body." His contemporary Maimonides also asks, "What determined 'the first day,' since there was no rotating sphere, and no sun?"
These interpreters were not just using figurative language about the circuit of the sun as it appears. They spoke in very clear terms about the rotations of the entire heavens, as Aristotelian cosmology demanded. For Rabbi Hoshaia the variant durations of the planets' orbits were an indication that the heavens were not as perfect as the Aristotelians would have liked to believe.
So too there is a planet which completes its circuit in twelve months such as the sun, and there is a planet which completes its circuit in twelve years, such as Jupiter, and there is a planet that completes its circuit in thirty days, such as the moon, and there is a planet that completes its circuit in thirty years, such as Saturn. The exceptions are the planets Mercury, Venus, and Mars, for these complete their circuit in four hundred eighty years.
These are not just observations about the length of a day, but about the fact that each of the heavenly spheres required a set amount of time to complete its circuit around the earth. Aquinas is one of the few interpreters who actively engages Aristotelian ideas. In response to Aristotle's Prime Mover, Aquinas argues that God is the Unmoved Mover Aristotle required.
A proof that the heavenly bodies are moved by the direct influence and contact of some spiritual substance, and not, like bodies of specific gravity, by nature, lies in the fact that whereas nature moves to one fixed end which having attained, it rests; this does not appear in the movement of heavenly bodies. Hence it follows that they are moved by some intellectual substances. Augustine appears to be of the same opinion when he expresses his belief that all corporeal things are ruled by God through the spirit of life.
The movement of the heavens was not theoretical or observational. It was mathematical and, more importantly, theological. That the heavens moved had been settled by Aristotle long ago. Now Aquinas was able to demonstrate that the movements of the heavens had real theological significance with God as the Unmoved Mover.
#### Summary and Conclusion
Aristotle and Ptolemy were influential Greek thinkers, to put it mildly. Aristotle was a philosopher whose ideas were heavily influenced by Plato and Platonism, in which perfection lay in the forms. Earth is but a shadow of the perfect heavens. Ptolemy's mathematical interests and acumen moved him beyond the metaphysical concerns of forms and into the theoretical potential of equations. Neither of these intellectual giants were devout men of Scripture. Their interests were not theological but philosophical and cosmological. However, their ideas were judged by Jews or Christians not on theological grounds but on the persuasiveness of their arguments, and rightfully so.
Of course, while these Jewish and Christian interpreters did not buy into every single tenet of Aristotelian cosmology, they did nonetheless need to reckon with it. They could not ignore it or dismiss it on the grounds that it was pagan in origin. On several occasions, Basil refers to "the wise men of the Greeks" in somewhat derogatory terms, suggesting Scripture must be thought of more highly than Greek philosophy. But even then he recognized the credible arguments put forward by the Greeks and felt compelled to counter with a rational response, if one could be found. Moreover, he not only conceded many of the Aristotelian concepts but also appealed to them on occasion to support his own exegesis. These interpreters were faced with the reality that the new cosmology made much more sense than the ancient cosmology and that Aristotelian cosmology had won the court of public consensus.
The world had changed drastically and dramatically around 400 B.C. In the ancient Near East, the earth was small, flat and round. It was surrounded by a treacherous, cosmic sea with unspeakable depths and unfathomable monsters. A dome in the sky separated the heavens above from the earth below, held back the heavenly seas and served as the ground floor of God's heavenly abode. Most of this changed with Aristotle. The earth was now a sphere, with various bodies of water separating numerous landmasses. The heavens were composed of seven spheres, one for each of the seven planets. God's throne was moved further from the earth to accommodate the spheres. Some ancient ideas were held over, though, such as the fixed stars on the firmament and the waters above the firmament.
New Testament authors were stuck between two worlds. On the one hand, their Scripture was the Hebrew Bible, which operated in the context of ancient Near Eastern cosmology. The new heavens and new earth of Revelation 21–22 are reminiscent of the cosmos as described in Genesis 1–2. When Jesus calms the stormy sea (Mt 8:26), he assumes his audience fears the chaotic cosmic ocean. In Acts 1:8 Jesus instructs his disciples to be witnesses "to the ends of the earth," suggesting his disciples thought there was an end to be reached. On the other hand, the New Testament authors' culture was sufficiently Greek to adapt some Aristotelian concepts, such as the third heaven (2 Cor 12:2) and levels in the grave (Lk 16:19-31).
The most notable trait we see among the Aristotelian-era interpreters is the willingness to adapt their interpretation of Scripture in light of new understandings of the physical universe. It was assumed that the cosmos was composed of seven spheres that rotated around the earth. This had implications for all sorts of biblical interpretations. The foundations of the earth could no longer be thought of in terms of physical columns, but were conceived as a metaphor for God's sustaining power. The greater light and lesser light had to be interpreted in terms of the amount of light the sun and moon emitted, rather than their size. The fact that Genesis 1 speaks of two heavens suddenly became unproblematic, since the Greek philosophers had determined several more than that. A global earth had to be reconciled with the possibility of people living on the other side of it. Whether there were waters above the firmament was discussed in light of a spherical firmament. Wherever Scripture touched on issues of cosmology, the interpreters had to contend with the Aristotelian cosmos.
# 6
## SCRIPTURE AND COPERNICAN COSMOLOGY
It is usually dangerous to generalize an entire century, let alone several centuries, according to a single defining element. However, thanks in large part to Jules Michelet's _History of France_ (1858), the term _Renaissance_ has done just that for Europe in the fourteenth to the seventeenth centuries. The term was canonized by Jacob Burckhardt in 1860 with the publication of _The Civilization of the Renaissance in Italy_. For better or worse, the term suits historians as a generic term for the general cultural European climate between medieval Christendom and the modern era.
For reasons too complicated to explore here, the ingredients necessary for the Renaissance were in place long before its official onset in the fourteenth century. For reasons equally complicated, the fertile lands of Italy served also as the fertile fields for the Renaissance. At the heart of the Renaissance was the recognition that successful business and efficient government required literacy, and literacy required education. Universities not only enlarged their enrollments but also shifted their educational emphasis from theological studies to more practical fields in the humanities. The humanists, as they were called, were interested in subjects like grammar, philosophy, rhetoric and history, which they learned by appealing to the classical era of the Greco-Roman period (ca. 332 B.C. to A.D. 395). Humanists were not uninterested in theological concerns or religious ideas, but they "stressed earthly fulfillment rather than preparation for paradise." So, while they were not unconcerned with matters of the church, they were more concerned with how they could improve their lives and the lives of their fellow humans. It was their contention that the best way to accomplish this was to reacquaint themselves with the art and literature of ancient Greece and Rome, which had never been surpassed, at least in the view of Petrarch, the father of humanism.
Thanks to the humanistic achievement of the period, the world's museums, churches and homes are now adorned with the paintings and sculptures of the artistic visionaries of the Renaissance. Michelangelo gave us sculptures of David and Moses, as well as his paintings _Pietà_ and _Creation of Adam_ in the Sistine Chapel. Leonardo da Vinci's _Last Supper_ and _Mona Lisa_ are among the most famous paintings of all time. Other masters of the period include Raphael ( _Madonna in the Meadow_ ), Donatello ( _Saint George_ and _David_ ), Botticelli ( _Venus_ ), Mantegna ( _The Dead Christ_ ) and Ghiberti ( _Gates of Paradise_ ).
**Table 6.1.** People and progress of the Renaissance
**Copernicus (1473–1543)**
**Galileo (1564–1642)**
**Kepler (1571–1630)** | 1492 Columbus rediscovers the New World
1517 Protestant Reformation begins
1519–1522 Magellan circumnavigates the globe
1590 Zacharias Janssen invents compound microscope
1597 Shakespeare writes _Romeo and Juliet_
1607 Jamestown founded
1628 William Harvey publishes _On the Motion of the Heart and Blood in Animals_
1667 John Milton publishes _Paradise Lost_
1676 Anton van Leeuwenhoek observes bacteria under microscope
---|---
#### Cosmological Revolutionaries
As impressive and enduring were the representational arts of the Renaissance, the advances in the sciences were perhaps even more impressive and equally enduring (see table 6.1). It was in this context of humanistic achievement that the likes of Copernicus, Galileo and Kepler upset the cosmological apple cart. Under the persistent scrutiny of these intellectual giants, Aristotle's system of spheres within spheres moving about the earth would prove no longer tenable. Despite the church's best efforts to silence the unbiblical doctrine of heliocentrism, a new cosmology emerged in which the sun usurped the earth as the center of the universe.
**_Copernicus._** Although the height of the Renaissance took place in Italy, the cosmological revolution that had been two thousand years in the making began humbly in the small Polish town of Torún. There, in 1473, Nicholas Kopernik was born to a merchant father who died when the young Kopernik was only ten years old. Following the death of his father, Nicholas's uncle, Lucas Watzenrode, who was well situated in life, assumed responsibility for Nicholas and his younger brother. Due to Uncle Lucas's societal position, the two boys were eventually afforded the distinguished honor of attending the prestigious University of Krakow. While at Krakow, Nicholas studied mathematics and astronomy. At the age of twenty-three he continued his studies in Italy at Bologna and Padua, but changed his course of study to liberal arts, canon law and medicine. His formal education culminated in his studies at the University of Ferrara, Italy, with a doctorate in canon law. With degree in hand at the age of thirty, he returned to Poland in 1503 to begin his lifetime clerical post at the Cathedral of Frombork.
Parish ministry may have been his career, and the one for which he had been formally trained, but astronomy remained his hobby and passion. It has been suggested that Kopernik, better known as Copernicus, was "one of the first scholars to study printed books in his own library." Among the books he held in his possession were Ptolemy's _Almagest_ , along with al-Battani's ninth-century corresponding astronomical tables. Copernicus entrenched himself in Ptolemy's work but became frustrated with the complexity of the Ptolemaic epicycles.
Therefore I also, having found occasion, began to meditate upon the mobility of the Earth. And although the opinion seemed absurd, nevertheless because I knew that others before me had been granted the liberty of constructing whatever circles they pleased in order to demonstrate astral phenomena, I thought that I too would be readily permitted to test whether or not, by the laying down that the Earth had some movement, demonstrations less shaky than those of my predecessors could be found for the revolutions of the celestial spheres.
Copernicus's discontent with the inadequate explanations for the structure of the cosmos yielded one of the greatest scientific advances of all time, and certainly the most significant to come along in two thousand years.
Using geometrical theorems, mathematical formulas and simple observations of the cosmos, Copernicus determined that the Aristotelian/Ptolemaic geocentric system could not withstand scrutiny. It was not until the year of his death in 1543, though, that he finally mustered the courage to publish _De Revolutionibus orbium coelestium_ , which translates to _On the Revolutions of the Heavenly Spheres_. There he posited the ingenious notion that the earth orbits the sun, along with the five planets, Mercury, Venus, Mars, Jupiter and Saturn. He was well aware that his ideas may not sit well with the holy see, as evidenced by these comments in his introduction to _Revolutions_ :
But if perchance there are certain "idle talkers" who take it upon themselves to pronounce judgment, although wholly ignorant of mathematics, and if by shamelessly distorting the sense of some passage in Holy Writ to suit their purpose, they dare to reprehend and to attack my work; they worry me so little that I shall even scorn their judgments as foolhardy.
Copernicus was convinced that there would be those who would oppose his views, but reminded his readers that a dogged commitment to a hyperliteralistic interpretation of Scripture led Lactantius, a "distinguished writer but hardly a mathematician," to defend a flat earth "in an utterly childish fashion." We see, then, that Copernicus was trying to alert his audience to the fact that we should allow the evidence to speak for itself, rather than allow potentially flawed interpretations of Scripture to muddle our judgment.
According to Thomas Kuhn, "The significance of the _De Revolutionibus_ lies . . . less in what it says than in what it caused others to say." Before looking at what others said, though, let us briefly summarize the ideas that spawned the Copernican Revolution. First, Copernicus did not set out to revolutionize anything. Remember, he was an ardent student of Ptolemy's _Almagest_. However, as he himself looked to the heavens, he could not reconcile what he saw with what he read. In chapters seven and eight of book one, he provides the reasons why his predecessors adhered to a geocentric cosmology, followed immediately with a reasoned solution for its problems. According to the old model, the further a celestial body is from earth, the faster its orbit must be due to the enlarged circumference of the sphere. As the spheres increase in size, the speed of their rotations approaches infinity, which defies logic and the laws of physics. Another problem with the Aristotelian system was its concept of a finite universe. If the heavens were finite, what lay beyond them would be nothing, and it makes little sense for the heavens to be held in place by nothing. Instead, Copernicus posits that the heavens as we know them are merely a finite hollow space within the infinite heavens. These conclusions, however, merely laid the theoretical framework for his ultimate argument, namely, that "it is more probably that the Earth moves than that it is at rest—especially in the case of the daily revolution, as it is the Earth's very own."
In chapters ten and eleven of _Revolutions_ , Copernicus articulates his innovative model of the heavenly movements. Rather than the heavenly spheres rotating around the earth, Copernicus demonstrates that a "threefold movement of the Earth" accounts for all of the celestial observations. The three movements are (1) daily rotation of the earth on its axis, (2) annual orbit of the earth around the sun and (3) seasonal shift in the tilt of the earth on its axis. The first movement accounts for the apparent celestial differences between night and day, such as the sunrise and sunset, and the waxing and waning of the constellations and planets. The second movement accounts for the movement of the zodiacal signs. He says, "In this way, for example, when the centre of the earth is traversing Capricorn, the sun seems to be crossing Cancer." The third movement explains the changes of the sun's position on the horizon, such that in the northern hemisphere daylight hours are longer in the summer and shorter in the winter. Copernicus maintained the circular orbit of the planets but shifted the center of the movement from the sun to the earth. By placing the sun at the center of the universe, Copernicus was able to account for nearly every conceivable mathematical and astronomical problem inherent in the Aristotelian system (see figure 6.1). Although his theory better accounts for the apparent retrograde movements of Venus and Mars in the night sky, his theory does not altogether explain the motions of the two planets. That would have to wait another sixty-six years, when Kepler would introduce the idea of elliptical orbits.
**Figure 6.1.** The Copernican cosmos
**_Galileo._** Two decades after Copernicus's death Galileo Galilei was born in the Tuscany village of Pisa on February 15, 1564. The famous tower was leaning even then. At the age of ten, his merchant family relocated about fifty miles inland to Florence, the heart of the Italian Renaissance, where Galileo began to study Greek, Latin and logic. In 1581 he enrolled at the University of Pisa to study medicine. It wasn't long before he earned the reputation for which he continues to be remembered, namely, as an intellectual who would not accept an argument without evidence. It was this inquisitive spirit that earned him the moniker "father of the scientific method." By the time his career as a mathematician came to an end, Galileo had held posts at the University of Pisa (1589–1592), the University of Padua (about twenty-five miles west of Venice; 1592–1610) and then again back in Pisa, where he concluded his career.
Galileo's claim to fame, of course, is his insistence that the Copernican system provided the only plausible explanation for the astronomical phenomena. But that was not always the case. In fact Galileo taught Aristotelian cosmology at the University of Padua until the mid-1590s. Then in 1595 he began to ponder the tides and concluded that the Copernican system of the earth's rotation on its axis, paired with its revolution of the sun, provided the best explanation. A year later the German mathematician-philosopher Johannes Kepler published _Mysterium cosmographicum_ , in which he demonstrated both the theoretical and astronomical superiority of the Copernican system. Kepler sent a copy of his book to Galileo, who replied, "I have preferred not to publish, intimidated by the fortune of our teacher Copernicus, who though he will be of immortal fame to some, is yet by an infinite number (for such is the multitude of fools) laughed at and rejected." Consequently, Galileo would wait seven years to publicly decry Aristotelianism, and another thirty-five years before his major treatise on Copernican cosmology would reach the press. Although his theory of the tides inevitably proved erroneous, it nonetheless formed the impetus for his investigation, then defense, of the Copernican system.
Although Galileo refrained from writing formally about the Copernican system, which he had come to adopt as his own, he became a vocal supporter of heliocentrism and a vocal critic of geocentrism. Two major events in the first decade of the seventeenth century only served to embolden his efforts. The first was astronomical; the second, technological. In the fall of 1604, a supernova appeared in the heavens. Incidentally, in 1572, when Galileo was a child, another supernova had been visible as well. At that time the Danish astronomer Tycho Brahe posited that the heavens were not unchangeable, as the Aristotelians argued. In fact supernovae were cause for concern in the old system, in which the heavens were deemed perfect and immutable. The appearance of these changing and new celestial bodies undermined that assumption. By sheer coincidence or divine providence, the last supernovae to explode did so during Galileo's lifetime, at the peak of the Copernican Revolution.
**Figure 6.2.** St. Mark's bell tower in Venice
Due to the immense interest in these celestial phenomena, Galileo was forced to defend publicly his anti-Aristotelian position, culminating in his publication of a pamphlet-length dialogue between a professor and a peasant, the latter of whose logic was presented as more reasonable than that of the professor. Although Galileo wrote the dialogue under a pseudonym, it did not sit well with his Aristotelian colleagues at the university.
The second event of significance was the invention of the telescope. Galileo was not the inventor of the telescope. That honor belongs to Hans Lipperhey, a Dutch eyeglass maker. When Galileo heard of it, though, he built one of his own within eight months. In 1609, excited to demonstrate his new device as well as to herald its merits for military and shipping uses, Galileo took a group of government officials to the top of Saint Mark's bell tower in Venice, the Campanile in Piazza San Marco (see figures 6.2 and 6.3). Having presented one of his new inventions to the doge of St. Mark's, Galileo suddenly found himself in the very good graces of the Venetian power brokers, landing him a prestigious lifetime position at the University of Padua, with a twofold increase in salary. A year later, however, he left the favorable intellectual atmosphere of the Venetian province and returned to the University of Pisa.
**Figure 6.3.** Modern plaque commemorating Galileo's inaugural use of the telescope
Although Galileo was well aware of the entrepreneurial benefits of the telescope, it was his astronomical observations with more powerful telescopes that would ultimately spell the demise of the Aristotelian system. In January of 1610, he pointed his instrument to Jupiter and discovered four moons orbiting the planet. The implications were profound, since it would be impossible to ever argue again that there is only one body, the earth, around which all others revolve. Galileo quickly published _Siderus Nuncius_ , or _Starry Messenger_ , in which he implored his fellow astronomers to set their scopes to the skies of Jupiter. Enamored of this discovery, he turned his eyeglass to other regions of the heavens, continually adding to the list of observations that would prove untenable in the Aristotelian system. The universe was much vaster than anyone could have possibly imagined before, as evidenced by the stellar construction of the Milky Way galaxy. Venus had moon-like phases, indicating that it also orbited the sun. The moon was not smooth but had mountains and valleys, and the sun had spots, both of which demonstrated celestial imperfections.
Kepler. Johannes Kepler and Galileo were contemporaries who agreed on the Copernican system as the best representation of physical cosmology, but they had contrasting methods for voicing their opinions. Whereas Galileo had raised the ire of the holy office on numerous occasions, Kepler quietly went about his work as a mathematician to prove the superiority of heliocentrism. What's more significant, though, is that Kepler not only demonstrated the merits of Copernicanism but also improved on it.
While Kepler was a mathematician by trade, his governing philosophy was that the universe and all its components adhere to providential laws of geometry. The Creator of this cosmos not only established the cosmos to follow geometrical principles but also gave humans the capacity to comprehend these principles. Laboring intensely over the structure of the cosmos, the idea of elliptical planetary orbits hit Kepler like a personal revelation from God. At least that's how he described it. "I believe it was by divine ordinance that I obtained by chance that which previously I could not reach by any pains; I believe that so much the more readily because I had always prayed to God to let my plan succeed, if Copernicus had told the truth." Despite a world that had been more than unkind to Kepler, he refused to accept it as anything but beautiful.
The true test for Kepler's theory of elliptical planetary orbits lay in the orbit of the planet Mars. Even though the Copernican model provided an improved explanation for the apparent retrograde movements of planets in the nocturnal sky, problems persisted, especially with respect to the observed orbit of Mars; "for no planet were the inadequacies of both the Ptolemaic and Copernican models rendered more starkly." This became especially apparent when in the late 1580s the Danish astronomer Tycho Brahe determined that Mars is closer in proximity to the earth than the sun. In 1600 Kepler waged a bet with Brahe's apprentice Christian Longomontanus that he could crack the riddle of Mars within one week. The complexities of the Mars problem proved so challenging that it actually took Kepler five years to decipher. Kepler lost the wager, but Aristotelianism was now poised to lose the entire pot.
#### Heliocentrism and Scripture
As John Dillenberger reminds us, the challenge of the new science as articulated by Copernicus, Galileo and Kepler was not that it lacked observational data to support its claims. The problem was that it was directly opposed to deeply seated "philosophical and theological assumptions" rooted in Aristotelianism. While Aristotle employed mathematics to support his observations, it was but one of the many tools at his disposal. Kepler, if we recall, relied exclusively on mathematical calculations, casting aside all theoretical notions that could not be substantiated by his equations. Despite his mathematical intentionality, Kepler managed to hold his mathematics in tension with his conviction that the cosmos still had a certain mystical quality about it.
Galileo, by contrast, preferred a more rational approach. In a letter to Christina, the grand duchess of Tuscany, he recognized that at times Scripture was at variance with nature, but that that should be of no concern.
Nature, on the other hand, never transgresses the laws to which it is subject, but is inexorable and unchanging, quite indifferent to whether its hidden reasons and ways of working are accessible to human understanding or not. Hence, any effect in nature which the experience of our senses places before our eyes, or to which we are led by necessary demonstrations, should on no account be called into question, much less condemned, because of a passage of Scripture whose words appear to suggest something different.
For Galileo, if God was responsible for both Scripture and the natural world, it was illogical to conceive a world in which the two would be in contradiction. Where there were apparent contradictions, the problem was that one of the two was being wrongly interpreted. From his perspective, given the choice between Scripture and science, the former provided the heaviest challenges for unequivocal interpretation.
As we might imagine, Galileo's assertion that the Book of Nature could supersede the Book of Scripture was cause for consternation among Christians throughout the European continent. While Christians have always recognized that nature was one means by which God revealed himself (Ps 19), the greatest revelation is the person and work of Jesus Christ as preserved for us in Holy Writ. Consequently, both Catholics and Protestants found reasons to dismiss Copernicanism on theological grounds.
**_Protestant Reformation._** The sixteenth century was a volatile period for the Roman Catholic Church. Not only did Copernicus dare to overturn Aristotelian cosmology, but this century was also the period in which the Protestant Reformation gained traction under the leadership of Martin Luther and John Calvin, most prominently. On October 31, 1517, Martin Luther posted his Ninety-Five Theses at the University of Wittenberg as a means of initiating public dialogue over the issue of the sale of indulgences, among other issues. Although Luther was not looking to start a movement of protest, his actions ultimately lead to what is commonly called the Protestant Reformation, thanks in large measure to factors beyond Luther's influence.
Protestants earned their name not simply because they were standing against the political abuses of the church. To set themselves apart from the Roman Catholic Church, they reacted against the whole stream of its traditions, including the papacy's stranglehold on Scripture. Under Roman authority, the common person need not bother with reading, let alone interpreting, the Bible. The priest had the divine right to both impart its message and parse its meaning. Without access to the Bible the layperson had no choice but to accept the priest's words as words from God himself. To confront the abuses promulgated by the holy office, the Reformers aimed to place the Bible in the hands of all believers. It had the desired positive effect, but also had an unintended consequence. As Peter Harrison demonstrates, "For prospective new readers of the Bible, functional literacy was challenge enough without having to confront the complexities of tropology, anagogy, and allegory." Since ordinary readers were not sophisticated readers, they were unable to detect shifts in genre, metaphor, analogy or other types of figurative language. As such, the "plain sense" became the standard interpretive method adopted by the Reformers, which also stood in stark contrast to the sometimes creative interpretations of the church fathers.
Martin Luther and John Calvin were the two most prominent figures of the Protestant Reformation. We have seen from the previous chapter that they also preferred to read Scripture according to its "plain sense." Unlike many of their lesser educated contemporaries, though, they were able to read the biblical text with a little more sophistication. Sometimes the "plain sense" made no sense, leading them to adopt one of three reading strategies: (1) admit that the nonsensical nature of the text was due to their inadequacies as human interpreters, (2) adopt an allegorical interpretation of the text or (3) apply reason to resolving the complexity of the text.
_Martin Luther_. Martin Luther died on February 18, 1546, just three years after the publication of Copernicus's _Revolutions_. For nearly his entire life, then, Luther lived and operated within an Aristotelian worldview. But he was not averse to scientific inquiry. As we have seen in the previous chapter, he was more than happy at times to concede issues of science and astronomy to the philosophers. Sometimes he even interpreted Scripture in light of what he knew about Aristotelian cosmology, such as the movements of the seven spheres or the five elements of nature. His preference was to interpret the Bible according to its "simple and true meaning," but his knowledge of the natural world occasionally left him confused.
Even though none of Luther's sermons or commentaries directly addresses Copernican cosmology, it seems from one of his _Table Talks_ , dated to 1539, that Luther had at least become familiar with Copernicus's ideas, but the precise extent to which Luther was willing to engage the new science is unclear. The most provocative statement attributed to Luther in response to the Copernican Revolution is found in his Table Talk dated June 4, 1539, in which one of his students reports him as saying:
There was mention of a certain astrologer who wanted to prove that the earth moves and not the sky, the sun, and the moon. This would be as if somebody were riding on a cart or in a ship and imagined that he was standing still while the earth and the trees were moving. [Luther remarked,] "So it goes now. Whoever wants to be clever must agree with nothing that others esteem. He must do something of his own. This is what that fellow does who wishes to turn the whole of astronomy upside down. Even in these things that are thrown into disorder I believe the Holy Scriptures, for Joshua commanded the sun to stand still and not the earth [Josh 10:12]."
Luther's _Table Talks_ are a little complicated to unravel. First, they were not published until 1566, twenty years after his death. Second, as the title of the work implies, the sayings were allegedly informal conversations between Luther and his students, so you might say they were "off the record." Third, on this particular entry, there are conflicting reports from two of his students. The above quotation comes from Anton Lauterbach, whereas another student, Johannes Aurifaber, reported Luther as saying, "That fool would upset the whole art of astronomy." In fact modern studies on Luther have concluded that Aurifaber's edition of Luther's talks contains embellishments and emendations. Luther's comments, if authentic, demonstrate a certain level of reticence toward the new science. However, considering that these remarks allegedly came four years prior to the publication of _Revolutions_ , we must wonder how much Luther had actually heard about and understood the heliocentric model.
It is hard to say exactly how Luther would have responded to the Copernican system had he been allotted the time to contemplate its implications on the interpretation of Scripture. We do know, however, that he was not a pure Aristotelian. Where Aristotle attributes the existence of creatures to the sun and its heat, Luther appeals to the biblical claim that it was the Word of God who created all things. Elsewhere Luther notes that Aristotle's claim that the heavens are not made of the elements is reasonable, but Luther is not sure about this. For Luther the sciences and Scripture need not be in conflict with one another, and they often inform one another. In a comment on the icy firmament, he remarks, "Even though this science has many superstitious elements, still it should not be completely disregarded; for as a whole it concerns itself with the observation and contemplation of the divine works, something which is a most worthy concern in a human being. Therefore men of the highest ability have engaged in it and have taken delight in it." So, although Luther agrees with Aristotle that the sun moves around the earth, which gives us our meaning of "day," he is willing to engage the sciences because "they are the result of plausible reasoning and contain the foundation for the arts" to better appreciate the world which God has made.
_John Calvin_. Until the latter half of the twentieth century it was commonly thought that Calvin was directly at odds with Copernicus's ideas. In 1896, Andrew Dickson White, the first president of Cornell University, claimed that Calvin asked indignantly, "Who will venture to place the authority of Copernicus above that of the Holy Spirit?" As it turns out, the quote attributed to Calvin by White has never been verified. Instead, it seems rather apparent that White had put words in Calvin's mouth to make a stronger case for the ideological divide between science and faith. These apocryphal sayings of Calvin were then relayed and popularized in 1935 by the philosopher Bertrand Russell in his _Religion and Science_. As it turns out, Calvin appears to have offered little, if any, direct response to the new astronomy.
In 1971 Richard Stauffer found the most likely link between Calvin and Copernican science. Rather than being located in the usual list of Old Testament cosmology texts, this interaction comes from Calvin's eighth sermon on 1 Corinthians 10–11, preached a little over a decade after the publication of _Revolutions_.
We will see some who are so deranged, not only in religion but who in all things reveal their monstrous nature, that they will say that the sun does not move, and that it is the earth which shifts and turns. When we see such minds we must indeed confess that the devil possess them, and that God sets them before us as mirrors, in order to keep us in his fear. So it is with all who argue out of pure malice, and who happily make a show of their imprudence. When they are told: "That is hot," they reply: "No, it is plainly cold." When they are shown an object that is black, they will say that it is white, or vice versa. Just like the man who said that snow is black; for although it is perceived and known by all to be white, yet he clearly wished to contradict the fact. And so it is that there are madmen who would try to change the natural order, and even to dazzle men's eyes and benumb their senses.
Calvin is not making a cosmological argument here, but he is clearly engaging the concept of Copernican cosmology as a perverse idea, one that contradicts nature. It may seem at first blush that Calvin is directly engaging Copernicus as one who says "the sun does not move" and "it is the earth which shifts and turns." Christopher Kaiser sees things differently, contending that Calvin is actually refuting his former student Sebastian Castellio, who had become a strong advocate of religious tolerance. Regardless of whom Calvin is responding to, there can be no doubt where he stands on the doctrine of heliocentrism. It is clear that Calvin had not acquiesced to the new science.
For Luther, Scripture was the motivating force for his geocentric dogmatism. Expectedly, for Calvin it was God's sovereignty.
Therefore, to be brief, let all readers know that they have with true faith apprehended what it is for God to be Creator of heaven and earth, if they first of all follow the universal rule, not to pass over in ungrateful thoughtlessness or forgetfulness those conspicuous powers which God shows forth in his creatures, and then learn so to apply it to themselves that their very hearts are touched. The first part of the rule is exemplified when we reflect upon the greatness of the Artificer who stationed, arranged, and fitted together the starry host of heaven in such a wonderful order that nothing more beautiful in appearance can be imagined; who so set and fixed some in their stations that they cannot move; who granted to others a freer course, but so as not to wander outside their appointed course; who so adjusted the motion of all that days and nights, months, years, and seasons of the year are measured off; who so proportioned the inequality of days, which we daily observe, that no confusion occurs.
The stability of the earth was clear evidence that God was in control and had attended to his creation in a powerful, yet caring, manner.
Like Luther, Calvin believed science complemented Scripture. The Bible was to be trusted on all matters, including science, but both men consistently reminded their readers that they were not the original audience of the biblical text. Since Calvin and his contemporaries knew more about science than the ancient Israelites, Calvin asserted that God spoke to them in the Bible through Moses, who "wrote in a popular style things which, without instruction, all ordinary persons, endued with common sense, are able to understand." So when God speaks of the firmament, it is not because there is necessarily a dome above the earth that holds back the water. Rather, it is because that is how the ancients would have understood it. This idea that God has condescended in his language to the limitations of human knowledge and comprehension is known as divine accommodation and will be taken up in more detail in the following chapter.
With the assistance of the doctrine of divine accommodation, Calvin was able to reconcile Scripture with science in areas that may have otherwise seemed irreconcilable. This does not mean that Calvin readily accepted every new scientific claim. As we have already seen, Calvin was heavily entrenched in Aristotelian cosmology and quite wary of Copernicanism. Nonetheless, he demonstrates on a number of occasions his willingness to concede matters of science to those who are trained in such matters. For example, in his commentary on the greater light and lesser light in Genesis, Calvin recognizes that astronomers had rightly concluded that Saturn is actually larger than the moon, even though the moon is called the "lesser light" by the author of Genesis.
Astronomers investigate with great labour whatever the sagacity of the human mind can comprehend. Nevertheless, this study is not to be reprobated, nor this science to be condemned, because some frantic persons are wont boldly to reject whatever is unknown to them. For astronomy is not only pleasant, but also very useful to be known: it cannot be denied that this art unfolds the admirable wisdom of God.
As with Luther, for Calvin the observational sciences played an important role in understanding the nature of God's creation. Unfortunately Calvin was positioned too closely to the Copernican Revolution to apply the doctrine of divine accommodation to this new science.
**_Roman Catholic Church._** It is unsurprising that neither Luther nor Calvin readily adopted the ideas of a Copernican cosmology. After all, Galileo remained an Aristotelian until around the age of thirty, approximately fifty years after the death of Copernicus. Furthermore, as Thomas Kuhn reminds us, _On the Revolutions of the Heavenly Spheres_ was not written for the masses; it was written for fellow astronomers, and even they were slow in recognizing its significance. It really wasn't until the seventeenth century when Galileo pressed the issue that Copernican cosmology received a broad hearing among the clergy. What they heard was not well received.
_Osiander_. The first reaction to _Revolutions_ from the Catholic viewpoint actually came in the form of a preemptive strike by one of the Church's clerics. As Copernicus neared the end of his life, a cleric by the name of Osiander helped see Copernicus's magnum opus through the printing process. Before it went to press, though, Osiander, in an effort to make the work more palatable to the papacy, added a preface that essentially undermined the entirety of the work by calling it an unproved hypothesis:
Since the newness of the hypotheses of this work—which sets the earth in motion and puts an immovable sun at the center of the universe—has already received a great deal of publicity, I have no doubt that certain of the savants have taken grave offense and think it wrong to raise any disturbances among liberal disciplines which have had the right set-up for a long time now. If, however, they are willing to weigh the matter scrupulously, they will find that the author of this work has done nothing which merits blame.
More to the point, he wrote that "it is not necessary that these hypotheses should be true, or even probably; but it is enough if they provide a calculus which fits the observations." Although Osiander had converted to Lutheranism prior to 1546, the objective of his preface was to establish a manner in which the Catholic Church could read Copernicus without alarm.
_Catholic tribunal on Galileo (1616)._ Under the assault of Copernicus's mathematical formulas and Galileo's observational evidence, the Aristotelian model could no longer withstand logical scrutiny. But scrutiny is not always logical. In 1614, the Dominican priest Tommaso Caccini publicly denounced Galileo from the pulpit, citing Acts 1:11 as reason enough not to doubt the accepted, official cosmological system. Playing on the names Galilei and Galilee, Caccini asked rhetorically, "Men of Galilee, why do you stand looking up toward heaven?" Caccini's Dominican superior eventually extended an apology, but the damage was done, for Galileo was now viewed with great suspicion, especially by Cardinal Bellarmine, "a fundamentalist for whom truth lay in the literal words of the Bible." Two years later, Bellarmine successfully petitioned an official committee to rule that Copernicanism was "foolish and absurd in philosophy, and formally heretical since it explicitly contradicts the sense of Holy Scripture in many places, according to the literal meaning of the words and according to the common interpretation and understanding of the Holy Fathers and the doctors of theology." Furthermore, they cited Joshua 10 as biblical support for Aristotelian, geocentric cosmology.
On the day when the LORD gave the Amorites over to the Israelites, Joshua spoke to the LORD; and he said in the sight of Israel,
> "Sun, stand still at Gibeon,
>
> and Moon, in the valley of Aijalon."
And the sun stood still, and the moon stopped, until the nation took vengeance on their enemies. (Josh 10:12-13)
Most of the men on the committee were Dominicans, none of whom were experts in astronomy. But that did not stop them from making pronouncements about it.
The verdict of the convention was twofold. First, the Catholic Church decreed Copernicus's _Revolutions_ be placed on the _Index of Prohibited Books_. Kepler was none too pleased with this outcome, for which he blamed Galileo: "Some, through their imprudent behavior, have brought things to such a point that the reading of the work of Copernicus, which remained absolutely free for eighty years, is now prohibited." It seems, though, that Kepler was not completely informed of the situation. In fact, _On the Revolutions of the Heavenly Spheres_ was not officially placed on the _Index of Prohibited Books_ but was merely forbidden to be read until corrections could be made to make its claims seem less scientific and more hypothetical. In 1620 an addendum of ten corrections was inserted into existing copies. Outside Italy, the corrections were ignored. The second outcome of the convention was to serve notice to Galileo that he was to cease and desist from promoting Copernicanism until he could provide indisputable proof. Bellarmine sums up the committee's opinion by stating that
if there were a real proof that the sun is the center of the universe, that the earth is in the third sphere, and that the sun does not go round the earth but the earth round the sun, then we should have to proceed with great circumspection in explaining passages of Scripture which appear to teach the contrary. . . . But I do not think there is any such proof since none has been shown me.
Galileo was spared a guilty verdict, but the hearings had the desired effect for the holy see. After his demoralizing defeat in Rome, Galileo returned to Florence and pursued less controversial endeavors, turning his attention to naval navigation systems.
_Inquisition of Galileo (1633)._ One of the presiding members of the tribunal was a progressive-thinking Jesuit by the name of Cardinal Maffeo Barberini. He and Galileo had formed a cordial relationship that served Galileo well into the early years of their relationship. It is thought that Barberini's diplomatic skill was the mitigating factor in tempering the judgment against Galileo. To Galileo's great delight, in 1623 Cardinal Barberini was elected pope, taking the name Urban VIII. Two years later the reinvigorated astronomer took to writing his _Dialogue Concerning the Two Chief World Systems—Ptolemaic and Copernican_ , which was published in 1632. In the meantime, Urban VIII gave Galileo two official church positions, leading the unwitting Galileo to the impression that he had an ally at the highest level. In fact, while Urban was impressed with Galileo's intellect, he knew it was politically imprudent to permit this rogue astronomer to carry on publicly with his Copernican ideas.
When _Dialogue_ was finally published, Pope Urban VIII reacted predictably, but not to Galileo. Written in the common language of Italian rather than the academic language of Latin, _Dialogue_ took shots at the Aristotelian position, and more importantly, at those who held those views dearly. Even though Galileo presented his viewpoint as a hypothesis, the manner in which he presented his hypothesis did not win him any favor with the holy see. Galileo's introduction set the historical context for his argument.
A salutary edict was published some years ago in Rome which, as a defence against the dangerous scandals of our present, imposed a timely silence on the opinion of Pythagoras concerning the mobility of the Earth. There were some who were so bold as to assert that this decree was the product not of judicious consideration but of ill-informed prejudice, and there were protests that adjudicators who were totally inexperienced in astronomical observations had no business clipping the wings of speculative thinkers by means of an over-hasty ban. I could not remain silent in the face of such presumptuous complaints, and as I was fully informed about this entirely prudent decision I resolved to appear on the stage of world opinion as a witness to the unvarnished truth.
Galileo states three objectives in the preface. First, experiments conducted on earth can neither prove nor disprove that the earth is stationary. Second, astronomical observations support the Copernican system. And third, he reiterates his earlier hypothesis that the tides make the best sense in a system in which the earth moves.
He called his work a dialogue because it "is not bound always to follow the strict rules of mathematics and so gives scope for occasional digressions, which are sometimes no less interesting than the main argument itself." In reality, it provided him the opportunity to make subtle yet pointed attacks on the previous cosmological model, all the while maintaining its guise as a hypothesis. He uses three characters to engage in the dialogue, all of whom are named for real people with whom he had been acquainted. Salviati, "a man of sublime intellect," represents Galileo's Copernican viewpoint. Salviati's counterpart is Simplicio, named after an Aristotelian philosopher "for whom the greatest obstacle to perceiving the truth was the fame he had acquired as an interpreter of Aristotle." Finally, Sagredo, "a man of distinguished birth and great intelligence," appears to be an objective third party, except that he consistently sides with Salviati.
Pope Urban VIII took great exception to the publication of _Dialogue_ on two counts. One is for the clear fact that Galileo had failed to report to Urban about the injunction imposed on him from the 1616 tribunal. Pope Urban felt betrayed by his former friend for subverting the church's ruling, making it necessary for the pontiff to take action on a controversial issue. The second was that Urban's own viewpoint was characterized in the book as "simple," coming from the perspective of Simplicio. Consequently, Urban VIII convened the Roman tribunal of the Inquisition in 1633. On June 16 of the same year, the verdict was reached, and six days later was rendered to Galileo. Since the verdict was merely "vehemently suspect of heresy," Galileo was spared the consequences that befell Giordano Bruno, who was burned at the stake on the charge of outright heresy in 1600. Instead, Galileo was forced to recant heliocentrism and was placed under house arrest, where he remained until his death in 1642. While captive, he was permitted to entertain only a handful of visitors, but he was able to maintain contact with the outside world via correspondence.
**_Integration of science and Scripture._** Initially, the response to Copernicanism in England paralleled what was happening on the Continent. William Barlow, Richard Burton and Thomas Overbury were among a few of the opponents of the new science in the first quarter of the seventeenth century. Perhaps the most vocal critic, though, was Alexander Ross, who stood as the upholder of truth against those he saw as conforming to the secular scientific agenda. Ross stood against Copernicanism in large part because of the implications that accommodating the inerrant Scriptures would undermine biblical authority.
It is but a conceit of yours to say, that the Scripture accommodates itself to the vulgar conceits, in saying, the Sun riseth and falleth. I warrant you, if the vulgar should conceive that the heavens were made of water, as the Gnostics held; or that the Sun and Moon were two ships, with the Manichees; or that the world was made of the sweat of the Aeons, with the Valentinians; or whatsoever absurd opinions they should hold, you would make the Scripture say so, and to accommodate itself to their conceits.
For Ross, standing against Copernicanism carried the same theological import as the early church's stand against the heretical movements of Gnosticism, Manichaeism and Valentinianism.
Ross's primary rival was John Wilkins, an Anglican clergyman and "principal founder both of the first enduring scientific society, the Royal Society of London, and of a revelation-free natural religion with a utilitarian ethic." In fact, he was the actual founder of neither. With respect to the latter, his views inadvertently paved the way for a purely naturalistic theology devoid of Christian substance, precisely as Ross had predicted. But the objective of the Royal Society was to integrate natural philosophy with the nature of God. They were convinced that our knowledge of God could be supplemented through the study of the natural world. Advances were being made not only in astronomy but in biology as well. In 1590 Zacharias Janssen invented the compound microscope, enabling Anton van Leeuwenhoek to be the first human to observe bacteria in 1676. In 1628 William Harvey published _On the Motion of the Heart and Blood in Animals_ , in which he explained the circulatory system. The wealth of discoveries made in the natural world made it clear to Wilkins and others in the Royal Society that there was much more to God's creation than first meets the eye.
The death of Aristotelian cosmology came with the publication of Isaac Newton's _Mathematical Principles of Natural Philosophy_ in 1687. Building off Descartes, Gilles de Roberval and Giovanni Borelli, Newton was able to provide "the first mathematically formulated explanation of all known celestial phenomena based on a single set of physical laws." With every criticism, Newton was able to counter not just with philosophical hypotheses but also with mathematical precision. But Newton was very careful not to describe the cosmos simply as a clock-like machine, as his harshest critic Gottfried Leibniz had done. For Newton, gravitation was the governing law for the motion of the heavenly bodies, but God was the ultimate Governor of the universe, without whom the entire system would cease to exist.
#### Summary and Conclusion
The seventeenth century, then, was a pivotal period for our current understandings of the world. Discoveries large and small were being made, with Christians at the fore. Understandably these new inquiries were initially met with resistance. The concern was there that pursuing natural explanations for the world would result in the demise of the faith. As humans dug deeper and deeper into the natural realm, many thought that God's activity within the natural world would be increasingly diminished. In retrospect, we see the fears were unfounded. The God of an infinite universe is no less omnipotent or sovereign than a God who sits on his throne beyond the outermost sphere. The God who has created countless planets, stars and galaxies cares no less for humans than the God who created the earth at the center of a geocentric system. In fact, as Owen Gingerich notes, Kepler's life as a Christian scientist demonstrates that "the very motivation for the scientific research can stem from a desire to trace God's handiwork." As Christians of great intellect and curiosity continued their investigation into the world that God created, the new science not only became more and more acceptable but also came to be understood as a fuller revelation of God's magnificent creation.
For two thousand years Aristotle's geocentric cosmos of spheres within spheres held the court of popular opinion. It unquestionably explained the machinations of the universe. The spherical earth stood at the center of revolving heavenly bodies, which completed their daily circuit around the earth, just as it appears. This system remained intact because there was no reason to question it. All it took was a look to the skies to verify its logic and validity. Humans don't move; the planets and stars do.
Not everyone was content to rely on common sense and subjective observation, though. After a lifetime of study, Copernicus resolved that Aristotle was wrong on one important point. The sun did not move about the earth; the earth and the planets moved about the sun. Many were willing to accept Copernicus's proposition as a helpful theoretical construct, but not as scientific truth. Even Galileo was among those who did not readily capitulate to Copernican ideas. It wasn't until he set out to solve the riddle of the tides that he became convinced of the Copernican system. His correspondence with Kepler only bolstered his resolve. As he grew more and more convinced, he also grew more and more courageous in the face of Catholic opposition. Finally, with the aid of the newly invented telescope, Galileo demonstrated not only that the earth revolves around the sun but also that the moon has texture, Jupiter has moons, Venus has moon-like phases and the universe is more expansive than anyone had previously imagined. Paired with the mathematical computations of Copernicus and Kepler, Galileo's heavenly observations ushered in the so-called Copernican Revolution.
The strong theological resistance to Copernicanism was natural. To be sure, some allowances had to be made under the Aristotelian model to account for certain readings of Scripture. For example, the firmament had to be moved to the outer reaches of the seven heavens, and the foundations of the earth had to be taken figuratively rather than literally. But the adaptations necessary for the Aristotelian model paled in comparison to those required of the Copernican model.
It must be remembered that for the holy office the interpretation of Scripture and the church's authority to interpret Scripture were two strands of the same thread. According to the Aristotelian model, humans maintained their pride of place as the pinnacle of God's creation. Since the church was _the_ divinely established institution to govern humanity, the Aristotelian model validated the church as the center of the universe, around which all of God's lesser creation revolved. If the Aristotelian model collapsed, so did the church's stake as the bond between heaven and earth.
For Protestants, the issue with Copernicanism was not one of central authority. In fact, it would seem that Protestants would have welcomed another voice to undermine the overbearing and overreaching authority of the Roman Catholic Church. Instead, Protestants likewise responded in opposition to the new science. For Protestants the main point of contention was its apparent violence against the "plain sense" meaning of Scripture. If the Bible says the earth does not move (Ps 104:5) and that God caused the sun, not the earth, to stand still (Josh 10:12), then there was no reason to dispute that. Although some, like Luther and Calvin, were willing to listen to the opinions of astronomers on cosmological matters, they simply lived too close to the revolution. They did not have the expertise to properly weigh the evidence, nor the chronological distance required to adequately process it.
Eventually the Aristotelian model succumbed to the Copernican model. Although the model was not perfect, it more accurately reflected the true nature of the cosmos than the Aristotelian model, which also proved more accurate than its predecessor. Kepler improved on the Copernican model by discovering the planets' elliptical orbits. Newton improved on it by explaining the movement of objects with his three laws of motion and his law of universal gravitational attraction. Einstein improved on our understanding of the universe again with his theory of relativity, such that modern astrophysicists can say that the universe is completely without a center. In other words, Copernicus was not completely correct in his conclusions, but that does not mean he was incorrect. Copernicus had the beginnings of a theory that was viable. His theory has not been overturned. It has merely been improved on by subsequent generations of astronomers who continue to discover and refine our understanding of the cosmos. What Copernicus did was to recognize a profound mathematical problem with the old system and to provide an explanation that resolved most of the difficulties. Whereas Aristotle's cosmology needed to be overthrown, Copernicus's cosmology merely needed clarification and refinement. This is the nature of science.
# Part Three
## SCRIPTURE _and_ SCIENCE
# 7
## COSMOLOGY AND THE AUTHORITY OF SCRIPTURE
That the biblical description of the cosmos does not comport with our modern understanding of it is not a novel idea. Ever since the discovery of the cache of ancient Near Eastern cosmological texts, interpreters have been well aware of the parallels between ancient Israel's view of the cosmos and that of her neighbors. Unfortunately, this aspect of Scripture's cultural context is vastly ignored by many otherwise good readers of the Bible.
In recent years those who are antagonistic toward the Bible as a viable source of divine revelation have capitalized on Christians' ignorance of these parallels in order to undermine the authority of Scripture. They enjoy pointing the unsuspecting believer to the Bible's scientific errors, superstition and myth. If they can sow the seeds of doubt in the minds of the fragile faithful, they just might finally succeed in wresting from impressionable intellectuals what little biblical influence remains, paving the way for a fully secular society, in which humans are free from any and all religious notions. The antagonists are counting on the fact that young Christians have either not encountered these views before or that they have been given simplistic answers that explain away the biblical evidence as actually affirming a modern cosmological system with a spherical earth in a heliocentric solar system within the Milky Way galaxy.
If someone's only experience with the Bible is one in which the ancient cosmological evidence is either disregarded—whether by overprotective teachers or by willful neglect—or dismissed as not applicable, what happens when these issues are brought to their attention? The response, all too often, is either continued ignorance or willful abandonment of the entire Christian enterprise. In either case it is unfortunate at best, and tragic at worst. In the case of the former, ignorance leads to a shallow faith, where sincere questions are given pat answers, theological complexities are brushed aside with blind faith, childlike faith never matures to a vibrant faith with deep roots that can withstand storms and droughts, and God is barely smarter than a fifth grader. In the words of the apostle Paul, it's a faith that still drinks milk and has not matured to the point of consuming meat (1 Cor 3:1-2). In the case of the latter, the tragedy is that having been seemingly duped on this issue, believers wonder where else they have been led astray by their trusted Christian leaders. They question whether anything they have been taught about the Bible or their faith has any validity.
#### The Context of Scripture
We began this journey together by recognizing that to be good students and readers of the Bible we must pay attention to the various contexts in which a particular text is written. We looked briefly at Boaz's sandal ceremony in Ruth 4 as an example of cultural context. Next we saw how an appreciation and understanding of Israel's geography was vital for comprehending the significance of Jeroboam erecting altars at Dan and Bethel (1 Kings 12:25-33). We then looked ever so briefly at the book of Haggai for the importance of ascertaining its historical and literary context.
Since the events of the Bible happened in a distant time and distant place, it takes some work on our part to interpret what the authors were attempting to communicate. They used idioms that require translation, such as "the little man in your eyes" (Prov 7:2), rendered "the apple of your eye" in most popular English translations. They spoke of unknown people (Girgashites, Perizites and Hivites [Deut 7:1]) and places (Shuah [Job 8:1], Naamah [Job 11:1], Shulam [Song 6:13]) that as of yet have not been located. They engaged in strange behavior that defies explanation (Jacob's sheep ritual [Gen 31], the ordeal of the bitter water [ _śo_ ṭ _ah_ ] to determine adultery [Num 5:11-31], and Saul summoning the spirit of Samuel [1 Sam 28:3-25]). They spoke in a dead language that used strange script, read from right to left in texts that originally lacked vowels. Simply put, study of the Bible requires hard work to make sense of what it meant in ancient times before we can make any sense of it today.
Some Christians like to think that all they need is the Bible and the Holy Spirit to hear God speak directly to them. Two passages in the Bible, however, remind us that sometimes it requires additional explanation. In 586 B.C. the Babylonians destroyed Jerusalem, demolished the temple and dethroned David, leading to the so-called Babylonian exile. Forty-seven years later the Persians overthrew the Babylonians as the dominant power broker in the region. King Cyrus issued his famous decree releasing all the captives to their homeland (Ezra 1:2-4). These former captives, now known as Judeans, rebuilt their homes and (eventually) the temple (515 B.C.) and the walls of the city (445 B.C.). The period of restoration wasn't complete, though, until Ezra renewed their commitment to the keeping of the law (Ezra 8–10). Standing at the newly erected Water Gate,
the priest Ezra brought the law before the assembly, both men and women and all who could hear with understanding. This was on the first day of the seventh month. He read from it facing the square before the Water Gate from early morning until midday, in the presence of the men and the women and those who could understand; and the ears of all the people were attentive to the book of the law. The scribe Ezra stood on a wooden platform that had been made for the purpose; and beside him stood Mattithiah, Shema, Anaiah, Uriah, Hilkiah, and Maaseiah on his right hand; and Pedaiah, Mishael, Malchijah, Hashum, Hash-baddanah, Zechariah, and Meshullam on his left hand. And Ezra opened the book in the sight of all the people, for he was standing above all the people; and when he opened it, all the people stood up. Then Ezra blessed the LORD, the great God, and all the people answered, "Amen, Amen," lifting up their hands. Then they bowed their heads and worshiped the Lord with their faces to the ground. Also Jeshua, Bani, Sherebiah, Jamin, Akkub, Shabbethai, Hodiah, Maaseiah, Kelita, Azariah, Jozabad, Hanan, Pelaiah, the Levites, helped the people to understand the law, while the people remained in their places. So they read from the book, from the law of God, with interpretation. They gave the sense, so that the people understood the reading. (Neh 8:2-8)
Ezra did not just read to the people and expect them to understand. He had at least thirteen professionals on hand to provide an interpretation for the laity. Similarly, in Acts 8, on the road from Jerusalem to Gaza, Philip encounters an Ethiopian who is reading from the scroll of Isaiah. When Philip asks him if he understands what he is reading, the Ethiopian responds, "How can I, unless someone guides me?" (Acts 8:31). The point is that sometimes we all need some help understanding what the Bible says.
A quick perusal of any modern translation of the Old Testament will reveal just how much we rely on others to help us understand what God has to say to us in the Scriptures. You'll see footnotes with references to Aramaic, Greek, Latin and Syriac, not to mention the ubiquitous phrase "meaning of Hebrew uncertain." Of course, your ability to read the Hebrew Bible at all is due to the diligent work of men and women who have devoted their professional lives to the study of the Semitic languages—Hebrew, Aramaic, Moabite, Phoenician, Ugaritic, even Arabic—the knowledge of which are essential for the translation of books like Job and Isaiah, whose vocabulary consists of an inordinate number of _hapax legomena_. Once the Bible has been translated into our mother tongue, there is still much that needs explanation. Biblical historians rely on the work of archaeologists, who unearth artifacts and texts. Archaeologists rely on the expertise of epigraphers and linguists who can date and translate texts. The more we are able to glean from these specialists, the less distant the ancient world becomes. The wise reader of Scripture listens to the wisdom of these scholars to inform their understanding of that foreign world.
Cosmology is simply another aspect of the foreignness of the ancient biblical world. Just as the ancient Hebrews spoke in a forgotten language, so they thought according to a forgotten worldview. They rarely traveled far from where they were born. Their lives consisted of basic subsistence—finding green pastures for their flocks or fertile land for their fields. Even if they were aware of plate tectonics, celestial orbits or hydraulic cycles, those matters were of little consequence for their survival. But they were concerned that the sun would shine, that rain would fall, that their ancestors were buried and that God (or the gods) was in control of it all.
#### Divine Accommodation
Education is a challenging prospect. The teacher must find a balance between providing the correct information or procedure without overwhelming the apprentice with corrections of every tedious misconception or error. No group of teachers is more aware of this than parents (especially parents of two-year-olds!). Despite the grand intentions of virtually every new parent to always give an answer, no matter how simple, to the eager toddler's incessant "why?" inevitably mommy and daddy succumb to the deluge by resorting to the time-tested response, "It just is!" It is not easy to explain complex issues to children who have not yet developed the capacity to deal with complexity. For example, a child might ask why a pebble sinks but an enormous ship floats. Of course, the correct answer has to do with water displacement, and if the rock were represented by a cube, the correct answer would go something like this:
The fluid exerts pressure on all faces of the cube. The forces exerted on each of the vertical faces are equal. Since the forces on the left and right faces, as well as the front and back faces, are equal and opposite, they cancel. The net force on the cube is due to the difference in pressures exerted on the top and bottom faces. The pressure on the top face is shown as _P_ top. The force exerted on the top face is _P_ top times its area, which is _x_ 2: forcetop = _P_ top _x_ 2. The pressure on the bottom face, _P_ bottom, is equal to the pressure on the top face plus the pressure due to differences in depths between the top and bottom faces. Therefore, the pressure on the bottom face is equal to _P_ top \+ _pgx,_ where p is the density of the fluid. The force exerted on the bottom face equals ( _P_ top \+ _pgx_ ) _x_ 2 _._ The difference in forces on the two faces is the net force on the cube: _P_ top _x_ 2 \+ p _gx_ 3 \- _P_ top _x_ 2 = p _gx_ 3. The quantity _x_ 3 is the volume of the cube and equals the volume of fluid displaced. The product p _gx_ 3 is the weight of the fluid displaced, demonstrating that the net upward force exerted on a submerged object is equal to the weight of fluid displaced.
This is known as the Archimedes principle and is utterly meaningless to most children—and adults, for that matter. While the explication of the Archimedes principle may be more correct than simply saying that the boat floats because of its shape, in reality the simple answer is actually preferred because it makes sense to the child. As the child grows older she can build on her basic knowledge of floatable shapes, until at some point in her educational experience she is ready to hear and comprehend the physical laws of fluid dynamics.
Historically speaking, Christian interpreters of Scripture have also noted that God condescends his language to the language of humanity. This is not to say that God is condescending but that he speaks down to the cognitive ability of his human audience. This is known as the doctrine of divine accommodation, defined by Kenton Sparks as "God's adoption in inscripturation of the human audience's finite and fallen perspective. Its underlying conceptual assumption is that in many cases God does not correct our mistaken human viewpoints but merely assumes them in order to communicate with us." Just as a father uses simple vocabulary and analogical language to communicate complex ideas to his children, so the heavenly Father accommodates his language to his children by speaking in his audience's mother tongue and also employing analogical language.
That God would need to accommodate his language to mere mortals is no more apparent than in the book of Job. While being subjected to an incessant verbal assault from his three friends, Job demands a hearing before the Judge of the universe, accusing him of callously oppressing Job, and failing to vindicate guiltless Job.
> There is no umpire between us,
>
> who might lay his hand on us both.
>
> If he would take his rod away from me,
>
> and not let dread of him terrify me,
>
> then I would speak without fear of him,
>
> for I know I am not what I am thought to be.
>
> I loathe my life;
>
> I will give free utterance to my complaint;
>
> I will speak in the bitterness of my soul.
>
> I will say to God, Do not condemn me;
>
> let me know why you contend against me.
>
> Does it seem good to you to oppress,
>
> to despise the work of your hands
>
> and favor the schemes of the wicked?
>
> Do you have eyes of flesh?
>
> Do you see as humans see?
>
> Are your days like the days of mortals,
>
> or your years like human years,
>
> that you seek out my iniquity and search for my sin,
>
> although you know that I am not guilty,
>
> and there is no one to deliver out of your hand? (Job 9:33–10:7)
To Job's chagrin, God remains silent. Job knows his vindicator lives (Job 19:25-26) and holds out hope that before he dies he will finally be able to face the God who on the one hand oppresses him and on the other hand is the only one who can vindicate him.
When Job and his now four friends have exhausted their conversation, God speaks. But God doesn't answer Job's questions or respond to the friends' accusations. Instead, he rattles off two chapters' worth of rhetorical questions.
Were you there when I laid the foundation of the earth? (38:4)
Have you entered into the springs of the sea? (38:16)
Have the gates of death been revealed to you? (38:17)
Can you bind the chains of the Pleiades, or loose the cords of Orion? (38:31)
Can you hunt the prey for the lion? (38:39)
Do you know when the mountain goats give birth? (39:1)
Do you give the horse its might? (39:19)
Is it by your wisdom that the hawk soars? (39:26)
The obvious answer is that Job has not, does not and cannot. God created the cosmos and everything in it, yet Job cannot even comprehend relatively modest concepts like why the ostrich has feathers but cannot fly (39:13). Job is not God, and whatever Job does know about God is that which God has revealed about himself to Job.
When God breaks his silence in those climactic chapters, he speaks in terms Job understands. He speaks Job's language, including faulty cosmology (38:4-38) and ancient Near Eastern mythology (41:1-34). It is not that we should understand God as prescribing this worldview, or even endorsing it. Instead, God chooses to condescend his language to accommodate Job's primitive mind.
Not only has God found it necessary to condescend to us in his language, but he has also condescended in his very being in the event of the incarnation.
> Let the same mind be in you that was in Christ Jesus,
>
> who, though he was in the form of God,
>
> did not regard equality with God
>
> as something to be exploited,
>
> but emptied himself,
>
> taking the form of a slave,
>
> being born in human likeness.
>
> And being found in human form,
>
> he humbled himself
>
> and became obedient to the point of death
>
> even death on a cross. (Phil 2:5-8)
The incarnation is the essence of the Christian faith. It is not the hope that God will be with us. It is the reality that God is with us. In the Old Testament God revealed himself through prophets, through priests, through visions and through the occasional personal encounter. When God did reveal himself, though, it was often accompanied by analogical language. Moses is hidden in the cleft of a rock so as not to see God's face (Ex 33:17-23). Ezekiel saw "something _like_ " amber, and "something _like_ " four living creatures that had human features (Ezek 1:4-5). Daniel saw "one _like_ a human being" (Dan 7:13). The incarnation, though, is not just God speaking about himself or revealing himself in veiled or guarded imagery. It is God revealing himself in the most recognizable fashion. As John Stackhouse notes, "The bottom line, in any case, is that in Jesus of Nazareth, we have God. We have not only a messenger from God, a representation of God, an example of devotion to God, a teacher of God's truth, a conveyor of God's power— _we have God_." In the incarnation God himself condescended to us in the most fundamental capacity. He made his incomprehensible, inconceivable, invisible self clearly comprehendible, conceivable and visible.
Based on the analogies of divine speech and the incarnation, biblical commentators have co-opted this notion of divine accommodation to account for pre-enlightened language in Scripture. For a sense of historical perspective, we will look at Basil of Caesarea and John Chrysostom from the fourth century, Thomas Aquinas from the thirteenth century and John Calvin from the sixteenth century. Employing terms such as _adopt_ , _adapt_ and _condescend_ , these scholars agree that God has accommodated his language to human conventions.
In his homily on Genesis 1, Basil takes up the notion of God speaking. Does God have lungs that produce air? Does God have a tongue to produce sounds? Basil is careful not to ascribe these anthropomorphic features to the Creator. Rather, he affirms that "God's will is established by the nod of his majesty in the things that he wishes to accomplish. And for the proper understanding of those who come to instruction, in the likeness of a voice of command we supposed that he spoke and adopted our forms in his speech to help us." The operative words here are "likeness" and "adopted." Basil did not view God as actually having spoken audible words, but believed that what God emitted could best be described according to human comprehension as a voice. Just as Jesus took on the appearance of man, so God's "speech" took on the form of human language.
Noting that both Paul (Col 1:16) and John (Jn 1:3) provide a fuller description of the initial creation act than does Genesis 1:1, Chrysostom draws on Paul's experience in Athens to explain the difference. When Paul spoke at the Areopagus in Athens, he was directed by the Holy Spirit to speak in terms the Athenians would understand (Acts 17:22-28). So Paul adjusted his presentation according to the cultural peculiarities of his audience. In the same way, Chrysostom argues that Moses spoke under the direction of the Holy Spirit in a "manner appropriate to his hearers." For Chrysostom the human race was not yet ready for the solid food as presented by Paul and John, so God communicated his message as milk to the early listeners. He clarifies his point by using an example from ordinary life: "Whereas teachers who have been entrusted by parents with the education of their children give them fundamentals of learning, those who receive the children from them at the next stage take them through more developed stages of learning." In his view, then, as the human race becomes more educated, God can take it to higher levels of learning, exchanging milk for solid food.
Commenting on the phrase "God saw that it was good" in Genesis 1:10, Chrysostom takes a tack similar to Basil. When we read about God "seeing," we shouldn't understand that to mean that God has a set of eyeballs with corneas, retinas and optic nerves that send signals to God's brain. Rather, "the Creator knew the beauty of the created thing before he created it, whereas we are human beings and encompassed with such limitations that we cannot understand it in any other way; accordingly, he directed the tongue of the blessed author to make use of the clumsiness of these words for the instruction of the human race." Of utmost importance for Chrysostom was recognizing that humans are incapable of comprehending divine speech unless the divine accommodates his speech to the finite limitations of human cognitive abilities.
In article 3 of question 68 in his _Summa Theologica_ , Thomas Aquinas takes up the matter of whether the firmament divides water from water. In typical fashion, Aquinas begins by raising three objections. First, since all water is essentially the same in its chemical makeup—or "of the same species" in Aquinas's terms—water "cannot be distinct from water by place." Second, even if water did have separate species, "it is not the firmament that distinguishes them." Third, "It is evident that the waters below do not reach up to the firmament," so the firmament cannot separate the water from the water. Having established through logical conclusions that the firmament does not divide water from water, Aquinas now must respond to the biblical text, which clearly states, "And God said, 'Let there be a dome in the midst of the waters, and let it separate the waters from the waters'" (Gen 1:6). For Aquinas there is only tension between what the text says and what must be true from natural philosophy if the text is read at a superficial level. In fact, that is exactly what certain "philosophers of antiquity" did when they "taught that not all corporeal things are confined beneath the heaven perceived by our senses, but that a body of water, infinite in extent, exists above that heaven." We see, then, that Aquinas was responding negatively to the pre-Aristotelian view of a three-tiered cosmos. He continues by claiming that although this might be the plain sense reading of Scripture, it is not the intended sense. Employing the language of divine accommodation, Aquinas concludes,
It should rather be considered that Moses was speaking to ignorant people, and that out of condescension to their weakness he put before them only such things as are apparent to sense. . . . Moses, then, while he expressly mentions water and earth, makes no express mention of air by name, to avoid setting before ignorant persons something beyond their knowledge.
Like Chrysostom before him, Aquinas utilizes the metaphor of the unlearned. Since the ancients were unable to comprehend higher-level concepts of the cosmos, God condescended in his language to accommodate their ignorance. For Aquinas, then, Scripture may not always comport with scientific investigation. However, it is not because Scripture misleads its readers, but because its readers are already misled. Rather than teaching correct cosmology to a generation who out of their lack of knowledge of the natural world simply would not get it, God stoops to their intellectual status and speaks to them according to their understanding, not his.
As we saw in the previous chapter, the doctrine of divine accommodation is most commonly associated with the Protestant Reformer John Calvin. I have already demonstrated how he utilized this approach in his commentary on the firmament in Genesis. It is in his _Institutes of the Christian Religion_ , though, that he most fully develops the doctrine, citing or alluding to the notion in multiple places. I will briefly discuss four such cases here.
First, while introducing his exposition on the prohibition of graven images, Calvin writes, "But as Scripture, having regard for men's rude and stupid wit, customarily speaks in the manner of the common folk." What may look like an endorsement or at least the condoning of false deities was simply God speaking into the ancient Hebrews' cultural milieu. Since idolatry permeated the ancient world, Scripture repeatedly strikes a contrast between the true God of Israel and the false "gods" of their neighbors, even though the God of Israel would not have seen the "gods" of the nations as legitimate deities.
Second, in his discussion of the Trinity, Calvin chastises the Manichees for their belief that God had human form.
The Anthropomorphites, also, who imagined a corporeal God from the fact that Scripture often ascribes to him a mouth, ears, eyes, hands, and feet, are easily refuted. For who even of slight intelligence does not understand that, as nurses commonly do with infants, God is wont in a measure to "lisp" in speaking to us? Thus such forms of speaking do not so much express clearly what God is like as accommodate the knowledge of him to our slight capacity. To do this he must descend far beneath his loftiness.
Notice how Calvin essentially says that God speaks to us in baby talk. As infants respond to babbles and coos, rather than sentences and paragraphs, so God limits his speech to the most basic of human communication.
Third, in book one of the _Institutes_ Calvin comments on the absence of the creation of angels in Genesis 1.
To be sure, Moses, accommodating himself to the rudeness of the common folk, mentions in the history of the Creation no other works of God than those which show themselves to our own eyes. Yet afterward when he introduces angels as ministers of God, one may easily infer that he, to whom they devote their effort and functions, is their Creator. Although Moses, speaking after the manner of the common people, did not in laying down basic principles immediately reckon the angels among God's creatures, yet nothing prevents us from conveying plainly and explicitly what Scripture elsewhere repeatedly teaches concerning them.
Here again Calvin accounts for an apparent oversight in Scripture to an intentional revelatory omission. To include the angelic realm in Genesis 1 would have only complicated matters and would actually detract from the central theme of Genesis 1, namely, that God is Lord over all.
The fourth example we will examine from Calvin's _Institutes_ concerns his explanation on reconciling the God of the Old Testament with the God of the New Testament.
Why, then, do we brand God with the mark of inconstancy because he has with apt and fitting marks distinguished a diversity of times? . . . Paul likens the Jews to children, Christians to young men. What was irregular about the fact that God confined them to rudimentary teaching commensurate with their age, but has trained us through a firmer and, so to speak, more manly discipline?
For Calvin, it is not that God has changed, but that his children have grown up. They have learned more of his character because God was able to speak to them in a more mature manner.
The doctrine of divine accommodation has its flaws. It can be pressed to account for any and every inconsistency in the Bible without merit. In fact, we have seen among Basil, Chrysostom, Aquinas and Calvin that it was used somewhat inconsistently at times. For example, Calvin could account for the firmament by divine accommodation but saw no reason to account for his own misguided understanding of Aristotelian cosmology. Nonetheless, it is helpful to remember that God does, in fact, speak to a particular culture according to its cultural conventions. More importantly, it is necessary to recognize that God revealed himself not according to modern, Western cultural conventions, but in an ancient time, in an ancient place and in an ancient language.
#### Conclusion
Some well-intentioned Christians will take offense at the suggestion that Scripture does not comport with modern scientific findings. For them such a proposal admits that the Bible contains errors, undermines Scriptural authority and starts us down the slippery slope of biblical liberalism. If the Bible is the Word of God, and God is the author of truth, then the Bible must be completely accurate about all things, even things of a scientific nature.
The concern is a valid one. On what basis do we as interpreters have the right to say that Scripture is perfectly precise on some points but open for reinterpretation on others? Of course, the answer to that question cannot be adequately handled in a paragraph or two. In fact, it has been the topic of discussion for a number of books in biblical studies in recent years. However, I can offer a few general comments that I think can be helpful in this respect.
First, the Bible never claims to be a scientific textbook. In fact, one would be hard pressed to find anyone who actually makes the assertion that it is, even among those for whom the first objection applies. The Bible's primary function is to demonstrate how God has worked in history for the redemption of humanity, ultimately pointing to the One who brings about that redemption. In fact, Jesus makes this explicitly clear in a speech to a group of Jews who had sought to kill him. "You search the scriptures because you think that in them you have eternal life; and it is they that testify on my behalf. Yet you refuse to come to me to have life" (Jn 5:39-40). For Jesus—and the rest of the New Testament authors as well—the purpose of Scripture was to help people find Jesus.
Second, it takes a certain degree of hubris to assume that even now humans have a full grasp of the nature of the cosmos. Suppose that God communicated the actual structure of the cosmos. Even with our technology, our vast study of deep space with powerful telescopes and satellites, do even we know enough to comprehend a divine explication of the universe, if in fact it is a _uni_ verse? At what point in history will the human race have matured enough for God to have "adult conversation" with his children? Imagine for a moment, though, that we have arrived and have gained all the knowledge there is to gain about the cosmos. Imagine if when God first spoke about the cosmos to the ancient Hebrews he had spoken about the universe we know to be true. What would that have meant to Moses or David or Isaiah? How would they have been able to make sense of that when everyone knew the world was a flat disk supported by pillars? From God's perspective, would it not make more sense for him to communicate with the conventions, customs and cultural trappings of his intended audience rather than those of its readers several millennia later? New parents do not speak to their infant as if she had earned a PhD. They speak to her according to her developmental stages. In the same way, God has spoken in history and through history according to the developmental stages of his children.
Other well-intentioned Christians will take offense at the suggestion that one must study the language and culture of the ancient Near East to have a proper understanding of biblical cosmology. They might assert that this raises the status of Old Testament scholars to a sort of pope, where only they hold the true knowledge of biblical interpretation. They will appeal to church history and wonder why Augustine, Aquinas, Calvin or Luther did not refer to the ancient Near Eastern material. How could these titans of biblical interpretation have been ignorant of these so-called formative and informative texts? If the ancient Near Eastern context is so important for our understanding of the Old Testament world, then why have interpreters only recently begun to utilize this information?
Here it is crucial to remember that the texts on which modern biblical scholars rely to glean cultural information were unknown for thousands of years. Outside the land of Israel, the Fertile Crescent was not considered a region of interest for exegetes, other than for contrastive purposes. The land was foreign and the languages were more foreign. Had they even had access to the cuneiform and hieroglyphic texts, it is unlikely they would have cared to try to read them. Their interests were exclusively theological, christological, pneumatological and ecclesiastical in nature. Inscriptions from Assyria, Babylon and Egypt would not have interested the church fathers, as they had no bearing on these essential concerns of the church.
The rediscovery of the lost world of ancient Mesopotamia and Egypt should not elicit skepticism toward interpretations that take this material into account any more than does the archaeological discovery of another clay pot, bronze sword or temple foundation. Virtually everything that is excavated from the Middle East provides some sort of insight into the life and culture of the biblical world. Each object provides a window, however small, into the lands in which the people traveled, the materials they used, the food they ate, the language they spoke and the way they thought. With every new discovery there is typically some degree of overreaction to the significance of the find. In time, though, cooler heads generally prevail, and the artifact receives the appropriate level of analysis and interpretation.
A helpful parallel for understanding the importance of these ancient texts is the Dead Sea Scrolls, discovered in several caves on the northwest coast of the Dead Sea between 1946 and 1956. Like the texts from Mesopotamia and Egypt unearthed a century earlier, these ancient scrolls had been stored away for over two thousand years before their discovery by a Bedouin shepherd boy. Although it took another half century for them to be published for public consumption, these texts ultimately provided invaluable insight into the formation of the Hebrew Bible and the thought world of the time of Jesus. In fact, with the discovery of the Dead Sea Scrolls we have a much clearer picture on the type of messianic expectations imposed on Jesus and the eccentric behavior of John the Baptist. Had we never found the Dead Sea Scrolls, we would still be able to make very good sense of the Gospels. However, armed with this newly found contextual information, the Gospels are much less opaque and we have a richer understanding of the thought world of first-century Palestine. Likewise, the rediscovery of the thousands of cuneiform and hieroglyphic texts from across the ancient Near East has provided us with a bounty of cultural data.
Biblical cosmology is ancient Near Eastern cosmology. Through the biblical authors God spoke in the language of the common folk. These authors wrote in their native tongue, whether that was Hebrew, Aramaic or Greek. They utilized cultural conventions, such as animal sacrifices, monarchies, patriarchies and polygamy. And they assumed the cultural thought world in which they operated on a daily basis. While some would argue that this aspect of the Bible undermines any of the divine qualities of its authority, it is important to remember that without the human element of Scripture there would be no access to the divine. As the Word of God condescended to dwell among us (Jn 1:14), so too did the words of God condescend to our level so they would have meaning to us. Scripture is authoritative not because it answers all of life's questions or resolves all the mysteries of science. Rather, Scripture is authoritative because it testifies on behalf of Jesus (Jn 5:39-40), the one to whom all authority in heaven and on earth has been given (Mt 28:18).
# 8
## THE AUTHORITY OF SCRIPTURE AND THE ISSUE OF SCIENCE
Psalm 19 celebrates the fact that God has revealed himself both in Scripture and in the natural world. Romans 1 echoes the same sense: "Ever since the creation of the world his eternal power and divine nature, invisible though they are, have been understood and seen through the things he has made" (Rom 1:20). The creation hymns in both the Old and New Testaments point to a God who is not threatened by creation. Instead, the wonder of the natural world points directly to the Creator.
Some Christians, however, do feel threatened by advances in science, which is rather unfortunate. Often this threat stems from the so-called God-of-the-gaps idea, in which it is only in the inexplicable that we find God. But as human investigation delves deeper into the mysteries of the universe—both at the macroscopic and microscopic levels—there is less and less to relegate to the mystery of the divine. In other words, the gap is narrowing, and this reality can be rather unnerving to those whose faith is contingent on the unfathomable wonders of the world.
This ought not be. If, as Scripture asserts, God reveals himself in creation, then the more we learn about his wondrous works, the more we learn about the God who fashioned them. In many respects, Christians have willingly adapted to scientific inquiry and have readily adopted the results of those inquiries despite a so-called biblical view to the contrary. We will look briefly at the field of medicine as a case in point.
#### The Authority of Scripture and Medicine
It is generally understood that Luke, the author of the third and fifth books of the New Testament, was a physician (Col 4:14). As such, it is all too often assumed that Luke would have attended a four-year medical school where as a student he would have learned human anatomy, biochemistry, embryology and immunology, among other important courses in biological health. Instead, Luke would have practiced medicine according to the custom of the ancient Greeks, like Hippocrates, who is best known for the Hippocratic Oath. For Hippocrates and others in the ancient Greek tradition of medicine, the standard course of medicine began with a "hypothesis," used as a technical medical term for ascertaining the root of the ailment. Disease, it was thought, was caused by a limited number of principles—such as hot, cold, wet and dry—which could be treated by applying the opposite principle. Luke, like his contemporaries, would not have known how to diagnose, let alone treat, infectious disease, cancer, tension headaches or the common cold. He would have suggested a hypothesis and treated it according to its opposite principle.
Imagine how different life would be today if doctors practiced health care according to the "biblical view of medicine." Other than the numerous healing miracles interspersed throughout its pages, the Bible does not have much to say on the matter, but it does provide a few guidelines on how to care for the sick. In the book of Leviticus, the proper course of treatment for "leprosy" (ṣ _āra_ ʿ _at_ ) was banishment from the camp until the condition cleared (Lev 13:45-46). Furthermore, biblical leprosy does not even fit the current medical definition of the disease, as it has various physical characteristics (Lev 13:1-3, 18-20, 24-25, 29-30, 40-44), could be seen on a building (Lev 14:55), could spread rather quickly (Lev 13:5-8) and probably did not even reach the region of Syria-Palestine until the Greco-Roman period. Many neurological diseases—such as strokes, paralysis and epilepsy—are challenging even with modern medical techniques. However, in the ancient world, the only hope for healing such conditions was divine intervention (1 Sam 25:36-38; Mk 9:14-29; Jn 5:2-9). Infertility was considered a curse, and the blessing of motherhood could only be attained if God opened the womb (e.g., Gen 17:15-17; 1 Sam 1:1-18; Lk 1:5-25). Several other physical ailments and illnesses are recounted in the biblical narratives. In not one of them does the Bible provide practical medical advice for proper and effective treatment. The patient would either get better—either naturally or supernaturally—or eventually perish with their condition.
Modern medicine has not only prolonged life but also greatly increased quality of life. Patient care, from diagnosis to remedy, involves clinical studies, laboratory experiments, microbiology, endocrinology and immunology. It requires the expert research of specialists in cell structure, chemical equations and pharmaceutical reactions. Scientists and physicians from numerous disciplines have made it their lives' work to detect illness or disease, improve treatments and discover cures so humans may live longer, healthier lives. We take for granted the successes that scientists and medical practitioners have made in the longevity and quality of life as a result of the intensive study of physiological systems. These medical advances were not made through a better reading of Scripture, but through a deeper study of the world created by the God revealed in Scripture. We are generally quite content to grant physicians the freedom to investigate and explore the mysteries of the human body, to search for cures for cancer and AIDS, or to give premature babies a realistic chance at living a full life. Why is it, then, that we are reluctant to allow other scientists the freedom to investigate and explore other arenas of God's creation, regardless of whether what they find aligns with our own understanding of Scripture?
Our propensity to appeal to the marvels of modern medicine against a biblical view of health care causes little, if any, alarm in the church. Reasonable Christians understand that the Bible did not, and could not, address contemporary health concerns. While they might take some minor health issues into their own hands, they recognize that certain medical diagnoses and procedures are best left to the experts. In fact I would go so far as to say that if a Bible-believing Christian suddenly broke out in painful boils, he would be more likely to visit his doctor than he would be to camp outside the city until it all cleared up.
#### The Authority of Scripture and Astronomy
It is not simply a modern notion that we should leave matters of scientific analysis to those who have devoted their lives to the study of a particular field. Several ancient biblical commentators made it a point to remind their readership that when it comes to the cosmos it is important to recognize that astronomers are better equipped to speak on the subject than the layperson. This was not always the case. In fact, it was not until the rise of scholasticism in the medieval period that theology became "queen of the sciences" and theological inquiry was subjected to empirical evidence.
Before we look at the specific comments from Aquinas, Maimonides, Luther and Calvin, there are several significant points to keep in mind. First, the ones making these comments also misunderstood the nature of the cosmos. Generally speaking, it was out of their lack of understanding that they appealed to the experts. However, it was also due to their humility that they recognized areas outside their own expertise. Second, as some of the greatest minds to contemplate the meaning of Scripture, they understood that faithful interpretation of the text required knowledge outside the text. Third, it was generally assumed that the ones who were engaged in the study of the cosmos were neither Christian nor Jew. In other words, even though these astronomers were not studying the skies to elucidate Scripture, biblical exegetes saw the value their study could provide for the elucidation of Scripture. Finally, there was a distinction, for Luther and Calvin especially, between astronomy and astrology. The former dealt with the study of the heavens, while the latter referred to the worship of the heavens. Whereas astronomy was deemed beneficial, astrology was rightfully considered idolatrous.
No ancient biblical interpreter amassed and assimilated more secondary source material into their arguments than Thomas Aquinas. In his _Summa Theologica_ , Aquinas engages St. Augustine, Ambrose, Basil, Chrysostom and other biblical exegetes. He also interacts with Greek philosophers, chief of whom is Aristotle. From Aquinas's perspective, Aristotle's arguments were not to be trivialized but to be deployed for the benefit of biblical exegesis. For example, in response to the question of whether the celestial luminaries are living beings, Aquinas alludes to Aristotle to demonstrate that their movement is dependent on God, meaning they cannot have the same kind of life as plants and animals.
A proof that the heavenly bodies are moved by the direct influence and contact of some spiritual substance, and not, like bodies of specific gravity, by nature, lies in the fact that whereas nature moves to one fixed end which having attained, it rests; this does not appear in the movement of heavenly bodies. Hence it follows that they are moved by some intellectual substances. Augustine appears to be of the same opinion when he expresses his belief that all corporeal things are ruled by God through the spirit of life.
Aquinas did not always agree with Aristotle, but he could not do biblical exegesis without accounting for and consulting with the premier cosmological thinker. It did not bother Aquinas in the least that Aristotle did not approach the cosmos from a biblical perspective. What mattered for Aquinas was that Aristotle had demonstrated his expertise in the field.
One of the authors with whom Aquinas liked to interact was the Jewish interpreter Maimonides, also known as Rambam—Rabbi Moses ben Maimonides. Like his contemporary Aquinas, Maimonides found it useful and necessary to incorporate Aristotle's cosmological ideas into his exposition of Scripture. In his discussion on the firmament, Maimonides asserts that the water above the firmament must "be understood in a figurative sense." Although Scripture speaks about the "extraordinary mysteries" of the firmament, Rambam thought it helpful to consult the meteorologists of the day to lend proper understanding to these phenomena. So he offers this directive: "Understand that which has been proved by Aristotle in his book _On Meteorology_ , and note whatever men of science have said on meteorological matters." As with Aquinas, Maimonides appeals to the astronomers for assistance in dealing with cosmological matters in Scripture, rather than relying on doctrinal dogmatism or spiritual speculation.
A few centuries later, both Martin Luther and John Calvin extolled the virtues of the astronomers in understanding God's universe. On the one hand, Luther insists that some things—like waters above the firmament—are beyond comprehension, and so he simply subscribes "to the Word even though I do not understand it." On the other hand, Luther accepts that Aristotle has provided a different conception of the heavens. Even though Luther does not fully endorse Aristotle's assessment, he appreciates its potential usefulness for biblical interpretation.
These ideas, to be sure, are not certain; nevertheless, they are useful for teaching because they are the result of plausible reasoning and contain the foundation for the arts. Therefore, it would be boorish to pay no attention to them or to regard them with contempt, especially since in some respects they are in agreement with experience.
Later he notes that even though astronomy is often rooted in superstition, it cannot be completely ignored, since "as a whole it concerns itself with the observation and contemplation of the divine works, something which is a most worthy concern in a human being." It was of little concern to Luther that "men of the highest ability" were engaged in the study of the cosmos apart from a biblical worldview. What was important to him was that the subject of their study had its origins in the divine. To study creation, regardless of the perspective one brought to that study, was to engage its Creator.
The waters above the firmament were no less vexing for Calvin. Again, it is counterintuitive to imagine water actually being above the firmament, which Calvin defines as "the empty space around the circumference of the earth." Operating from an Aristotelian perspective, with spheres within spheres, it is utterly unimaginable that the Bible could actually mean what it seems to mean. The "plain sense" of Scripture appears to be lacking any sense.
For it appears opposed to common sense, and quite incredible, that there should be waters above the heaven. Hence some resort to allegory, and philosophize concerning angels; but quite beside the purpose. For, to my mind, this is a certain principle, that nothing is here treated of but the visible form of the world. He who would learn astronomy, and other recondite arts, let him go elsewhere.
Ultimately Calvin would explain the waters above the firmament as figurative language for rain clouds. But he was not interested in delving into the scientific peculiarities of the passage. Neither was he resistant to those who could provide a better understanding of Scripture through scientific investigation.
Despite the fact that Aristotle was a Greek philosopher whose cosmology was deeply rooted in Platonic dualism, Christians—and Jews, for that matter—had widely accepted his explanation of things. That Aristotle did not use Scripture to guide his understanding of the cosmos was of little consequence. Instead of rejecting his model on grounds that it did not start from a biblical perspective, Christians and Jews adapted Aristotelian language to fit biblical theology. The effective cause for the motions of the celestial spheres Aristotle called the Unmoved Mover, an impersonal, nondivine entity that simply keeps the spheres in motion. The Unmoved Mover was eternal, but so was the cosmos, meaning the Unmoved Mover did not create the cosmos. For Aristotle, then, the Unmoved Mover would be comparable to a car engine. The engine did not create the car; it just causes the car to move.
Aristotle's cosmology was largely incompatible with a biblical view of God and the origins of the cosmos. However, since his model was based on the best observational methods of the time and provided a compelling explanation for the movements of the celestial bodies, biblical interpreters granted his cosmological conclusions, but nuanced his argument to fit their theological paradigms. What Aristotle termed the Unmoved Mover, Christians simply called God. Whereas Aristotle's Unmoved Mover was impersonal, theologians said God was personal. While Aristotle's universe was eternally coexistent with the Unmoved Mover, Scripture states that the heavens and earth had a beginning, when God spoke them into existence. In other words, Aristotle's model was recognized as authoritative in matters of cosmology, but redefined and adapted in matters of theology.
#### The Authority of Scripture and Human Origins
There is much to be learned from church history regarding the relationship between Scripture and the sciences. We have seen examples where the two have coexisted quite compatibly. We have also witnessed the debacle that was the Galilean Inquisition. With the intent of upholding a high view of Scripture, good science was censored for the sake of traditional theology. Biblical blinders covered the eyes of sound science. Unfortunately the drama that unfolded in the middle of the sixteenth century is being played out again in the twenty-first century. The fight rages on between the authority of Scripture and the authenticity of science. Where the battle once raged over whether the earth was the center of the cosmos, the conflict now revolves around the issue of human origins.
When Charles Darwin published _On the Origin of Species by Means of Natural Selection_ in 1859, it was met with skepticism from cleric and naturalist alike. After all, many if not most naturalists also thought "that each species had been independently created and remained fixed and unchanged throughout its existence." Even as he penned his paradigm-shifting masterpiece, Darwin knew that it would not sit well within certain sectors of the Christian community. He anticipated the rejection of his theory based on the human propensity to be defensive of long-held convictions and to "hide our ignorance under such expressions as the 'plan of creation,' 'unity of design,' etc., and to think that we give an explanation when we only restate a fact." In language that sounds eerily similar to that of Copernicus in the foreword to _On the Revolutions of the Heavenly Spheres_ , Darwin continues by stating that "any one whose disposition leads him to attach more weight to unexplained difficulties than to the explanation of a certain number of facts will certainly reject the theory."
Darwin's task was not to undermine the role of a Creator but to attempt to explain what that creation process looked like. Responding to the burgeoning backlash from the religious community, Darwin released a second edition of _Origin of Species_ one year after its initial publication. In this revised version, he made more explicit his conviction that natural selection was not at odds with creation and there is "no good reason why the views given in this volume should shock the religious feelings of anyone." Appealing to ecclesiastical support for his defense, he noted that a "celebrated author and divine has written to me that 'he has gradually learnt to see that it is just as noble a conception of the Deity to believe that He created a few original forms capable of self-development into other and needful forms, as to believe that He required a fresh act of creation to supply the voids caused by the action of His laws.'" Darwin, in other words, was not trying to shock Christendom with his discoveries in natural biology, but to situate them in a context in which those who held to a high view of Scripture could also accept the realities of the natural world, at least as he articulated them. This is no more evident than in his closing sentence:
There is grandeur in this view of life, with its several powers, having been originally breathed by the Creator into a few forms or into one; and that, whilst this planet has gone cycling on according to the fixed law of gravity, from so simple a beginning endless forms most beautiful and most wonderful have been, and are being, evolved.
For Darwin, the notion of natural selection does not diminish his view of the Creator but fortifies it because it demonstrates how the Creator brought life into existence and established the laws by which new forms would continue to be created.
Although Darwin's home was not the least bit irreligious, the family's creed consisted of an odd mix of Unitarianism and orthodox Anglicanism. Darwin participated in that faith, but his wife was mostly responsible for nurturing their daughter Annie. For Charles, intellectual challenges like the problem of suffering and the dubious nature of miracles made belief especially trying to his faith, but he dared not abandon it. It was a fragile faith, though, and when in 1875 his daughter Annie died at the age of ten, his faith had all but completely faded. Nonetheless, even in _The_ _Descent of Man_ , generally regarded as the more base and naturalistic of his two works, Darwin responds to Archbishop Sumner's metaphysical concerns over his theory of natural selection, asserting that the question of "whether there exists a Creator and Ruler of the Universe . . . has been answered in the affirmative by the highest intellects that have ever lived." While arguing that humans developed over time through natural processes, Darwin still affirmed, even if unconvincingly, that the processes were guided by the hand of the Creator.
In the years following the publication of _Origin of Species_ and _Descent of Man_ , biblical commentators were forced to consider if or how Darwin's ideas could be incorporated into a Christian view of theology and anthropology. Could the gradation of species be reconciled with the creation accounts of Genesis 1–2? Did evolutionary theory contradict one of the pillars of Christian theology, that God was the maker of heaven and earth? How could Darwin's ideas on the descent of humanity be reconciled with the _imago Dei_ , that humans are created in the image of God? As it happened, just as biblical interpreters had adopted Aristotle's cosmological model without adopting his theology, some exegetes were willing to consider the same possibility in terms of human origins. Others were not.
A little less than forty years after the publication of _Descent of Man_ , a series of ninety essays was commissioned "to set forth the fundamentals of the Christian faith" and "to combat the inroads of liberalism." These essays came to be known as _The Fundamentals_ , and those who would align themselves with these teachings would later be identified as "fundamentalists." The impressive list of contributors included names like James Orr, Benjamin B. Warfield, George F. Wright, C. I. Scofield, Thomas Spurgeon and G. Campbell Morgan. Their essays covered a wide array of topics, such as historical criticism, the existence of God, inspiration of Scripture, sin, atonement, evangelism, prayer and the deity of Christ, among many others.
Within _The Fundamentals_ , the issue of human origins was well represented. Among these essays we find the full spectrum of evangelical positions regarding human origins. At one end of the spectrum is Dyson Hague's "The Doctrinal Value of the First Chapters of Genesis." At the other end of the spectrum is James Orr's "Science and Christian Faith." George F. Wright offers a middle position in his essay, "The Passing of Evolution." It bears repeating that each of these positions was deemed compatible with fundamentalism and efficacious in preventing liberalism from undermining biblical authority.
Using language and tone that still resonates quite strongly in some circles within evangelicalism today, Hague unapologetically clarifies the stakes in the debate of human origins.
The Book of Genesis is the seed in which the plant of God's Word is enfolded. It is the starting point of God's gradually-unfolded plan of the ages. Genesis is the plinth of the pillar of the Divine revelation. It is the root of the tree of the inspired Scriptures. It is the source of the stream of the holy writings of the Bible. If the base of the pillar is removed, the pillar falls. If the root of the tree is cut out, the tree will wither and die. If the fountain head of the stream is cut off, the stream will dry up.
Hague argues that if Genesis is not treated as historical narrative, the Bible cannot be authoritative and it cannot be divine revelation. His contention is not that science and Scripture are at odds with each other. On the contrary: "This sublime order is just the order that some of the foremost of the nineteenth and twentieth century scientists have proclaimed." For Hague, then, scientific finds will always and only concord with what we already see in Scripture. He concludes by demonstrating the theological implications of Darwinian notions of human descent:
A lowered anthropology always means a lowered theology, for if man was not a direct creation of God, if he was a mere indirect development, through slow and painful process, of no one knows what, or how, or why, or when, or where, the main spring of moral accountability is gone. The fatalistic conception of man's personal and moral life is the deadly gift of naturalistic evolution to our age.
To concede to Darwin is to concede that human existence is meaningless, that the fall of humanity was fictional and the incarnation of Christ was unnecessary.
James Orr, who also wrote the essay "The Virgin Birth of Christ" in _The Fundamentals_ , takes a rather different approach to the issue of human origins than did Hague. Orr's chief concern is that all too often a false dichotomy is established, according to which Christians must choose between science and faith. Unfortunately this hostility has meant that
grievous mistakes have often been made, and unhappy misunderstandings have arisen, on one side and the other, in the course of the progress of science—that new theories and discoveries, as in astronomy and geology, have been looked on with distrust by those who thought that the truth of the Bible was being affected by them—that in some cases the dominant church sought to stifle the advance of truth by persecution—this is not to be denied. It is an unhappy illustration of how the best of men can at times err in matters which they imperfectly understand, or where their prejudices and traditional ideas are affected.
Harkening back to the Inquisition of Galileo in 1633, Orr notes that errors can be made at both ends of the spectrum. At one extreme are those who attempt to undermine the authority of Scripture by misappropriating scientific data to demonstrate a contradiction that does not exist. At the other extreme are those who demand "that the Bible be taken as a textbook of the newest scientific discoveries, and trying by forced methods to read these into them." Orr does not feel constrained by the biblical text to argue for a six-thousand-year-old earth any more than he feels constrained by Scripture to assert a geocentric view of the cosmos. For Orr, the laws of nature are an expression of God's providential sovereignty, rather than evidence against it. He closes his essay by appealing to God's two books of revelation: Scripture and nature, each of which enlightens the other, neither of which contradicts the other.
In "The Passing of Evolution," George Wright contends for a position somewhere between Hague's complete dismissal of Darwin's theory and Orr's willingness to harmonize Scripture with the laws of nature. Wright begins with the assertion that "the word evolution is innocent enough, and has a large range of legitimate use," noting that the Bible itself incorporates evolutionary language as the acts of creation move from lower life forms to higher life forms. Wright not only is unalarmed by the idea of evolution but also endorses a limited version of it, remarking that Darwin's theory took into account the role of the Creator, who "in the beginning breathed the forces of life into several forms of plants and animals, and at the same time endowed them with the marvelous capacity for variation which we know they possess." In fact Wright even suggests that if evolution were proved true, it would only strengthen the argument that a designer was responsible. Where Wright does take great exception to evolution is with so-called neo-Darwinists, naturalists who demand "that all organic beings had been equally independent of supernatural forces." Ultimately, for Wright, the notion of evolution is consistent with Scripture so long as it includes at its core the stipulation that the process require divine design.
There is one more figure from the early twentieth century who deserves some attention on this matter. Benjamin B. Warfield is one of the most influential and enduring biblical scholars in American Calvinism. His contribution to _The Fundamentals_ was the essay "The Deity of Christ." In addition to several full-length monographs, Warfield wrote numerous works on biblical authority and Christian theology. He is perhaps most noted, however, for his work on the doctrine of biblical inerrancy. Along with A. A. Hodge, he coauthored the seminal essay on the topic in 1906, in which they narrowly define inspiration as the manner in which God attended to the entire process of revelation, from the transmission of the text to its canonical close. Decades after Warfield's death, Samuel Craig compiled a collection of Warfield's essays on the subject titled _Inspiration and Authority of the Bible_. In short, one would be hard pressed to find someone more committed to the authority of Scripture in the early twentieth century than B. B. Warfield.
Besides his important contributions on biblical inspiration, Warfield also wrote extensively on providing a biblical response to Darwinism. Warfield grew up in the bluegrass region of central Kentucky, where his father William bred livestock using methods that drew heavily on Darwin's theory of natural selection. Benjamin was thus raised in an environment in which Darwinian thought had a positive pragmatic purpose. As Mark Noll and David Livingstone describe it, Warfield "had met the theory empirically, in the feedlot, rather than as merely a question of theology." Having been reared in a context where the family's livelihood benefited from the theory of natural selection, the staunch proponent of biblical inerrancy would make a strong case for the compatibility of evolution and the doctrine of creation.
Warfield's contribution to the discussion on the authority of Scripture and human origins is perhaps best summarized in his essay "Creation, Evolution, and Mediate Creation," published in 1901. In this essay Warfield draws the distinction between creation and evolution, theistic evolution and mediate creation. Creation is the act by which God originates something new without modifying something old. Evolution, by contrast, is only modification of a preexistent form. In theistic evolution, God creates all the original material, but then modifications occur by means of evolutionary processes. For Warfield, none of these options are viable theological options. Warfield finds the solution in the doctrine of mediate creation. According to this view, "to create is not only to make something out of nothing but also to produce out of this inapt material something above what the powers intrinsic in it are capable of producing." In other words, God did not create _immediately_ (at once), but _mediately_ (over time). Warfield finds in mediate creation a more robust view of God, who did not just create once in the original composition of material substance, but continues to create anew "whenever and wherever during the course of God's providential government anything comes into being for the production of which natural causes are inadequate." Warfield is not even opposed to using the term _evolution_ , so long as the term is rightly understood as God's providential hand in the formation of new creatures, rather than the modification of previous forms. With these qualifications, "the Christian man has as such no quarrel with evolution."
Hopefully we can find in this brief survey of four of the founders of fundamentalism some historical insight into how evangelicals can respectfully engage this contentious issue pertaining to the authority of Scripture and human origins. There is room for disagreement now, just as there was room for disagreement among the most ardent fundamentalists. If we have learned anything from the history of the church, though, we will take care not to ignore biologists, geologists and chemists simply for the sake of standing on the inspiration of Scripture. Cardinal Bellarmine has already demonstrated the futility of that posture. Instead, as James Orr reminds us, we must be attentive to all the ways God reveals himself to us, and to all the ways that Scripture and science inform each other.
#### The Authority of Scripture and Science
In an essay for the _New York Observer_ , Charles Hodge wrote about the importance of interpreting Scripture in light of scientific discoveries. As this book has shown, science has demonstrated that the earth does not have pillars, the heavens don't have a dome and the sun does not move around the earth. Hodge asks, rhetorically, "Shall we go on to interpret the Bible as to make it teach the falsehood that the sun moves around the earth, or shall we interpret it by science, and make the two harmonize?" For Hodge—and Orr, Wright and Warfield, for that matter—the Christian witness diminishes when its followers make erroneous statements about the natural world yet expect to be believed on matters concerning the supernatural world. To this end, I conclude with a timely and timeless excerpt from Augustine:
Usually, even a non-Christian knows something about the earth, the heavens, and the other elements of this world, about the motion and orbit of the stars and even their size and relative positions, about the predictable eclipses of the sun and moon, the cycles of the years and the seasons, about the kinds of animals, shrubs, stones, and so forth, and this knowledge he holds to as being certain from reason and experience. Now, it is a disgraceful and dangerous thing for an infidel to hear a Christian, presumably giving the meaning of Holy Scripture, talking nonsense on these topics; and we should take all means to prevent such an embarrassing situation, in which people show up vast ignorance in a Christian and laugh it to scorn. The shame is not so much that an ignorant individual is derided, but that people outside the household of faith think our sacred writers held such opinions, and, to the great loss of those for whose salvation we toil, the writers of our Scripture are criticized and rejected as unlearned men. If they find a Christian mistaken in a field which they themselves know well and hear him maintaining his foolish opinions about our books, how are they going to believe those books in matters concerning the resurrection of the dead, the hope of eternal life, and the kingdom of heaven, when they think their pages are full of falsehoods and on facts which they themselves have learnt from experience and the light of reason? Reckless and incompetent expounders of Holy Scripture bring untold trouble and sorrow on their wiser brethren when they are caught in one of their mischievous false opinions and are taken to task by those who are not bound by the authority of our sacred books. For then, to defend their utterly foolish and obviously untrue statements, they will try to call upon Holy Scripture for proof and even recite from memory many passages which they think support their position, although they understand neither what they say nor the things about which they make assertion.
Theses sage words from Augustine remind us that when we pit Scripture against science, or written revelation against natural revelation, we are defending the faith not from secularism but from sincerity. Sincere Christians with sincere questions are not helped by artful interpretations of Scripture that ignore the realities of the world God created. As humanity presses on to unmask more and more mysteries of the cosmos, let us consider Calvin, Aquinas, Maimonides and Ambrose, who entreat us to let those trained in studying the natural world speak on matters pertaining to such. Let us recall Kepler, who could not imagine a God who would conceal his harmonious and melodious creation from inquiring minds. Let us appeal to Augustine, who models for us an appropriate tension between the authority of Scripture and authenticity of scientific investigation. The God who created the cosmos and spoke through Scripture is not threatened by their coexistence, but revels in revealing himself through both.
#
## NOTES
#### Chapter 1: Scripture in Context
See Irene Collins, "Charles Dickens and the French Revolution," _Literature and History_ 1, no. 1 (1990): 40-57.
See Thomas Krüger, _Qoheleth: A Commentary_ , Hermeneia (Minneapolis: Fortress, 2004), pp. 5-8, or my own "Debating Wisdom: The Role of Voice in Qoheleth," _CBQ_ 76 (July 2012): 476-91, for a summary of the possible ways to interpret the literary structure of Ecclesiastes.
The present outline is based on the year-date formula. Another plausible division is based on the prophetic oracles, in which case chap. 1 would consist of two units: 1:1-2 and 1:3-15.
Genre analysis is, to some extent, a subjective enterprise. On the importance of genre in the Old Testament, see V. Philips Long, _The Art of Biblical History_ , Foundations of Contemporary Interpretation 5 (Grand Rapids: Zondervan, 1994), pp. 27-57. See also James L. Bailey's exceptional treatment of the subject from a New Testament perspective, "Genre Analysis," in _Hearing the New Testament: Strategies for Interpretation_ , ed. Joel B. Green, 2nd ed. (Grand Rapids: Eerdmans, 2010), pp. 141-65.
You can see Steinberg's cover at www.condenaststore.com/-sp/The-New-Yorker-Cover-View-of-the-World-from-9th-Avenue-March-29-1976-Prints_i8553097_.htm.
See David K. Naugle, _Worldview: The History of a Concept_ (Grand Rapids: Eerdmans, 2002), p. 58.
Immanuel Kant, _Critique of Judgment: Including the First Introduction_ , trans. and intro. Werner S. Pluhar, with a foreword by Mary J. Gregor (Indianapolis: Hackett, 1987), pp. 111-12.
John H. Walton, _Genesis 1 as Ancient Cosmology_ (Winona Lake, IN: Eisenbrauns, 2011), p. 2.
Ibid., p. 3.
John H. Walton, _The Lost World of Genesis One: Ancient Cosmology and the Origins Debate_ (Downers Grove, IL: IVP Academic, 2009), p. 16.
Richard J. Clifford, "Creation in the Psalms," in _Creation in the Biblical Traditions_ , ed. Richard J. Clifford and John J. Collins, CBQMS 24 (Washington, DC: Catholic Biblical Association of America, 1992), p. 69.
Sandra L. Richter, _The Epic of Eden: A Christian Entry into the Old Testament_ (Downers Grove, IL: IVP Academic), p. 101.
See P. Seely, "The Geographical Meaning of 'Earth' and 'Seas' in Genesis 1–10," _WTJ_ 59 (1997): 231-55.
See, e.g., Shimon Bakon, "Two Hymns to Wisdom: Proverbs 8 and Job 28," _JBQ_ 36, no. 4 (2008): 222-30.
Luis I. J. Stadelmann, _The Hebrew Conception of the World: A Philosophical and Literary Study_ , AnBib 39 (Rome: Pontifical Biblical Institute, 1970).
Ibid., p. 9.
#### Chapter 2: Ancient Near Eastern Cosmologies
See Piotr Bienkowski and Alan Millard, eds., _Dictionary of the Ancient Near East_ (Philadelphia: University of Pennsylvania Press, 2000), p. ix.
Marc Van de Mieroop, _A History of the Ancient Near East ca. 3000–323_ BC, Blackwell History of the Ancient World (Oxford: Blackwell, 2004), p. 2.
For a fuller treatment on the rediscovery of the ancient Near East, see Christopher B. Hayes, _Hidden Riches: A Sourcebook for the Comparative Study of the Hebrew Bible and Ancient Near East_ (Louisville: Westminster John Knox, 2014), pp. 17-37; and Mark W. Chavalas, "Assyriology and Biblical Studies: A Century and a Half of Tension," in _Mesopotamia and the Bible: Comparative Explorations,_ ed. M. W. Chavalas and K. L. Younger Jr. (Grand Rapids: Baker Academic, 2002), pp. 21-67.
Helen Whitehouse, "Egypt in European Thought," in Jack M. Sasson, _Civilizations of the Ancient Near East_ (Peabody, MA: Hendrickson, 1995), 1:20.
T. G. H. James, "Rediscovering Egypt of the Pharaohs," in Sasson, _Civilizations of the Ancient Near East_ , 4:2755.
For a succinct account of the rediscovery of Akkadian texts, see Benjamin R. Foster, _Before the Muses: An Anthology of Akkadian Literature_ , vol. 1, _Archaic, Classical, Mature_ (Bethesda, MD: CDL, 1993), pp. 6-13.
A. Kirk Grayson, _Assyrian Rulers of the Early First Millennium_ BC _, I (1114–859_ BC _)_ , The Royal Inscriptions of Mesopotamia Assyrian Periods 2 (Toronto: University of Toronto Press, 1991), p. 7.
W. G. Lambert and Alan R. Millard, _Atra-hasis: The Babylonian Story of the Flood_ (Winona Lake, IN: Eisenbrauns, 1999), p. 3.
Geoffrey D. Summers, "Boghazköy," in _Dictionary of the Ancient Near East_ , ed. Piotr Bienkowski and Alan Millard (Philadelphia: University of Pennsylvania Press, 2000), pp. 54-55.
Gregory McMahon, "Hittites in the OT," _ABD_ 3:233.
Gregory McMahon, "Hittite Texts and Literature," _ABD_ 3:228-31.
Michael D. Coogan, and Mark S. Smith, eds., _Stories from Ancient Canaan_ , 2nd ed. (Louisville: Westminster John Knox, 2012), p. 3.
Bill T. Arnold, and David B. Weisberg, "A Centennial Review of Friedrich Delitzsch's 'Babel und Bibel' Lectures," _JBL_ 121 (Autumn 2002): 442.
Friedrich Delitzsch, _Babel and Bible: Two Lectures Delivered Before the Members of the Deutsche Orient-gesellschaft in the Presence of the German Emperor, v. 1-4_ , ed. C. H. W. Johns (London: Williams and Norgate, 1903), p. 7.
K. Lawson Younger, "The 'Contextual Method': Some West Semitic Reflections," in _The Context of Scripture_ , vol. 3, _Archival Documents from the Biblical World_ , ed. W. W. Hallo and K. L. Younger (Leiden: Brill, 2003), pp. xxxvi-xxxvii. Regarding parallelomania, see esp. Samuel Sandmel's "Parallelomania," _JBL_ 81 (March 1962): 1-13.
John H. Walton, _The Lost World of Genesis One: Ancient Cosmology and the Origins Debate_ (Downers Grove, IL: IVP Academic, 2009), pp. 13-14.
Michael C. Astour, "Overland Trade Routes in Ancient Western Asia," in Sasson, _Civilizations of the Ancient Near East_ , 3:1403.
George F. Bass, "Sea and River Craft in the Ancient Near East," in Sasson, _Civilizations of the Ancient Near East_ , 3:1421-32.
Stephanie Dalley, _Myths from Mesopotamia: Creation, the Flood, Gilgamesh, and Others_ , Oxford World's Classics (Oxford: Oxford University Press, 1989), pp. 238-77, esp. 255-57; W. G. Lambert, _Babylonian Creation Myths_ , Mesopotamian Civilizations 16 (Winona Lake, IN: Eisenbrauns, 2014), pp. 3-277.
Lambert and Millard, _Atra-hasis_ , pp. 42-45; Dalley, _Myths of Mesopotamia_ , pp. 1-38.
James P. Allen, trans., "From the Memphite Theology," in Hallo and Younger, _Context of Scripture_ , vol. 1, _Canonical Compositions from the Biblical World_ , p. 39.
Benjamin R. Foster, _From Distant Days: Myths, Tales, and Poetry of Ancient Mesopotamia_ (Bethesda, MD: CDL, 1995), pp. 112-13. For a more technical treatment of this epic, see Jamie R. Novotny, _The Standard Babylonian Etana Epic_ , SAACT II (Helsinki: Neo-Assyrian Text Corpus Project, 2001).
Othmar Keel, _The Symbolism of the Biblical World: Ancient Near Eastern Iconography and the Book of Psalms_ , trans. Timothy J. Hallett (Winona Lake, IN: Eisenbrauns, 1997), p. 37.
John A. Wilson, "Egypt: The Nature of the Universe," in _The Intellectual Adventure of Ancient Man: An Essay on Speculative Thought in the Ancient Near East_ , ed. Henri Frankfort et al., 4th ed. (Chicago: University of Chicago Press, 1946), p. 45.
Wayne Horowitz, _Mesopotamian Cosmic Geography_ , Mesopotamian Civilizations 8 (Winona Lake, IN: Eisenbrauns, 2011), pp. 30-32.
Ibid., p. 194.
A sampling of these references may be found in Mark W. Chavalas, ed., _The Ancient Near East: Historical Sources in Translation_ (Oxford: Blackwell, 1996). See esp. Benjamin Studevent-Hickman, "The Construction of the Gipar and the Installation of the En-Priestess for Nanna of Karzid," pp. 55-56; Christopher Morgan, "The Construction of a New Capital," pp. 153-56; Kyle R. Greenwood, "Tiglath-pileser I's Subjugation of the Nairi Lands," pp. 157-60; and Sarah C. Melville, "Adad-Nirari II," pp. 280-85.
Dalley, _Myths from Mesopotamia_ , p. 51.
Miriam Lichtheim, _Ancient Egyptian Literature_ , vol. 2, _The New Kingdom_ (Berkeley: University of California Press, 2006), p. 227.
John L. Foster, _Hymns, Prayers, and Songs: An Anthology of Ancient Egyptian Lyric Poetry_ , SBLWAW 8 (Atlanta: Scholars Press, 1996), p. 73.
Horowitz, _Mesopotamian Cosmic Geography_ , p. 98.
Maureen Gallery Kovacs, _The Epic of Gilgamesh_ (Stanford, CA: Stanford University Press, 1989), p. 76.
The Kassite Dynasty ruled in Babylon from 1595 B.C. to 1157 B.C. See H. W. F. Saggs, _Babylonians: Peoples of the Past_ (Berkeley: University of California Press, 2000), pp. 113-27; Bill T. Arnold, "Babylonians," in _Peoples of the Old Testament World_ , ed. Alfred J. Hoerth, Gerald L. Mattingly and Edwin M. Yamauchi (Grand Rapids: Baker, 1994), pp. 43-75. Stored in the temple as a record of transactions in the presence of the deities, a _kudurru_ "was made of stone and was inscribed with the terms of a gift or contract including the name of the beneficiary, as well as with the divine names and curses. It bore pictorial symbols or emblems of the gods" (Kathryn E. Slanski, _The Babylonian Entitlement_ _narûs_ _(kudurrus): A Study in Their Form and Function_ , ASOR 9 [Boston: American Schools of Oriental Research, 2003], p. 26).
John H. Walton, _Genesis 1 as Ancient Cosmology_ (Winona Lake, IN: Eisenbrauns, 2011), p. 96.
Dalley, _Myths from Mesopotamia_ , p. 291.
Foster, _Hymns, Prayers, and Songs_ , p. 5.
Erik Hornung, _The Ancient Egyptian Books of the Afterlife_ , trans. D. Lorton (Ithaca, NY: Cornell University Press, 1999), pp. 55-56.
See James P. Allen, _Genesis in Egypt: The Philosophy of Ancient Egyptian Creation Accounts_ , Yale Egyptological Studies 2 (New Haven, CT: Yale University Press, 1988), p. 4.
Mark Smith, _On the Primaeval Ocean: The Carlsberg Papyri 5_ , CNI Publications 26 (Copenhagen: Museum Tusculanum Press, 2002), p. 193.
A minor, and more ambiguous, view is found in the fourth-century Egyptian sarcophagus, mentioned earlier. See fig. 2.2. According to Keel, "the two bent arms, which at an early stage come to embody 'life force,' may have originally (and more precisely) denoted 'uplifting power'" (Keel, _Symbolism of the Biblical World_ , p. 39). Due to Egypt's emphasis on being over substance, it is not too surprising to find evidence of an upholding power in Egypt.
Lambert, _Babylonian Creation Myths_ , pp. 372-73.
For a detailed discussion on the Mesopotamian view of the netherworld in the third millennium B.C., see Dina Katz, _The Image of the Netherworld in the Sumerian Sources_ (Bethesday, MD: CDL, 2003).
Dalley, _Myths from Mesopotamia_ , p. 155.
Alan Lenzi, "An Incantation Prayer: Ghosts of My Family 1," in _Reading Akkadian Prayers and Hymns: An Introduction_ , ed. Alan Lenzi, ANEM 3 (Atlanta: Society of Biblical Literature, 2011), p. 143.
See, e.g., Coogan and Smith, _Stories from Ancient Canaan_ , p. 137.
See T. J. Lewis, "Dead," _DDD_ , pp. 223-31.
Horowitz, _Mesopotamian Cosmic Geography_ , p. 351.
See, e.g., _Nergal and Ereshkigal_ , in Dalley, _Myths from Mesopotamia_ , pp. 165-77.
Dalley, _Myths from Mesopotamia_ , p. 89.
W. G. Lambert, _Babylonian Wisdom Literature_ (repr., Winona Lake, IN: Eisenbrauns, 1999), p. 71.
John H. Taylor, _Death and the Afterlife in Ancient Egypt_ (Chicago: University of Chicago Press, 2001), p. 186.
Ibid., p. 13.
See, e.g., Utterance 440 in Miriam Lichtheim, _Ancient Egyptian Literature_ , vol. 1, _The Old and Middle Kingdoms_ (Berkeley: University of California Press, 1973), p. 44.
Hornung, _Ancient Egyptian Books of the Afterlife_ , p. 34.
On the dating of these texts, see Hornung, _Ancient Egyptian Books of the Afterlife_ , pp. 27-28.
For a detailed discussion of this text, see Andreas Schweitzer, _The Sungod's Journey Through the Netherworld: Reading the Ancient Egyptian Amduat,_ trans. D. Lorton (Ithaca, NY: Cornell University, 2010); and Hornung, _Ancient Egyptian Books of the Afterlife_ , pp. 33-56.
See Horowitz, _Mesopotamian Cosmic Geography_ , p. 263.
J. Edward Wright, _The Early History of Heaven_ (Oxford: Oxford University Press, 2000), p. 13.
Foster, _From Distant Days_ , p. 34.
See Horowitz, _Mesopotamian Cosmic Geography_ , p. 265.
For a detailed study of astral sciences in the ancient world, see Hermann Hunger and David Pingree, _Astral Sciences in Mesopotamia_ , Handbook of Oriental Studies, Part One: The Ancient Near East and Middle East 44 (Leiden: Brill, 1999); Francesca Rochberg, _The Heavenly Writing: Divination, Horoscopy, and Astronomy in Mesopotamian Culture_ (Cambridge: Cambridge University Press, 2004).
Francesca Rochberg, "Mesopotamian Cosmology," in _A Companion to the Ancient Near East_ , ed. D. C. Snell, Blackwell Companions to the Ancient World (Oxford: Blackwell, 2005), p. 349.
Horowitz, _Mesopotamian Cosmic Geography_ , p. 153.
_Pennsylvania Sumerian Dictionary Project_ , University of Pennsylvania Museum of Anthropology and Archaeology, 2006, <http://psd.museum.upenn.edu/epsd1/nepsd-frame.html>; see also Hermann Hunger and David Pingree, _MUL.APIN: An Astronomical Compendium in Cuneiform_ , AfO 24 (Horn, Austria: Berger & Söhne, 1989).
N. M. Swerdlow, _The Babylonian Theory of the Planets_ (Princeton, NJ: Princeton University Press, 1998).
Alexander Jones, "A Study of Babylonian Observations of Planets Near Normal Stars," _Archive for History of Exact Sciences_ 58 (2004): 475-536.
_CAD_ K, p. 45.
_CAD_ B, p. 217.
This phenomenon is still observable today by fixing a slow-exposure camera on the North Star over the duration of the night. If the photographer centers Polaris in her camera, the resulting image is that of a pinwheel of light rotating around the Polaris hub.
Jeffrey L. Cooley, "An OB Prayer to the Gods of the Night," in Lenzi, _Reading Akkadian Prayers and Hymns_ , p. 82.
Benjamin R. Foster, _Before the Muses: An Anthology of Akkadian Literature_ , vol. 2, _Mature, Late_ (Bethesda, MD: CDL, 1993), pp. 646-75.
Wolfgang Heimpel, "The Sun at Night and the Doors of Heaven in Babylonian Texts," _JCS_ 28 (1986): 146.
Ibid., p. 150.
Hunger and Pingree, _MUL.APIN_ , ii, 1-6.
Wright, _Early History of Heaven_ , p. 33. For specific examples, see Heimpel, "The Sun at Night," pp. 132-40.
Cooley, "Prayer to the Gods of the Night," p. 82.
Ibid., p. 75.
Horowitz, _Mesopotamian Cosmic Geography_ , p. 266.
For a detailed discussion on this tablet, see Christopher E. Woods, "The Sun-God Tablet of Nabû-apla-iddina Revisited," _JCS_ 56 (2004): 23-103.
Henri Frankfort, _The Art and Architecture of the Ancient Orient_ , 5th ed. (New Haven, CT: Yale University Press, 1996), p. 202.
Wright, _Early History of Heaven_ , pp. 36-37.
See Kyle R. Greenwood, "A Shuilla: Marduk 2," in Lenzi, _Reading Akkadian Prayers and Hymns_ , p. 320; Greenwood, "The Hearing Gods of the Assyrian Royal Inscriptions," _JANER_ 10 (2010): 211-18.
Paul H. Seely, "The Geographical Meaning of 'Earth' and 'Seas' in Genesis 1:10," _WTJ_ 59 (1997): 240-42.
Thorkild Jacobsen, _The Treasures of Darkness: A History of Mesopotamian Religion_ (New Haven, CT: Yale University Press, 1976), p. 204.
Lichtheim, _New Kingdom,_ pp. 37, 41; Seely, "Geographical Meaning," p. 243.
Wilson, "Egypt," p. 45.
John H. Walton, _Ancient Near Eastern Thought and the Old Testament: Introducing the Conceptual World of the Hebrew Bible_ (Grand Rapids: Baker Academic, 2006), p. 176.
Horowitz, _Mesopotamian Cosmic Geography_ , p. 326.
See Coogan and Smith, _Stories from Ancient Canaan_ , p. 138; Christoph Uehlinger, "Leviathan," _DDD_ , p. 511.
Horowitz, _Mesopotamian Cosmic Geography_ , p. 335.
Martha T. Roth, _Law Collections from Mesopotamia and Asia Minor_ , SBLWAW 6, 2nd ed. (Atlanta: Scholars Press, 1997), p. 81.
Dalley, _Myths from Mesopotamia_ , p. 105.
Horowitz, _Mesopotamian Cosmic Geography_ , p. 342.
Foster, _Before the Muses_ , p. 850.
Jeremy Black and Anthony Green, _Gods, Demons and Symbols of Ancient Mesopotamia: An Illustrated Dictionary_ , illustrated by Tessa Rickards (Austin: University of Texas Press, 2000), p. 75.
"Enki and the World Order," _Electronic Text Corpus of Sumerian Literature_ , 2001, lines 309-17, <http://etcsl.orinst.ox.ac.uk/section1/tr113.htm>.
Horowitz, _Mesopotamian Cosmic Geography_ , pp. 262-63.
Coogan and Smith, _Stories from Ancient Canaan_ , p. 118.
Horowitz, _Mesopotamian Cosmic Geography_ , p. 262.
Leonard H. Lesko, "Ancient Egyptian Cosmogonies and Cosmology," in _Religion in Ancient Egypt: Gods, Myths, and Personal Practice_ , ed. B. E. Shafer (Ithaca, NY: Cornell University Press, 1991), p. 116.
Karl Butzer, _Early Hydraulic Civilization in Egypt: A Study in Cultural Ecology_ (Chicago: University of Chicago Press, 1976), pp. 18-20.
Smith, _On the Primaeval Ocean_ , p. 196.
Adriaan de Buck, _The Egyptian Coffin Texts_ , vol. 2, _Texts of Spells 76-143_ , OIP 49 (Chicago: University of Chicago Press, 1938), pp. 1-43.
Responses to these nontraditional viewpoints will be the focus of chaps. 5–6.
#### Chapter 3: Cosmology in Scripture
Some scholars describe the three tiers as consisting of the heavens, earth and netherworld. See, e.g., Luis I. J. Stadelmann, _The Hebrew Conception of the World_ , AnBib 39 (Rome: Pontifical Biblical Institute, 1970). However, this position fails to take into account two factors. First, although the netherworld is often depicted as the antithesis of heaven, it is also quite clear that its location lies within the depths of the earth. Second, the seas are an integral part of the ancient Near Eastern worldview, accounting for weather, floods and chaos.
In fact the argument could be made that this view was not limited to the Near East but was true throughout the ancient world.
Gregory A. Boyd and Paul R. Eddy, _Across the Spectrum: Understanding Issues in Evangelical Theology_ , 2nd ed. (Grand Rapids: Baker Academic, 2002), p. 25; Richard J. Clifford, "Creation in the Psalms," in _Creation in the Biblical Traditions_ , ed. Richard J. Clifford and John J. Collins, CBQMS 24 (Washington, DC: Catholic Biblical Association of America, 1992), p. 69; Peter Enns, _Inspiration and Incarnation: Evangelicals and the Problem of the Old Testament_ (Grand Rapids: Baker Academic, 2005), p. 54; Norman K. Gottwald, _The Hebrew Bible: A Socio-Literary Introduction_ (Philadelphia: Fortress, 1985), p. 476; Othmar Keel, _The Symbolism of the Biblical World: Ancient Near Eastern Iconography and the Book of Psalms_ , trans. Timothy J. Hallett (Winona Lake, IN: Eisenbrauns, 1997), p. 35; Sandra L. Richter, _The Epic of Eden: A Christian Entry into the Old Testament_ (Downers Grove, IL: IVP Academic, 2008); Ernest C. Lucas, "Cosmology," in _Dictionary of the Old Testament: Pentateuch_ , ed. T. Desmond Alexander and David W. Baker (Downers Grove, IL: InterVarsity Press, 2003), pp. 130-39; David Tsumura, _Creation and Destruction: A Reappraisal of the Chaoskampf Theory in the Old Testament_ (Winona Lake, IN: Eisenbrauns, 2005), pp. 65-72; John H. Walton, _Genesis 1 as Ancient Cosmology_ (Winona Lake, IN: Eisenbrauns, 2011), pp. 86-100.
In both Job and Zechariah, the noun _śā_ ṭ _ān_ is prefixed with the definite article, thus my translation, "The Satan." Scholars are fairly unanimous that the name in both Job and Zechariah function as a title rather than as a personal name. See, e.g., Marvin Pope, _Job: Introduction, Translation, and Notes_ , AB 15, 3rd ed. (Garden City, NY: Doubleday, 1973), p. 9; Carol L. Meyers and Eric M. Meyers, _Haggai, Zechariah 1–8: A New Translation with Introduction and Commentary_ , AB 25B (Garden City, NY: Doubleday, 1987), p. 183.
John E. Hartley, _The Book of_ _Job_ , NICOT (Grand Rapids: Eerdmans, 1988), p. 73.
Deut 13:7; 28:49, 64; 33:17; 1 Sam 2:10; Job 28:24; Ps 2:8; 22:27; 46:9; 48:10; 59:13; 61:2; 65:5; 67:7; 72:8; 98:3; 135:7; Prov 17:24; 30:4; Is 5:26; 24:16; 40:28; 41:5, 9; 42:10; 43:6; 45:22; 48:20; 49:6; 52:10; 62:11; Jer 10:13; 16:19; 25:31, 33; 51:16; Dan 4:22; Mic 5:4; Zech 9:10; Mt 12:42; Mk 13:27; Lk 11:31; Acts 1:8; 13:47.
Paul H. Seely, "The Geographical Meaning of 'Earth' and 'Seas' in Genesis 1:10," _WTJ_ 59 (1997): 239.
Marcus Jastrow, ed., _A Dictionary of the Targumim, the Talmud Babli and Yerushalmi, and the Midrashic Literature_ (New York: Judaica, 1996), p. 430; Michael Sokoloff, _A Syriac Lexicon: A Translation from the Latin, Correction, Expansion, and Update of C. Brockelmann's_ Lexicon Syriacum (Winona Lake, IN: Eisenbrauns, 2009), p. 421.
For a detailed discussion of this issue, see Robert J. Schneider, "Does the Bible Teach a Spherical Earth?," _Perspectives on Science and Faith_ 53 (2001): 159-69.
Hartley, _Book of Job_ , p. 329.
John N. Oswalt, _The Book of Isaiah: Chapters 40–6_ , NICOT (Grand Rapids: Eerdmans, 1998), p. 67; R. N. Whybray, _Isaiah 40–66_ , NCB (Grand Rapids: Eerdmans, 1981), pp. 56-57.
See, e.g., Aristotle, _On the Heavens_ , trans. W. K. Guthrie, LCL (Cambridge, MA: Harvard University Press, 1986), pp. 154-55.
Henry George Liddell, Robert Scott and Henry Stuart Jones, _A Greek-English Lexicon_ , 9th ed. with revised supplement (Oxford: Clarendon, 1996), p. 364.
Is 22:18 offers a possible alternative Hebrew word for ball, namely _dûr_ , although the evidence is not convincing. The immediate context of Is 22:18 seems to suggest a spherical object, but in Is 29:3, the only other place where the word occurs, it clearly connotes something ring-shaped. The Septuagint offers no help here as it translates _dûr_ (Hebrew _dwr_ ) as _dwd_ ("David") due to the similar-looking letters of _d_ and _r_ in the Hebrew script.
See also Izak Cornelius, "The Visual Representation of the World in the Ancient Near East and the Hebrew Bible," _JNSL_ 20 (1994): 201.
Another Greek word, _katabolē_ , refers to the foundations of the world in terms of its beginnings rather than its structure.
N. H. Tur-Sinai, _The Book of Job: A New Commentary_ (Jerusalem: Kiryath Sepher, 1957), p. 381.
Pope, _Job_ , p. 183.
Hartley, _Book of Job_ , p. 366.
See Moses Buttenwieser, _The Book of Job_ (London: Hodder & Stoughton, 1922), p. 281; Robert L. Alden, _Job_ , NAC 11 (Nashville: Broadman & Holman, 1993), p. 259.
For a similar interpretation, see Norman C. Habel, _The Book of Job: A Commentary_ , OTL (Philadelphia: Westminster, 1985), pp. 371-72.
For a detailed study of the netherworld in the Old Testament, see Philip S. Johnston, _Shades of Sheol: Death and Afterlife in the Old Testament_ (Downers Grove, IL: InterVarsity Press, 2002).
See also Job 10:21; 16:22.
Manfred Hutter, "Abaddon," _DDD_ , p. 1.
For a detailed but concise summary of this issue, see Theodore J. Lewis, "Dead, Abode of the," _ABD_ , 2:101-5.
Pope ( _Job_ , p. 43) states, "Just as Death had a first-born, xviii 13, so the various forms of pestilence may have been thought of as Resheph's children." Likewise, William J. Fulco notes that "trouble doesn't just come from the earth; no, man is faced with preternatural powers, evil spirits always ready to rise up from the underworld to assail him—that's how inevitable trouble is" ( _The Canaanite God Rešep_ , American Oriental Series 8 [New Haven, CT: American Oriental Society, 1976], p. 59).
Mark S. Smith, _The Priestly Vision of Genesis 1_ (Minneapolis: Fortress, 2010), p. 76.
Job 9:8; Ps 104:2; Is 40:22; 42:5; 44:24; 45:12; 48:13; 51:13, 16; Jer 10:12; 51:15; Zech 12:1.
Hartley, _Book of Job_ , p. 193.
Norman C. Habel ("He Who Stretches Out the Heavens," _CBQ_ 34 [1972]: 423) sees the tent-canopy imagery in light of ancient Near Eastern theophanies, whereby the "heavens are Yahweh's sacred 'tent,' the celestial holy place for his epiphanies on high."
Gen 1:6, 7 (3×), 8, 14, 15, 17, 20; Ps 19:2; 150:1; Ezek 1:22, 23, 25, 26; 10:1; Dan 12:3.
The word is also attested in the Phoenician text KAI 38:1 as _mrq_ ʿ. Herbert Donner and Wolfgang Röllig, _Kanaanäische und aramäische Inschriften_ (Wiesbaden: Harrassowitz, 2002), 1:9.
Luis Stadelmann, _The Hebrew Conceptions of the World_ , AnBib 39 (Rome: Pontifical Biblical Institute, 1970), p. 60.
Most modern translations of Ps 19:4 follow the LXX, Vulgate and the Syriac Peshitta. So the NRSV reads, "yet their voice goes out through all the earth." The Hebrew text translates as "their line" instead of "their voice," where the Hebrew word for line, _qāw_ , refers to a measuring line or tape measure. We will return to this issue in more depth in chap. 4.
See Baruch Halpern, "Late Israelite Astronomies and the Early Greeks," in _From Gods to God: The Dynamics of Iron Age Cosmologies_ , ed. M. J. Adams, FAT 63 (Tübingen: Mohr Siebeck, 2009), p. 445.
James K. Bruckner, _Exodus_ , NIBC 2 (Peabody, MA: Hendrickson, 2008), p. 227.
See J. Edward Wright, _The Early History of Heaven_ (Oxford: Oxford University Press, 2000), p. 56; Paul H. Seely, "The Firmament and the Water Above, Part I: The Meaning of _Raqia_ ʿ in Gen 1:6-8," _WTJ_ 53 (1991): 227-40.
See, e.g., Hartley, _Book of Job_ , p. 366; Pope, _Job_ , p. 184; Samuel Rolles Driver and George Buchanan, _A Critical and Exegetical Commentary on the Book of Job: Together with a New Translation_ , ICC (New York: Charles Scribner's Sons, 1921), 1:222.
John H. Walton, _Ancient Near Eastern Thought and the Old Testament: Introducing the Conceptual World of the Hebrew Bible_ (Grand Rapids: Baker Academic, 2006), p. 168.
English translations of _šāmayim_ vary greatly. The NRSV and NIV are fairly consistent in using "sky" or "air" when referring to the lower heavens, while the ESV and NASB fairly consistently use "heaven" or "heavens" for both the upper heavens and the lower heavens. However, none of these translations are perfectly consistent in their translations. Occasionally the NRSV and NIV will use "heaven" with reference to the lower heavens (e.g., Is 13:10; Jer 8:2), while the ESV and NASB will sometimes use "sky" (e.g., Prov 30:19).
See Cornelis Houtman, _Der Himmel im Alten Testament: Israels Weltbild und Weltanschauung_ , OtSt 30 (Leiden: Brill, 1993), p. 11.
Gen 1:26, 28; 2:20; 6:7; 7:3, 23; 1 Sam 17:44, 46; 2 Sam 21:10; 1 Kings 14:11; 16:4; 21:24; Job 12:7; 28:21; 35:11; Ps 8:8; 50:11; 79:2; 104:12; Jer 4:25; 7:33; 9:10; 15:3; 16:4; 19:7; 34:20; Ezek 29:5; 31:6, 13; 32:4; 38:20; Dan 2:38; 4:12, 21; Hos 2:18; 4:3; 7:12; Zeph 1:3. In all but four cases, the corresponding Hebrew phrase is ʿ _ôp haššāmayim_ , "bird of the heavens." At Ps 8:8; Dan 4:12, 21, the authors opt for a different word for bird, ṣ _ipôr_. The NRSV diverges from the Hebrew text at Ps 50:11. Where the Hebrew reads "birds of the mountains," the NRSV follows the LXX and translates "birds of the air." Most modern translations follow the Hebrew text here.
See also Job 20:6; 38:37; Ps 57:10; 77:17; 108:4.
See also Deut 4:11; Dan 7:13.
There are instances when clouds appear in the upper heavens; these clouds are not rain clouds but clouds that clothe God with splendor. See, e.g., Job 22:14.
See Brian N. Peterson, "Cosmology," in _Dictionary of the Old Testament: Prophets_ , ed. J. Gordon McConville and Mark J. Boda (Downers Grove, IL: InterVarsity Press, 2012), p. 96.
Stadelmann, _Hebrew Conception of the World_ , p. 66. Stadelmann notes that "nowhere in the Old Testament is there any mention of the region through which the sun travels between the time of its setting until its rising the next morning. The biblical authors did not accept the conception of the sun's journey through the nether world."
See, e.g., Jeffrey Cooley's discussion on Job 9:7-9 in _Poetic Astronomy in the Ancient Near East: The Reflexes of Celestial Science in Ancient Mesopotamia, Ugaritic, and Israelite Narrative_ (Winona Lake, IN: Eisenbrauns, 2013), pp. 320-23.
Edouard Lipínski, "Shemesh," _DDD_ , p. 810.
Oswalt, _Book of Isaiah_ , p. 321; Neil Bone, "Sky Notes," _Journal of the British Astronomical Association_ 119 (2009): 108; G. E. Kurtik, "The Identification of Inanna with the Planet Venus: A Criterion for the Time Determination of the Recognition of Constellations in Ancient Mesopotamia," _Astronomical and Astrophysical Transactions_ 17 (1999): 501.
Citing evidence from the _Damascus Document_ from the Dead Sea Scrolls, Cooley suggests reading _kiyyun_ as a reference to cultic paraphernalia, in parallel with "images," which the worshipers have made for themselves ( _Poetic Astronomy_ , pp. 237-45).
Ludwig Koehler and Walter Baumgartner, _The Hebrew and Aramaic Lexicon of the Old Testament_ (Leiden: Brill, 2001), 1:672.
Walter Bauer, William F. Arndt and F. Wilbur Gingrich, _A Greek-English Lexicon of the New Testament and Other Early Christian Literature_ , 2nd ed. (Chicago: University of Chicago Press, 1979), p. 666.
See also Eccles 12:2; Is 30:26; 60:19-20; Jer 31:35; Ezek 32:7; Hab 3:11.
According to a study published by NASA, between fifty-four and sixty-nine total solar eclipses have occurred every century since 2000 B.C. Including partial eclipses, the number escalates to an average of about 225 annually. Fred Espenak and Jean Meeus, _Five Millennium Catalog of Solar Eclipses: -1999 to +3000 (2000_ _BCE_ _to 3000_ _CE_ _)—Revised_ (Hanover, MD: NASA, 2009), <http://eclipse.gsfc.nasa.gov/5MCSE/TP2009-214174.pdf>.
2 Chron 36:23; Ezra 1:2; 5:11, 12; 6:9; 7:10, 12, 21, 23; Neh 1:4, 5; 2:4, 20; Ps 136:26; Dan 2:18, 19, 37, 44; 5:23 ("Lord of heaven"); Jon 1:9. It is interesting to note that each of these occurrences is found in later texts that date to the postexilic period, that is, after 539 B.C. See my note in "A Shuilla: Anu 1," in _Reading Akkadian Prayers and Hymns: An Introduction_ , ed. Alan Lenzi, ANEM 3 (Atlanta: Society of Biblical Literature, 2011), p. 233.
In three separate places we find the phrase "highest heaven" as a reference to God's sovereign dwelling place (Deut 10:14; 1 Kings 8:27; 2 Chron 2:6). A literal rendering of the Hebrew phrase is "the heavens and the heaven of heavens."
Mitchell G. Reddish, "Heaven," _ABD_ 3:90.
Jeffrey H. Tigay, _Deuteronomy_ , JPS Torah Commentary (Philadelphia: Jewish Publication Society, 1996), p. 107.
Houtman, _Der Himmel_ , p. 332.
Samuel A. Meier, _Themes and Transformations in Old Testament Prophecy_ (Downers Grove, IL: IVP Academic, 2009), p. 19.
In his dream at Bethel, Jacob sees angels ascending and descending on a stairway connecting heaven and earth. The account of the vision "reflects the ancient Near Eastern notion that the earthly temple was a scale model of the deity's heavenly residence. A stairway connected the two abodes, with a gate situated at the top of the stairway at the entrance of the cosmic dwelling." Greenwood, "Anu 1," pp. 224-25.
Gabriel and Michael are the only two named angels in the Old Testament. In the Hellenistic period (ca. 332–27 B.C.), many more angels were named. John J. Collins, "Gabriel," _DDD_ , pp. 338-39.
For a detailed discussion of the Satan in the Old Testament, see Cilliers Breytenbach and Peggy L. Day, "Satan," _DDD_ , pp. 726-32; Ryan E. Stokes, "The Devil Made David Do It . . . or Did He? The Nature, Identity, and Literary Origins of the Satan in 1 Chronicles 21:1," _JBL_ 128 (2009): 91-106.
N. T. Wright, _Surprised by Hope: Rethinking Heaven, the Resurrection, and the Mission of the Church_ (San Francisco: HarperOne, 2008), p. 45.
See Thorkild Jacobsen, _The Treasures of Darkness: A History of Mesopotamian Religion_ (New Haven, CT: Yale University Press, 1976), p. 20.
Wright, _Early History of Heaven_ , p. 59.
Keel and Uehlinger link the "Queen of Heaven" with astral worship, stating, "The cult of the 'Host of Heaven' in Iron Age IIC appears to have been analogous to that of the 'Queen of Heaven,' depicted primarily as an astral cult oriented toward the stars of the night sky" (Othmar Keel and Christoph Uehlinger, _Gods, Goddesses, and Images of God in Ancient Israel_ , trans. Timothy H. Trapp [Minneapolis: Fortress, 1998], p. 370). Houtman is less convinced. "The designation of 'Queen of Heaven' qualifies its bearer as a mighty, universal and leading goddess. In the ancient Near East similar designations were borne by prominent divinities such as the Babylonian Assyrian goddess Ishtar and the West Semitic goddesses Anat and Astarte. They have several traits of character in common and are generally regarded as fertility goddesses. It is doubtful whether they are characterized by their title as astral divinities. With regard to Ishtar and Astarte such an interpretation is possible—they are equated with Venus—, but with regard to Anat, for instance, the identification with a heavenly body is not likely" (Cornelis Houtman, "Queen of Heaven," _DDD_ , p. 678).
Fabrizio Lelli, "Stars," _DDD_ , p. 813.
See Meier Lubetski, "New Light on Old Seas," _JQR_ 68 (1977): 65-77.
Douglas Stuart hints at this reading by interpreting the passage to mean that the enemy will be "removed far away" ( _Hosea–Jonah_ , WBC 31 [Dallas: Word, 1989], p. 259).
Ralph L. Smith, _Micah–Malachi_ , WBC 32 (Dallas: Word, 1984), p. 289; Joyce G. Baldwin, _Haggai, Zechariah, Malachi: An Introduction and Commentary_ , TOTC 24 (Downers Grove, IL: InterVarsity Press, 1972), p. 203; David Allan Hubbard, _Joel and Amos: An Introduction and Commentary_ , TOTC 22b (Downers Grove, IL: InterVarsity Press, 1989), p. 63.
For a helpful discussion on the eastern and western seas, see Carol L. Meyers and Eric M. Meyers, _Zechariah 9–14: A New Translation with Introduction and Commentary_ , AB 25C (New York: Doubleday, 1993), pp. 437-38.
See Cornelius, "Visual Representation," pp. 211-18.
Literally he is the king's "third," "on whose hand the king leans." Mordechai Cogan and Hayim Tadmor provide a helpful, though complicated, summary of the possible meanings of the "third," Hebrew _šālîš_ : "Besides its obvious connections with _šālōš_ , 'three,' clues have been sought in almost every language of the ancient Near East without consensus. . . . Contextually there is no clear statement as to the function of the _šālîš_. Only Exod 14:7 hints at his possible service in the chariot corps, but Exod 15:4 does not support this interpretation. Nor does the pictorial evidence: Egyptian reliefs of the New Kingdom depict two-man crews on chariots in battle scenes with the Hittites, whose wagons also contain only two men. Only those chariots belonging to Sea Peoples ('Philistines') are manned by a crew of three. By the late eighth century, three-man crews became standard in Assyria. . . . The _šālîš_ —in 1 Kgs 9:22; 2 Kgs 7:2, 7, 19; 9:25; 15:25—is an officer, perhaps of 'third rank'" (Mordechai Cogan and Hayim Tadmor, _2 Kings: A New Translation with Introduction and Commentary_ , AB 11 [New York: Doubleday, 1988], pp. 81-82).
Walton, _Ancient Near Eastern Thought_ , pp. 176-77.
Tsumura, _Creation and Destruction_ , p. 50.
The Hebrew phrase translated as Red Sea is _yam sûp_ , which is best translated as "sea of reeds." Our modern translations follow both the Septuagint and the Latin Vulgate. In the Old Testament _yam sûp_ refers to various bodies of water, including the Gulf of Aqabah and the Gulf of Suez, the northern fingers of the Red Sea that surround the Sinai Peninsula. Most Bible maps reflect the modern scholarly consensus that the _yam sûp_ crossed by the Israelites was in the Bitter Lakes region, north of the Gulf of Suez. See Peter Enns, "Exodus Route and the Wilderness Itinerary," in Alexander and Baker, _Dictionary of the Old Testament: Pentateuch_ , pp. 272-80; James K. Hoffmeier, "The Exodus and Wilderness Narratives," in _Ancient Israel's History: An Introduction to Issues and Sources_ , ed. Bill T. Arnold and Richard S. Hess (Grand Rapids: Baker Academic, 2014), pp. 46-90, esp. pp. 78-80.
Walton, _Ancient Near Eastern Thought_ , p. 177.
In the modern debate between the Bible and science that is so prevalent in evangelicalism today, there are heated arguments about whether the flood of Gen 6–9 was global or local. If one takes into consideration the biblical view of the cosmos, it should be evident that the ancients would have thought of the flood as being universal, but not global. That is, it covered the entirety of the earth, but since the earth was not considered a sphere, it could not have been global. Moreover, the whole earth would have only been what was known to the audience of the narrative, namely, the Near East. So, on the question of whether the flood was local or global, the answer is yes. It was a universal flood from an ancient perspective, but a local flood from a modern point of view.
J. A. Emerton, "Leviathan and ltn: The Vocalization of the Ugaritic Word for Dragon," _VT_ 32 (1982): 327-31.
Christoph Uehlinger, "Leviathan," _DDD_ , p. 511.
Klaas Spronk, "Rahab," _DDD_ , p. 685. It will be shown in the next chapter that the Old Testament has different perspectives on the means by which God created the universe.
George C. Heider, "Tannin," _DDD_ , p. 836.
See Marten Stolz, "Sea," _DDD_ , pp. 737-42.
#### Chapter 4: Cosmology and Cosmogony in Scripture
Matthew Williams, _Two Gospels from One: A Comprehensive Text-Critical Analysis of the Synoptic Gospels_ (Grand Rapids: Kregel, 2006), p. 22.
See, e.g., Mark Goodacre, _The Synoptic Problem: A Way Through the Maze_ (New York: T & T Clark, 2001), pp. 13-55; Kurt Aland, ed., _Synopsis of the Four Gospels: English Edition_ , rev. ed. (New York: American Bible Society, 1985).
Mark S. Smith notes, "In ancient Israel, people told the creation story in different ways, as we see in various biblical books. There are allusions to the creation story in the prophets (for example, Jer. 10:12; Amos 4:13, 9:6; Zech 12:1), and it is recounted in various wisdom books (Prov. 8:22-31; Job 26:7-13, 38:1-11; Ben Sira 1:3-4, 24:3-9). The creation story was also a topic in Israel's worship (Pss. 74:12-17, 89:11-13, 90:2, and 148). These passages show us that in ancient Israel many different creation accounts existed, not just one single creation story. In fact, these passages indicate that there were various ways of telling the creation story." Mark S. Smith, _The Priestly Vision of Genesis 1_ (Minneapolis: Fortress, 2010), p. 11.
St. Thomas Aquinas, _Summa Theologica_ , trans. Fathers of the English Dominican Province (New York: Benziger, 1948), 1:346 (part 1, q. 70, art. 1).
Thomas refers to days one through three as "form," and days four through six as "fulness." W. H. Griffith Thomas _, Genesis: A Devotional Commentary_ (Grand Rapids: Eerdmans, 1946), p. 29.
Gordon Wenham observes "that although there are ten announcements of the divine words and eight commands actually cited, all the formulae are grouped in sevens" ( _Genesis 1–15_ , WBC 1 [Waco: Word, 1987], p. 6).
In the Hebrew text, only days six and seven have the definite article. Literally the days of Gen 1 read as follows: one day, a second day, a third day, a fourth day, a fifth day, the sixth day (lit. "a day, the sixth"), the seventh day.
For a detailed analysis of the stylistic nature of Gen 1, see C. John Collins, _Genesis 1–4: A Linguistic,_ _Literary, and Theological Commentary_ (Phillipsburg, NJ: P & R, 2006).
John H. Walton, _The Lost World of Genesis One: Ancient Cosmology and the Origins Debate_ (Downers Grove, IL: IVP Academic, 2009), p. 19.
A merism is a literary or rhetorical device used to encompass the entirety of something by pairing the extreme opposites of that entity, like "near and far" or "young and old."
Nahum Sarna, _Genesis_ , JPS Torah Commentary (Philadelphia: Jewish Publication Society, 1989), p. 5.
See, e.g., Brevard S. Childs, _Old Testament Theology in a Canonical Context_ (London: SCM, 1985), pp. 223-24; Hermann Gunkel, _Schöpfung und Chaos in Urzeit und Endzeit: Eine religionsgeschichtliche Untersuchung über Gen 1 und Ap Joh 12_ (Göttingen: Vandenhoeck und Ruprecht, 1895); Gerhard von Rad, _Genesis: A Commentary_ , trans. J. H. Marks, rev. ed., OTL (Philadelphia: Westminster, 1973), p. 51.
David Toshio Tsumura, "Genesis and Ancient Near Eastern Stories of Creation and Flood: An Introduction," in _"I Studied Inscriptions from Before the Flood_ " _:_ _Ancient Near Eastern, Literary, and Linguistic Approaches to Genesis 1–11_ , ed. Richard S. Hess and David Toshio Tsumura (Winona Lake, IN: Eisenbrauns, 1994), p. 33.
John H. Walton, _Genesis 1 as Ancient Cosmology_ (Winona Lake, IN: Eisenbrauns, 2011), p. 141.
Umberto Cassuto, _A Commentary on the Book of Genesis: From Adam to Noah_ (Jerusalem: Magnes, 1961), pp. 31-32.
Wenham, _Genesis 1–15_ , p. 20.
Paul H. Seely, "The Firmament and the Water Above: Part I: The Meaning of _raqia_ ʾ in Gen 1:6-8," _WTJ_ 53 (1991): 228.
Walter Vogels, "The Cultic and Civil Calendars of the Fourth Day of Creation (Gen 1, 14b)," _SJOT_ 11, no. 2 (1997): 175.
Collins, _Genesis 1–4_ , p. 241.
"The _sea monsters_ [ _tannînīm_ ] . . . are especially noteworthy, since to the Canaanites this was an ominous word, standing for the powers of chaos confronting Baal in the beginning. Here they are just magnificent creatures (like Leviathan in Ps. 104:26; Jb. 41), enjoying God's blessing with the rest (22). Although in some scriptures these names will symbolize God's enemies (e.g. Is. 27:1), taunted in the very terms in which Baal exults over them, no doubt is left by this chapter that the most fearsome of creatures were from God's good hand. There may be rebels in His kingdom, but no rivals" (Derek Kidner, _Genesis: An Introduction and Commentary_ , TOTC 1 [Downers Grove, IL: InterVarsity Press, 1967], p. 49).
Collins, _Genesis 1–4_ , p. 72.
_2 Enoch_ 33.1; _Letter of Barnabas_ 15.1-5; _Babylonian Talmud, Sanhedrin_ 97a; Irenaeus, _Against Heresies_ 5.23.2 ( _ANF_ 1:551-52); Lactantius, _Divine Institutes_ 7.14 ( _ANF_ 7:211-12); Augustine, _City of God_ 12.12 (trans. Marcus Dods [New York: Modern Library, 1993]); Basil of Caesarea, _Hexaemeron_ 2.8 ( _NPNF_ 2 8:64-65); St. Ephraim, _Hymns on the Nativity_ 19 ( _NPNF_ 2 13:261-62); Gregory of Nyssa, _Against Eunomius_ 1.26 ( _NPNF_ 2 5:68-71).
See Walton, _Genesis 1 as Ancient Cosmology_ , pp. 178-92; Bernard F. Batto, "The Sleeping God: An Ancient Near Eastern Motif of Divine Sovereignty," in _In the Beginning: Essays on Creation Motifs in the Ancient Near East and the Bible_ , Siphrut 9 (Winona Lake, IN: Eisenbrauns, 2013), pp. 139-57.
For a compelling account of how Gen 2 serves as the theological core of the Bible, see Sandra L. Richter, _The Epic of Eden: A Christian Entry into the Old Testament_ (Downers Grove, IL: IVP Academic, 2008).
Sarna, _Genesis_ , p. 16. To this list we may also add Gen 6:9. Marten H. Woudstra, "The _Toledot_ of the Book of Genesis and Their Redemptive-Historical Significance," _CTJ_ 5 (1970): 186. Frank M. Cross, _Canaanite Myth and Hebrew Epic: Essays in the History of the Religion of Israel_ (Cambridge, MA: Harvard University Press, 1973), pp. 302-5.
Wenham, _Genesis 1–15_ , p. 49.
Walton, _Genesis 1 as Ancient Cosmology_ , p. 102. See also Ronald A. Simkins, _Creator and Creation: Nature in the Worldview of Ancient Israel_ (Peabody, MA: Hendrickson, 1994), pp. 138-44.
Gordon J. Wenham, "Sanctuary Symbolism in the Garden of Eden Story," in Hess and Tsumura, _I Studied Inscriptions_ , p. 399.
Note that at the second giving of the law in Deuteronomy, the rationale for the Sabbath was not the creation, but the exodus event (Deut 5:12-15). In fact, in terms of Old Testament theology, the exodus event has more significance than any other event, including creation. Moreover, in Heb 4 the author invites his audience to enter into the Sabbath rest, suggesting that the Sabbath is not a day but an eschatological event. See, e.g., David L. Allen, _Hebrews: An Exegetical and Theological Exposition of Holy Scripture_ , NAC 35 (Nashville: B & H, 2010), p. 284. As F. F. Bruce states, rest "is evidently an experience which they do not enjoy in their present mortal life, although it belongs to them as a heritage, and by faith they may live in the good of it here and now" (F. F. Bruce, _The Epistle to the Hebrews: The English Text with Introduction_ , _Exposition and Notes_ [Grand Rapids: Eerdmans, 1964], p. 78).
See, e.g., Charles Augustus Briggs and Emilie Grace Briggs, _A Critical and Exegetical Commentary on the Book of Psalms_ , ICC 16a (Edinburgh: T & T Clark, 1969), p. 163.
See J. Ross Wagner, "From the Heavens to the Heart: The Dynamics of Psalm 19 as Prayer," _CBQ_ 61 (1999): 245-61; Jeffrey L. Cooley, "Psalm 19: A Sabbath Song," _VT_ 64 (2014): 177-95.
See James K. Hoffmeier, "'The Heavens Declare the Glory of God': The Limits of General Revelation," _Trinity Journal_ 21 (2000): 17-24; Sheri L. Klouda, "The Dialectical Interplay of Seeing and Hearing in Psalm 19 and Its Connection to Wisdom," _BBR_ 10, no. 2 (2000): 192.
Daniel G. Ashburn, "Creation and the Torah in Psalm 19," _JBQ_ 22, no. 3 (2004): 243.
Julian Morgenstern, "Psalms 8 and 19A," _HUCA_ 19 (1945–1946): 512.
Hermann Gunkel, _The Psalms: A Form-Critical Introduction_ _with an Introduction by James Muilenburg_ , trans. T. M. Horner (Philadelphia: Fortress, 1967), p. 13; Gunkel, _An_ _Introduction to the Psalms: The Genres of the Religious Lyric of Israel_ , completed by J. Begrich, trans. J. D. Nogalski (Macon, GA: Mercer University Press, 1998), p. 82.
There is some debate whether God's dividing the seas in Ps 74:13 refers to the initial creative act or the splitting of the sea during the exodus. As Hans-Joachim Kraus notes, it may not be an either/or proposition: "Even though the mythical elements unquestionably predominate, undoubtedly also conceptions of ancient Israelite salvation history are present" (Hans-Joachim Kraus, _Psalms 60–150_ , trans. H. C. Oswald, Continental Commentary [Minneapolis: Fortress, 1993], p. 99).
John Oswalt, "The Myth of the Dragon and Old Testament Faith," _EvQ_ 49 (1977): 163-72.
Patrick D. Miller, "The Poetry of Creation: Psalm 104," in _God Who Creates: Essays in Honor of W. Sibley Towner_ , ed. W. P. Brown and S. D. McBride Jr. (Grand Rapids: Eerdmans, 2000), pp. 87-103.
In Ps 104 Leviathan "is demythologized as a mere creature who 'frolics' in the sea. Indeed, the sea itself, rather than symbolizing chaos, is presented as a realm under God's blessing" (Craig C. Broyles, _Psalms_ , NIBC 11 [Peabody, MA: Hendrickson, 1999], p. 400).
Gunkel, _An Introduction to the Psalms_ , p. 46.
It makes sense to read the challenging Ps 137 in light of its canonical context. God had indeed been faithful to Israel in the past. Now that Israel was in exile, they could recall that faithfulness to be with them during these trying times. Though they would like retributive justice, vengeance belongs to the Lord.
See also Kathryn M. Schifferdecker, "Creation Theology," in _Dictionary of the Old Testament: Wisdom, Poetry and Writings_ , ed. Tremper Longman III and Peter Enns (Downers Grove, IL: InterVarsity Press, 2008), pp. 63-71.
#### Chapter 5: Scripture and Aristotelian Cosmology
I. Crystal, "The Scope of Thought in Parmenides," _ClQ_ 52 (2002): 216. For an accessible summary of the life and works of Parmenides, see John Palmer, "Parmenides," in _The Stanford Encyclopedia of Philosophy_ , ed. Edward N. Zalta, summer 2012 ed., <http://plato.stanford.edu/archives/sum2012/entries/parmenides/>.
Carl Huffman, "Philolaus," in Zalta, _The Stanford Encyclopedia of Philosophy_ , <http://plato.stanford.edu/archives/sum2012/entries/philolaus/>.
Aristotle, _Metaphysics Books X–XIV, Oeconomica and Magna Moralia_ , trans. G. C. Armstrong, LCL (Cambridge, MA: Harvard University Press, 1977), p. 159 (12.8).
Timothy Ferris, _Coming of Age in the Milky Way_ (New York: HarperCollins, 1988), p. 26.
Edward Grant, _Science and Religion, 400_ BC _–_ AD _1550: From Aristotle to Copernicus_ (Baltimore: Johns Hopkins University Press, 2004), pp. 33-34.
Aristotle, _Metaphysics_ , p. 159 (12.8).
Harry Lee Poe and Jimmy H. Davis, _God and the Cosmos: Divine Activity in Space, Time and History_ (Downers Grove, IL: IVP Academic, 2012), p. 151.
J. L. E. Dreyer, _A History of Astronomy from Thales to Kepler_ , rev. ed. (New York: Dover, 1953), p. 121.
C. M. Linton, _From Eudoxus to Einstein: A History of Mathematical Astronomy_ (Cambridge: Cambridge University Press, 2004), p. 34.
Aristotle, _Physics_ 8.258b, 10 [Wicksteed, LCL].
Helge S. Kragh, _Conceptions of Cosmos from Myths to the Accelerating Universe: A History of Cosmology_ (Oxford: Oxford University Press, 2007), p. 23.
Aristotle, _On the Heavens_ 2.8.289b [Guthrie, LCL].
Cited in Edward Rosen, "The Dissolution of the Solid Celestial Spheres," _Journal of the History of Ideas_ 46 (1985): 14.
See, e.g., the discussion on Macrobius and Calcidius in Bruce S. Eastwood, _Ordering the Heavens: Roman Astronomy and Cosmology in the Carolingian Renaissance_ , Medieval and Early Modern Science 8 (Leiden: Brill, 2007).
According to Kragh, "It is believed that this alternative was first proposed by the Alexandrian mathematician Apollonius, who is especially known for his unified theory of conic sections, including the circle, parabola, ellipse, and hyperbola. . . . Apollonius' writings on astronomy have not survived, but his idea was developed by Hipparchus, who was the first to supply it with numerical parameters based on observations" ( _Conceptions of Cosmos_ , p. 28).
Ptolemy, _Almagest_ 1.1.
Ferris, _Coming of Age in the Milky Way_ , pp. 28-29.
Robert Wilson, _Astronomy Through the Ages: The Story of the Human Attempt to Understand the Universe_ (Princeton, NJ: Princeton University Press, 1997), p. 37.
Kragh, _Conceptions of Cosmos_ , p. 25.
For a detailed description of the mathematical equations used by Hipparchus and Ptolemy, see Linton, _From Eudoxus to Einstein_ , pp. 51-83, and Kitty Ferguson, _Measuring the Universe: Our Historic Quest to Chart the Horizons of Space and Time_ (New York: Walker, 1999), p. 20.
Using the equation r=c/2π, where c=39,375 km as calculated by Eratosthenes, one earth radius is approximately 6,267 km.
Kragh, _Conceptions of Cosmos_ , p. 31; G. J. Toomers, "Ptolemy and His Greek Predecessors," in _Astronomy Before the Telescope_ , ed. C. Walker (New York: St. Martin's, 1996), p. 91.
This calculation is based on the actural mean radius of the earth of 6,371 km.
See G. E. R. Lloyd, _Aristotle: The Growth and Structure of His Thought_ (Cambridge: Cambridge University Press, 1968), p. 287.
Richard Kraut, "Plato," in Zalta, _The Stanford Encyclopedia of Philosophy_ , fall 2013 ed., <http://plato.stanford.edu/archives/fall2013/entries/plato/>.
Norman Melchert, _The Great Conversation: A Historical Introduction to Philosophy_ , 5th ed. (New York: Oxford University Press, 2006), pp. 181-83.
Ed L. Miller and Jon Jensen, _Questions That Matter: An Invitation to Philosophy_ , 6th ed. (Boston: McGraw-Hill, 2009), p. 56.
Gnosticism was a religious and philosophical movement pervasive in the first and second centuries A.D. Deemed heretical by the church, its foundational principle was "the commitment to a radical anticosmic dualism in which all that is material—the world and the body—is seen as evil and as the creation of a lesser, inferior god" (David M. Scholer, "Gnosis, Gnosticism," in _Dictionary of the Later New Testament and Its Developments_ , ed. Ralph P. Martin and Peter H. Davids [Downers Grove, IL: InterVarsity Press, 1997], p. 401).
For a splendid study on how the early Christian interpreters read the Genesis accounts, see Peter C. Bouteneff, _Beginnings: Ancient Christian Readings of the Biblical Creation Narratives_ (Grand Rapids: Baker Academic, 2008).
Martin Luther, _Lectures on Genesis, Chapters 1–5_ , ed. Jaroslav Pelikan, trans. George V. Schick, Luther's Works 1 (St. Louis: Concordia, 1958), p. 41.
Philo, _Life of Moses_ 2.133 [Colson, LCL].
Moses Maimonides, _The_ _Guide for the Perplexed_ , trans. M. Friedländer, 2nd ed. (New York: Dover, 1904), p. 213.
Luther, _Lectures on Genesis_ , p. 26.
Basil of Caesarea, _The Syriac Version of the Hexaemeron_ , trans. R. W. Thompson, Corpus Scriptorum Christianorum Orientalium 551, Scriptorus Syri 223 (Louvain: Peeters, 1995), p. 27.
Jacob Neusner, trans., _Genesis Rabbah_ : _The Judaic Commentary to the Book of Genesis—A New American Translation_ , vol. 1, _Parashiyyot One Through Thirty-Three on Genesis 1:1 to 8:4_ , Brown Judaic Studies 104 (Atlanta: Scholars Press, 1985), p. 100.
See, e.g., Joel S. Allen, _Jewish Biblical Legends: Rabbinic Wisdom for Christian Readers_ (Eugene, OR: Cascade, 2013).
Lactantius, _Divine Institutes_ 24 ( _ANF_ 7:94).
Lactantius, _Divine Institutes_ 24 ( _ANF_ 7:95).
Saint Augustine, _The_ _City of God_ 16.9 (trans. Marcus Dods [New York: Modern Library, 1993], p. 532).
Isidore Epstein, J. H. Hertz and Maurice Simon, _Hebrew-English Edition of the Babylonian Talmud, Translated into English with Notes, Glossary, and Indices_ (London: Soncino, 1984), _Pesa_ ḥ _im_ 94a.
Ferguson, _Measuring the Universe_ , p. 20. According to Lucio Russo ("Ptolemy's Longitudes and Eratosthenes' Measurement of the Earth's Circumference," _Mathematics and Mechanics of Complex Systems_ 1 [2013]: 69), this value was first posited by F. Hultsch ( _Griechische und römische Metrologie_ [Berlin: Weidmann, 1882]). More recent studies, particularly by D. Rawlins ("The Eratosthenes–Strabo Nile Map: Is It the Earliest Surviving Instance of Spherical Cartography? Did It Supply the 5000 Stades Arc for Eratosthenes' Experiment?," _Archive for History of Exact Sciences_ 26, no. 3 [1982]: 211-19), argue for a stade value of 185 kilometers.
Philo, _On the Creation_ 18.
Theophilus, _To Autolycus_ 2.13 ( _ANF_ 2:99).
St. John Chrysostom, _Homilies on Genesis 1–17_ , trans. Robert C. Hill, FC 74 (Washington, DC: Catholic University of America Press, 1986), p. 35.
John Calvin, _Commentary on the Book of Psalms_ , vol. 4, _Psalms 93–150_ , trans. J. Anderson, Calvin's Commentaries 6 (Grand Rapids: Baker, 1981), p. 148.
Martin Luther, _First Lectures on the Psalms_ , vol. 2, _Psalms 76–126_ , trans. Herbert J. A. Bouman, Luther's Works 11 (St. Louis: Concordia, 1976), p. 323.
Martin Luther, _Lectures on Isaiah Chapters 40–66_ , trans. Herbert J. A. Bouman, Luther's Works 17 (St. Louis: Concordia, 1972), p. 164.
John Calvin, _Commentary on the Prophet Isaiah_ , vol. 2, _Isaiah 33–66_ , trans. W. Pringle, Calvin's Commentaries 8 (Grand Rapids: Baker, 1981), p. 478.
Mt 13:35; 25:34; Lk 11:50; Jn 17:24; Eph 1:4; Heb 4:3; 9:26; 1 Pet 1:20; Rev 13:8; 17:8.
See Grant R. Osborne, "Resurrection," in _Dictionary of Jesus and the Gospels_ , ed. Joel B. Green and Scot McKnight (Downers Grove, IL: InterVarsity Press, 1992), p. 675; Gary G. Porton, "Sadducees," _ABD_ 5:892.
Neusner, _Parashiyyot_ , p. 5.
Although the earliest iterations of what would become the Apostles' Creed date to the early second century A.D., the phrase "he descended into hell" ( _descendit ad inferna_ ) does not appear in any Latin forms of the creed until A.D. 359 in the Fourth Formula of Sirmium. See J. N. D. Kelly, _Early Christian Creeds_ , 3rd ed. (New York: Continuum, 2006), pp. 101, 378.
For a brief review of the early Christian concept of hell as the abode of sinner and saint, see John Yates, "'He Descended Into Hell': Creed, Article, and Scripture, Part I," _Churchman_ 102, no. 3 (1988): 240-50.
Dante Alighieri, _The Divine Comedy_ , vol. 1, _The Inferno_ , trans. John D. Sinclair (Oxford: Oxford University Press, 1961).
Mt 5:22, 29-30; 10:28; 18:9; 23:15, 33; Mk 9:43, 45, 47; Lk 12:5.
Jan N. Bremmer, "Hades," _DDD_ , p. 382.
William Hansen, _Classical Mythology: A Guide to the Mythical World of the Greeks and Romans_ (Oxford: Oxford University Press, 2004), pp. 179-80.
Joel B. Green, _The Gospel of Luke_ , NICNT (Grand Rapids: Eerdmans, 1997), p. 605.
_Testament of Abraham_ 20.14; E. P. Sanders, "Testament of Abraham," in _The Old Testament Pseudepigrapha_ , vol. 1, _Apocalyptic Literature and Testaments_ , ed. James H. Charlesworth (Garden City, NY: Doubleday, 1983), p. 895.
Green, _Luke_ , p. 607.
Hansen, _Classical Mythology_ , pp. 294-95.
Basil, _Hexaemeron_ , p. 32.
Ibid., p. 33.
Ibid.
Ibid., p. 34.
F. I. Andersen, "2 (Slavonic Apocalypse of) Enoch," in Charlesworth, _Apocalyptic Literature and Testaments_ , pp. 149-50.
Philo, _On the Creation_ 38.113 [Colson and Whitaker, LCL].
Maimonides, _Guide for the Perplexed_ , p. 214.
Luther, _Lectures on Genesis_ , p. 26.
St. Thomas Aquinas, _Summa Theologica_ , trans. Fathers of the English Dominican Province (New York: Benziger, 1948), 1:341 (part 1, q. 68, art. 3).
Ambrose, _Hexaemeron_ 2.2 (in Ambrose, _Hexaemeron, Paradise, and Cain and Abel_ , trans. J. J. Savage, FC 42 [Washington, DC: Catholic University of America Press, 2003], p. 60).
Epstein, Hertz and Simon, _Hebrew-English Edition of the Babylonian Talmud,_ Ḥ _agigah_ 12b.
_Song of the Three_ was a later addition to the book of Daniel and contains a hymn sung by Shadrach, Meshach and Abednego while enduring the fiery furnace at the hand of Nebuchadnezzar (Dan 4).
Theophilus, _To Autolycus_ 2.13 ( _ANF_ 2:100).
Chrysostom, _Homilies on Genesis 1–17_ , p. 35.
Neusner, _Parashiyyot_ , p. 37.
Harry E. Gaylord, "3 (Greek Apocalypse of) Baruch," in Charlesworth, _Apocalyptic Literature and Testaments_ , p. 665.
Origen, _Homilies on Genesis and Exodus_ , trans. Ronald E. Heine, FC 71 (Washington, DC: Catholic University of America Press, 1982), p. 49.
Chrysostom, _Homilies on Genesis_ , p. 35.
Basil, _Hexaemeron_ , p. 35.
Neusner, _Parashiyyot_ , p. 55.
Ibid., p. 55.
Ibid., p. 56.
Luther, _Lectures on Genesis_ , p. 41.
John Calvin, _Commentaries on the First Book of Moses Called Genesis_ , trans. J. King, Calvin's Commentaries 1 (Grand Rapids: Baker, 1979), p. 86.
J. Richard Middleton writes, "Whatever we think about the intermediate state (and I acknowledge that belief in such a state is dear to many Christians), it is clear from Scripture that heaven is not the final destination of the redeemed. . . . Not only is the term 'heaven' never used in Scripture for the eternal destiny of the redeemed, but also continued use of 'heaven' to name the Christian eschatological hope may well divert our attention from the legitimate expectation for the present transformation of our earthly life to conform to God's purposes. Indeed, to focus our expectation on an otherworldly salvation has the potential to dissipate our resistance to societal evil and the dedication needed to work for the redemptive transformation of this world" ( _A New Heaven and a New Earth: Reclaiming Biblical Eschatology_ [Grand Rapids: Baker Academic, 2014], p. 237).
Dante Alighieri, _The Paradiso_ , trans. J. Ciardi (New York: Penguin, 1970), pp. 327-32.
Calvin, _Isaiah_ , p. 411.
S. E. Robinson, trans., "The Testament of Our Father Adam," in Charlesworth, _Apocalyptic Literature and Testaments_ , p. 993.
Andersen, "2 (Slavonic Apocalypse of) Enoch," p. 110.
_Babylonian Talmud, Sanhedrin_ 109a (in Epstein, Hertz and Simon _, Hebrew-English Edition_ ).
_Taanith_ 9b (in Epstein, Hertz and Simon _, Hebrew-English Edition_ ).
Josephus, _Antiquities of the Jews_ 1.1.30.
Neusner, _Parashiyyot_ , p. 41.
Theophilus, _To Autolycus_ 2.13 ( _ANF_ 2:100).
Chrysostom, _Homilies on Genesis 1–17_ , p. 55.
Basil, _Hexaemeron_ , pp. 34-35.
_St. Augustine on Genesis: Two Books on Genesis and On the Literal Interpretation of Genesis: An Unfinished Book_ , trans. Roland J. Teske, FC 84 (Washington, DC: Catholic University of America Press, 1991), p. 168.
Maimonides, _Guide for the Perplexed_ , p. 215.
Ibid., p. 215.
Aquinas, _Summa Theologica_ , 1:339-40 (part 1, q. 68, art. 2).
Luther, _Lectures on Genesis_ , p. 26.
Calvin, _Genesis_ , p. 79.
Ibid., p. 80.
The farthest known galaxy from Earth is MACS0647-JD, viewed by NASA's Hubble Telescope in 2011. "NASA Great Observatories Find Candidate for Most Distant Object in the Universe to Date," NASA, November 15, 2011, www.nasa.gov/mission_pages/hubble/science/distance-record.html.
Philo, _On the Creation_ 23.70 [Colson and Whitaker, LCL].
Philo, _Allegorical Interpretation_ 1.2 [Colson and Whitaker, LCL].
Basil, _Hexaemeron_ , p. 28.
Aquinas, _Summa Theologica_ , 1:336.
Maimonides, _Guide for the Perplexed_ , p. 212.
Neusner, _Parashiyyot_ , p. 101.
Aquinas, _Summa Theologica_ , 1:349.
Basil, _Hexaemeron_ , p. 35.
Ibid., p. 33.
#### Chapter 6: Scripture and Copernican Cosmology
Wallace K. Ferguson, _The Renaissance_ , Berkshire Studies in European History (New York: Holt, Rinehart and Winston, 1940), p. 1.
Paul Johnson, _The Renaissance: A Short History_ , Modern Library Chronicles (New York: Modern Library, 2002), p. 3.
John R. Hale, "The Origins of the Renaissance," in _The Renaissance_ , ed. S. P. Thompson, Turning Points in World History (San Diego: Greenhaven, 2000), p. 30.
Ibid., p. 47.
For a survey of the Renaissance art and artists, see De Lamar Jensen, _Renaissance Europe: Age of Recovery and Reconciliation_ (Lexington, MA: Heath, 1981), pp. 133-60.
Owen Gingerich, _The Eye of Heaven: Ptolemy, Copernicus, Kepler_ (New York: American Institute of Physics, 1993), p. 161.
Robert Wilson, _Astronomy Through the Ages: The Story of the Human Attempt to Understand the Universe_ (Princeton, NJ: Princeton University Press, 1997), p. 53.
Timothy Ferris, _Coming of Age in the Milky Way_ (New York: HarperCollins, 2003), p. 63.
Willis, _Astronomy Through the Ages_ , p. 53.
Nicolaus Copernicus, _On the Revolutions of Heavenly Spheres_ , trans. C. G. Wallis, Great Minds Series (Amherst, NY: Prometheus, 1995), p. 6.
Ibid., p. 7.
Ibid.
Thomas Kuhn, _The Copernican Revolution: Planetary Astronomy in the Development of Western Thought_ (New York: Vintage Books, 1957), p. 135.
Copernicus, _On the Revolutions of Heavenly Spheres_ , p. 18 (1.8).
Ibid., p. 28 (1.10).
Clarice Swisher, "Galileo Galilei: A Lifelong Struggle for a New Science," in _Galileo_ , ed. Clarice Swisher (San Diego: Greenhaven, 2001), pp. 13-34.
I. S. Glass, _Revolutionaries of the Cosmos: The Astro-Physicists_ (Oxford: Oxford University Press, 2009), pp. 8-39.
Annibale Fantoli, _Galileo: For Copernicanism and for the Church_ , trans. G. V. Coyne, 3rd ed. (Notre Dame, IN: University of Notre Dame Press, 2003), p. 58.
J. L. E. Dreyer, _A History of Astronomy from Thales to Kepler_ , rev. ed. (New York: Dover, 1953), p. 373.
Glass, _Revolutionaries of the Cosmos_ , p. 14.
On Galileo's faulty assumptions regarding the tides, see Paolo Palmieri, "Re-examining Galileo's Theory of the Tides," _Archive for the History of Exact Sciences_ 53 (1998): 223-375.
William R. Shea and Mark Davie, trans., _Galileo: Selected Writings_ , Oxford World's Classics (Oxford: Oxford University Press, 2012), p. xi.
Glass, _Revolutionaries of the Cosmos_ , p. 15. Incidentally, in 1618 three comets appeared in successive order, further undermining the unchangeable nature of the heavens.
Swisher, _Galileo_ , p. 19.
Glass, _Revolutionaries of the Cosmos_ , p. 16.
A doge (pronounced _dōjh_ ) is "the title of the chief magistrate in the formerly existing republics of Venice and Genoa" ( _The Oxford English Dictionary_ , 2nd ed. [Oxford: Oxford University Press, 1999], 4:926).
Fantoli, _Galileo_ , p. 83.
Kitty Ferguson, _Measuring the Universe: Our Historic Quest to Chart the Horizons of Space and Time_ (New York: Walker, 1999), p. 89.
Max Caspar, _Kepler_ (New York: Dover, 1993), p. 62.
Ibid.
Ferris, _Coming of Age in the Milky Way_ , p. 75.
Ibid., p. 78.
Dreyer, _History of Astronomy_ , p. 362.
Gingerich, _Eye of Heaven_ , p. 314.
John Dillenberger, _Protestant Thought and Natural Science: A Historical Interpretation_ (Nashville: Abingdon, 1960), p. 79.
Shea and Davie, _Galileo_ , p. 67.
Dillenberger, _Protestant Thought and Natural Science_ , p. 89.
Indulgences were spiritual favors initiated by Pope Leo X to fund the renovations for St. Peter's Basilica in Rome. According to the church, the purchase of an indulgence would cleanse the customer of his or her sins. Ironically, "the refurbishment of the great basilica that is now the pride of Roman Catholicism indirectly helped foment the Protestant Reformation" (Justo L. González, _The Story of Christianity_ , vol. 2, _The Reformation to the Present Day_ , rev. ed. [San Francisco: HarperSanFrancisco, 1984], p. 27).
Ibid., p. 21.
Peter Harrison, _The Bible, Protestantism, and the Rise of Natural Science_ (Cambridge: Cambridge University Press, 1998), p. 114.
Martin Luther, _Lectures on Genesis, Chapters 1–5_ , ed. Jaroslav Pelikan, trans. George V. Schick, Luther's Works 1 (St. Louis: Concordia, 1958), p. 18.
Martin Luther, _Table Talk_ , ed. T. G. Tappert, Luther's Works 54 (Philadelphia: Fortress, 1967), pp. 358-59.
Dillenberger, _Protestant Thought and Natural Science_ , p. 38.
Owen Gingerich, _The Book Nobody Read: Chasing the Revolutions of Nicolaus Copernicus_ (New York: Walker, 2004), p. 136.
Luther, _Table Talk_ , pp. xv-xix.
Luther, _Lectures on Genesis_ , pp. 29, 52, 58, 127.
Ibid., pp. 31-32.
Ibid., p. 27.
Andrew Dickson White, _History of Warfare of Science with Theology in Christendom_ , vol. 1 (New York: Appleton, 1896), 1:127.
Robert White, "Calvin and Copernicus: The Problem Reconsidered," _CTJ_ 15 (1980): 234.
Edward Rosen, _Copernicus and His Successors_ (London: Hambeldon, 1995), pp. 161-72.
Cited in White, "Calvin and Copernicus," pp. 236-37.
Christopher B. Kaiser, "Calvin, Copernicus, and Castellio," _CTJ_ 21 (1986): 5-31.
John Calvin, _The Institutes of the Christian Religion_ , ed. John T. McNeill, trans. Ford Lewis Battles, LCC 20 (Philadelphia: Westminster, 1973), 1:181.
Kaiser, "Calvin, Copernicus, and Castellio," p. 6.
John Calvin, _Commentaries on the First Book of Moses Called Genesis_ , trans. J. King, Calvin's Commentaries 1 (Grand Rapids: Baker, 1979), p. 86.
Much more will be said on this in the following chapter.
Calvin, _Commentaries on First Book of Moses Called Genesis,_ pp. 86-87.
Kuhn, _The Copernican Revolution_ , pp. 188-89.
Copernicus, _On the Revolutions of Heavenly Spheres_ , p. 3.
Ibid.
Swisher, _Galileo_ , p. 23.
Glass, _Revolutionaries of the Cosmos_ , p. 21.
Ernan McMullin, "The Church's Ban on Copernicanism, 1616," in _The Church and Galileo_ , ed. E. McMullin (Notre Dame, IN: University of Notre Dame, 2005), p. 152.
Glass, _Revolutionaries of the Cosmos_ , p. 25.
Ferris, _Coming of Age in the Milky Way_ , p. 98.
Glass, _Revolutionaries of the Cosmos_ , p. 25.
Ferguson, _Measuring the Universe_ , p. 98.
Ferris, _Coming of Age in the Milky Way_ , p. 97.
Michael H. Shank, "Setting the Stage: Galileo in Tuscany, the Veneto, and Rome," in McMullin, _The Church and Galileo_ , p. 71.
Shea and Davie, _Galileo_ , p. 124.
Ibid., p. 125.
Ibid.
Ibid., p. 126.
Ibid., p. 125.
Glass, _Revolutionaries of the Cosmos_ , p. 31.
McMullin, "The Church's Ban on Copernicanism," p. 177.
Francesco Beretta, "Galileo, Urban VIII, and the Prosecution of Natural Philosophers," in McMullin, _The Church and Galileo_ , p. 252.
Swisher, _Galileo_ , pp. 30-31.
Dillenberger, _Protestant Thought and Natural Science_ , p. 104.
Alexander Ross, cited in ibid., p. 107.
Manichaeism was a form of Gnosticism formulated by the Syro-Babylonian Mani, whose theology was heavily influenced by Eastern religious thought. Its primary doctrine was that a "precosmic invasion of the realm of light by the forces of darkness had resulted in the present intermingling of good and evil, the divine substance being imprisoned in matter. In Jesus the Son of God came to save his own soul, lost in Adam" (John F. Matthews, "Manichaeism," in _The Oxford Classical Dictionary_ , ed. S. Hornblower and A. Spawforth, 3rd ed. [Oxford: Oxford University Press, 1996], p. 917). Valentinianism was named after the Roman emperor Valentinian (A.D. 364–375), who demonstrated exceptional tolerance toward pagans and heretics alike (R. S. O. Tomlin, "Valentinianism," in Hornblower and Spawforth, _Oxford Classical Dictionary_ , p. 1576).
Stephen F. Mason, "Bishop John Wilkins, F. R. S. (1614–72): Analogies of Thought-Style in the Protestant Reformation and Early Modern Science," _Notes and Records in the Royal Society of London_ 46 (1992): 1.
Helge S. Kragh, _Conceptions of Cosmos from Myths to the Accelerating Universe: A History of Cosmology_ (Oxford: Oxford University Press, 2007), p. 70.
Owen Gingerich, _God's Universe_ (Cambridge, MA: Harvard University Press, 2006), p. 77.
Not everyone agrees that the Roman Catholic Church programmatically affirmed Aristotelianism on metaphysical grounds. Among those who disabuse this theory see, for example, Dennis Danielson, "That Copernicanism Demoted Humans from the Center of the Cosmos," in _Galileo Goes to Jail and Other Myths About Science and Religion_ , ed. R. L. Numbers (Cambridge, MA: Harvard University Press, 2009), pp. 50-58; and David Bentley Hart, _Atheist Delusions_ (New Haven, CT: Yale University Press, 2009), pp. 56-74. However, David C. Lindbergh notes that for the medieval church, "[a] broad mastery of the Aristotelian works . . . left the distinct impression that the only road to truth was Aristotelian demonstration" ("The Medieval Church Encounters Classical Tradition: Saint Augustine, Roger Bacon, and the Handmaiden Metaphor," in _When Science and Christianity Meet_ , ed. D. C. Lindbergh and R. L. Numbers [Chicago: University of Chicago, 2003], pp. 7-32, esp. p. 23). Although it is true that many of the finest scientific minds worked within the framework of the Catholic Church and that some factions of the church were willing to entertain innovative scientific ideas, the institution itself was very much beholden to Aristotelianism, in large part due to the influence of Thomas Aquinas.
Newton's three laws of motion are (1) inertia: objects in motion tend to stay in motion and objects at rest tend to stay at rest unless acted on by an outside force; (2) acceleration: force equals mass times acceleration (F = ma); (3) action and reaction: for every action there is an equal but opposite reaction. His law of universal gravitation holds the heavens together. See Douglas C. Giancoli, _Physics: Principles with Application_ , 5th ed. (Upper Saddle River, NJ: Prentice Hall, 1998), pp. 103, 126.
Stephen Hawking, "Quantum Cosmology," in Stephen Hawking and Roger Penrose, _The Nature of Space and Time_ (Princeton, NJ: Princeton University Press, 1996), pp. 75-103.
#### Chapter 7: Cosmology and the Authority of Scripture
The Christian doctrine of perspicuity does not state that the Bible is clear on all things but that it is clear on those matters that are essential to salvation. In other words, multiple readers of the Bible might come away with rather diverse opinions on baptism, church governance or the second coming of Christ. However, when it comes to the issue of salvation, the Bible is very clear.
The Hebrew text says "and the Levites," suggesting that the thirteen interpreters were in addition to the Levites.
For a more thorough discussion of this issue see Iain Provan, "'How Can I Understand, Unless Someone Explains It to Me?' (Acts 8:30-31): Evangelicals and Biblical Hermeneutics," _BBR_ 17.1 (2007): 1-36.
A _hapax legomenon_ (plural _hapax legomena_ ) is a word that appears only one time in a given corpus of texts. In terms of the Hebrew Bible, it refers to a word that has only one occurrence in the entire canon. Both Job and Isaiah contain sixty absolute _hapax legomena_ , that is, words that have no derivative form elsewhere in the canon. Due to the vast number of _hapax_ in the books, translators must rely on cognate languages to make sense of the biblical text.
Rusty L. Myers, _The Basics of Physics_ , Basics of the Hard Sciences (Westport, CT: Greenwood, 2006), p. 118.
Kenton L. Sparks, _God's Words in Human Words: An Evangelical Appropriation of Critical Biblical Scholarship_ (Grand Rapids: Baker Academic, 2008), pp. 230-31.
See John E. Hartley _, The Book of_ _Job_ , NICOT (Grand Rapids: Eerdmans, 1988), p. 295.
See the discussion of Leviathan in chap. 3.
John G. Stackhouse Jr., "Jesus Christ," in _The Oxford Handbook of Evangelical Theology_ , ed. G. R. McDermott (Oxford: Oxford University Press, 2010), p. 147.
Basil of Caesarea, _The Syriac Version of the Hexaemeron_ , trans. R. W. Thomson, Corpus Scriptorum Christianorum Orientalium 551 (Louvain: Peeters, 1995), p. 26.
St. John Chrysostom, _Homilies on Genesis 1–17_ , trans. Robert C. Hill, FC 74 (Washington, DC: Catholic University of America Press, 1986), p. 34.
Ibid.
Ibid., p. 58.
St. Thomas Aquinas, _Summa Theologica_ , trans. Fathers of the English Dominican Province (New York: Benziger, 1948), 1:340.
Ibid.
Ibid., 1:341.
Ibid.
Ibid.
See also ibid., 1:336, 347.
John Calvin, _Institutes of the Christian Religion_ , ed. John T. McNeill, trans. Ford Lewis Battles, LCC 20 (Philadelphia: Westminster, 1960), 1:99 (1.11.1).
Ibid., 1:121 (1.13.1).
Ibid., 1:162 (1.14.3).
Ibid., 1:463 (2.11.13).
See, among others, Peter Enns, _Inspiration and Incarnation: Evangelicals and the Problem of the Old Testament_ (Grand Rapids: Baker Academic, 2005); A. T. B. McGowan, _The Divine Authenticity of Scripture: Retrieving an Evangelical Heritage_ (Downers Grove, IL: IVP Academic, 2007); Sparks, _God's Words in Human Words_ ; N. T. Wright, _Scripture and the Authority of God: How to Read the Bible Today_ (San Francisco: HarperOne, 2011); Carlos R. Bovell, _Rehabilitating Inerrancy in a Culture of Fear_ (Eugene, OR: Wipf & Stock, 2012); John H. Walton and Brent D. Sandy, _The Lost World of Scripture: Ancient Literary Culture and Biblical Authority_ (Downers Grove, IL: IVP Academic, 2013); Craig L. Blomberg, _Can We Still Believe the Bible? An Evangelical Engagement with Contemporary Questions_ (Grand Rapids: Baker Academic, 2014).
On the question of a multiverse, see Bernard Carr, ed., _Universe or Multiverse?_ (Cambridge: Cambridge University Press, 2007).
#### Chapter 8: The Authority of Scripture and the Issue of Science
Mark J. Schiefsky, _Hippocrates on Ancient Medicine_ , ed. J. Scarborogh, P. J. Van Der Eijk and A. Hanson, Studies in Ancient Medicine 28 (Leiden: Brill, 2005), pp. 111-19.
For a more detailed review of the subject, see Max Sussman, "Sickness and Disease," _ABD_ 6:6-15.
Ibid., 6:10.
As a matter of full disclosure, I should confess that my wife is a physician. Next to the birth of our three children, the proudest moment I have as her husband was when she recited the Hippocratic Oath and was hooded as a doctor of medicine.
Of course, there are fringe groups who do, in fact, seek to operate with a "biblical view" of medicine, thus declining medical treatment for their children or rejecting blood transfusions.
For more on scholasticism, see Justo L. González, _The History of Christianity_ , vol. 1, _The Early Church to the Dawn of the Reformation_ (San Francisco: HarperSanFrancisco, 1984), pp. 311-19.
St. Thomas Aquinas, _Summa Theologica_ , trans. Fathers of the English Dominican Province (New York: Benziger, 1948), 1:349 (part 1, q. 70, art. 3).
Moses Maimonides, _The_ _Guide for the Perplexed_ , trans. M. Friedländer, 2nd ed. (New York: Dover, 1956), p. 215.
Ibid.
Martin Luther, _Lectures on Genesis, Chapters 1–5_ , ed. Jaroslav Pelikan, trans. George V. Schick, Luther's Works 1 (St. Louis: Concordia, 1958), p. 26.
Ibid., p. 27.
Ibid., p. 31.
Ibid.
John Calvin, _Commentaries on the First Book of Moses Called Genesis_ , trans. J. King, Calvin's Commentaries 1 (Grand Rapids: Baker, 1979), p. 78.
Ibid., p. 79.
Istvan Bodnar, "Aristotle's Natural Philosophy," in _The Stanford Encyclopedia of Philosophy_ , spring 2012 ed., <http://plato.stanford.edu/archives/spr2012/entries/aristotle-natphil/>.
Elizabeth A. Johnson, _Ask the Beasts: Darwin and the God of Love_ (New York: Bloomsbury, 2014), p. 30.
Charles Darwin, _On the Origin of Species by Means of Natural Selection, or the Preservation of Favoured Races in the Struggle for Life_ (London: John Murray, 1859), p. 482.
Ibid.
Ibid., p. 481.
Ibid.
See Johnson, _Ask the Beasts_ , pp. 33-35.
Darwin, _Origin of Species_ , p. 490.
Randal Keynes, _Darwin, His Daughter, and Human Evolution_ (New York: Riverhead, 2002), p. 131.
Charles Darwin, _Descent of Man, and Selection in Relation to Sex_ (New York: Appleton, 1872), 1:63.
It is important to recognize that Darwin was not the only naturalist to publish the gradation of species. The preface to _Origin of Species_ contains a detailed overview of approximately two dozen other naturalists who had made similar observations. That there was gradation of the species was gaining momentum in the scientific community. While Darwin's voice was certainly the loudest and most influential, his voice was but one among a large choir.
R. A. Torrey et al., eds., _The Fundamentals: The Famous Sourcebook of Foundational Biblical Truths_ (Grand Rapids: Kregel, 1990).
Dyson Hague, "The Doctrinal Value of the First Chapters of Genesis," in Torrey et al., _The Fundamentals_ , pp. 101-14.
James Orr, "Science and Christian Faith," in Torrey et al., _The Fundamentals_ , pp. 125-34.
George F. Wright, "The Passing of Evolution," in Torrey et al., _The Fundamentals_ , pp. 613-25.
Hague, "Doctrinal Value," p. 101.
Ibid., p. 107.
Ibid., p. 112.
James Orr, "The Virgin Birth of Christ," in Torrey et al., _The Fundamentals_ , pp. 269-77.
Orr, "Science and Christian Faith," p. 126.
Ibid., p. 130.
Wright, "The Passing of Evolution," p. 613.
Ibid., p. 616.
Ibid., p. 615.
Benjamin B. Warfield, "The Deity of Christ," in Torrey et al., _The Fundamentals_ , pp. 261-66.
See Mark A. Noll and David N. Livingstone, eds., _B. B. Warfield: Evolution, Science, and Scripture; Selected Writings_ (Grand Rapids: Baker, 2000), p. 15.
Archibald A. Hodge and Benjamin B. Warfield, "Inspiration," _The Presbyterian Review_ 6 (April 1881): 225-60.
Benjamin B. Warfield, _Inspiration and Authority of the Bible_ , ed. Samuel G. Craig (Philadelphia: P & R, 1948).
Paul Helm, "B. B. Warfield's Path to Inerrancy: An Attempt to Correct Some Serious Misunderstandings," _WTJ_ 72 (2010): 23-42.
William Warfield, _The Theory and Practice of Cattle-Breeding_ (Chicago: Sanders, 1889).
Noll and Livingstone, _B. B. Warfield_ , p. 29.
For a more robust discussion on how the Princetonians handled the challenges of evolution, see David N. Livingstone, _Dealing with Darwin: Place, Politics, and Rhetoric in Religious Engagement with Evolution_ (Baltimore: Johns Hopkins University Press, 2014), pp. 157-96.
B. B. Warfield, "Creation, Evolution, and Mediate Creation," _The Bible Student_ (1901): 1-8; reprinted in Noll and Livingstone, _B. B. Warfield_ , pp. 197-210 (further page references are to this printing).
Ibid., p. 204.
Ibid., p. 209.
Ibid., p. 210.
Charles Hodge, "The Bible in Science," _New York Observer_ , March 26, 1863, pp. 98-99; cited in Mark A. Noll, _The Scandal of the Evangelical Mind_ (Grand Rapids: Eerdmans, 1994), p. 184.
St. Augustine, _The Literal Meaning of Genesis_ , ed. J. Quasten, W. J. Burghardt and T. C. Lawler, ACW 41 (New York: Paulist Press, 1982), 1:42-43.
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## IMAGE CREDITS
Figure 1.1: Originally published in Sandra L. Richter, _The Epic of Eden_ (Downers Grove, IL: InterVarsity Press, 2009).
Figure 2.1: Kim Walton. The British Museum.
Figure 2.2: Kim Walton. The Metropolitan Museum of Art, New York.
Figure 2.3: Kim Walton. The Louvre.
Figure 2.4: Werner Forman Archive / Bridgeman Images.
Figure 2.5: E. A. W. Budge / Wikimedia Commons.
Figure 2.6: Kim Walton. The British Museum.
Figure 2.7: ©Baker Publishing Group and Dr. James C. Martin. Courtesy of the British Museum, London, England.
Figure 2.8: E. A. Wallis Budge (1857–1937) / Wikimedia Commons.
Figure 2.9: Tech. Sgt. Christopher Marasky.
Figure 2.10: ©Baker Publishing Group and Dr. James C. Martin. Courtesy of the British Museum, London, England.
Figure 2.11: ©Baker Publishing Group and Dr. James C. Martin. Courtesy of the British Museum, London, England.
Figure 2.12: Werner Forman Archive / Bridgeman Images.
Figure 5.3: Kyle Greenwood.
Figure 6.2: Kyle Greenwood.
Figure 6.3: Kyle Greenwood.
#
## AUTHOR AND WORK INDEX
_(Page numbers refer to print edition.)_
_1_ _Enoch_ , 140
_2_ _Enoch_ , 109, 137, 139, 142, 149, 150
_2_ _Esdras_ , 135, 139, 140
_3_ _Baruch_ , 145, 150
Allen, James P., 40, 49
Ambrose, 144, 208, 221
Aquinas, Thomas, 105-6, 144, 153, 155-56, 198-99, 208-9, 221
_Summa_ _Theologica_ , 105, 144, 153, 155, 156, 198-99, 208-9
Aristotle, 69, 77, 123-58, 162-69, 171-77, 183-85, 208-11
_Metaphysics_ , 124, 125
_On_ _Meteorology_ , 209
_On_ _the_ _Heavens_ , 77, 127
_Physics_ , 126
Arnold, Bill T., 36, 47
_Atrahasis_ , 35, 40
Augustine, 105, 134-35, 152, 208-9, 220-21
_City_ _of_ _God_ , 109, 135
_On_ _the_ _Literal_ _Interpretation_ _of_ _Genesis_ , 152, 220
_Babylonian_ _Map_ _of_ _the_ _World_ , 41-42, 43, 63
_Babylonian_ _Talmud_ , 109, 135, 144, 150
Basil, 133, 134, 141-42, 145, 151-52, 155, 157, 197
Batto, Bernard F., 109
_Book_ _of_ _Two_ _Ways_ , 53
_Books_ _of_ _the_ _Netherworld_ , 54
Bouteneff, Peter C., 132
Buttenwieser, Moses, 80
Calvin, John, 138, 146, 149, 153-54, 170-71, 173-76, 199-201, 208, 210-11, 221
_Commentary_ _on_ _Genesis_ , 146, 154, 175, 176, 210
_Commentary_ _on_ _Psalms_ , 138
_Institutes_ _of_ _the_ _Christian_ _Religion_ , 175, 199-201
_Chaldean_ _Account_ _of_ _Genesis_ , 35
Chavalas, Mark W., 34, 44
Childs, Brevard, 107
Chrysostom, 137, 144-45, 151, 197-98
Clifford, Richard J., 25-26, 72
Code of Hammurabi, 46, 64
Coffin Texts, 67, 72
Collins, C. John, 106, 109
Cooley, Jeffrey L., 59, 60-61, 88
Copernicus, Nicholas, 69, 145, 159-85, 212
_On_ _the_ _Revolutions_ _of_ _the_ _Heavenly_ _Spheres_ , 162, 163, 171, 172, 174, 176, 177, 178, 212
Cornelius, Izak, 78, 96
Cross, Frank Moore, 111
Dalley, Stephanie, 40, 44, 48, 51-52, 64
Dante, 139, 149
Darwin, Charles, 212-19
_Descent_ _of_ _Man_ , _The_ , 213-14
_On_ _the_ _Origin_ _of_ _Species_ , 212-13, 214
Delitzsch, Friedrich, 36
_Descent_ _of_ _Ishtar_ _into_ _the_ _Netherworld_ , 50, 51, 60, 81
_Enki_ _and_ _the_ _World_ _Order_ , 65
Enns, Peter, 72, 99, 202
_Enuma_ _Elish_ , 40, 57
_Epic_ _of_ _Baal_ , 63, 65
_Epic_ _of_ _Erra_ _and_ _Ishum_ , 47-48
_Epic_ _of_ _Gilgamesh_ , 44, 46, 50, 52, 64
_Etana_ _Epic_ , 42, 63
Ferguson, Kitty, 129, 135, 167, 178
Ferris, Timothy, 124, 128, 161, 168, 178
Foster, Benjamin R., 35, 42, 57, 59, 64
Foster, John L, 45, 48
_Founding_ _of_ _Eridu_ , 50
Frankfort, Henri, 61
_Fundamentals_ , _The_ , 214-17
Galileo, 69, 160, 164-68, 169-70, 177-81, 183, 216
_Dialogue_ _Concerning_ _the_ _Two_ _Chief_ _World_ _Systems_ , 179-80
_Starry_ _Messenger_ , 167
_Genesis_ _Rabbah_ , 133, 134, 139, 142, 144, 145
Gingerich, Owen, 161, 169, 172, 183
Glass, I. S., 165, 166, 177-78, 180
González, Justo J., 170, 208
Grant, Edward, 124
Greenwood, Kyle, 20, 44, 61, 90, 92
Gunkel, Hermann, 107, 115, 117
Habel, Norman C., 80, 83
Hague, Dyson, 215-16
Hartley, John E., 74, 76, 80, 83, 85, 195
Hodge, Archibald A., 217
Hodge, Charles, 219-20
Hornung, Erik, 49, 53-55
Horowitz, Wayne, 43, 46, 52, 55, 57, 58, 61, 63-66
Houtman, Cornelis, 86, 91, 94
Hunger, Hermann, 58, 60
Jacobsen, Thorkild, 63, 93
Johnson, Elizabeth A., 212-13
Josephus, 151
Kant, Immanuel, 24
Keel, Othmar, 42, 49-50, 72, 94
Kepler, Johannes, 69, 160, 165, 168-69, 178, 183, 185, 221
_Mysterium_ _cosmographicum_ , 165
Kovacs, Maureen Gallery, 46
Kragh, Helge S., 126-27, 129, 182
Kuhn, Thomas, 162, 176
Lactantius, 109, 134-35, 162
Lambert, W. G., 35, 40, 50, 52
Lichtheim, Miriam, 44, 53, 63
Livingstone, David N., 217-18
Luther, Martin, 132, 133, 138, 143, 146, 153-54, 170-73, 174, 175, 176, 208, 210
_Lectures_ _on_ _Genesis_ , 132, 133, 143, 146, 153, 171, 173, 210
_Table_ _Talks_ , 171-72
Maimonides, Moses, 133, 143, 152-53, 155, 209, 221
_Memphite_ _Theology_ , 40
Millard. A. R., 34-35, 40
Miller, Patrick D., 116-17
_Nergal_ _and_ _Ereshkigal_ , 50, 52
Neusner, Jacob, 133, 139, 144-45, 151, 156
Newton, Isaac, 182, 185
Noll, Mark A., 217-18
Orr, James, 214, 215, 216, 219
Philo, 132-33, 135, 143, 155
_Allegorical_ _Interpretation_ _of_ _Genesis_ , 155
_Life_ _of_ _Moses_ , 132-33
_On_ _the_ _Creation_ _of_ _the_ _World_ , 135, 143, 155
Pingree, David, 58, 60
Poe, Harry Lee, 126
Pope, Marvin H., 74, 79-80, 82, 85
_Prayer_ _to_ _the_ _Gods_ _of_ _the_ _Night_ , 59, 60
Ptolemy, 69, 127-29, 156-57, 161, 163
_Almagest_ , _The_ , 128, 161, 163
Pyramid Texts, 53
Rad, Gerhard von, 107
_Report_ _of_ _Wenamun_ , 44
Richter, Sandra L., 26, 72, 110
Sandmel, Samuel, 37
Sarna, Nahum, 107, 111
Seeley, Paul, 27, 62-63, 76, 85, 108
Smith, Mark, 49, 67
Smith, Mark S., 36, 52, 63, 83, 104
_Song_ _of_ _the_ _Three_ , 144, 149
Sparks, Kenton L., 194, 202
Stadelmann, Luis I. J., 28, 71, 84, 88
Sun-God Tablet of Nabu-apla-iddina, 61, 62
_Testament_ _of_ _Abraham_ , 141
_Testament_ _of_ _Adam_ , 149
Theophilus, 137, 144, 151
Tsumura, David Toshio, 72, 97, 107
Uehlinger, Christoph, 63, 94, 100
Walton, John, 25, 38, 47, 63, 72, 85, 97, 100, 106-7, 109, 111, 202
Warfield, B. B., 214, 217-19
Wright, George F., 214, 215, 217, 219
Wright, J. Edward, 56, 60-61, 85, 94
Wright, N. T., 93, 202
Younger, K. Lawson, Jr., 37
## SUBJECT INDEX
_(Page numbers refer to print edition.)_
accommodation, divine, 193-201
ancient Near East, 25-29, 33-69, 71-72, 82-83, 92-94, 101-2, 104-5, 132, 136-37, 139, 157, 203-4
Apsu, 40, 57, 62, 64-65, 97
birds, 25, 39, 82, 85-87, 108-10, 114, 117
cosmos, three-tiered, 25-29, 38-40, 47, 68-69, 71-73, 86, 101-2, 103-19, 132, 157-58, 199
deep, 27-28, 62-65, 68, 80, 94, 97-102, 107, 113, 117, 118
dew, 40, 65-66, 95, 151
earth, 25-27, 39-40, 41-55, 68-69, 73-82, 101-2, 105-19, 123-30, 132-41, 154-58, 161-64, 182-85
circumference, 74, 129, 135, 154
depths of, 50-55, 68, 80-82, 101, 139-41, 148
dimensions, 41-45, 74-78, 113, 133-37
foundations, 27, 45-50, 68, 78-80, 101, 118, 137-38, 158
four corners, 43-44, 78, 136
shape, 41-42, 75-78, 123-24, 133-37, 154
evolution, 212-19
exodus, the, 99, 116, 118
firmament, 55-58, 59-62, 65-69, 68, 71, 73, 77, 82-85, 90-94, 95-97, 101-2, 107-8, 123, 126-27, 143-45, 149-54, 157-58, 175, 184, 198, 209-11
four winds, 43-44, 136
genre, 21, 40-41, 171
grave, 51-52, 64, 80-82, 139
heaven(s), 25-26, 38-40, 55-61, 65-66, 68, 82-94, 95-96, 101-2, 105-19, 141-49, 156-58
and earth, 83, 106, 111, 211
heliocentrism and, 169-85
lower, 58-61, 68, 85-90, 101-2
upper, 58, 60-61, 68, 85, 89-94, 96, 101-2, 147-49
Leviathan, 63, 100, 109, 116, 117
Marduk, 40, 50, 57
moon, 26, 39, 58-61, 87-89, 108, 114, 117, 124, 125-29, 142-44, 145-46, 158, 168, 176, 177-78, 181, 183
MUL.APIN, 58, 60
netherworld, 46-49, 50-55, 59-60, 80-82, 113
planet, 26, 58-60, 73, 87-89, 102, 108, 113, 114, 124-30, 141-44, 154-56, 162-64, 168, 183
Rahab, 100-101
rain, 40, 65-66, 68, 95-97, 150-51, 193, 211
Scripture
authority of, 181-85, 189-204, 205-21
context of, 17-29, 34-38, 156-58, 189-93, 203-4
sea, 27, 39-40, 61-69, 94-102, 103-19, 149-54, 157
Sheol, 27, 80-82, 98, 101, 139
snow, 40, 65-67, 68, 95, 133-34
stars, 26, 39, 58-59, 61, 87-89, 92-94, 108, 113, 114, 126-27, 129, 141-44, 146, 157, 183
sun, 26, 39, 45, 48-49, 54, 58-60, 68-69, 87-89, 108, 115, 117, 124, 129, 141-43, 145-46, 155,162-64, 168
Tannin(im), 100, 101, 109, 116
weather, 41, 65-68, 94, 95-97, 99, 114
worldview, 23, 24-29, 37-41, 72-73, 93, 101-2, 104-5, 192, 196, 210
## SCRIPTURE INDEX
_(Page numbers refer to print edition.)_
**O LD TESTAMENT**
**Genesis**
1, _25_ , _47_ , _72_ , _83_ , _100_ , _104_ , _105_ , _106_ , _107_ , _108_ , _109_ , _110_ , _111_ , _116_ , _119_ , _137_ , _139_ , _142_ , _158_ , _197_ , _200_ , _201_
1–2, _157_ , _214_
1–4, _106_ , _109_
1–10, _27_
1–11, _107_
1–15, _106_ , _108_ , _111_
1–17, _137_ , _144_ , _151_ , _197_
1:1, _133_ , _137_ , _141_ , _143_ , _197_
1:1–2:3, _111_
1:2, _97_
1:6, _84_ , _143_ , _144_ , _149_ , _198_
1:6-7, _153_
1:6-8, _84_ , _95_ , _108_
1:7, _84_
1:8, _141_ , _143_
1:10, _62_ , _76_ , _198_
1:14, _108_
1:16, _88_ , _145_
1:18, _93_
1:21, _101_ , _109_
1:26, _86_ , _155_
1:26-27, _155_
1:28, _86_
2, _96_ , _104_ , _110_ , _111_
2:4, _110_
2:5-24, _111_
2:6, _97_ , _150_
2:9, _102_ , _111_
2:10, _111_
2:11-12, _111_
2:20, _86_
3, _110_
3:22-24, _102_
3:24, _92_ , _111_
5:21, _93_
6–7, _100_
6–9, _40_ , _99_ , _100_ , _108_
6:7, _86_
6:9, _111_
6:17, _99_
7:3, _86_
7:11, _96_
7:11-12, _100_
7:23, _86_
8:2, _96_
11:1-9, _145_
13:17, _74_
17:15-17, _207_
19:1, _92_
24, _90_
24:3, _90_
24:7, _90_
25:19, _111_
26:19, _97_
27:28, _99_
28:12, _92_
31, _190_
37:2, _111_
49:25, _98_
**Exodus**
9:22-34, _96_
9:23, _95_
15:5, _98_
20:8-11, _104_ , _112_
20:11, _73_ , _112_ , _119_
24, _84_
24:10, _84_ , _90_
25–40, _111_
25:8, _108_
25:10-31, _111_
25:17-22, _111_
26:32, _85_
27:20, _108_
33:17-23, _196_
35:8, _108_
39:3, _84_ , _145_
**Leviticus**
13:1-3, _206_
13:5-8, _206_
13:18-20, _206_
13:24-25, _206_
13:29-30, _206_
13:40-44, _206_
13:45-46, _206_
14:55, _206_
19:34, _37_
24:2, _108_
**Numbers**
4:1-49, _108_
5:11-31, _190_
6:23, _98_
11:8, _74_
16:38, _84_ , _145_
**Deuteronomy**
4:11, _87_
4:15-19, _93_
5:12-15, _112_
6:5, _19_
7:1, _190_
8:7, _97_
10:14, _90_
11:11, _150_
13:7, _74_
28:12, _96_ , _99_
28:23, _99_
28:49, _74_ , _75_
28:64, _74_
33:13, _98_
33:17, _74_
**Joshua**
6:22-25, _37_
10, _177_
10:12, _172_ , _184_
10:12-13, _178_
10:12-14, _88_
**Judges**
3:20, _117_
5:4, _86_
5:20, _94_
16:25, _85_
**Ruth**
4, _190_
4:13-15, _37_
**1 Samuel**
1:1-18, _207_
2:8, _79_
2:10, _74_ , _75_
12:17, _99_
17:44, _86_
17:46, _86_
25:36-38, _206_
28:3-25, _190_
**2 Samuel**
12:7, _21_
18:33, _117_
21:10, _86_
22:8, _84_
22:18, _85_
24:10-17, _92_
**1 Kings**
6, _111_
6:20, _111_
6:29-35, _111_
7:6, _85_
7:9-11, _78_
8:27, _90_
8:35, _99_
12:25-33, _19_ , _190_
12:26, _19_
14:11, _86_
16:4, _86_
16:25-33, _38_
16:31, _37_
17:19, _117_
18:1, _99_
18:45, _87_
21:24, _86_
22:19, _92_
**2 Kings**
2:11, _93_
3, _37_
6:25, _97_
7, _96_
7:1-2, _21_
7:2, _22_ , _71_ , _96_
7:19, _96_
16:3, _38_
19:35, _92_
21:3, _94_
21:6, _38_
23:4, _94_
23:10, _140_
23:12, _117_
**1 Chronicles**
16:30, _137_
21:1, _93_
**2 Chronicles**
2:6, _90_
6:27, _99_
36:23, _90_
**Ezra**
1:1-4, _112_
1:2, _90_
1:2-4, _191_
4, _112_
5:11, _90_
5:12, _90_
6, _112_
6:9, _90_
7:10, _90_
7:12, _90_
7:21, _90_
7:23, _90_
8–10, _191_
**Nehemiah**
1:4, _90_
1:5, _90_
2:4, _90_
2:20, _90_
4–5, _112_
4:21, _88_
6, _112_
8, _112_
8:2-8, _191_
9:1, _99_
9:6, _73_ , _104_ , _112_ , _113_
9:6-31, _112_
9:11, _98_
**Job**
1, _74_
1:6, _92_ , _93_
1:6-12, _93_
1:7, _74_ , _93_
2:1, _92_ , _93_
2:1-7, _93_
2:2, _93_
5:7, _82_
7:7-10, _81_
7:12, _101_
8:1, _190_
9:7, _88_
9:7-9, _88_
9:8, _83_
9:33–10:7, _195_
10:2-3, _113_
10:21, _81_
11, _80_
11:1, _190_
11:7-9, _80_
12:7, _86_
12:15, _99_
16:22, _81_
17:13, _82_
17:16, _82_
19:25-26, _195_
20:6, _87_
22, _90_
22:12, _87_
22:12-14, _90_
22:14, _76_ , _87_
26, _84_
26:5, _98_
26:7, _79_ , _80_
26:7-13, _104_
26:10, _76_ , _77_
26:11, _85_
28, _27_
28:21, _86_
28:24, _74_
35:5, _87_
35:11, _86_
36:27, _150_
37:1-6, _96_
38, _114_
38:1-11, _104_
38:2-11, _104_
38:2-38, _113_
38:4, _113_ , _137_
38:4-6, _78_
38:5, _84_ , _113_
38:6, _113_
38:7, _94_ , _113_
38:8, _108_ , _113_
38:9, _113_
38:10-11, _113_
38:16, _97_ , _113_
38:17, _113_
38:18, _113_
38:19, _113_
38:22, _96_ , _113_
38:22-24, _96_
38:24, _113_
38:24-26, _113_
38:25, _113_
38:28-29, _113_
38:30, _113_
38:31-32, _113_
38:34, _113_
38:37, _87_ , _113_
41:1, _100_
**Psalms**
2:8, _74_
8, _115_
8:3-4, _114_
8:5, _155_
8:8, _86_
11:4, _91_
19, _170_
19:1-6, _114_
19:2, _84_ , _115_
19:4, _84_ , _115_
19:6, _115_
19:7-14, _114_
22:27, _74_
29:10, _96_
33:7, _97_
36:5, _87_
46:9, _74_
48:10, _74_ , _75_
50:1, _88_
50:11, _86_
57:10, _87_
59:13, _74_
60–150, _116_
61:2, _74_
65:5, _74_
67:7, _74_
68:22, _98_
69:1-2, _82_
69:14-15, _98_
72:8, _74_ , _75_ , _95_
74:13, _116_
74:17, _115_
75:3, _85_
76–126, _138_
77:14, _99_
77:17, _87_
78:15, _97_
79:2, _86_
89:8-10, _100_
93–150, _138_
95:3, _116_
95:3-5, _81_
95:4-5, _116_
98:3, _74_
102:25, _137_
104, _117_
104:2, _83_
104:3, _154_
104:5, _137_ , _184_
104:12, _86_
107:18, _82_
108:4, _87_
113:3, _88_
135:6, _99_
135:7, _74_
136:26, _90_
137, _117_
137:7, _96_
147:16-18, _96_
148:1-4, _92_
148:4, _95_ , _154_
150:1, _84_
**Proverbs**
3:19-20, _73_
7, _118_
7–8, _118_
7:2, _190_
8, _27_ , _118_
8:22-31, _27_ , _28_ , _118_
8:22-36, _104_
8:23-26, _28_
8:24, _97_
8:27, _76_ , _77_
8:27-28, _28_
8:29, _28_
17:24, _74_
30:4, _74_
30:19, _85_
**Ecclesiastes**
1:5, _88_
12:2, _89_
12:3, _96_
**Song of Solomon**
6:13, _190_
**Isaiah**
4, _99_
5:26, _74_
6, _91_ , _92_
6:2, _92_
6:3, _91_
11:12, _78_
13:10, _85_ , _89_
13:13, _84_ , _85_
14, _88_
14:12, _87_ , _88_
22:18, _77_
24:16, _74_
24:18, _96_
24:18-20, _79_
27:1, _100_
29:3, _77_
30:26, _89_
33–66, _138_
38:10, _82_
40, _83_
40–66, _77_
40:12, _104_ , _118_
40:21, _85_
40:22, _76_ , _83_
40:28, _74_
41:5, _74_
41:9, _74_
41:18, _97_
42:5, _83_
42:10, _74_
43:2, _82_
43:6, _74_
44:12-13, _77_
44:13, _77_
44:24, _83_
45:12, _83_
45:22, _74_ , _75_
48:13, _83_ , _137_ , _138_
48:20, _74_
49:6, _74_
51:10, _98_ , _99_
51:13, _83_
51:16, _83_
52:10, _74_ , _75_
55:10, _95_
60:19-20, _89_
62:11, _74_
63:3, _98_
66, _92_
66:1, _91_
**Jeremiah**
4:25, _86_
5:22, _108_
7, _140_
7:18, _94_
7:33, _86_
8:2, _85_
9:10, _86_
9:21, _96_
10:9, _84_ , _145_
10:12, _83_
10:13, _74_ , _96_
15:3, _86_
16:4, _86_
16:19, _74_
19:7, _86_
25:31, _74_
25:31-33, _75_
25:33, _74_
31:35, _88_ , _89_
34:20, _86_
44:17-25, _94_
51:15, _83_
51:16, _74_ , _96_
**Lamentations**
3:6, _82_
**Ezekiel**
1:4-5, _196_
1:5-11, _111_
1:22, _84_ , _92_
1:23, _84_
1:25, _84_
1:26, _84_ , _90_
1:26-28, _92_
7:2, _78_
10, _93_
10:1, _84_
29:5, _86_
31:3-5, _98_
31:6, _86_
31:13, _86_
32:4, _86_
32:7, _89_
38:20, _86_
41:8, _85_
47, _96_ , _111_
47:1, _111_
**Daniel**
2:18, _90_
2:19, _90_
2:37, _90_
2:38, _86_
2:44, _90_
4, _75_ , _144_
4:10-11, _75_
4:10-12, _136_
4:12, _86_
4:21, _86_
4:22, _74_
4:37, _93_
5:23, _90_
7:13, _87_ , _196_
8:10, _87_
8:16, _92_
9:21, _92_
12:1, _92_
12:3, _84_
**Hosea**
2:18, _86_
4:3, _86_
7:12, _86_
9:17, _89_
13:3, _96_
**Joel**
2:20, _95_
**Amos**
4:13, _104_
5:26, _88_
7:4, _99_
8:12, _95_
9:2, _81_
9:6, _96_ , _104_
**Obadiah**
4, _87_
**Jonah**
1:9, _90_
2:3-5, _98_
2:6-7, _82_
**Micah**
5:4, _74_
7:19, _98_
**Nahum**
1:4, _101_
**Habakkuk**
3:8, _101_
3:10, _98_ , _99_
3:11, _89_
**Zephaniah**
1:3, _86_
**Haggai**
1, _112_
1:1, _19_
2:6, _84_ , _85_
**Zechariah**
1–8, _74_
3:2, _93_
9–14, _95_
9:10, _74_ , _95_
12:1, _83_ , _104_
14:8, _95_
**Malachi**
1:11, _88_
3:10, _96_
**A POCRYPHA**
**2 Baruch**
21:4, _145_
**3 Baruch**
2:1, _150_
3:7, _145_
**2 Esdras**
7:36, _140_
7:74-75, _139_
**N EW TESTAMENT**
**Matthew**
3:2, _148_
3:16, _147_
4, _136_
4:8, _136_
4:8-11, _136_
4:17, _148_
5:22, _140_
5:29-30, _140_
5:34-35, _147_
6:9, _90_
6:10, _148_
8:6, _103_
8:25, _103_
8:26, _157_
10:7, _148_
10:28, _140_
12:42, _74_ , _136_
13:35, _138_
18:9, _140_
21:1-11, _103_
22:34-40, _103_
22:37, _19_
23:15, _140_
23:20-22, _147_
23:33, _140_
24:29, _145_
25:34, _138_
28:18, _204_
**Mark**
1:10, _147_
1:16-20, _10_
4:38, _103_
9:14-29, _206_
9:43, _140_
9:45, _140_
9:47, _140_
11:1-11, _103_
12:28-34, _103_
12:30, _19_
13:24, _145_
13:27, _74_ , _136_
**Luke**
1:5-25, _207_
7:6, _103_
8:24, _103_
10:25-28, _103_
10:27, _19_
11:31, _74_ , _136_
11:50, _138_
12:5, _140_
16:19-31, _141_ , _158_
16:23, _80_
19:28-40, _103_
**John**
1:3, _197_
1:14, _204_
5:2-9, _206_
5:39-40, _202_ , _204_
17:24, _138_
**Acts**
1:8, _74_ , _75_ , _136_ , _157_
1:11, _177_
7:56, _147_
8, _192_
8:30-31, _192_
8:31, _192_
13:47, _74_ , _136_
17:22-28, _197_
**Romans**
1, _205_
1:20, _205_
10:18, _136_
**1 Corinthians**
3:1-2, _190_
10–11, _174_
15:50-57, _80_
**2 Corinthians**
12:2, _142_ , _158_
**Ephesians**
1:4, _138_
4:9, _139_
4:10, _147_
**Philippians**
2:5-8, _196_
**Colossians**
1:16, _197_
4:14, _206_
**Hebrews**
4, _112_
4:3, _138_
4:14, _147_
7:26, _147_
8:1-2, _147_
9:26, _138_
**1 Peter**
1:20, _138_
**2 Peter**
2:4, _141_
**Jude**
13, _89_
**Revelation**
1, _136_
1:7, _136_
4:2, _147_
5:13, _148_
7:1, _78_ , _136_
8:12, _145_
13:8, _138_
14, _73_
17:8, _138_
20:8, _78_ , _136_
20:11, _148_
21–22, _111_ , _148_ , _157_
21:12, _111_
21:18-21, _111_
21:23, _145_
22, _96_
22:1, _111_
22:2, _102_ , _111_
#
## PRAISE FOR _SCRIPTURE AND COSMOLOGY_
"In the modern conversation about science and Scripture we can easily get the impression that throughout history Christian interpreters spoke with a clear and unanimous voice, upholding Scripture against science. This book not only gives us a clear understanding of the view of the cosmos found in the ancient world and in Scripture, it helps us see the many issues that biblical interpreters have struggled with throughout the centuries. It thus provides important information to help us sort through the issues that face us today."
**John H. Walton,** Wheaton College
"Scientific discoveries have caused us to view the universe in completely different ways than the biblical writers. This book not only explains these differences but shows how Christians can understand them in theologically beneficial ways that enhance our readings of Scripture. Instead of being a threat to Christian belief, modern science can help us read the Bible better and deepen our appreciation of God's beauty. Because of modern science we will never again be able to read the Bible in the ways that ancient Christians did. Greenwood shows us the way forward by giving us a theologically rich reading of Scripture that embraces scientific advances. If Christianity is going to survive in the West, it must adopt the approach to reading the Bible that Greenwood offers us in this book."
**Charles Halton,** assistant professor in theology, Houston Baptist University
"A very thorough survey, from the ancient Near East as the setting of the Bible through the Christian West's use of the Bible in cosmological theories. And a very sensible closing chapter on the authority of Scripture and the issue of science, respecting the Bible for what it is and for what it is not. Even when we disagree on particular judgments along the way, we owe our thanks to Dr. Greenwood for this indispensable resource and for the friendly, learned and reverent tone throughout."
**C. John Collins,** professor of Old Testament, Covenant Theological Seminary
"What does the universe look like? From the three-tiered cosmos of the ancient Near Eastern peoples, to the spheres of Aristotle, to the heliocentric model of Copernicus, to evolutionary biology, God's people have lived through thousands of years of change in the prevailing view of the universe. How have readers throughout history worked to take Scripture seriously in light of new scientific discoveries? Filled with rich historical and biblical detail and thorough scholarly references, this book shines the light of history on today's debates over Scripture and science."
**Deborah Haarsma,** president of BioLogos
"The Bible reveals God in ways that speak to all cultures, but does so from its human authors' own ancient cultures. Kyle Greenwood's _Scripture and Cosmology_ explores one particular cross-cultural pressure point, the structure of the cosmos, by tracing this theme through the culture of the ancient Near East, the biblical writings and biblical interpreters who worked when early modern cosmological ideas were taking root. This example helpfully clarifies some of the difficulties Christians face as they seek God's revelation for today's culture."
**Rob Barrett,** The Colossian Forum
"Kyle Greenwood provides us with fascinating details of the ancient Near Eastern view of our universe. His thorough biblical analysis shows how this view permeates the Bible, giving us a better understanding of the message that God has for us in his Word. _Scripture and Cosmology_ will be a vital resource for everyone seeking to understand the Scriptures."
**Randy Isaac,** executive director, American Scientific Affiliation
#
## ABOUT THE AUTHOR
**Kyle Greenwood** (PhD, Hebrew Union College) is associate professor of Old Testament and Hebrew language at Colorado Christian University. He is the author of several studies of the Old Testament in its ancient Near Eastern environment.
#
## MORE TITLES FROM INTERVARSITY PRESS
**_God and the Cosmos_**
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**_The Lost World of Genesis One_**
978-0-8308-6149-1
**_Science, Creation and the Bible_**
978-0-8308-6815-5
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_InterVarsity Press
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_©2015 by Kyle Greenwood_
_All rights reserved. No part of this book may be reproduced in any form without written permission from InterVarsity Press._
_InterVarsity Press® is the book-publishing division of InterVarsity Christian Fellowship/USA®, a movement of students and faculty active on campus at hundreds of universities, colleges and schools of nursing in the United States of America, and a member movement of the International Fellowship of Evangelical Students. For information about local and regional activities, visit_ _intervarsity.org_ _._
_Scripture quotations, unless otherwise noted, are from the_ New Revised Standard Version of the Bible, _copyright 1989 by the Division of Christian Education of the National Council of the Churches of Christ in the USA. Used by permission. All rights reserved._
_Cover design: Cindy Kiple_
_Images:_ The Creation of the World, _closed doors of the triptych_ The Garden of Earthly Delights _by Hieronymus Bosch at Prado, Madrid, Spain / Bridgeman Images_
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_ISBN 978-0-8308-9870-1 (digital)
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* * *
**Library of Congress Cataloging-in-Publication Data**
_Greenwood, Kyle.
Scripture and cosmology : reading the Bible between the ancient world and modern science / Kyle Greenwood.
1 online resource.
Includes bibliographical references and index.
Description based on print version record and CIP data provided by publisher; resource not viewed.
ISBN 978-0-8308-9870-1 (eBook) -- ISBN 978-0-8308-4078-6 (pbk. : alk. paper)
1. Biblical cosmology. 2. Bible and science. I. Title.
BS651
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2015023988_
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| {
"redpajama_set_name": "RedPajamaBook"
} | 1,897 |
Peristil (grč. περιστύλιον) (arhit.) - slobodan prostor, okružen stubovima i natkriven; predvorje ili hodnik sa stubovima.
U Hrvatskoj je najpoznatiji primjer splitski Peristil, trg ispred prvostolnice Sv. Dujma u Starom gradu u Splitu.
Izvori
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https://visitsplit.com/hr/528/peristil
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Arhitektura | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 1,360 |
\section{Introduction}
Models of growing random trees have been widely studied for their connections with algorithms~\cite{devroye1998} and networks~\cite{ergun2002}; they have been used to model, among others, epidemic spread~\cite{moon1974} and pyramid schemes~\cite{gastwirthbhattacharya1984}.
See the survey \cite{smythemahmoud1994} and the book \cite{drmota2009} for a review of the literature.
In this paper, we consider a large family of such models that generalizes some well-studied cases, such as the uniform recursive tree or the plane oriented recursive tree, whose study dates back at least to~\cite{narapoport1970} and~\cite{szymanski1987} respectively.
For these simpler models, the first order for the height has been proved by Pittel~\cite{pittel1994} and the second and third orders in the asymptotic expansion can be deduced from similar results for the maximum of branching random walks.
The models of trees that we consider here can be seen as inhomogeneous versions of these simpler ones.
The first order for their height has been obtained recently in~\cite{senizergues2021} by one of the authors, and we prove here that the second and third orders are still similar to those appearing in the maximum of branching random walks, even though no direct connection can be used in this case.
We first present our model and results, and then discuss in more details some related works from the literature,
as well as the link between our model and branching random walks.
\subsection{Definition of the model and assumptions}
\paragraph{Definition of WRTs}
We define the model of weighted recursive trees, first introduced in \cite{borovkov2006} by Borovkov and Vatutin.
For any sequence of non-negative real numbers $(w_n)_{n\geq 1}$ with $w_1>0$, we define the distribution $\wrt((w_n)_{n\geq 1})$ on sequences of growing rooted trees, which is called the \emph{weighted recursive tree with weights $(w_n)_{n\geq 1}$}.
We construct a sequence of rooted trees $(\mathtt{T}_n)_{n\geq 1}$ starting from $\mathtt{T}_1$ containing only one root-vertex $\mathtt{u}_1$ and let it evolve in the following manner: the tree $\mathtt{T}_{n+1}$ is obtained from $\mathtt{T}_n$ by adding a vertex $\mathtt{u}_{n+1}$ with label $n+1$. The father of this new vertex is chosen to be the vertex with label $K_{n+1}$, where
\begin{align*}
\forall k\in \{1,\dots,n\}, \qquad \Ppsq{K_{n+1}=k}{\mathtt{T}_n}\propto w_k.
\end{align*}
Whenever we have any sequence of real numbers $(x_n)_{n\geq 1}$, we write $\boldsymbol x=(x_n)_{n\geq 1}$ in a bold font as a shorthand for the sequence itself, and $(X_n)_{n\geq 1}$ with a capital letter to denote the sequence of partial sums defined for all $n\geq 1$ as $X_n\coloneqq \sum_{i=1}^nx_i$. In particular, we do so for sequences of weights $(w_n)_{n\geq 1}$, so that $W_n$ always denotes the sum of the $n$ first weights.
Some of our assumptions are expressed using the Landau big-O notation: we write $x_n=\grandO{y_n}$ if there exists a constant $C$ such that $\abs{x_n}\leq C \abs{y_n}$ for all $n\geq 1$.
\paragraph{Assumptions}
We assume that we work with a sequence $\boldsymbol w$ which satisfies the following assumption for some $\gamma > 0$,
\begin{align} \tag{$\mathcal H_{1,\gamma}$} \label{eq:assumption_1}
\exists \lambda >0,\ \exists\alpha\in\intervalleoo{0}{1} :
W_n = \lambda \cdot n^\gamma + O \left( n^{\gamma-\alpha} \right),
\end{align}
as $n \to \infty$.
Moreover, we assume in parts of the paper that
\begin{align} \tag{$\mathcal H_2$} \label{eq:assumption_2}
\sum_{i=n}^\infty \left( \frac{w_i}{W_i} \right)^2
= O \left( \frac{1}{n} \right).
\end{align}
Associated to the constant $\gamma$, we define another constant $\theta > 0$ as the unique positive solution to the following equation
\begin{align}\label{eq:definition_theta}
1+\gamma\left(e^\theta-1-\theta e^\theta \right) = 0.
\end{align}
Under assumption \eqref{eq:assumption_1} on the sequence of weights $(w_n)_{n\geq 1}$, it was shown in \cite{senizergues2021} that the height of the tree satisfies
\begin{align}\label{eq:asymptotic for the height first order}
\frac{\haut(\mathtt{T}_n)}{\log n}\underset{n \rightarrow\infty}{\longrightarrow} \gamma e^{\theta}
\end{align}
almost surely.
\subsection{Main results}
Our results consist in computing the next order terms for the asymptotic behaviour \eqref{eq:asymptotic for the height first order}, which contains a logarithmic correction followed by a term of constant order. This is contained is the following theorem.
\begin{theorem} \label{thm:height_WRT}
Under assumptions \eqref{eq:assumption_1} and \eqref{eq:assumption_2}, the following sequence of random variables is tight
\[
\left( \haut(\mathtt{T}_n) - \gamma e^{\theta} \log n + \frac{3}{2 \theta} \log \log n \right)_{n \geq 2}.
\]
\end{theorem}
In the case of the upper bound for the height, we have a more precise result, requiring only assumption \eqref{eq:assumption_1}, which gives an explicit bound for the tail distribution of the height.
This bound should be optimal up to the value of the constant $C=C(\boldsymbol w)$.
\begin{theorem} \label{thm:upper_bound_height_WRT}
Under assumption \eqref{eq:assumption_1}, there exists $C > 0$ such that for any $n,x \geq 1$,
\[
\Pp{\haut(\mathtt{T}_n) \geq \gamma e^{\theta} \log n - \frac{3}{2 \theta} \log \log n + x}
\leq C x e^{-\theta x}.
\]
\end{theorem}
The next theorem ensures that
the set of vertices in $\mathtt{T}_n$ having height close to $\haut(\mathtt{T}_n)$
are not all close parents, meaning that some of them have a most recent common ancestor that is of height of constant order.
This has the effect that the diameter of the tree is close to twice its height (which is an obvious upper-bound for the diameter).
This is stated in the following theorem.
\begin{theorem} \label{thm:diameter_WRT}
Under assumptions \eqref{eq:assumption_1} and \eqref{eq:assumption_2}, the following sequence of random variables is tight
\[
\left( \diam(\mathtt{T}_n) - 2\gamma e^{\theta} \log n + \frac{3}{\theta} \log \log n \right)_{n \geq 2}.
\]
\end{theorem}
\paragraph{The case of i.i.d. weights}
A natural setting to consider is to consider the case where we run the model starting with an i.i.d.\@ random sequence of weights $(\mathsf w_n)_{n\geq 1}$, say with law $\mu$ on $\intervalleoo{0}{\infty}$.
In this case it is quite easy to check that, if $\mu$ admits a moment of order $2$, then the random sequence $(\mathsf w_n)_{n\geq 1}$ almost surely satisfies \eqref{eq:assumption_1} with $\gamma=1$, and also \eqref{eq:assumption_2}. Remark that the value of $\theta$ associated to $\gamma=1$ by \eqref{eq:definition_theta} is $\theta=1$.
This directly allows to apply Theorem~\ref{thm:height_WRT} and Theorem~\ref{thm:diameter_WRT} in this setting.
If $\mu$ only has a moment of order $1+\epsilon$ for some positive $\epsilon$, then we still have the fact that the random sequence $(\mathsf w_n)_{n\geq 1}$ almost surely satisfies \eqref{eq:assumption_1} with $\gamma=1$.
In this case, we get that the result of Theorem~\ref{thm:upper_bound_height_WRT} holds conditionally on the sequence $(\mathsf w_n)_{n\geq 1}$.
Integrating this over the sequence $(\mathsf w_n)_{n\geq 1}$ entails that at least the upper-bound in Theorem~\ref{thm:height_WRT} is true, \emph{i.e}
\begin{equation}
\sup _{n\geq 1}\Pp{\haut(\mathtt{T}_n) \geq e \log n - \frac{3}{2} \log \log n + b} \underset{b\rightarrow \infty}{\longrightarrow}0.
\end{equation}
We remark that this statement in the case of random weights is weaker than the one for deterministic weights, as the speed of the convergence to $0$ is not explicit here.
In the statement of Theorem~\ref{thm:upper_bound_height_WRT}, the constant $C$ appearing on the right-hand side depends on the sequence of weights in a non-explicit way, and getting the same tail bound as in Theorem~\ref{thm:upper_bound_height_WRT} would require to integrate the value of this non-explicit function over the law of the sequence $(\mathsf w_n)_{n\geq 1}$.
\subsection{Application to preferential attachment trees}
We introduce here another family of growing trees and explain how to apply the results of Theorem~\ref{thm:height_WRT}, Theorem~\ref{thm:upper_bound_height_WRT} and Theorem~\ref{thm:diameter_WRT} to this other setting.
\paragraph{Definition of PATs}
We define a process on growing random trees called the \emph{preferential attachment tree with additive fitnesses}, or $\pa$ for short.
This model depends on a sequence $\mathbf{a}=(a_i)_{i\geq 1}$ of non-negative numbers, which represent the initial fitnesses of the vertices.
For non-constant sequences $\mathbf{a}$, this model was introduced for the first time in \cite{ergun2002} by Erg\"un and Rodgers.
As before, we iteratively construct a sequence of rooted trees $(\mathtt{P}_n)_{n\geq 1}$ starting from $\mathtt{P}_1$ containing only one root-vertex $\mathtt{u}_1$ labelled $1$, and evolving in the following manner.
The tree $\mathtt{P}_{n+1}$ is obtained from $\mathtt{P}_n$ by adding a vertex $\mathtt{u}_{n+1}$ with label $n+1$.
The father of this new vertex is chosen to be the vertex with label $J_{n+1}$, where
\begin{align*}
\forall k\in \{1,\dots,n\}, \qquad \Ppsq{J_{n+1}=k}{\mathtt{P}_n}\propto \deg_{\mathtt{P}_n}^+(\mathtt{u}_k)+a_k,
\end{align*}
where $\deg_{\mathtt{P}_n}^+(\mathtt{u}_k)$ denotes the out-degree of $\mathtt{u}_k$ in the tree $\mathtt{P}_n$.
In the particular case where $n = 1$, we set $J_2=1$, even in the case $a_1=0$ for which the last display does not make sense.
\paragraph{Connection with WRTs with a random sequence of weights}
First recall that, for $a,b>0$, the distribution $\mathrm{Beta}(a,b)$ has density $\frac{\Gamma(a+b)}{\Gamma(a)\Gamma(b)}\cdot x^{a-1}(1-x)^{b-1} \cdot \ind{0\leq x\leq 1}$ with respect to Lebesgue measure.
If $b=0$ and $a>0$, we use the convention that the distribution $\mathrm{Beta}(a,b)$ is a Dirac mass at $1$.
Now, \cite[Theorem~1.1]{senizergues2021} tells us the following.
For any sequence $\mathbf a$ of fitnesses, we define the associated random sequence $\boldsymbol{\mathsf w}^\mathbf a=(\mathsf{w}^\mathbf{a}_n)_{n\geq 1}$ through its corresponding partial sums $\mathsf{W}^\mathbf{a}_n=\sum_{k=1}^{n}\mathsf{w}^\mathbf{a}_n$ as
\begin{equation}\label{def:random weight associated to sequence of fitnesses}
\mathsf{w}^\mathbf{a}_1=\mathsf{W}^\mathbf{a}_1 \coloneqq 1
\qquad \text{and} \qquad
\forall n\geq 2, \quad \mathsf{W}^\mathbf{a}_n \coloneqq \prod_{k=1}^{n-1}\beta_k^{-1},
\end{equation}
where the $(\beta_k)_{k\geq 1}$ are independent with respective distribution $\mathrm{Beta}(A_k+k,a_{k+1})$, and $A_k \coloneqq \sum_{i=1}^{k}a_i$.
Then,
the distributions $\pa(\mathbf a)$ and $\wrt(\boldsymbol{\mathsf w}^\mathbf a)$ coincide.
The strategy to apply our results to preferential attachment trees is to use this connection and to check that under some assumptions on the sequence $\mathbf a$, the corresponding random sequence of weights $(\mathsf{w}^\mathbf{a}_n)_{n\geq 1}$ almost surely satisfies the assumptions of our theorems.
\paragraph{Almost sure behaviour of \texorpdfstring{$(\mathsf{w}^\mathbf{a}_n)_{n\geq 1}$}{(wna)}}
We assume here that the sequence of fitnesses $\mathbf a=(a_i)_{i\geq1}$ satisfies
\begin{align}\label{eq:assumption_1 fitness sequence}\tag{$\mathcal H_{1,\zeta}^{\mathrm{PAT}}$}
A_n\coloneqq \sum_{i=1}^na_i=\zeta\cdot n + \grandO{n^{1-\delta}},
\end{align}
for some $\zeta>0$ and some $\delta>0$.
Then \cite[Proposition~1.3]{senizergues2021} tells us that under this assumption for the sequence $\mathbf a$, the random sequence $(\mathsf{w}^\mathbf{a}_n)_{n\geq 1}$ almost surely satisfies \eqref{eq:assumption_1} with $\gamma=\frac{\zeta}{\zeta+1}$.
This allows us to apply Theorem~\ref{thm:upper_bound_height_WRT} to preferential attachment trees with any sequence of fitnesses satisfying \eqref{eq:assumption_1 fitness sequence}, and obtain the following corollary.
\begin{corollary}\label{cor:upper bound on the height for PAT}Under assumption \eqref{eq:assumption_1 fitness sequence} for the sequence of fitnesses $\mathbf{a}$, we have
\[\sup_{n\geq 1} \Pp{\haut(\mathtt{P}_n)\geq \gamma e^\theta \log n -\frac{3}{2\theta} \log\log n +b}\underset{b \rightarrow\infty }{\longrightarrow} 0,\]
with $\gamma=\frac{\zeta}{\zeta+1}$ and $\theta$ defined from $\gamma$ as in \eqref{eq:definition_theta}.
\end{corollary}
In order to also get the lower bound given by Theorem~\ref{thm:height_WRT}, we need to assume some additional hypothesis on the sequence $\mathbf a$, namely
\begin{align}\label{eq:assumption_2 fitness sequence}\tag{$\mathcal H_2^{\pa}$}
\sum_{i=1}^{n}a_i^2=\grandO{n}.
\end{align}
The following lemma, proved in the appendix, then ensures that under \eqref{eq:assumption_1 fitness sequence} and \eqref{eq:assumption_2 fitness sequence}, the random sequence $(\mathsf{w}^\mathbf{a}_n)_{n\geq 1}$ almost surely satisfies \eqref{eq:assumption_2}, so that the assumptions of Theorem~\ref{thm:height_WRT} and Theorem~\ref{thm:diameter_WRT} are satisfied.
\begin{lemma}\label{lem:remainder sum p_i square for PAT}
If the sequence $\mathbf{a}$ satisfies \eqref{eq:assumption_1 fitness sequence} and \eqref{eq:assumption_2 fitness sequence}, then almost surely
\begin{align*}
\sum_{i=n}^{\infty}\left(\frac{\mathsf{w}^\mathbf{a}_i}{\mathsf{W}^\mathbf{a}_i}\right)^2 = \grandO{n^{-1}}.
\end{align*}
\end{lemma}
This allows us to get the following analog of Theorem~\ref{thm:height_WRT} and Theorem~\ref{thm:diameter_WRT} in the context of preferential attachment trees.
\begin{corollary}\label{cor:height and diameter for PAT}Under the assumptions \eqref{eq:assumption_1 fitness sequence} and \eqref{eq:assumption_2 fitness sequence} for the sequence of fitnesses $\mathbf{a}$, the sequences
\[\left(\haut(\mathtt{P}_n)- \gamma e^\theta \log n +\frac{3}{2\theta} \log\log n\right)_{n\geq 1}\]
and
\[\left(\diam(\mathtt{P}_n)- 2\gamma e^\theta \log n +\frac{3}{\theta} \log\log n\right)_{n\geq 1}\]
are tight, where $\gamma=\frac{\zeta}{\zeta+1}$ and $\theta$ is defined from $\gamma$ as in \eqref{eq:definition_theta}.
\end{corollary}
\paragraph{The case of i.i.d. fitnesses} As for the case of WRTs, a natural model is to start from a sequence $\mathbf{a}=(a_i)_{i\geq 1}$ that is i.i.d.\ with some distribution $\mu$ over $\intervallefo{0}{\infty}$ that is not concentrated on $0$.
From the discussion above, we see that if $\mu$ has a moment of order $1+\epsilon$ for some positive $\epsilon$, then \eqref{eq:assumption_1 fitness sequence} holds almost surely and Corollary~\ref{cor:upper bound on the height for PAT} applies where $\zeta$ is the first moment of $\mu$.
If furthermore $\mu$ has a second moment, then $\mathbf a$ satisfies \eqref{eq:assumption_2 fitness sequence} almost surely and so, thanks to Lemma~\ref{lem:remainder sum p_i square for PAT}, the conclusions of Corollary~\ref{cor:height and diameter for PAT} hold.
\subsection{Related works and comments}
An asymptotic expansion for the height of recursive trees identical to Theorem~\ref{thm:height_WRT} has already been obtained for some specific models.
The first result of this type has been shown by Drmota~\cite{drmota2003} and Reed~\cite{reed2003} for binary search trees: these trees are a sequence of random subtrees of the infinite binary tree, recursively built by adding new vertices uniformly at random among all the possible sites.
Note that these trees do not enter in the framework of WRTs.
The simplest WRT is the uniform recursive tree, obtained by taking all weights equal to 1.
In this case, the asymptotic expansion has been obtained by Addario-Berry and Ford \cite{addario-berryford2013}.
Slight modifications of the uniform recursive tree have also been covered: Hoppe trees, where all weights except $w_1$ equal 1, have been studied in \cite{leckeyneininger2013}, and another extension, where finitely many weights are different from 1, in \cite{hiesmayrislak2020}.
The asymptotic expansion in Theorem~\ref{thm:height_WRT} is also similar to the one for the maximal position in a branching Brownian motion \cite{bramson1978,bramson1983} or a branching random walk \cite{hushi2009,addario-berryreed2009,aidekon2013}.
More generally, this behaviour for the maximum is shared by the universality class of log-correlated fields, see \cite{arguin2017} for a review.
For this large class of models, the maximum should behave asymptotically as
\begin{equation}\label{eq:general asymptotic expansion}
v \log n - \frac{3}{2 \beta_c} \log \log n+ O(1),
\end{equation}
where $n$ is the number of particles involved, $v$ is a constant depending on the model and $\beta_c$ is the critical inverse temperature of the system.
The fact that in our case $\beta_c = \theta$ can be seen from the fact that $\theta$ is the smallest real number such that a vertex $\mathtt{u}_i$ chosen in $\mathtt{T}_n$ proportionally to $\frac{w_i}{W_n} e^{\theta \haut(\mathtt{u}_i)}$ has a height asymptotically equivalent to $\haut(\mathtt{T}_n)$, see Lemma~\ref{lem:many_to_one} and \cite{senizergues2021}.
Furthermore, note that the precise upper tail in Theorem~\ref{thm:upper_bound_height_WRT} is known to be optimal for branching random walks, up to the value of the constant.
Connections between recursive trees and branching processes have been widely used since the works of Pittel \cite{pittel1984,pittel1994} and Devroye \cite{devroye1986,devroye1987,devroye1998}.
In particular the height of the uniform recursive tree can be deduced from the counterpart for branching random walks as follows. Consider a continuous-time branching random walk, starting with one particle at position 0 at time 0
and where each particle lives during an exponential time with parameter 1, during which it stays at position $h$ where it was born, and then splits into two particles at positions $h$ and $h+1$.
If $\tau_n$ denotes the first time where $n$ particles are alive in this branching random walk, then the distribution of the positions of the particles at time $\tau_n$ is the same as the distribution of the heights of vertices in the uniform recursive tree $\mathtt{T}_n$.
Since $\tau_n = \log n + O(1)$ in probability, the asymptotic development in Theorem~\ref{thm:height_WRT} for the uniform recursive tree follows directly from the result of Aïdékon \cite{aidekon2013}.
Note that Addario-Berry and Ford \cite{addario-berryford2013} used a different connection with branching random walks to prove the asymptotic expansion for the height of the uniform recursive tree.
It is important to note that in the case of a general WRT, we cannot directly deduce Theorem~\ref{thm:height_WRT} from the result for branching random walks.
We can still link the tree $\mathtt{T}_n$ to an \textit{inhomogeneous} continuous-time branching random walk defined as follows.
Let $\mathrm{Exp}(\lambda)$ denote the exponential distribution with parameter $\lambda$.
We start with one particle at position $0$ at time $0$ with an $\mathrm{Exp}(w_1)$ lifetime.
When a particle at position $h$ with an $\mathrm{Exp}(w_i)$ lifetime dies, it split into two particles, one at $h$ with an $\mathrm{Exp}(w_i)$ lifetime and another at $h+1$ with an $\mathrm{Exp}(w_k)$ lifetime, if this is the $(k-1)$-th death event in the whole process.
Then, with $\tau_n$ defined as before, the distribution of the positions of the particles at time $\tau_n$ is the same as the distribution of the heights of the vertices in the tree $\mathtt{T}_n$ with distribution $\wrt((w_n)_{n\geq 1})$.
However, in addition to being inhomogeneous, the branching random walk defined here does not satisfy the branching property: the progeny of a particle depends on the progeny of the other particles alive at the same time.
Consequently, results from the literature cannot be directly applied to this model.
Nonetheless, we managed to adapt the methods used to prove asymptotics for the maximum of branching random walks (e.g.\@ in \cite{aidekon2013}) directly in context of weighted recursive trees, see Section~\ref{subsection:organization} for an overview of the proof.
In the case of preferential attachment trees with additive fitnesses with a constant sequence $\mathbf a$,
we believe that the same type of comparison with a branching random walk as above could lead directly to the asymptotic expansion \eqref{eq:general asymptotic expansion}; however, we have failed to find a reference for that fact in the literature.
For non-constant sequences $\mathbf{a}$, deterministic or i.i.d., this connection would break down
and obtaining such an asymptotic expansion would again not straightforwardly follow from known results.
A natural question is the convergence in distribution of the height of weighted recursive trees after centering as in Theorem~\ref{thm:height_WRT}.
This convergence has been proved for branching Brownian motion \cite{bramson1983,lalleysellke1987} and for non-lattice branching random walks \cite{aidekon2013} and the limit is a randomly shifted Gumbel random variable.
In the case of a lattice branching random walk (such as the ones mentioned before), no general result has been established so far and one can only hope that the centered height oscillates around a non-universal limiting distribution \cite{lifshits2012,corre2017}.
For recursive trees, this convergence is known only for binary search trees: it has been shown by Drmota \cite{drmota2003}, via analytic methods, and by Corre~\cite{corre2017}, who uses the connection with a similar continuous-time branching random walk as the one above and gives a different description of the limit than that of Drmota.
Another future direction of study would be the case where \eqref{eq:assumption_1} is not satisfied, in particular where $W_n$ grows sub- or super-polynomially. This is not done in this paper, but we expect universality to break in these cases.
Last, we mention some other contributions about WRTs that investigate other properties than the height, under various assumptions for the behaviour of the sequence of weights $(w_n)_{n\geq 1}$.
The model of WRT has been introduced by Borovkov and Vatutin in \cite{borovkov2006},
in which they study the asymptotic behaviour of the height of the $n$-th vertex, as well as some properties on the degree of vertices in the tree, under the assumption that the weights have a certain product form.
Recently, Mailler and Uribe Bravo \cite{maillerbravo2019} proved the convergence of the weighted profile of the tree to a Gaussian, in the sense of weak convergence, for a variety of random sequences $(w_n)_{n\geq 1}$ that exhibit a very wide range of asymptotic behaviours.
Convergence of the profile in a strong sense is also proved in \cite{senizergues2021}, under assumptions that ensure that the weights behave more or less polynomially, similar to the ones in this paper.
Also recently, Lodewijks and Ortgiese studied in \cite{lodewijks2020} a similar model of weighted random graphs (which contains the case of trees) under the assumption that $(w_n)_{n\geq 1}$ is i.i.d.\@ with some distribution $\mu$.
Under a first moment assumption on $\mu$, they prove the convergence of the empirical distribution of the degrees and the weights of vertices in the graph.
They also describe the behaviour of the maximal degree under several different assumptions for the tail of $\mu$.
The convergence of the degree distribution in the i.i.d.\ setting can also be seen as a particular case of some results by Iyer in \cite{iyer2020} and by Fountoulakis, Iyer, Mailler and Sulzbach in \cite{fountoulakis2019}, both times proved in a more general model of growing graphs.
\subsection{Overview of the paper}
\label{subsection:organization}
The paper is mainly dedicated to the proof of Theorem~\ref{thm:height_WRT} concerning the height of weighted recursive trees and this proof is split into two parts: the upper bound and the lower bound. For the upper bound, we actually prove Theorem~\ref{thm:upper_bound_height_WRT} which implies the upper bound in Theorem~\ref{thm:height_WRT}.
Theorem~\ref{thm:diameter_WRT}, concerning the diameter of the trees, is a byproduct of the proof of the lower bound in Theorem~\ref{thm:height_WRT}.
Concerning preferential attachment trees, the only result we need to show is Lemma~\ref{lem:remainder sum p_i square for PAT} and it is proved in Appendix~\ref{section:PAT}.
Our strategy is to adapt the methods used to prove the asymptotic expansion of the maximum of a branching random walk and, for this, we rely on the same basic tools: many-to-one and many-to-two lemmas.
These lemmas, established in Section~\ref{sec:many-to-few}, allow us to compute the first and second moment of quantities of the form
\[
\sum_{i=1}^{n} \frac{w_i}{W_n} \cdot e^{\theta\haut(\mathtt{u}_i)}\cdot F(\haut(\mathtt{u}_i(1)),\haut(\mathtt{u}_i(2)),\dots ,\haut(\mathtt{u}_i(n))),
\]
where $\mathtt{u}_i(k)$ denotes the closest ancestor of $\mathtt{u}_i$ in $\mathtt{T}_k$, and $F$ is a real-valued function.
We call the sequence $(\haut(\mathtt{u}_i(1)),\dots ,\haut(\mathtt{u}_i(n)))$ the \emph{trajectory} of vertex $\mathtt{u}_i$ in the construction of $\mathtt{T}_n$.
The first moment of the quantity appearing in the last display is expressed in terms of $\Ec{F(H_1,H_2,\dots,H_n)}$, where $(H_i)_{i\geq 1}$ is a time-inhomogeneous random walk, whose step distributions depend on the $w_i$'s.
The expression for the second moment involves two random walks that coincide at the beginning of their trajectory and that are then only weakly dependent: this differs from the behaviour observed in branching random walks where the trajectories of two different particles are independent after their splitting point.
These lemmas rely on a coupling result from \cite{maillerbravo2019}, which describes a joint construction of the tree as well as two distinguished vertices in the tree, in a way that makes the trajectory of those vertices easy to analyze.
In Section~\ref{section:upper_bound}, we prove Theorem~\ref{thm:upper_bound_height_WRT}, which implies the upper bound in Theorem~\ref{thm:height_WRT}.
Its proof relies only on first moment calculations using the many-to-one lemma.
The first step is to prove that for $K$ large enough, with high probability, for any $n\geq1$ we have $\haut(\mathtt{u}_n) \leq \gamma e^\theta \log n +K$, and we then work on this event in order to prevent the first moment from blowing up.
The end of the argument is then close to the method used by Aïdékon \cite{aidekon2013} for branching random walks: we use a first moment calculation on the number of high vertices on the aforementioned event, dealing separately with vertices whose trajectory reach a high point too soon, each leading to a large cluster of high vertices.
The lower bound in Theorem~\ref{thm:height_WRT} is established in Section~\ref{section:lower_bound}. We use a first and second moment calculation on a well-chosen quantity $Q_n$, which is the total weight of sufficiently high vertices in $\mathtt{T}_n$ whose trajectory has stayed below an appropriate barrier (see \eqref{def:Q_n^(N)}).
For the branching random walk, this calculation usually shows that $\P(Q_n > 0) \geq c$ with $c$ a positive constant and one can conclude using the branching property: wait until there is a large number $N$ of particles alive and then each of these particles has a probability $c$ of having a very high descendant, independently of each other.
In our case, this second step of the argument is harder to justify: the subtrees rooted at the $N$ first vertices are not independent and do not necessarily satisfy our assumptions (some of them can even be finite).
Therefore, we use a different approach to show directly that $\P(Q_n > 0) \to 1$ as $n \to \infty$.
This can be shown via a first and second moment calculation on $Q_n$ only if typically the most recent common ancestor of two vertices contributing to $Q_n$ is the root.
To this end, we first choose a very constraining barrier so that the most recent common ancestor has to be typically in the first $O(1)$ vertices.
Then, we consider a modified tree $\mathtt{T}_n^{(N)}$, where we transfer the weights of the $N$ first vertices to the root.
We actually do our calculation on this tree, for which the most recent common ancestor of two vertices contributing to $Q_n$ is the root with high probability when $N \to \infty$.
Since the height of $\mathtt{T}_n^{(N)}$ is stochastically dominated by the height of $\mathtt{T}_n$, this is sufficient.
In Section~\ref{section:diameter}, we prove Theorem~\ref{thm:diameter_WRT} showing that the diameter of the tree is twice its height, up to a $O(1)$ term. The upper bound is trivial and the lower bound follows from the fact that, in the tree $\mathtt{T}_n^{(N)}$, we can find with high probability two very high vertices whose most recent common ancestor is the root.
We also need precise estimates for the time-inhomogeneous random walks appearing in the many-to-one and many-to-two lemmas. These random walks have Bernoulli jumps with smaller and smaller parameters and therefore known results cannot be directly applied.
In Section~\ref{section:RW}, we compare these random walks with a time-homogeneous random walk with Poisson jumps to establish these estimates. Note that this section has to be written in a relative generality, so that the same result can be applied in different contexts in the paper.
Throughout the paper, $C$ and $c$ denote positive constants that can only depend on the weights $(w_i)_{i\geq 1}$ and that can change from line to line. Typically, $C$ should be thought as sufficiently large and $c$ as sufficiently small.
For sequences $(a_n)_{n\geq1}$ and $(b_n)_{n\geq1}$ of real numbers, we say that $a_n = O(b_n)$ as $n \to \infty$ if there is a constant $C$, depending only on the weights $(w_i)_{i\geq 1}$, such that $\abs{a_n} \leq C \abs{b_n}$ for any $n \geq 1$.
Let $\ensemblenombre{N} \coloneqq \{0,1,2,\dots\}$ and, for $a,b \in \ensemblenombre{R}$, $\intervalleentier{a}{b} \coloneqq \intervalleff{a}{b} \cap \ensemblenombre{Z}$.
\section{Distinguished points and many-to-few lemmas}
\label{sec:many-to-few}
\subsection{Some terminology}
\paragraph{Recursive trees}
Recursive trees on $n$ vertices are rooted trees whose vertices are labeled with the integers $1$ to $n$ such that the labels along any path starting from the root form a strictly increasing sequence.
We denote $\mathbb{T}_n$ the set of such trees.
Note that the root is necessarily the vertex with label $1$.
According to these definitions, the sequence $(\mathtt{T}_n)_{n\geq 1}$ constructed in the introduction takes its values in $\bigcup_{n\geq 1}\mathbb T_n$.
We also introduce
\begin{align*}
\mathbb{T}^\bullet_n \coloneqq \enstq{(\mathtt{t}, \mathtt{u})}{\mathtt{t}\in \mathbb{T}_n,\ \mathtt{u} \in \mathtt{t}}, \quad \text{and} \quad \mathbb{T}^{\bullet\bullet}_n \coloneqq \enstq{(\mathtt{t},\mathtt{u},\mathtt{v})}{\mathtt{t}\in \mathbb{T}_n,\ \mathtt{u} \in \mathtt{t},\ \mathtt{v}\in \mathtt{t}},
\end{align*}
the set of recursive trees of size $n$ endowed with respectively one or two distinguished vertices.
\paragraph{Labels and ancestors of a vertices} For any $(\mathtt{t},\mathtt{u})\in\mathbb{T}_n^{\bullet}$, we write $\mathrm{lab}(\mathtt{u})$ for the label of vertex $\mathtt{u}$ in the tree $\mathtt{t}$, which is an integer between $1$ and $n$.
For any $k\leq n $ we write $\mathtt{u}(k)$ for the most recent ancestor of $\mathtt{u}$ that has label smaller than or equal to $k$.
For any $(\mathtt{t},\mathtt{u},\mathtt{v}) \in \mathbb{T}^{\bullet\bullet}_n$, we denote $\mathtt{u}\wedge \mathtt{v}$ the most recent common ancestor of $\mathtt{u}$ and $\mathtt{v}$ in the tree $\mathtt{t}$.
\subsection{Model with two distinguished vertices}
We introduce here a very useful construction of the trees $(\mathtt{T}_n)_{n\geq 1}$ which is coupled with the choice of some distinguished vertices on those trees. It is due to Mailler and Uribe Bravo \cite[Section~2.4]{maillerbravo2019}.
For $n\geq 2$, let $B_n$ and $\widetilde{B}_n$ be two independent Bernoulli random variables with parameter $\frac{w_{n}}{W_{n}}$, independent for all $n\geq 2$.
For $n\geq 1$, let $J_n$ be a random variable on $\{1,\dots, n\}$ such that $\Pp{J_n=k}=\frac{w_k}{W_n}$, also independent of all other random variables.
We define a sequence $((\mathtt{T}_n,\mathtt{D}_n,\widetilde{\mathtt{D}}_n))_{n\geq 1}$, where at each time $n\geq 1$ we have $(\mathtt{T}_n,\mathtt{D}_n,\widetilde{\mathtt{D}}_n)\in \mathbb T_n^{\bullet \bullet }$, by the following procedure.
\begin{itemize}
\item The tree with distinguished vertex $(\mathtt{T}_1,\mathtt{D}_1,\widetilde{\mathtt{D}}_1)$ is the only recursive tree with one vertex and the vertices $\mathtt{D}_1$ and $\widetilde{\mathtt{D}}_1$ are equal to this vertex.
\item At every step $n \geq 1$, conditionally on $(\mathtt{T}_n,\mathtt{D}_n,\widetilde{\mathtt{D}}_n)$,
\begin{itemize}
\item if $(B_{n+1},\widetilde{B}_{n+1})=(1,0)$, the tree $\mathtt{T}_{n+1}$ is obtained by attaching a new vertex $\mathtt{u}_{n+1}$ to the distinguished vertex $\mathtt{D}_n$, and setting $\mathtt{D}_{n+1}=\mathtt{u}_{n+1}$, and $\widetilde{\mathtt{D}}_{n+1}=\widetilde{\mathtt{D}}_n$,
\item if $(B_{n+1},\widetilde{B}_{n+1})=(0,1)$, the tree $\mathtt{T}_{n+1}$ is obtained by attaching a new vertex $\mathtt{u}_{n+1}$ to the distinguished vertex $\widetilde{\mathtt{D}}_n$, and setting $\mathtt{D}_{n+1}=\mathtt{D}_{n}$, and $\widetilde{\mathtt{D}}_{n+1}=\mathtt{u}_{n+1}$,
\item if $(B_{n+1},\widetilde{B}_{n+1})=(0,0)$, the tree $\mathtt{T}_{n+1}$ is obtained by attaching a new vertex $\mathtt{u}_{n+1}$ to the vertex $\mathtt{u}_{J_n}$, and setting $\mathtt{D}_{n+1}=\mathtt{D}_{n}$, and $\widetilde{\mathtt{D}}_{n+1}=\widetilde{\mathtt{D}}_n$,
\item if $(B_{n+1},\widetilde{B}_{n+1})=(1,1)$, the tree $\mathtt{T}_{n+1}$ is obtained by attaching a new vertex $\mathtt{u}_{n+1}$ to the distinguished vertex $\mathtt{D}_n$, and setting $\mathtt{D}_{n+1}=\mathtt{u}_{n+1}$, and $\widetilde{\mathtt{D}}_{n+1}=\mathtt{u}_{n+1}$.
\end{itemize}
\end{itemize}
The following proposition is \cite[Proposition~9]{maillerbravo2019}, slightly rephrased for our purposes.
\begin{proposition}{\cite[Proposition~9]{maillerbravo2019}}\label{prop: construction deux points distingués}
The sequence $(\mathtt{T}_n)_{n\geq 1}$ defined above has distribution $\wrt(\boldsymbol{w})$.
Furthermore, for any $n\geq 1$, conditionally on $\mathtt{T}_n$, the points $\mathtt{D}_n$ and $\widetilde{\mathtt{D}}_n$ are sampled on $\mathtt{T}_n$ independently with distribution $\mu_n$, where $\mu_n$ is the probability measure supported on $\mathtt{T}_n$ such that for any $1\leq k \leq n$ we have $\mu_n(\{\mathtt{u}_k\})= \frac{w_k}{W_n}$.
This entails that for any $n\geq 1$ and any function $\Phi \colon \mathbb{T}^{\bullet\bullet}_n \to \ensemblenombre{R}$, we have
\begin{align}\label{eq:égalité en loi deux points distingués}
\Ec{\Phi(\mathtt{T}_n,\mathtt{D}_n,\widetilde{\mathtt{D}}_n)}=\Ec{\sum_{1\leq i,j\leq n}\frac{w_i w_j}{W_n^2}\Phi(\mathtt{T}_n,\mathtt{u}_i,\mathtt{u}_j)}.
\end{align}
For a function $\Psi \colon \mathbb{T}^{\bullet}_n \to \ensemblenombre{R}$, this can be re-written as
\begin{align}\label{eq:égalité en loi un point distingué}
\Ec{\Psi(\mathtt{T}_n,\mathtt{D}_n)}=\Ec{\sum_{1\leq i\leq n}\frac{w_i}{W_n}\Psi(\mathtt{T}_n,\mathtt{u}_i)}.
\end{align}
\end{proposition}
\paragraph{Remarks about the construction}
In the previous construction, we can remark that the sequence $(\mathtt{D}_n)_{n \geq 1}$ is non-decreasing in the genealogical order so that for any $k\leq n$ we have $\mathtt{D}_n(k)=\mathtt{D}_k$. This is not the case for $(\widetilde{\mathtt{D}}_n)_{n \geq 1}$. Also, we can write
\begin{align}\label{eq:hauteur point distingué est somme de bernoulli}
\forall 1\leq k \leq n, \quad \haut(\mathtt{D}_n(k))= \haut(\mathtt{D}_k)= \sum_{i=2}^{k}B_i.
\end{align}
Denoting $I_n \coloneqq \max \{1\leq k \leq n : B_k=\widetilde{B}_k=1 \}$ with the convention that $B_1=\widetilde{B}_1=1$ to make the last set non-empty, we can also write
\begin{align*}
\forall 1\leq k \leq n, \quad \haut(\widetilde{\mathtt{D}}_n(k))=\begin{cases} \sum_{i=2}^{k}B_i &\text{if } k\leq I_n\\
\sum_{i=2}^{I_n}B_i + \sum_{i=I_n+1}^{n}\widetilde{B}_i &\text{otherwise}
\end{cases}
\end{align*}
Note that $I_n$ is equal to $\mathrm{lab}(\mathtt{D}_n\wedge \widetilde{\mathtt{D}}_n)$, the label of the most recent common ancestor between $\mathtt{D}_n$ and $\widetilde{\mathtt{D}}_n$.
\subsection{Change of measures and many-to-one}
\paragraph{Change of measure}
For any $n\geq 1$ the tree with two distinguished vertices $(\mathtt{T}_n,\mathtt{D}_n,\widetilde{\mathtt{D}}_n)$ defined above only depends on the sequences $(B_i)_{2\leq i \leq n}$, $(\widetilde{B}_i)_{2\leq i \leq n}$ and $(J_i)_{1\leq i \leq n-1}$.
Recall $\theta > 0$ is defined by \eqref{eq:definition_theta}.
We can introduce $\P_{\theta}$ in such a way that
\begin{align}
\frac{\mathop{}\mathopen{}\mathrm{d} \P_{\theta}}{\mathop{}\mathopen{}\mathrm{d} \P}
= \frac{\prod_{i=2}^n e^{\theta B_i}}{Z_n}
= \frac{e^{\theta \haut(\mathtt{D}_n)}}{Z_n},
\end{align}
where
\begin{align}
Z_n
\coloneqq \Ec{e^{\theta \haut(\mathtt{D}_n)}}=\Ec{\prod_{i=2}^n e^{\theta B_i}}
= \prod_{i=2}^{n}\left(1+(e^{\theta}-1)\frac{w_i}{W_i}\right).
\end{align}
Then, under this new measure, the random variables $(\widetilde{B}_i)_{2\leq i \leq n}$ and $(J_i)_{1\leq i \leq n}$ still have the same distribution and $(B_i)_{2\leq i \leq n}$ are independent Bernoulli r.v.\@ with respective parameter $p_i$ where
\begin{align}\label{eq:parametres bernoulli apres tilt exponentiel}
p_i\coloneqq \frac{e^{\theta}\frac{w_i}{W_i}}{1+(e^{\theta}-1)\frac{w_i}{W_i}}.
\end{align}
\begin{remark}
In general, we could define $\P_{z}$ in the same way for any other value $z\in \ensemblenombre{R}$ but in this won't be needed for our analysis.
\end{remark}
\paragraph{Many-to-one}
We first focus on the case of one distinguished point and use Proposition~\ref{prop: construction deux points distingués} for functions $\Psi$ which are defined in such a way that, for any $(\mathtt{t},\mathtt{u})\in \mathbb T_n^{\bullet}$,
\begin{align*}
\Psi(\mathtt{t},\mathtt{u})= F(\haut(\mathtt{u}(1)),\haut(\mathtt{u}(2)),\dots ,\haut(\mathtt{u}(n))),
\end{align*}
for some function $F:\ensemblenombre{N}^n\rightarrow \ensemblenombre{R}$.
Using Proposition~\ref{prop: construction deux points distingués} and the discussion above, we can write
\begin{align*}
\Ec{\sum_{i=1}^{n}\frac{w_i}{W_n}e^{\theta\haut(\mathtt{u}_i)}\Psi(\mathtt{T}_n,\mathtt{u}_i)}
&= \Ec{e^{\theta\haut(\mathtt{D}_n)}\Psi(\mathtt{T}_n,\mathtt{D}_n)} \\
&= Z_n\cdot \mathbb{E}_{\theta}\left[\Psi(\mathtt{T}_n,\mathtt{D}_n)\right] \\
&= Z_n\cdot \mathbb{E}_{\theta}\left[F(\haut(\mathtt{D}_n(1)),\haut(\mathtt{D}_n(2)),\dots ,\haut(\mathtt{D}_n(n)))\right]
\end{align*}
Using the description of the sequence $(\haut(\mathtt{D}_n(k)))_{1\leq k \leq n}$ from the sequence $(B_2,B_3,\dots ,B_n)$ in \eqref{eq:hauteur point distingué est somme de bernoulli} and the description \eqref{eq:parametres bernoulli apres tilt exponentiel} of the distribution of $(B_2,B_3,\dots ,B_n)$ under $\P_{\theta}$ yields the following statement.
\begin{lemma}[Many-to-one] \label{lem:many_to_one}
For any function $F:\ensemblenombre{N}^n\rightarrow \ensemblenombre{R}$ we have
\begin{align*}
\Ec{\sum_{i=1}^{n}\frac{w_i}{W_n} e^{\theta\haut(\mathtt{u}_i)}
\cdot F(\haut(\mathtt{u}_i(1)),\haut(\mathtt{u}_i(2)),\dots ,\haut(\mathtt{u}_i(n)))}
= Z_n\cdot \Ec{F(H_1,H_2,\dots,H_n)},
\end{align*}
where $(H_1,H_2,\dots , H_n)$ is such that
\begin{align*}
H_k=\sum_{i=2}^{k}\ind{U_i\leq p_i},
\end{align*}
for $(U_i)_{i\geq 2}$ i.i.d.\@ uniform random variables on the interval $\intervalleoo{0}{1}$ under $\P$ and $(p_i)_{i\geq 2}$ defined in \eqref{eq:parametres bernoulli apres tilt exponentiel}.
\end{lemma}
\subsection{Many-to-two}
We now apply the same line of reasoning in the case of two distinguished points.
We fix a function $F:\ensemblenombre{N}^n\rightarrow\ensemblenombre{R}$ and we define a function $\Psi \colon \mathbb T_n^{\bullet}\rightarrow \ensemblenombre{R}$ by
\begin{equation}
\Psi(\mathtt{t} ,\mathtt{u}) \coloneqq F(\haut(\mathtt{u}(1)),\haut(\mathtt{u}(2)),\dots ,\haut(\mathtt{u}(n))).
\end{equation}
We also fix a function $f \colon \intervalleentier{1}{n}\rightarrow \ensemblenombre{R}$.
We can use \eqref{eq:égalité en loi deux points distingués} for the function $\Phi:\mathbb T_n^{\bullet \bullet}\rightarrow\ensemblenombre{R}$ such that for every $(\mathtt{t},\mathtt{u},\mathtt{v})\in \mathbb T_n^{\bullet \bullet}$,
\begin{align*}
\Phi(\mathtt{t},\mathtt{u},\mathtt{v})= f(\mathrm{lab}(\mathtt{u}\wedge \mathtt{v}))\cdot e^{\theta\haut(\mathtt{u})} \cdot \Psi(\mathtt{t},\mathtt{u})\cdot e^{\theta\haut(\mathtt{v})}\cdot \Psi(\mathtt{t},\mathtt{v}).
\end{align*}
This yields
\begin{align}\label{eq:many-to-two premiere etape}
\Ec{\sum_{1\leq i,j\leq n}\frac{w_i w_j}{W_n^2}\Phi(\mathtt{T}_n,\mathtt{u}_i,\mathtt{u}_j)}
&=\Ec{f(\mathrm{lab}(\mathtt{D}_n\wedge \widetilde{\mathtt{D}}_n))\cdot e^{\theta \haut(\mathtt{D}_n)} \cdot e^{\theta\haut(\widetilde{\mathtt{D}}_n)}\cdot \Psi(\mathtt{T}_n,\mathtt{D}_n) \cdot \Psi(\mathtt{T}_n,\widetilde{\mathtt{D}}_n)}\notag\\
&= \Ec{f(I_n)\cdot e^{\theta \haut(\mathtt{D}_n)} \cdot e^{\theta\haut(\widetilde{\mathtt{D}}_n)}\cdot \Psi(\mathtt{T}_n,\mathtt{D}_n) \cdot \Psi(\mathtt{T}_n,\widetilde{\mathtt{D}}_n)}\notag\\
&= Z_n\cdot \mathbb{E}_{\theta}\left[f(I_n)\cdot e^{\theta\haut(\widetilde{\mathtt{D}}_n)}\cdot \Psi(\mathtt{T}_n,\mathtt{D}_n) \cdot \Psi(\mathtt{T}_n,\widetilde{\mathtt{D}}_n)\right]\notag\\
&= Z_n \cdot \sum_{\ell=1}^n \P_{\theta}(I_n=\ell)\cdot f(\ell) \cdot \mathbb{E}_{\theta} \left[e^{\theta\haut(\widetilde{\mathtt{D}}_n)}\cdot \Psi(\mathtt{T}_n,\mathtt{D}_n) \cdot \Psi(\mathtt{T}_n,\widetilde{\mathtt{D}}_n) \ \middle| \ I_n=\ell\right],
\end{align}
where we can compute
\begin{align}\label{eq:loi de In}
\P_{\theta}\left(I_n=\ell\right)=p_\ell q_\ell\cdot \prod_{i=\ell+1}^{n}\left(1-p_iq_i\right),
\end{align}
setting $q_i \coloneqq \frac{w_i}{W_i}$ and recalling the definition of $p_i$ in \eqref{eq:parametres bernoulli apres tilt exponentiel}, with the convention that $p_1=1$.
We can then rewrite the expression appearing in the $\ell$-th term of the sum appearing in \eqref{eq:many-to-two premiere etape} as
\begin{align*}
&\mathbb{E}_{\theta} \left[e^{\theta\haut(\widetilde{\mathtt{D}}_n)}\cdot \Psi(\mathtt{T}_n,\mathtt{D}_n) \cdot \Psi(\mathtt{T}_n,\widetilde{\mathtt{D}}_n) \ \middle| \ I_n=\ell\right]\\
&=\mathbb{E}_{\theta} \left[e^{\theta\haut(\widetilde{\mathtt{D}}_n)}\cdot F(\haut(\mathtt{D}_n(1)),\dots ,\haut(\mathtt{D}_n(n))) \cdot F(\haut(\widetilde \mathtt{D}_n(1)),\dots ,\haut(\widetilde \mathtt{D}_n(n))) \ \middle| \ I_n=\ell\right].
\end{align*}
The random variables in the conditional expectation of the last display only depend on the sequences of Bernoulli random variables $(B_2,\dots, B_n)$ and $(\widetilde{B}_2,\dots, \widetilde{B}_n)$ and so does the conditioning.
By working out explicitly the distribution of $(B_2,\dots B_n,\widetilde{B}_2,\dots, \widetilde{B}_n)$ under $\mathbb P_{\theta}(\ \cdot\ \vert I_n=\ell)$ we can rewrite the last display as
\begin{align}\label{eq:expression avant de biaiser le deuxieme spine}
\Ec{e^{\theta \widetilde{H}^\ell_n}\cdot F(H^\ell_1,\dots , H^\ell_n)\cdot F(\widetilde{H}^\ell_1,\dots,\widetilde{H}^\ell_n)}
\end{align}
where the sequences $(H^\ell_i)_{1\leq i \leq n}$ and $(\widetilde{H}^\ell_i)_{1\leq i \leq n}$ are defined from two sequences $(U_i)$ and $(V_i)$ of i.i.d.\ uniform random variables on $\intervalleoo{0}{1}$ under $\P$ as follows. For all $1\leq i\leq n$,
\begin{equation}\label{eq:definition H^l}
H_i^\ell\coloneqq\sum_{j=2}^{i}\ind{U_j\leq p^\ell_j}, \qquad \text{where} \qquad p^\ell_i\coloneqq \begin{cases}
p_i \quad &\text{for} \quad i<\ell,\\
1 &\text{for}\quad i=\ell,\\
\frac{p_i (1-q_i)}{1-p_iq_i} &\text{for} \quad i>\ell,\\
\end{cases}
\end{equation}
and
\begin{equation*}
\widetilde{H}^\ell_i= \begin{cases}
H^\ell_i & \text{if} \quad i\leq \ell,\\
H^\ell_\ell+\sum_{j=\ell+1}^i\ind{V_j\leq \tilde{q}^\ell_j} & \text{if} \quad i> \ell,
\end{cases}
\end{equation*}
where $\tilde{q}^\ell_i\coloneqq q_i\ind{U_i>p_i^\ell}=q_i\cdot \ind{H^\ell_i=H^\ell_{i-1}}$ for all $\ell+1\leq i \leq n$.
Remark that the $(p^\ell_i)_{2\leq i\leq n}$ are deterministic but the $(\tilde{q}^\ell_i)_{\ell+1\leq i \leq n}$ are random.
We transform further the expression \eqref{eq:expression avant de biaiser le deuxieme spine}.
\begin{align*}
& \Ec{e^{\theta \widetilde{H}^\ell_n}\cdot F(H^\ell_1,\dots , H^\ell_n)\cdot F(\widetilde{H}^\ell_1,\dots, \widetilde{H}^\ell_n)} \\
& =\Ec{e^{\theta H^\ell_\ell}\cdot F(H^\ell_1,\dots , H^\ell_n)\cdot \Ecsq{e^{\theta(\widetilde{H}^\ell_n-\widetilde{H}^\ell_\ell)} F(\widetilde{H}^\ell_1,\dots, \widetilde{H}^\ell_n)}{(H^\ell_i)_{1\leq i \leq n}}}
\end{align*}
We can rewrite the conditional expectation using a change of measure as follows:
\[
\Ecsq{e^{\theta(\widetilde{H}^\ell_n-\widetilde{H}^\ell_\ell)} F(\widetilde{H}^\ell_1,\dots, \widetilde{H}^\ell_n)}{(H^\ell_i)_{1\leq i \leq n}}
=\prod_{i=\ell+1}^{n}(1+(e^{\theta}-1)\tilde{q}^\ell_j) \cdot \Ecsq{F(\overline{H}_1^\ell, \dots, \overline{H}^\ell_n)}{(H^\ell_i)_{1\leq i \leq n}},
\]
where $(\overline{H}_i^\ell)_{1\leq i \leq n}$ is defined as
\begin{equation}\label{eq:definition overline H^l}
\overline{H}^\ell_i= \begin{cases}
H^\ell_i & \text{if} \quad i\leq \ell,\\
H^\ell_\ell+\sum_{j=\ell+1}^i\ind{V_j\leq \tilde{p}^\ell_j}& \text{if} \quad i> \ell,
\end{cases}
\end{equation}
where
\begin{equation*}
\tilde{p}^\ell_i\coloneqq \frac{e^{\theta}\tilde{q}^\ell_i}{1+(e^{\theta}-1)\tilde{q}^\ell_i}=p_i\cdot \ind{H^\ell_i=H^\ell_{i-1}} .
\end{equation*}
In the end, we have
\begin{align*}
&\Ec{e^{\theta \widetilde{H}^\ell_n}\cdot F(H^\ell_1,\dots , H^\ell_n)\cdot F(\widetilde{H}^\ell_1,\dots, \widetilde{H}^\ell_n)} \\
&= \Ec{e^{\theta H^\ell_\ell}\cdot
\left( \prod_{i=\ell+1}^{n}\left(1+(e^{\theta}-1)q_i \ind{H^\ell_i=H^\ell_{i-1}}\right) \right)
\cdot F(H^\ell_1,\dots , H^\ell_n)\cdot F(\overline{H}_1^\ell, \dots, \overline{H}^\ell_n)}.
\end{align*}
This yields the following statement.
\begin{lemma}[Many-to-two] \label{lem:many-to-two}
For any $n\geq 1$ and any functions $F \colon \ensemblenombre{N}^n \to \ensemblenombre{R}$ and $f \colon \intervalleentier{1}{n} \to \ensemblenombre{R}$, we have
\begin{align*}
& \mathbb{E}\Biggl[ \sum_{1\leq i,j\leq n}
\frac{w_iw_j}{W_n^2} f(\mathrm{lab}(\mathtt{u}_i\wedge \mathtt{u}_j))
\cdot e^{\theta\haut(\mathtt{u}_i)} F(\haut(\mathtt{u}_i(1)),\dots ,\haut(\mathtt{u}_i(n)))
\cdot e^{\theta\haut(\mathtt{u}_j)} F(\haut(\mathtt{u}_j(1)),\dots ,\haut(\mathtt{u}_j(n))) \Biggr] \\
& = Z_n \sum_{\ell=1}^n \P_{\theta}(I_n=\ell) \cdot f(\ell)\cdot
\mathbb{E}\Biggl[ e^{\theta H^\ell_\ell} \prod_{i=\ell+1}^{n}\left(1+(e^{\theta}-1)q_i \ind{H^\ell_i=H^\ell_{i-1}}\right)
\cdot F(H^\ell_1,\dots , H^\ell_n)\cdot F(\overline{H}_1^\ell, \dots, \overline{H}^\ell_n)
\Biggr],
\end{align*}
where the random sequences $(H_i^\ell)_{1\leq i \leq n}$ and $(\overline{H}_i^\ell)_{1\leq i \leq n}$ appearing above are defined in \eqref{eq:definition H^l} and in \eqref{eq:definition overline H^l}, respectively.
\end{lemma}
\section{Upper bound for the height}
\label{section:upper_bound}
The goal of this section is to prove Theorem~\ref{thm:upper_bound_height_WRT}, which implies in particular the upper bound in Theorem~\ref{thm:height_WRT}. Hence, we work under assumption \eqref{eq:assumption_1}, but not necessarily under assumption \eqref{eq:assumption_2}.
\subsection{Preliminaries}
We first state several consequences of assumption \eqref{eq:assumption_1}, which guarantees the existence of
$\lambda> 0$ and $\alpha\in\intervalleoo{0}{1}$ such that
$W_n = \lambda \cdot n^\gamma + O \left( n^{\gamma-\alpha} \right)$.
By \cite[Lemma~3.4]{senizergues2021}, it follows that
\begin{align} \label{eq:consequence_assumption_1}
\sum_{i=1}^n \frac{w_i}{W_i}
= \gamma \log n
+ \cst + O(n^{-\alpha})
\qquad \text{and} \qquad
\sum_{i=n}^\infty \left( \frac{w_i}{W_i} \right)^2
= O(n^{-\alpha}).
\end{align}
Hence, for any $n \geq 0$, we have
\begin{align} \label{eq:bound_Z_n}
Z_n
\leq \exp \left( (e^{\theta}-1) \sum_{i=1}^n \frac{w_i}{W_i} \right)
\leq C n^{\gamma(e^{\theta}-1)},
\end{align}
where we recall $C$ denotes a positive constant depending only on $(w_i)_{i\geq 1}$ that can change from line to line.
Moreover, recalling the definition of $p_n$ in \eqref{eq:parametres bernoulli apres tilt exponentiel}, it follows from \eqref{eq:consequence_assumption_1} that
\begin{align} \label{eq:bound_sum_p_j}
\sum_{j=1}^n p_j
= \gamma e^\theta \log n
+ \cst' + O(n^{-\alpha})
\qquad \text{and} \qquad
\sum_{j=n}^\infty p_j^2
\leq C n^{-\alpha},
\end{align}
as well as the following bound, obtained by subtracting the first part of \eqref{eq:consequence_assumption_1} at $n-1$ and to the one at $n$,
\begin{align} \label{eq:upper_bound_p_n}
p_n \leq e^\theta \frac{w_n}{W_n} \leq C n^{-\alpha}.
\end{align}
We use these bounds repetitively throughout the section, sometimes without mentioning them.
Recall the random walk $(H_i)_{i\geq 1}$, which appears after applying the many-to-one lemma (see Lemma~\ref{lem:many_to_one}), has Bernoulli$(p_i)$ jumps.
In order to work with an approximately time-homogeneous and centered random walk,
we introduce, for any $k \geq 0$,
\begin{align*}
i_k & \coloneqq \inf \left\{ i \geq 1 : \sum_{j=2}^i p_j \geq k \right\},
\end{align*}
and $i_0 \coloneqq 1$. Moreover, we set
\begin{equation}\label{eq:definition Sk}
S_k \coloneqq H_{i_k} - k.
\end{equation}
This random walk fits the framework of Section~\ref{section:RW} with $\mathbf j=(i_k)_{k\geq 0} $ and $\mathbf r = (p_j)_{j\geq 2}$.
We need the following estimates for this time change.
Note that \eqref{eq:bound_sum_p_j} implies that
\begin{align} \label{eq:bound_i_k}
k - C
\leq \gamma e^{\theta} \log i_k
\leq k + C.
\end{align}
For any $n \geq 1$, let $\tau(n)$ denote the smallest integer $t$ such that $i_t \geq n$. It follows from \eqref{eq:bound_i_k} that
\begin{align} \label{eq:bound_tau(n)}
\gamma e^{\theta} \log n - C
\leq \tau(n)
\leq \gamma e^{\theta} \log n + C.
\end{align}
Moreover, in our case, the quantities introduced in \eqref{eq:def_delta}, which appear in the estimates for the random walk $(S_k)_{k\geq 0}$, can be bounded as follows
\begin{equation} \label{eq:bounds_delta_eta}
\delta_k \leq p_{i_k}
\leq C e^{-ck},
\qquad
\Delta_k \leq 1
\qquad \text{and} \qquad
\eta_k \leq C \exp\left(-c k^c\right),
\end{equation}
using \eqref{eq:upper_bound_p_n}, \eqref{eq:bound_i_k} and \eqref{eq:bound_sum_p_j}.
\begin{remark}
We repetitively need upper bounds for quantities of the form
\begin{align} \label{eq:quantity}
& \Ec{e^{\theta\haut(\mathtt{u}_n)}
F(\haut(\mathtt{u}_n(i_0)),\haut(\mathtt{u}_n(i_1)),\dots,\haut(\mathtt{u}_n(i_{t-1})))
g(\haut(\mathtt{u}_n)) },
\end{align}
with $n \geq 1$, $t \coloneqq \tau(n)$ and $F \colon \ensemblenombre{R}^{t} \to \ensemblenombre{R}_+$ and $g \colon \ensemblenombre{R} \to \ensemblenombre{R}_+$ measurable functions.
In order to avoid the repetition of the same argument, we explain here how we proceed.
Using the dynamics of the construction, conditionally on the tree $\mathtt{T}_{n-1}$, the vertex $\mathtt{u}_n$ is the child of any vertex $\mathtt{u}_j$ with $1\leq j\leq n-1$ with probability $\frac{w_j}{W_{n-1}}$. Note that in that case we have $\haut(\mathtt{u}_n)=\haut(\mathtt{u}_j(n-1))+1$.
Taking the conditional expectation with respect to $\mathtt{T}_{n-1}$, we get that \eqref{eq:quantity} equals
\begin{align*}
& \Ec{\sum_{j=1}^{n-1} \frac{w_j}{W_{n-1}}
e^{\theta(\haut(\mathtt{u}_j(n-1))+1)}
F(\haut(\mathtt{u}_j(i_0)),\dots,\haut(\mathtt{u}_j(i_{t-1})))
g(\haut(\mathtt{u}_j(n-1))+1) } \\
& \leq \frac{W_{i_t}}{W_{n-1}}
\Ec{\sum_{j=1}^{i_t} \frac{w_j}{W_{i_t}}
e^{\theta(\haut(\mathtt{u}_j(i_t))+1)}
F(\haut(\mathtt{u}_j(i_0)),\dots,\haut(\mathtt{u}_j(i_{t-1})))
g(\haut(\mathtt{u}_j(i_t))+1) },
\end{align*}
using $i_t \geq n \geq n-1$ to add non-negative terms in the sum and noting that, for $j \leq n-1$, $\mathtt{u}_j(n-1) = \mathtt{u}_j = \mathtt{u}_j(i_t)$.
Applying the many-to-one lemma (Lemma~\ref{lem:many_to_one}), the right-hand side of the last displayed equation equals
\begin{align*}
\frac{W_{i_t}}{W_{n-1}} Z_{i_t} e^{\theta}
\Ec{F(H_{i_0},\dots,H_{i_{t-1}})
g(H_{i_t}+1) },
\end{align*}
By \eqref{eq:bound_i_k} and \eqref{eq:bound_tau(n)}, note that $i_t \leq C n$ for any $n \geq 2$ and it follows from \eqref{eq:assumption_1} that $W_{i_t}/W_{n-1} \leq C$.
Combining the above and using \eqref{eq:bound_Z_n}, we get
\begin{equation} \label{eq:one_to_one}
\Ec{e^{\theta\haut(\mathtt{u}_n)}
F(\haut(\mathtt{u}_n(i_0)),\dots,\haut(\mathtt{u}_n(i_{t-1})))
g(\haut(\mathtt{u}_n)) }
\leq C n^{\gamma(e^{\theta}-1)}
\Ec{F(H_{i_0},\dots,H_{i_{t-1}})
g(H_{i_t}+1) }.
\end{equation}
\end{remark}
\subsection{Introducing the first barrier}
\begin{lemma} \label{lem:first_barrier}
Recall $\tau(n) \coloneqq \min\{ t \in \ensemblenombre{N} : i_t \geq n\}$. There exists $C > 0$, such that, for any integer $K \geq 0$,
\[
\P \left( \exists n \geq 1 : \haut(\mathtt{u}_n) > \tau(n) + K \right)
\leq C (K+1) e^{-\theta K}.
\]
\end{lemma}
Note that by \eqref{eq:bound_tau(n)}, a similar statement could be made with $\gamma e^{\theta} \log n$ instead of $\tau(n)$.
However, this formulation is more convenient to prove and fits exactly our future purpose.
\begin{proof}
Let $B \coloneqq \{ \exists n \geq 1 : \haut(\mathtt{u}_n) > \tau(n) + K \}$ denote the event we want to control.
Distinguishing according to the first integer $n$ such that $\haut(\mathtt{u}_n) > \tau(n) + K$, we have $B = \bigcup_{n\geq2} B_n$ where we set
\[
B_n \coloneqq \{ \haut(\mathtt{u}_n) > \tau(n) + K,\ \forall m < n,
\haut(\mathtt{u}_m) \leq \tau(m) + K \}.
\]
On the event $B_n$, we have $\haut(\mathtt{u}_n(n-1)) \leq \tau(n-1) + K \leq \tau(n) + K$.
But, on the other hand, note that $\haut(\mathtt{u}_n(n-1)) = \haut(\mathtt{u}_n) - 1$ so we necessarily have $\haut(\mathtt{u}_n) = \tau(n) + K +1$.
Hence, keeping only part of the constraints, we have
\begin{align*}
\P(B_n)
& \leq \Pp{\haut(\mathtt{u}_n) = \tau(n) + K + 1, \forall k < \tau(n), \haut(\mathtt{u}_n(i_k)) \leq k + K} \\
& = e^{-\theta(\tau(n)+K + 1)} \cdot
\Ec{e^{\theta \haut(\mathtt{u}_n)} \1_{\{\haut(\mathtt{u}_n) = \tau(n) + K + 1\}}
\1_{\{\forall k < \tau(n),\ \haut(\mathtt{u}_n(i_k)) \leq k + K\}}} \\
& \leq C e^{-\theta(\tau(n)+K)} n^{\gamma(e^{\theta}-1)}
\Pp{H_{i_{\tau(n)}} +1 = \tau(n) + K + 1,\
\forall k < \tau(n), H_{i_k} \leq k + K},
\end{align*}
applying \eqref{eq:one_to_one}. Recalling the definition of the walk $(S_k)$ in \eqref{eq:definition Sk}, this last probability equals
\begin{align*}
\Pp{S_{\tau(n)} = K,\ \forall k < \tau(n), S_k \leq K}
& \leq \frac{C (K+1)}{\tau(n)^{3/2}},
\end{align*}
by Lemma~\ref{lem:upper_bound_RW_double_barrier} and \eqref{eq:bounds_delta_eta}.
Therefore, using \eqref{eq:bound_tau(n)} and $\gamma (e^{\theta}- 1 -\theta e^{\theta})=-1$, we finally obtain
\begin{align*}
\P(B_n)
& \leq \frac{C (K+1) e^{-\theta K}}{n (\log n)^{3/2}},
\end{align*}
and the result follows by summing over $n \geq 2$.
\end{proof}
\subsection{Proof of the upper bound for the height}
We now state and prove a key lemma for the proof of Theorem~\ref{thm:upper_bound_height_WRT}.
Let
\begin{align*}
x_n & \coloneqq \left\lfloor \frac{3}{2\theta} \log \log n \right\rfloor.
\end{align*}
\begin{lemma} \label{lem:upper_bound_WRT}
There exist constants $C,c>0$ such that for any integers $L,K \geq 0$, $a \geq K$ and $n \geq 1$, we have, setting $t \coloneqq \tau(n)$,
\begin{align*}
& \P \Bigg( \exists \mathtt{u} \in \mathtt{T}_n :
\haut(\mathtt{u}) = t-x_n+a,\
\max_{k \in \intervalleentier{0}{t}} \haut(\mathtt{u}(i_k)) - k \leq K,\
\max_{k \in \intervalleentier{t/2}{t}} \haut(\mathtt{u}(i_k)) - k = -x_n + a + L\Bigg) \\
& \leq C (K+1) e^{-\theta L/4} e^{-\theta a}.
\end{align*}
\end{lemma}
The proof of this lemma is very close to the proof of Lemma~3.3 of Aïdékon \cite{aidekon2013} for the branching random walk, up to additional technicalities due to our model.
\begin{proof}
For brevity, we introduce $S_k(\mathtt{u}) \coloneqq \haut(\mathtt{u}(i_k)) - k$, which is exactly what is transformed into $S_k$ after applying the many-to-one lemma.
Let $E$ denote the event we are interested in.
We first distinguish according to the instant $j \in \intervalleentier{t/2}{t}$ where $\max_{k \in \intervalleentier{t/2}{t}} S_k(\mathtt{u})$ is reached: we introduce, for any $1\leq m\leq n$, the event
\[
E_j(m)
\coloneqq \Bigl\{
S_t(\mathtt{u}_m) = -x_n+a,\
\max_{k \in \intervalleentier{0}{t}} S_k(\mathtt{u}_m) \leq K,\
\max_{k \in \intervalleentier{t/2}{t}} S_k(\mathtt{u}_m) = S_j(\mathtt{u}_m) = -x_n + a + L
\Bigr\}
\]
and then $E_j \coloneqq \bigcup_{1\leq m \leq n} E_j(m)$.
Note here that $i_t \geq n \geq m$ so $\mathtt{u}_m(i_t) = \mathtt{u}_m$ and therefore $S_t(\mathtt{u}_m) = \haut(\mathtt{u}_m) - t$.
By the union bound, we have $\Pp{E} \leq \sum_{j \in \intervalleentier{t/2}{t}} \Pp{E_j}$, so we now have to bound $\Pp{E_j}$.
For this, we distinguish the cases $t/2 \leq j \leq t-2b$ and $t-2b < j \leq t$ with
\[
b \coloneqq \left\lceil \frac{2}{\theta} e^{\theta L/2} \right\rceil,
\]
which satisfies $b > L$ for any $L\geq0$.
Moreover, we can restrict ourselves to the case where $L \leq K-a+x_n$, otherwise the probability in the lemma is simply zero.
This implies that $L \leq x_n$ and therefore $b \leq \frac{2}{\theta} (\log n)^{3/4}+1$.
Hence, we consider from now $n$ large enough (independently of $K,a,L$) such that $b \leq t/8$.
The case where $n$ is small is immediate by choosing the constant $C$ in the lemma large enough.
Start with the case $t/2 \leq j \leq t-2b$. We write, recalling that $S_t(\mathtt{u}_m) = \haut(\mathtt{u}_m) - t$,
\begin{align} \label{eq:first_bound_P(E_j)}
\Pp{E_j}
& \leq \Ec{ \sum_{m=1}^n \1_{E_j(m)}}
= e^{-\theta(t - x_n+a)}
\sum_{m=1}^n \Ec{ e^{\theta \haut(\mathtt{u}_m)} \1_{E_j(m)}}.
\end{align}
We fix some $m \in \llbracket 1,n \rrbracket$ and let $s = \tau(m)$ be the smallest integer such that $i_s \geq m$.
If $s \leq t-L-1$, we have $\mathtt{u}_m(i_{t-L-1}) = \mathtt{u}_m$ and therefore, on the event $E_j(m)$,
\[
S_{t-L-1}(\mathtt{u}_m)
= \haut(\mathtt{u}_m)-t+L+1
= S_t(\mathtt{u}_m)+L+1
= - x_n + a + L+1,
\]
which is a contradiction because $t-L-1 \geq t-b-1 \geq t/2$ and on that event we have $\max_{k \in \intervalleentier{t/2}{t}} S_k(\mathtt{u}_m)\leq - x_n + a + L$.
Hence, the event $E_j(m)$ is empty for any $m \leq i_{t-L-1}$ and we can restrict ourselves to the case $m \in \llbracket i_{t-L-1} + 1,n \rrbracket$.
Then, we have $j \leq t-2b \leq t-L-1 \leq s-1$, so $E_j(m)$ is contained in the event
\[
\biggl\{
\haut(\mathtt{u}_m)-s = - x_n+a+t-s,\
\max_{k \in \intervalleentier{0}{s-1}} S_k(\mathtt{u}_m) \leq K,\
\max_{k \in \intervalleentier{t/2}{s-1}} S_k(\mathtt{u}_m) = S_j(\mathtt{u}_m) = - x_n + a + L
\biggr\}.
\]
Applying \eqref{eq:one_to_one} with $m$ and $s$ instead of $n$ and $t$, we get
\begin{align*}
& \Ec{ e^{\theta \haut(\mathtt{u}_m)} \1_{E_j(m)}} \\
& \leq C m^{\gamma(e^{\theta}-1)}
\P \biggl( S_s+1 = -x_n+a+t-s,\
\max_{k \in \intervalleentier{0}{s-1}} S_k \leq K,\
\max_{k \in \intervalleentier{t/2}{s-1}} S_k = S_j = -x_n + a + L \biggr) \\
& \leq C m^{\gamma(e^{\theta}-1)}
\Pp{\max_{k \in \intervalleentier{0}{j}} S_k \leq K,\
\max_{k \in \intervalleentier{t/2}{j}} S_k = S_j = -x_n + a + L } \\
& \hspace{3.64cm} {} \cdot
\Pp{\overline{S}_{s-j} = t-s-1-L,\
\max_{k \in \intervalleentier{0}{s-j}} \overline{S}_k \leq 0},
\end{align*}
applying the Markov property at time $j$, setting $\overline{S}_k \coloneqq S_{j+k} - S_j$ and using that $s \geq t-L$ to extend $\max_{k \in \intervalleentier{0}{s-j-1}} \overline{S}_k$ to the time $k = s-j$.
Note that the random walk $\overline{S}$ fits also the framework of Section~\ref{section:RW}
and that the quantities in \eqref{eq:def_delta} are bounded as follows in that case: $\Delta_k \leq 1$ and $\eta_k \leq C e^{ct^c}$ for any $k \geq 0$, using that $j \geq t/2$.
Applying Lemma~\ref{lem:upper_bound_RW_double_barrier}, we get
\begin{align*}
\Pp{\overline{S}_{s-j} = t-s-1-L,
\max_{k \in \intervalleentier{0}{s-j}} \overline{S}_k \leq 0}
& \leq \frac{C (L+2+s-t)}{(s-j)^{3/2}}
\leq \frac{C (L+1)}{(t-b-j)^{\frac32}},
\end{align*}
where the last inequality comes from the fact that $s\geq t-L>t-b> j$.
On the other hand, applying Lemma~\ref{lem:upper_bound_RW_double_barrier} and \eqref{eq:bounds_delta_eta}, we have
\begin{align*}
\Pp{\max_{k \in \intervalleentier{0}{j}} S_k \leq K,
\max_{k \in \intervalleentier{t/2}{j}} S_k = S_j = -x_n + a + L }
& \leq
\begin{cases}
\frac{C(K+1)}{t^{3/2}} \vphantom{\frac{p}{\frac{p}{p}}}
& \text{if } \frac{3t}{4} \leq j \leq t, \\
\frac{C(K+1) (x_n+1)}{t^{3/2}}
& \text{if } \frac{t}{2} \leq j < \frac{3t}{4},
\end{cases}
\end{align*}
where in the second case we simply omit the constraint $\max_{k \in \intervalleentier{t/2}{j}} S_k \leq -x_n + a + L$ and use that $K+x_n-a-L \leq x_n$.
Coming back to \eqref{eq:first_bound_P(E_j)} and using \eqref{eq:bound_tau(n)}, we proved
\begin{align*}
\Pp{E_j}
& \leq C e^{-\theta a} (\log n)^{3/2} n^{-\theta \gamma e^{\theta}} \sum_{m=i_{t-L-1}+1}^{n-1}
\Ec{ e^{\theta \haut(\mathtt{u}_m)} \1_{E_j(m)}} \\
& \leq C e^{-\theta a} (\log n)^{3/2}
\cdot \frac{(K+1)}{t^{3/2}}
\left(1 + x_n \1_{t/2 \leq j < 3t/4} \right)
\cdot \frac{(L+1)}{(t-b-j)^{3/2}},
\end{align*}
bounding the number of terms in the sum by $n$ and using that $\gamma(e^{\theta}-1-\theta e^{\theta}) = -1$.
Hence, we get
\begin{align*}
\sum_{j=t/2}^{t-2b} \Pp{E_j}
& \leq C e^{-\theta a} (K+1) (L+1)
\left(
\sum_{j=t/2}^{3t/4-1}
\frac{(1+x_n)}{(t-b-j)^{3/2}}
+
\sum_{j=3t/4}^{t-2b}
\frac{1}{(t-b-j)^{3/2}}
\right) \\
& \leq C e^{-\theta a} (K+1) (L+1)
\left(
\frac{\log \log n}{(\log n)^{1/2}}
+
\frac{1}{b^{1/2}} \right).
\end{align*}
Since $b \leq \frac{2}{\theta} (\log n)^{3/4}+1$, we have $\log \log n/(\log n)^{1/2} \leq C/b^{1/2}$.
Then, recalling the definition of~$b$, this gives the desired bound for this part of the sum over~$j$.
We now deal with the case $t-2b < j \leq t$.
Note that, forgetting the constraints on $S_k(\mathtt{u})$ for $k > j$,
\begin{align*}
E_j
& \subset \Bigl\{ \exists u \in \mathtt{T}_{i_j} :
\max_{k \in \intervalleentier{0}{j}} S_k(\mathtt{u}) \leq K,\
\max_{k \in \intervalleentier{t/2}{j}} S_k(\mathtt{u}) = S_j(\mathtt{u}) = -x_n+a+L
\Bigr\}.
\end{align*}
Then, proceeding similarly as before,
\[
\Pp{E_j}
\leq e^{-\theta(j -x_n+a+L)} \sum_{m=i_{j-1}+1}^{i_j}
\mathbb{E}\Bigl[ e^{\theta \haut(\mathtt{u}_m)}
\1_{\lbrace\max_{k \in \intervalleentier{0}{j}} S_k(\mathtt{u}_m) \leq K\rbrace}
\1_{\lbrace\max_{k \in \intervalleentier{t/2}{j}} S_k(\mathtt{u}_m) = S_j(\mathtt{u}_m) = -x_n+a+L\rbrace} \Bigr],
\]
where we noted that the event in the indicator function is empty if $m \leq i_{j-1}$ because in that case $S_{j-1}(\mathtt{u}_m) = S_{j}(\mathtt{u}_m) +1$.
In particular, note that here $\tau(m)=j$.
Using \eqref{eq:one_to_one} as before, the last expectation is smaller than
\begin{align*}
&C m^{\gamma(e^{\theta}-1)}
\Pp{\max_{k \in \intervalleentier{0}{j-1}} S_k \leq K,\
\max_{k \in \intervalleentier{t/2}{j-1}} S_k \leq -x_n+a+L,\
S_j+1 = -x_n+a+L}\\
&\leq C m^{\gamma(e^{\theta}-1)} \frac{(K+1)}{t^{3/2}},
\end{align*}
by Lemma~\ref{lem:upper_bound_RW_double_barrier}, noting that $j \geq t-2b \geq 3t/4$.
Hence, we get
\begin{align*}
\sum_{j=t-2b+1}^{t} \Pp{E_j}
& \leq C e^{-\theta (a+L)} (K+1)
\sum_{j=t-2b+1}^{t} \sum_{m=i_{j-1}+1}^{i_j}
(i_j)^{\gamma(e^{\theta}-1)} e^{-\theta j}
\leq C e^{-\theta (a+L)} (K+1) b
\end{align*}
using that $e^{-\theta j} \leq C (i_j)^{-\theta \gamma e^{\theta}}$, bounding the number of terms in the sum over $m$ by $i_j$ and using again that $\gamma(e^{\theta}-1-\theta e^{\theta}) = -1$.
This concludes the proof.
\end{proof}
We can now proceed to the proof of Theorem~\ref{thm:upper_bound_height_WRT}, which implies the upper bound in Theorem~\ref{thm:height_WRT}.
\begin{proof}[Proof of Theorem~\ref{thm:upper_bound_height_WRT}]
Setting $t \coloneqq \tau(n)$ and using \eqref{eq:bound_tau(n)}, it is enough to prove, for any $b \geq 1$,
\begin{align*}
\Pp{\exists \mathtt{u} \in \mathtt{T}_n : \haut(\mathtt{u}) \geq t-x_n+b}
& \leq C b e^{-\theta b}.
\end{align*}
For this, we first apply Lemma~\ref{lem:first_barrier} with $K = b$ to work on the event $\{\forall m \geq 1,\ \haut(\mathtt{u}_m) \leq \tau(m) + b \}$.
Then, we apply Lemma~\ref{lem:upper_bound_WRT} with all possible values of $a\geq b$ and $L\geq 0$, and $K=b$. The result follows from a union-bound.
\end{proof}
\section{Lower bound for the height}
\label{section:lower_bound}
\subsection{Strategy}
For any integer $N\geq 1$, we construct a new tree $\mathtt{T}_n^{(N)}$ from $\mathtt{T}_n$: we first remove all vertices with labels 2 through $N$ and then attach all of them and all of their children to the root.
Note that $\mathtt{T}_n^{(N)}$ has distribution $\wrt(\boldsymbol{w}^{(N)})$,
where the sequence of weights $\boldsymbol w^{(N)}$ is related to the sequence $\boldsymbol w$ as follows:
\begin{align} \label{eq:def_w^(N)}
w_i^{(N)}=
\begin{cases}
W_N & \text{if} \quad i=1,\\
0 & \text{if} \quad 2\leq i\leq N,\\
w_i & \text{if} \quad i\geq N+1.
\end{cases}
\end{align}
In other words, the sequence $\boldsymbol w^{(N)}$ is obtained from $\boldsymbol w$ by "transferring" all the weight of vertices $2$ to $N$ to the first vertex, and leaving the rest unchanged.
Our aim is to prove a lower bound for the height of $\mathtt{T}_n^{(N)}$, and the lower bound for $\mathtt{T}_n$ follows because $\haut(\mathtt{T}_n) \geq \haut(\mathtt{T}_n^{(N)})$.
We introduce the following quantities associated to this new sequence of weights $\boldsymbol w^{(N)}$:
\[
W_n^{(N)} \coloneqq \sum_{j=2}^n w_j^{(N)}
\qquad
p_n^{(N)} \coloneqq
\frac{e^{\theta}\frac{w_n^{(N)}}{W_n^{(N)}}}
{1+(e^{\theta}-1)\frac{w_n^{(N)}}{W_n^{(N)}}},
\qquad
i_k^{(N)} \coloneqq \inf \left\{ i \geq 1 : \sum_{j=2}^i p_j^{(N)} \geq k \right\}.
\]
As before we define
\[
x_n \coloneqq \left\lfloor \frac{3}{2\theta} \log \log n \right\rfloor.
\]
Then, for some $K \geq 0$, the quantity we use for our first and second moment argument is the following: for $n=i_t^{(N)}$,
\begin{equation} \label{def:Q_n^(N)}
Q_n^{(N)}
\coloneqq \sum_{m=1}^{n} \frac{w_m^{(N)}}{W_n^{(N)}}
e^{\theta \haut(\mathtt{u}_m)}
\ind{\haut(\mathtt{u}_m) = t - x_n}
\ind{\max_{k \in \intervalleentier{0}{t/2}} \haut(\mathtt{u}_m(i_k^{(N)})) - k \leq K}
\ind{\max_{k \in \intervalleentier{t/2}{t}} \haut(\mathtt{u}_m(i_k^{(N)})) - k \leq -x_n},
\end{equation}
where $\haut(\mathtt{u}_m)$ refers implicitly to the height of $\mathtt{u}_m$ in $\mathtt{T}_n^{(N)}$. Note that the dependence of $Q_n^{(N)}$ in $K$ is also kept implicit.
The following lemma gives bounds for the first and second moment of $Q_n^{(N)}$ and is proved in Sections \ref{subsection:first_moment_Q} and \ref{subsection:second_moment_Q}.
\begin{lemma} \label{lem:first_and_second_moment}
For any $\varepsilon > 0$, there exist $K_0(\varepsilon),N_0(\varepsilon),n_0(\varepsilon)$ such that for any $K \geq K_0(\varepsilon)$, $N \geq N_0(\varepsilon)$ and $n \geq n_0(\varepsilon)$ such that $n = i_t^{(N)}$ for some $t \geq 1$,
we have
\begin{align}
\Ec{Q_n^{(N)}}
& \geq \frac{Z_n^{(N)}}{t^{3/2}} \cdot (1-\varepsilon) \sqrt{\frac{2}{\pi}}
\frac{K}{\rho^-},
\label{eq:first_moment_Q_n} \\
\Ec{\left( Q_n^{(N)} \right)^2}
& \leq \left( \frac{Z_n^{(N)}}{t^{3/2}} \cdot (1+\varepsilon) \sqrt{\frac{2}{\pi}}
\frac{K}{\rho^-} \right)^2,
\label{eq:second_moment_Q_n}
\end{align}
where the constant $\rho^-$ is defined in Section~\ref{subsection:known_results_RW}.
\end{lemma}
\begin{proof}[Proof of the lower bound in Theorem~\ref{thm:height_WRT}]
Consider some $b \geq 0$.
The tree $\mathtt{T}_n$ is higher than $\mathtt{T}_n^{(N)}$ so
\begin{align}
\Pp{\haut(\mathtt{T}_n) \geq \gamma e^{\theta} \log n - x_n - b}
& \geq \Pp{\haut(\mathtt{T}_n^{(N)}) \geq \gamma e^{\theta} \log n - x_n - b} \nonumber \\
& \geq \Pp{\haut(\mathtt{T}_m^{(N)}) \geq t + \gamma e^{\theta} \log N + C_0 - x_m - b},
\end{align}
with $t$ such that $i_t^{(N)} \leq n < i_{t+1}^{(N)}$ and $m \coloneqq i_t^{(N)}$ and using that $t \geq \gamma e^\theta (\log n - \log N)-C_0$ by \eqref{eq:estimate_i_k^(N)}, where $C_0$ is a constant.
Now fix some $\varepsilon$.
We take $K=K_0(\varepsilon)$ and $N = N_0(\varepsilon)$ given by Lemma~\ref{lem:first_and_second_moment} and assume that $n$ is large enough such that $m \geq n_0(\varepsilon)$.
Then, with $b = \gamma e^{\theta} \log N + C_0$, we get
\begin{align*}
\Pp{\haut(\mathtt{T}_n) \geq \gamma e^{\theta} \log n - x_n - b}
\geq \Pp{\haut(\mathtt{T}_m^{(N)}) \geq t - x_m}
\geq \Pp{Q_m^{(N)} > 0}
\geq \frac{\mathbb{E}[Q_m^{(N)}]^2}{\mathbb{E}[(Q_m^{(N)})^2]},
\end{align*}
by Cauchy--Schwarz inequality.
By Lemma~\ref{lem:first_and_second_moment}, for any $\varepsilon > 0$, there exists $b \in \ensemblenombre{R}$ such that
\begin{align*}
\Pp{\haut(\mathtt{T}_n) \geq \gamma e^{\theta} \log n - x_n - b}
\geq \frac{(1-\varepsilon)^2}{(1+\varepsilon)^2},
\end{align*}
which proves the lower bound in Theorem~\ref{thm:height_WRT}.
\end{proof}
\subsection{Preliminaries}
Recall we work with an initial sequence $\boldsymbol w$ that satisfies assumption \eqref{eq:assumption_1} for some $\gamma>0$ and \eqref{eq:assumption_2}.
In this section, we list some bounds for the quantities depending on the modified sequence $\boldsymbol w^{(N)}$.
Anytime we add a superscript $(N)$ to a symbol that was implicitly a function of the weight sequence $\boldsymbol{w}$, it corresponds to the analog object for the weight sequence $\boldsymbol w^{(N)}$.
Constants $C,c>0$ that can change from line to line and $O(\dots)$ terms can only depend on the initial sequence $\boldsymbol w$, but \textbf{not} on $N$.
Moreover, we denote by $\kappa_N$ a quantity that depends only on $N$, tends to 0 as $N \to \infty$ and can change from line to line.
It follows from \eqref{eq:consequence_assumption_1} that, for $n \geq N+1$,
\begin{align} \label{eq:sum_w_i^(N)}
\sum_{i=2}^{n}\frac{w_i^{(N)}}{W_i^{(N)}}
& = \sum_{i=N+1}^{n}\frac{w_i}{W_i}
=\gamma (\log n - \log N) + \kappa_N + O(n^{-\alpha}), \\
\label{eq:sum_p_i^(N)}
\sum_{i=2}^{n}p^{(N)}_i
& = \sum_{i=N+1}^{n}p_i
= \gamma e^{\theta} (\log n - \log N) + \kappa_N + O(n^{-\alpha}), \\
\label{eq:bound_Z_n^(N)}
Z_n^{(N)}
& = \prod_{i=N+1}^{n}\left(1+(e^{\theta}-1)\frac{w_i}{W_i}\right)
= \left( \frac{n}{N} \right)^{\gamma(e^{\theta}-1)}
\exp \left( \kappa_N + O(n^{-\alpha}) \right).
\end{align}
Moreover, we have, for any $n \geq 1$,
\begin{align} \label{eq:bound_p_i^(N)}
p_n^{(N)}\leq C n^{-\alpha},
\end{align}
and, by assumption \eqref{eq:assumption_2},
\begin{align} \label{eq:sum_p_i^(N)_square}
\sum_{i=n}^\infty \left( p^{(N)}_i \right)^2
= \sum_{i=n \vee N}^\infty \left( p_i \right)^2
\leq \frac{C}{n \vee N}.
\end{align}
Concerning the time change $i_k^{(N)}$, one can check that, for any $k \geq 1$,
\begin{align} \label{eq:estimate_i_k^(N)}
i_k^{(N)}
= N\cdot \exp\left(\frac{k}{\gamma e^{\theta}} + \kappa_N + O \left(e^{-ck}\right) \right),
\end{align}
using \eqref{eq:bound_p_i^(N)} and the fact that $i_k^{(N)} \geq i_1^{(N)} \geq N+1$.
Note that the last display hold for $i_k^{(N)}\vee N$ for all $k\geq 0$.
The remaining part of this section is dedicated to the proof of Lemma~\ref{lem:first_and_second_moment}.
From now on, we consider the tree associated to the sequence $\boldsymbol w^{(N)}$, but we \textbf{omit the dependence on} $N$ in notation, writing for example $w_i$ instead of $w_i^{(N)}$.
\subsection{First moment}
\label{subsection:first_moment_Q}
In this section, we prove \eqref{eq:first_moment_Q_n}.
Applying the many-to-one lemma and setting $S_k \coloneqq H_{i_k} - k$, we have
\begin{align*}
\Ec{Q_n}
& = Z_n \cdot
\Pp{S_t = - x_n,\
\max_{k \in \intervalleentier{0}{t/2}} S_k \leq K,\
\max_{k \in \intervalleentier{t/2}{t}} S_k \leq -x_n}
\geq Z_n \cdot (1-\varepsilon) \sqrt{\frac{2}{\pi}}
(K-1) \frac{1}{\rho^- t^{3/2}},
\end{align*}
applying Lemma~\ref{lem:estimate_RW_double_barrier} and noting that $R^-(0) = 1$.
The result follows.
\subsection{Second moment}
\label{subsection:second_moment_Q}
In this section, we prove \eqref{eq:second_moment_Q_n}, up to Lemma~\ref{lem:estimates_RW_for_second_moment}, which we prove in Section \ref{subsection:applying_the_RW_estimates}. Recall we assumed $n=i_t$.
We apply the many-to-two lemma (Lemma~\ref{lem:many-to-two}) with
\[
F(\haut(\mathtt{u}(1)),\dots ,\haut(\mathtt{u}(n)))
\coloneqq
\ind{\haut(\mathtt{u}(n)) = t - x_n}
\ind{\max_{k \in \intervalleentier{0}{t/2}} \haut(\mathtt{u}(i_k)) - k \leq K}
\ind{\max_{k \in \intervalleentier{t/2}{t}} \haut(\mathtt{u}(i_k)) - k \leq -x_n},
\]
in order to get
\begin{align} \label{eq:first_bound_second_moment_Q_n}
\Ec{ Q_n^2 }
& \leq Z_n^2 \cdot
\sum_{\ell=1}^n \frac{\P_{\theta}(I_n=\ell)}{Z_\ell}
\cdot
\Ec{e^{\theta H^\ell_\ell}\cdot F(H^\ell_1,\dots , H^\ell_n) \cdot F(\overline{H}_1^\ell, \dots, \overline{H}^\ell_n)},
\end{align}
where we bounded $\prod_{i=\ell+1}^{n} (1+(e^{\theta}-1)q_i \ind{H^\ell_i=H^\ell_{i-1}})$ by $\prod_{i=\ell+1}^{n} (1+(e^{\theta}-1)q_i)= Z_n/Z_\ell$.
The following lemma gives us bounds for the expectation on the right-hand side of \eqref{eq:first_bound_second_moment_Q_n}. We postpone its proof to the next section.
\begin{lemma} \label{lem:estimates_RW_for_second_moment}
Let $1 \leq \ell \leq n$ and let $s$ be the smallest integer such that $i_s \geq \ell$. Let $K \geq 0$ and $N \geq K^{2}$.
\begin{enumerate}
\item\label{lem:estimates_RW_for_second_moment:it:large s} If $s \geq 3t/4$, then
\[
\Ec{e^{\theta H^\ell_\ell}\cdot F(H^\ell_1,\dots , H^\ell_n) \cdot F(\overline{H}_1^\ell, \dots, \overline{H}^\ell_n)}
\leq
\frac{C e^{\theta (s-x_n)}}{(t-s)^3+1} \frac{(K +1)}{t^{3/2}}.
\]
\item\label{lem:estimates_RW_for_second_moment:it:intermediate s} If $1 \leq s < 3t/4$, then
\[
\Ec{e^{\theta H^\ell_\ell}\cdot F(H^\ell_1,\dots , H^\ell_n) \cdot F(\overline{H}_1^\ell, \dots, \overline{H}^\ell_n)}
\leq
\frac{C e^{\theta (s+K)}}{t^3} \frac{(K +1)}{s^{3/2}}.
\]
\item\label{lem:estimates_RW_for_second_moment:it:first term} If $\ell = 1$, we consider some $\varepsilon > 0$ and let $K_0$ and $n_0$ be the constants given by Lemma~\ref{lem:estimate_RW_double_barrier}.
If $n \geq n_0$ and $K \in \llbracket K_0, n^{1/4} \rrbracket$, then
\[
\Ec{e^{\theta H^\ell_\ell}\cdot F(H^\ell_1,\dots , H^\ell_n) \cdot F(\overline{H}_1^\ell, \dots, \overline{H}^\ell_n)}
\leq
\left( (1+\varepsilon) \sqrt{\frac{2}{\pi}}
\frac{(K+ C N^{-c})}{\rho^- t^{3/2}} \right)^2.
\]
\end{enumerate}
\end{lemma}
We now apply this lemma to conclude the proof of \eqref{eq:second_moment_Q_n}.
We break the sum on the right-hand side of \eqref{eq:first_bound_second_moment_Q_n} into three terms $T_1 + T_2 + T_3$, where $T_1$ corresponds to the part where $\ell = 1$, $T_2$ to the part $2 \leq \ell \leq i_{\lceil 3t/4 \rceil - 1}$ and $T_3$ to the part $i_{\lceil 3t/4 \rceil - 1} < \ell \leq n$.
First note that, for any $k \geq 1$,
\begin{align*}
\P_{\theta}(I_n=k)
= p_k q_k\cdot \prod_{i=k+1}^{n}\left(1-p_iq_i\right)
\leq p_k q_k \leq p_k^2,
\end{align*}
recalling that $q_k = w_k/W_k \leq p_k$.
Start with $T_1$, which is the main term.
Since $Z_1 = 1$ and $p_1=1$, we get by Lemma~\ref{lem:estimates_RW_for_second_moment}\ref{lem:estimates_RW_for_second_moment:it:first term}
\begin{align} \label{eq:bound_T_1}
T_1
\leq \left( (1+\varepsilon) \sqrt{\frac{2}{\pi}}
\frac{(K+ C N^{-c})}{\rho^- t^{3/2}} \right)^2,
\end{align}
as soon as $K \geq K_0$ and $n \geq n_0$.
We now deal with $T_2$: applying Lemma~\ref{lem:estimates_RW_for_second_moment}\ref{lem:estimates_RW_for_second_moment:it:intermediate s}, we get
\begin{align*}
T_2
& \leq \sum_{s=1}^{\lceil 3t/4 \rceil - 1}
\sum_{\ell = i_{s-1}+1}^{i_s}
\frac{p_\ell^2}{Z_\ell}
\cdot \frac{C e^{\theta (s+K)}}{t^3} \frac{(K +1)}{s^{3/2}} \\
& \leq \frac{C e^{\theta K}}{t^3} (K+1)
\left(
\sum_{\ell = N+1}^{i_1} p_\ell^2
+
\sum_{s=2}^{\lceil 3t/4 \rceil - 1}
\frac{e^{\theta s}}{s^{3/2}}
\left( \frac{N}{i_{s-1}} \right)^{\gamma(e^{\theta}-1)}
\sum_{\ell = i_{s-1}+1}^{i_s}
p_\ell^2
\right),
\end{align*}
using \eqref{eq:bound_Z_n^(N)} when $s \geq 2$ and simply $Z_\ell \geq 1$ in the case $s=1$.
Then, using \eqref{eq:sum_p_i^(N)_square} for both terms
and applying \eqref{eq:estimate_i_k^(N)} to $i_{s-1}$ in the case $s \geq 2$ (bounding the $\kappa_N$ term by a constant independent of $N$), we get
\begin{align}
T_2
& \leq \frac{C e^{\theta K}}{t^3} (K+1)
\left(
\frac{1}{N}
+
\sum_{s=1}^{\lceil 3t/4 \rceil - 1}
\frac{e^{\theta s}}{s^{3/2}}
\cdot
\left( e^{-s/\gamma e^{\theta}} \right)^{\gamma(e^{\theta}-1)}
\cdot
\frac{e^{-s/\gamma e^{\theta}}}{N}
\right)
\leq \frac{C e^{\theta K}}{t^3} \frac{(K+1)}{N}, \label{eq:bound_T_2}
\end{align}
using that $1+\gamma (e^\theta-1-\theta e^\theta) = 0$.
Finally, we deal with $T_3$: applying Lemma~\ref{lem:estimates_RW_for_second_moment}\ref{lem:estimates_RW_for_second_moment:it:large s}, we get
\begin{align*}
T_3
\leq \sum_{s=\lceil 3t/4 \rceil}^t
\sum_{\ell = i_{s-1}+1}^{i_s}
\frac{p_\ell^2}{Z_\ell}
\cdot \frac{C e^{\theta (s-x_n)}}{(t-s)^3+1} \frac{(K +1)}{t^{3/2}}
\leq \frac{C e^{- \theta x_n}}{t^{3/2}} \frac{(K+1)}{N}
\sum_{s=\lceil 3t/4 \rceil}^t
\frac{1}{(t-s)^3+1},
\end{align*}
where in the second inequality we proceed as for $T_2$ (note that the sum w.r.t.\@ $\ell$ is identical).
Noting that the sum over $s$ is bounded by a constant and
$e^{-\theta x_n} \leq C/(\log i_t)^{3/2} \leq C/t^{3/2}$ by \eqref{eq:estimate_i_k^(N)}, it follows that
\begin{align} \label{eq:bound_T_3}
T_3
\leq \frac{C}{t^3} \frac{(K+1)}{N}.
\end{align}
Combining \eqref{eq:bound_T_1}, \eqref{eq:bound_T_2} and \eqref{eq:bound_T_3}, we finally get
\begin{align*} \label{eq:final_bound_Q^2}
\Ec{ Q_n^2 }
& \leq \frac{Z_n^2}{t^3} \cdot
\left(
\left( (1+\varepsilon) \sqrt{\frac{2}{\pi}}
\frac{(K+ C N^{-c})}{\rho^-} \right)^2
+ \frac{C(K+1)e^{\theta K}}{N}
+ \frac{C(K+1)}{N}
\right).
\end{align*}
This concludes the proof of \eqref{eq:second_moment_Q_n}.
\subsection{Applying the random walk estimates}
\label{subsection:applying_the_RW_estimates}
In this section, we prove Lemma~\ref{lem:estimates_RW_for_second_moment}. For this, we need the following lemma.
\begin{lemma} \label{lem:interactions}
There exist $C,c > 0$ such that, for any integers $t > s \geq 0$, $K\geq 0$, $\ell \geq 1$ and $N \geq K^{2}$, on the event $\{ \forall k \in \intervalleentier{0}{t}, H^\ell_{i_k} - k \leq K \}$, we have
\[
\sum_{i = i_s+1}^{i_{s+1}} p_i \ind{H^\ell_i \neq H^\ell_{i-1}}
\leq C \cdot N^{-1/4} \cdot e^{-c s}.
\]
\end{lemma}
\begin{proof}
We work on the event $\{ \forall k \in \intervalleentier{0}{t}, H^\ell_{i_k} - k \leq K \}$ so we have
\[
\sum_{i = i_s+1}^{i_{s+1}} \ind{H^\ell_i \neq H^\ell_{i-1}}
\leq H^\ell_{i_{s+1}}
\leq s+1 + K.
\]
Using successively the Cauchy-Schwarz inequality, the last display and \eqref{eq:sum_p_i^(N)_square} we have
\begin{equation*}
\sum_{i = i_s+1}^{i_{s+1}} p_i \ind{H^\ell_i \neq H^\ell_{i-1}}
\leq \sqrt{\sum_{i = i_s+1}^{i_{s+1}} \ind{H^\ell_i \neq H^\ell_{i-1}}}\cdot\sqrt{\sum_{i = i_s+1}^{i_{s+1}} p_i^2} \leq \sqrt{s+1 + K} \cdot \frac{C}{\sqrt{i_s\vee N}}.
\end{equation*}
Thanks to \eqref{eq:estimate_i_k^(N)}, which holds for $s\geq 1$, we can write $N\vee i_s\geq C\cdot N\cdot \exp(cs)$, which holds for any $s\geq 0$, for some $c>0$.
Using the condition that $K\leq N^{\frac12}$ we get
\begin{align*}
\sum_{i = i_s+1}^{i_{s+1}} p_i \ind{H^\ell_i \neq H^\ell_{i-1}}
\leq C \cdot N^{-\frac14}\cdot \left(\frac{s+1+N^{\frac12}}{N^{\frac12}}\right)^{\frac12}\cdot \exp\left(-\frac{cs}{2}\right)
\leq C\cdot N^{-\frac14} \cdot e^{-cs},
\end{align*}
where, we recall, we allow the values of the constants $C,c>0$ to change along the computation. This finishes the proof of the lemma.
\end{proof}
In the proof of Lemma~\ref{lem:estimates_RW_for_second_moment}, we apply several times the results of Section~\ref{section:RW} to a variety of different random walks.
All the results of Section~\ref{section:RW} depend on two sequences $(\mathbf r, \mathbf j)$ and in particular the error terms are expressed using the quantities introduced in \eqref{eq:def_delta}.
In the following lemma, we provide bounds for those error terms that apply uniformly in all the cases that arise in the proof of Lemma~\ref{lem:estimates_RW_for_second_moment}.
\begin{lemma}\label{lem:uniform error bounds}
There exist $C,c>0$ such that for any integers $t>s\geq 0,\ K\geq 0,\ \ell\geq 1$ being such that $i_s\geq \ell$, for $N\geq \sqrt{K}$, the following inequalities jointly hold for the quantities below defined in \eqref{eq:def_delta} for a family of $(\mathbf{r},\mathbf{j})$ that depends on $s, N,K$, which we describe below
\begin{align*}
\delta_k^{(\mathbf{r},\mathbf{j})}&\leq C\cdot N^{-c}\cdot e^{-c(k+s)}, \quad \text{for all } 1\leq k \leq t-s, \\ \Delta_{t-s}^{(\mathbf{r},\mathbf{j})}&\leq C\cdot N^{-c}\cdot e^{-cs},\\
\eta_{t-s}^{(\mathbf{r},\mathbf{j})}&\leq C\cdot N^{-c}\cdot e^{-ct}.
\end{align*}
The inequalities above hold jointly for $\mathbf{j}=(i_{k+s}-i_s+1)_{k\geq 0}$, which implicitly depends on $N$, and $\mathbf{r}= (p_{i_s-1+i})_{i\geq 2}$ or $ (p^\ell_{i_s-1+i})_{i\geq 2}$ or any realisation of $(\tilde{p}^\ell_{i_s-1+i})_{i\geq 2}$ on the event $\{ \forall k \in \intervalleentier{0}{t}, H^\ell_{i_k} - k \leq K \}$.
\end{lemma}
\begin{proof} Let $s\geq 0$ and $(\mathbf{r},\mathbf{j})$ as in the lemma. For any $1\leq k \leq t-s$, we can write
\begin{align*}
\delta_k^{(\mathbf{r},\mathbf{j})}
& = \abs{\Ec{Y_k^{(\mathbf{r},\mathbf{j})}}- 1}= \abs{\sum_{j=j_{k-1}+1}^{j_k} r_j -1}
\leq \abs{\sum_{i=i_{k+s-1}+1}^{i_{k+s}} p_i - 1} + \sum_{i=i_{k+s-1}+1}^{i_{k+s}} \abs{r_{i+1-i_s} - p_i}.
\end{align*}
The first term of the last display is bounded above by $(p_{i_{k+s-1}} \1_{k+s-1 \geq 1} + p_{i_{k+s}})$ which is smaller than $C N^{-\alpha} e^{-\alpha(k+s)}$ using \eqref{eq:bound_p_i^(N)}. Then, we consider the different choices of $\mathbf{r}$.
\begin{itemize}
\item If
$\mathbf{r}= (p_{i_s-1+i})_{i\geq 2}$, then the second sum is identically equal to $0$.
\item If $\mathbf{r}=(p^\ell_{i_s-1+i})_{i\geq 2}$, then recalling the definition \eqref{eq:definition H^l}, for $i>\ell$ we have
\[\abs{p^\ell_i - p_i} = \abs{\frac{p_i (1-q_i)}{1-p_iq_i}-p_i}= \abs{\frac{p_i q_i (1-p_i)}{1-p_i q_i}}\leq Cp_i^2,\]
so that using \eqref{eq:sum_p_i^(N)_square} and \eqref{eq:estimate_i_k^(N)} allows us to bound the sum by $C\cdot N^{-1}\cdot e^{-c(k+s)}$.
\item Last, if $\mathbf{r}$ is any realisation of $(\tilde{p}^\ell_{i_s-1+i})_{i\geq 2}$ on the event $\{ \forall k \in \intervalleentier{0}{t}, H^\ell_{i_k} - k \leq K \}$, recalling that
$\tilde{p}^\ell_i = p_i \ind{H^\ell_i=H^\ell_{i-1}}$ we have
\[\sum_{i=i_{k+s-1}+1}^{i_{k+s}} \abs{r_{i+1-i_s} - p_i}= \sum_{i=i_{k+s-1}+1}^{i_{k+s}} p_i \ind{H^\ell_i \neq H^\ell_{i-1}}
\leq C N^{-1/4} e^{-c(k+s)},\]
using Lemma~\ref{lem:interactions}.
\end{itemize}
In the end, by tuning the constants $C,c>0$, we have that in any case, for all $1\leq k \leq t-s$,
\begin{align*}
\delta_k^{(\mathbf{r},\mathbf{j})}&\leq C\cdot N^{-c} \cdot e^{-cs}.
\end{align*}
From there, it is easy to get that
\begin{align*}
\Delta_{t-s}^{(\mathbf{r},\mathbf{j})}
& \leq \sum_{k=1}^{t-s} \delta_k^{(\mathbf{r},\mathbf{j})}\leq \sum_{k=1}^{t-s} C\cdot N^{-c}\cdot e^{-c(k+s)}
\leq C\cdot N^{-c} \cdot e^{-cs}.
\end{align*}
Then, for any of our choices of $\mathbf{r}$, we have $r_i\leq p_{i_s-1+i}$ for all $i\geq 2$. This allows us to write
\begin{align*}
\eta_{t-s}^{(\mathbf{r},\mathbf{j})}&\leq 2 \left( \sum_{j = i_{\lfloor (t-s)^{1/4} \rfloor+s}+1}^{i_t} p_j^2 + \sum_{j=\lfloor (t-s)^{1/4} \rfloor}^{t-s} \delta_j^{(\mathbf{r},\mathbf{j})} \right)\\
&\leq \frac{C}{i_{\lfloor (t-s)^{1/4} \rfloor+s}}
+ C N^{-c} e^{-c(\lfloor (t-s)^{1/4} \rfloor+s)}
\leq C\cdot N^{-c}\cdot e^{-ct},
\end{align*}
where we use \eqref{eq:sum_p_i^(N)_square}, \eqref{eq:estimate_i_k^(N)} and our previous estimate on $\delta_j^{(\mathbf{r},\mathbf{j})}$ for $1\leq j \leq t-s$. This finishes the proof of the lemma.
\end{proof}
\begin{proof}[Proof of Lemma~\ref{lem:estimates_RW_for_second_moment}]
We set $E(\ell) \coloneqq \mathbb{E} [ e^{\theta H^\ell_\ell}
F(H^\ell_1,\dots,H^\ell_n)
F(\overline{H}_1^\ell, \dots, \overline{H}^\ell_n)]$.
\textbf{Part~\ref{lem:estimates_RW_for_second_moment:it:large s}}. We consider the case $s \geq 3t/4$.
Recalling that $\overline{H}_j^\ell = H_j^\ell$ for $j \leq \ell$, we have
\begin{align*}
E(\ell)
& = \Ec{e^{\theta H^\ell_\ell}
F(H^\ell_1,\dots,H^\ell_n) \cdot
\Ppsq{\overline{H}_{i_t}^\ell = t-x_n,\
\max_{k \in \intervalleentier{s}{t}} \overline{H}_{i_k}^\ell - k \leq -x_n}
{H^\ell, \overline{H}_{i_s}^\ell}}.
\end{align*}
This last conditional probability is equal to
\begin{align*}
\Ppsq{\overline{S}_{t-s} = -x_n - \overline{H}_{i_s}^\ell + s,\
\max_{k \in \intervalleentier{0}{t-s}} \overline{S}_k \leq -x_n-\overline{H}_{i_s}^\ell+s}
{H^\ell, \overline{H}_{i_s}^\ell},
\end{align*}
where $\overline{S}_k \coloneqq (\sum_{j=1}^k \overline{Y}_{\!\!j}) -k$
with $\overline{Y}_{\!\!j} \coloneqq \sum_{i=i_{j+s-1}+1}^{i_{j+s}} \1_{V_i \leq \tilde{p}^\ell_i}$, recalling that
$\tilde{p}^\ell_i = p_i \ind{H^\ell_i=H^\ell_{i-1}}$ and the $V_i$ are i.i.d.\@ uniformly distributed over $(0,1)$ and independent of $H^\ell$ and $\overline{H}_{i_s}^\ell$.
The distribution of $\overline{S}$ then corresponds to that of $S^{(\mathbf r, \mathbf j)}$, for $\mathbf r=(\tilde{p}^\ell_{i-1+i_s})_{i\geq 2}$ and $\mathbf j=(i_{k+s}-i_s+1)_{k\geq 0}$, in the setting of Section~\ref{section:RW}.
Applying Lemma~\ref{lem:upper_bound_RW_double_barrier} with $K=0$, $a=-x_n - \overline{H}_{i_s}^\ell + s$ and $n=t-s$ to bound this probability, we get that the above display is smaller than
\begin{align*}
C \left(\Delta_{\lfloor n^{1/4} \rfloor}^{(\mathbf r,\mathbf j)} +1 \right) \frac{(-x_n - \overline{H}_{i_s}^\ell + s+1)}{(t-s)^{3/2}+1}
+ \eta_{t-s}^{(\mathbf r,\mathbf j)}\leq \frac{C (-x_n - \overline{H}_{i_s}^\ell + s+1)}{(t-s)^{3/2}+1},
\end{align*}
where the inequality is due to Lemma~\ref{lem:uniform error bounds}.
Hence, we have
\begin{align*}
E(\ell)
& \leq \Ec{e^{\theta H^\ell_\ell}
F(H^\ell_1,\dots,H^\ell_n)
\frac{C (-x_n-\overline{H}_{i_s}^\ell+s +1)}{(t-s)^{3/2}+1}} \\
&\leq \Ec{e^{\theta H^\ell_\ell}
F(H^\ell_1,\dots,H^\ell_n)
\frac{C (-x_n-H_\ell^\ell+s +1)}{(t-s)^{3/2}+1}},
\end{align*}
where we used that $\overline{H}_{i_s}^\ell \geq H_\ell^\ell$.
Then, setting for brevity $B \coloneqq \{ \max_{k \in \intervalleentier{0}{t/2}} H_{i_k}^\ell - k \leq K,\ \max_{k \in \intervalleentier{t/2}{s-1}} H_{i_k}^\ell - k \leq -x_n \}$, we have
\begin{align*}
E(\ell)
\leq \Ec{ e^{\theta H^\ell_\ell} \1_B \cdot
\frac{C (-x_n-H_\ell^\ell+s+1)}{(t-s)^{3/2}+1}
\cdot
\Ppsq{
\max_{k \in \intervalleentier{s}{t}} H_{i_k}^\ell - k \leq -x_n = H_{i_t}^\ell - t}
{H^\ell_{i_s}}
}.
\end{align*}
We apply Lemma~\ref{lem:upper_bound_RW_double_barrier} again to bound the conditional probability appearing in the last display.
In that case the considered random walk is
$\widetilde{S}_k \coloneqq (\sum_{j=1}^k \widetilde{Y}_j) -k$
with $\widetilde{Y}_j \coloneqq \sum_{i=i_{j+s-1}+1}^{i_{j+s}} \1_{U_i \leq p^\ell_i}$, recalling that
$p^\ell_i = p_i (1-q_i)/(1-p_iq_i)$.
The distribution of $\widetilde{S}$ then corresponds to that of $S^{(\mathbf r, \mathbf j)}$, for $\mathbf r=(p^\ell_{i-1+i_s})_{i\geq 2}$ and $\mathbf j=(i_{k+s}-i_s+1)_{k\geq 0}$, and the conditional probability above can be written as
\begin{align*}
\Ppsq{\widetilde{S}_{t-s} = -x_n - H_{i_s}^\ell + s,\
\max_{k \in \intervalleentier{0}{t-s}} \widetilde{S}_k \leq -x_n-H_{i_s}^\ell+s}
{H_{i_s}^\ell}.
\end{align*}
Applying again Lemma~\ref{lem:upper_bound_RW_double_barrier} and Lemma~\ref{lem:uniform error bounds} as before, it follows that
\begin{align*}
E(\ell)
& \leq \Ec{e^{\theta H^\ell_\ell}
\1_B \cdot
\frac{C(-x_n-H_\ell^\ell+s +1)}{(t-s)^{3/2}+1} \cdot
\frac{(-x_n-H_{i_s}^\ell+s +1)}{(t-s)^{3/2}+1} } \\
& \leq \Ec{ e^{\theta H^\ell_{i_{s-1}}}
\1_B \cdot
\frac{(-x_n-H_{i_{s-1}}^\ell+s +1)^2}{(t-s)^3+1} },
\end{align*}
using that $H_{i_s}^\ell \geq H_\ell^\ell \geq H_{i_{s-1}}^\ell$ and that
$\mathbb{E} \bigl[ e^{\theta (H^\ell_\ell-H^\ell_{i_{s-1}})} \bigr] \leq C$.
Finally, we apply Lemma~\ref{lem:exponential_RW_double_barrier} to the random walk $S_k \coloneqq (\sum_{j=1}^k Y_j) -k$
with $Y_j \coloneqq \sum_{i=i_{j-1}+1}^{i_j} \1_{U_i \leq p_i}$, and we get
\begin{align*}
E(\ell)
& \leq \frac{C}{(t-s)^3+1}
e^{\theta (s-1-x_n)} \frac{(K +1)}{(s-1)^{3/2}}.
\end{align*}
This concludes the proof of Part~\ref{lem:estimates_RW_for_second_moment:it:large s}.
\textbf{Part~\ref{lem:estimates_RW_for_second_moment:it:intermediate s}}.
First note that $E(\ell)$ is smaller than
\begin{align*}
\mathbb{E} \Bigl[ e^{\theta H^\ell_\ell}
F(H^\ell_1,\dots,H^\ell_n)
\cdot
\ind{\overline{H}_{i_t}^\ell = t-x_n,\
\max_{k \in \intervalleentier{s}{(s+t)/2}} \overline{H}_{i_k}^\ell - k \leq K,\
\max_{k \in \intervalleentier{(s+t)/2}{t}} \overline{H}_{i_k}^\ell - k \leq -x_n}
\Bigr],
\end{align*}
where we replaced the barrier at $-x_n$ by a barrier at $K$ at some points.
We integrate w.r.t.\@ the random walk $\overline{S}$ as before, it follows from Lemma~\ref{lem:uniform error bounds} and Lemma~\ref{lem:upper_bound_RW_double_barrier} that
\begin{align*}
E(\ell)
& \leq \Ec{e^{\theta H^\ell_\ell}
F(H^\ell_1,\dots,H^\ell_n) \cdot
\frac{C (K-H_\ell^\ell+s +1)}{(t-s)^{3/2}+1}}.
\end{align*}
Then, we integrate w.r.t.\@ the random walk $S$ similarly and get, by Lemma~\ref{lem:uniform error bounds} and Lemma~\ref{lem:upper_bound_RW_double_barrier},
\begin{align*}
E(\ell)
& \leq \Ec{ e^{\theta H^\ell_{i_{s-1}}}
\ind{\max_{k \in \intervalleentier{0}{s}} H_{i_k}^\ell - k \leq K}
\frac{C(K-H_{i_{s-1}}^\ell+s +1)^2}{(t-s)^3+1} }.
\end{align*}
Finally, applying Lemma~\ref{lem:exponential_RW_double_barrier}, we get the announced result.
\textbf{Part~\ref{lem:estimates_RW_for_second_moment:it:first term}}. We are in the case $\ell = 1$, so $H^\ell_\ell = 0$ and $E(\ell)$ equals
\begin{align*}
\Ec{F(H^\ell_1,\dots,H^\ell_n)
\Ppsq{\overline{H}_{i_t}^\ell = t-x_n,
\max_{k \in \intervalleentier{0}{t/2}} \overline{H}_{i_k}^\ell - k \leq K,
\max_{k \in \intervalleentier{t/2}{t}} \overline{H}_{i_k}^\ell - k \leq -x_n}
{H^\ell}}.
\end{align*}
Then, we apply Lemma~\ref{lem:estimate_RW_double_barrier} to the random walk $\overline{S}$, noting that $R^-(0) = 1$, to get
\begin{align*}
E(\ell)
\leq (1+\varepsilon) \sqrt{\frac{2}{\pi}}
\frac{(K+ C N^{-c})}{\rho^- t^{3/2}}
\Ec{F(H^\ell_1,\dots,H^\ell_n)}.
\end{align*}
Applying Lemma~\ref{lem:estimate_RW_double_barrier} to the random walk $S$, the result follows.
\end{proof}
\section{Diameter of the tree}
\label{section:diameter}
\begin{proof}[Proof of Theorem~\ref{thm:diameter_WRT}]
First note that we have $\diam(\mathtt{T}_n) \leq 2 \haut(\mathtt{T}_n)$ so the upper bound follows directly from Theorem~\ref{thm:height_WRT}.
Now we fix some $\varepsilon >0$ and we want to prove that there exists $b \in \ensemblenombre{R}$ such that
\begin{align*}
\limsup_{n\to\infty}
\Pp{\diam(\mathtt{T}_n) \geq 2 \gamma e^{\theta} \log n - \frac{3}{\theta} \log \log n - b}
\geq 1-\varepsilon.
\end{align*}
For this, we use notation and results from Section~\ref{section:lower_bound}.
By an argument similar to the proof of the lower bound in Theorem~\ref{thm:height_WRT}, it is enough to prove that for $N$ large enough
\begin{align*}
\limsup_{t\to\infty} \Pp{\diam(\mathtt{T}_n^{(N)}) \geq 2t - 2x_n}
\geq 1-\varepsilon,
\end{align*}
where $n \coloneqq i_t^{(N)}$ and $\mathtt{T}_n^{(N)}$ has distribution $\wrt(\boldsymbol{w}^{(N)})$, where the sequence of weights $\boldsymbol w^{(N)}$ is defined in \eqref{eq:def_w^(N)}.
In the rest of this proof, we work only with the tree $\mathtt{T}_n^{(N)}$ for some fixed $N$ that is chosen large enough depending on $\varepsilon$ afterwards.
Therefore, from now on, we omit the dependence in $N$ in the notation of the various quantities we are considering (including $w_m^{(N)}$).
Recall that, for some $K \geq 0$, we consider
\begin{align*}
Q_n
& \coloneqq \sum_{m=1}^{n} \frac{w_m}{W_n}
e^{\theta \haut(\mathtt{u}_m)}
\1_{B_m}, \\
B_m
& \coloneqq
\left\{ \haut(\mathtt{u}_m) = t - x_n,\
\max_{k \in \intervalleentier{0}{t/2}} \haut(\mathtt{u}_m(i_k)) - k \leq K,\
\max_{k \in \intervalleentier{t/2}{t}} \haut(\mathtt{u}_m(i_k)) - k \leq -x_n \right\}.
\end{align*}
Observe that if there are two vertices in $\mathtt{T}_n^{(N)}$ at height $t - x_n$ whose most recent common ancestor is the root, then the diameter of $\mathtt{T}_n^{(N)}$ is at least $2t - 2x_n$.
Hence, recalling that $\mathtt{u} \wedge \mathtt{v}$ denotes the most recent common ancestor of vertices $\mathtt{u}$ and $\mathtt{v}$, we have
\begin{align*}
\Pp{\diam(\mathtt{T}_n^{(N)}) \geq 2t - 2x_n}
& \geq \Pp{ \exists \mathtt{u},\mathtt{v} \in \mathtt{T}_n^{(N)}:
\haut(\mathtt{u}) = \haut(\mathtt{v}) = t - x_n,\
\mathtt{u} \wedge \mathtt{v} = \mathtt{u}_1} \\
&\geq \Pp{\mathcal{T}_1 > 0},
\end{align*}
where we set
\begin{align*}
\mathcal{T}_1
& \coloneqq \sum_{\ell,m=1}^{n}
\frac{w_\ell w_m}{(W_n)^2}
e^{\theta \haut(\mathtt{u}_\ell)} e^{\theta \haut(\mathtt{u}_m)}
\1_{B_\ell} \1_{B_m}
\ind{\mathrm{lab}(\mathtt{u}_\ell \wedge \mathtt{u}_m) = 1}.
\end{align*}
Note that $\mathcal{T}_1$ is a part of the sum obtained when developing $Q_n^2$ and the remaining part satisfies
\begin{align*}
\Ec{Q_n^2- \mathcal{T}_1}
& = \Ec{\sum_{\ell,m=1}^{n}
\frac{w_\ell w_m}{(W_n)^2}
e^{\theta \haut(\mathtt{u}_\ell)} e^{\theta \haut(\mathtt{u}_m)}
\1_{B_\ell} \1_{B_m}
\ind{2 \leq \mathrm{lab}(\mathtt{u}_\ell \wedge \mathtt{u}_m) \leq n} }
\leq T_2 + T_3,
\end{align*}
by the many-to-two lemma (Lemma~\ref{lem:many-to-two}),
where $T_2$ and $T_3$ were defined in Section~\ref{subsection:second_moment_Q} as parts of the sum on the right-hand of \eqref{eq:first_bound_second_moment_Q_n} corresponding to $2 \leq \ell \leq i_{\lceil 3t/4 \rceil - 1}$ and $i_{\lceil 3t/4 \rceil - 1} < \ell \leq n$ respectively.
Then, we proved in \eqref{eq:bound_T_2} and \eqref{eq:bound_T_3} that
\begin{align*}
T_2 + T_3
\leq \frac{Z_n^2}{t^3} \cdot \frac{C(K+1)e^{\theta K}}{N}
\leq \varepsilon \Ec{Q_n}^2,
\end{align*}
where the second inequality follows from \eqref{eq:first_moment_Q_n} for $K,N,n$ large enough depending on $\varepsilon$ only.
Therefore, we get
\begin{align*}
\Pp{\mathcal{T}_1 > 0}
& \geq \Pp{Q_n > \frac{1}{2} \Ec{Q_n},\
Q_n^2- \mathcal{T}_1 < \frac{1}{4} \Ec{Q_n}^2} \\
& \geq 1
- \Pp{Q_n \leq \frac{1}{2} \Ec{Q_n} }
- \Pp{Q_n^2 - \mathcal{T}_1 \geq \frac{1}{4} \Ec{Q_n}^2} \\
& \geq 1
- \frac{4 \Var \left(Q_n\right)}{\Ec{Q_n}^2}
- 4 \varepsilon,
\end{align*}
applying Chebyshev and Markov inequalities.
By Lemma~\ref{lem:first_and_second_moment}, we have $\Var(Q_n) \leq \varepsilon \mathbb{E}[Q_n]^2$ for $K,N,n$ large enough depending on $\varepsilon$ only.
Hence, we proved that for $K,N,n$ large enough,
\begin{align*}
\Pp{\diam(\mathtt{T}_n^{(N)}) \geq 2t - 2x_n}
\geq \Pp{\mathcal{T}_1 > 0}
\geq 1 - 6 \varepsilon,
\end{align*}
which concludes the proof.
\end{proof}
\begin{appendix}
\section{Random walk estimates}
\label{section:RW}
The goal of this section is to prove estimates for the probability of events involving a certain inhomogeneous random walk $(S_k)$.
We work in the following framework: let $\mathbf{r}=(r_i)_{i\geq 2}$ be a sequence of real numbers in the interval $\intervalleff{0}{1}$.
Then, let $\mathbf{j}=(j_k)_{k \geq 0}$ be an increasing sequence of integers with $j_0 = 1$.
We introduce the following processes that depend on $\mathbf{r}$ and~$\mathbf{j}$
\begin{align*}
Y_k^{(\mathbf{r},\mathbf{j})} & \coloneqq \sum_{j=j_{k-1}+1}^{j_k} \ind{U_j \leq r_j},
\qquad \text{for } k \geq 1, \\
S_k^{(\mathbf{r},\mathbf{j})} & \coloneqq \left( \sum_{\ell=1}^k Y_\ell^{(\mathbf{r},\mathbf{j})} \right) - k,
\qquad \text{for } k \geq 0,
\end{align*}
where $(U_j)_{j\geq2}$ is a sequence of i.i.d.\@ uniform random variable over $(0,1)$.
Finally, we define
\begin{align}
\begin{split} \label{eq:def_delta}
& \delta_k^{(\mathbf{r},\mathbf{j})} \coloneqq \abs{\Ec{Y_k^{(\mathbf{r},\mathbf{j})}}-1},
\qquad
\Delta_k^{(\mathbf{r},\mathbf{j})}
\coloneqq \max_{0 \leq \ell \leq k} \abs{\Ec{S_\ell^{(\mathbf{r},\mathbf{j})}}}, \\
& \eta_k^{(\mathbf{r},\mathbf{j})} \coloneqq 2 \left( \sum_{j = j_{\lfloor k^{1/4} \rfloor}+1}^{j_k} r_j^2 \right) + 2 \left( \sum_{\ell=\lfloor k^{1/4} \rfloor}^k \delta_\ell^{(\mathbf{r},\mathbf{j})} \right).
\end{split}
\end{align}
which are non-negative numbers appearing in error terms.
Throughout the paper, we make use of the estimates proved in this section for several choices of $(\mathbf{r},\mathbf{j})$.
In particular, for a fixed $(\mathbf{r},\mathbf{j})$, it is useful to apply the results for the walk $(S_{k+s}^{(\mathbf{r},\mathbf{j})}-S_{s}^{(\mathbf{r},\mathbf{j})})_{k\geq 0}$ which has the same distribution as $(S_k^{(\mathbf{r}',\mathbf{j}')})_{k\geq 0}$ where $\mathbf{r}'=(r_{j_s+i-1})_{i\geq 2}$ and $\mathbf{j}'=(j_{s+k}-j_s+1)_{k\geq 0}$.
In this section, we are going to make the dependency in $(\mathbf{r},\mathbf{j})$ implicit because those sequences are chosen in different ways throughout the paper.
\subsection{A coupling with an homogeneous random walk}
The goal of this section is to prove the following lemma, which allows us to apply known results on homogeneous random walks.
\begin{lemma} \label{lem:comparison_S_Stilde}
For any $m \geq 0$, there exists a random walk $\widehat{S}$ with jump distribution $\mathrm{Poisson}(1) - 1$ such that
\[
\Pp{ \exists k \in \llbracket 0,n-m \rrbracket : S_{k+m}-S_m \neq \widehat{S}_k }
\leq 2 \left( \sum_{j = j_m+1}^{j_n} r_j^2 \right)
+ 2 \left( \sum_{k=m}^n \delta_k \right).
\]
\end{lemma}
It is proved easily by replacing each $Y_\ell$ by a $\mathrm{Poisson}(1)$ r.v.\@ using the following lemma.
\begin{lemma} \label{lem:comparison_Y_Poisson}
Let $q_1,\dots,q_n$ be non-negative real number, $V_1,\dots,V_n$ be independent r.v.\@ uniformly distributed over $(0,1)$ and $Y \coloneqq \sum_{i=1}^n \ind{V_i \leq q_i}$.
There exists a r.v.\@ $Z$ with distribution $\mathrm{Poisson}(1)$ such that
\[
\Pp{Y \neq Z}
\leq 2 \left( \sum_{i=1}^n q_j^2 \right)
+ 2 \abs{\mathbb{E}[Y] - 1}.
\]
\end{lemma}
\begin{proof} On the one hand, it follows from \cite[Proposition~1]{lecam1960} that the total variation distance between the distribution of $Y$ and the distribution $\mathrm{Poisson}(\mathbb{E}[Y])$ is at most $\sum_{i=1}^n q_i^2$.
On the other hand, by \cite[Equation (2.2)]{adelljodra2006}, the total variation distance between $\mathrm{Poisson}(\mathbb{E}[Y])$ and $\mathrm{Poisson}(1)$ is at most $\abs{\mathbb{E}[Y] - 1}$.
The result follows.
\end{proof}
\subsection{Known results on the homogeneous random walk}
\label{subsection:known_results_RW}
In this section, we state some known results concerning homogeneous random walks. We work in the particular case of the walk $\widehat{S}$, which jumps with distribution $\mathrm{Poisson}(1) - 1$. Hence we are in the so-called lattice case, because the walk $\widehat{S}$ can take only integer values.
We first introduce $\mathrm R$ the renewal function of the first strict ascending ladder height process of the random walk $\widehat{S}$.
For $x \geq 0$,
\begin{align*}
\mathrm R(x)
\coloneqq
\sum_{k = 0}^\infty
\Pp{H_k \leq x},
\end{align*}
where $(H_k)_{k\in\ensemblenombre{N}}$ is the first strict ascending ladder height process: we set $\tau_0 \coloneqq 0$, $H_0 \coloneqq 0$ and, for $k \geq 1$, $\tau_k \coloneqq \inf \{ n > \tau_{k-1} : \widehat{S}_n > \widehat{S}_{\tau_{k-1}} \}$ and $H_k \coloneqq \widehat{S}_{\tau_k}$.
Since $\mathbb{E}[\widehat{S}_1] = 0$ and $\mathbb{E}[(\widehat{S}_1)^2] < \infty$, by Feller \cite[Theorem~XVIII.5.1 (5.2)]{feller1971}, we have $\mathbb{E}[H_1] < \infty$.
Thus, it follows from Feller's \cite[p.\@ 360]{feller1971} renewal theorem that there exists a constant $\rho > 0$ such that
\begin{equation} \label{eq:equivalent_function_R}
\frac{\mathrm R(x)}{x}
\xrightarrow[x \to \infty]{}
\rho.
\end{equation}
Moreover, we denote by $\mathrm R^-$ the renewal function of the first strict ascending ladder height process for the random walk with jump $1-\mathrm{Poisson}(1)$ and by $\rho^-$ the constant such that $\mathrm R^-(x) / x \to \rho^-$ as $x \to \infty$.
We now state a result which is a direct corollary of \cite[Proposition~2.8]{pain2018}.
Let $(\gamma_n)_{n\in \ensemblenombre{N}}$ be a sequence of positive numbers such that $\gamma_n = o(\sqrt{n})$ as $n\to \infty$.
Then, for all $\lambda \in (0,1)$,
\begin{align} \label{eq:estimate_RW_double_barrier}
\Pp{\max_{k \leq \lfloor \lambda n \rfloor} \widehat{S}_k \leq K,\
\max_{\lfloor\lambda n\rfloor \leq i \leq n} \widehat{S}_i \leq L,\
\widehat{S}_n = L - a}
= \sqrt{\frac{2}{\pi}}
\frac{\mathrm R(K) \mathrm R^-(a)}{n^{3/2} \rho \rho^-}
(1 + \petito{1}),
\end{align}
as $n \to \infty$, uniformly in $K \in [0,\gamma_n]$, $L \in [-\gamma_n, \gamma_n]$ and $a \in [0, \gamma_n] \cap (L + \ensemblenombre{Z})$.
Moreover, Lemma~2.4 of A\"idékon and Shi \cite{aidekonshi2014} shows the following upper bound: for $\lambda \in (0,1)$,
there exists $C >0$ depending on $\lambda$ such that for all $a \geq 0$, $K \geq 0$, $L \in\ensemblenombre{R}$ and $n \geq 0$, we have
\begin{align} \label{eq:upper_bound_RW_double_barrier}
\Pp{\max_{k \leq \lfloor \lambda n \rfloor} \widehat{S}_k \leq K,\
\max_{\lfloor\lambda n\rfloor \leq i \leq n} \widehat{S}_i \leq L,\
\widehat{S}_n = L - a}
\leq
\frac{C(K+1)(a+1)}{n^{3/2}+1}.
\end{align}
\subsection{Estimates on random walk \texorpdfstring{$S$}{S}}
\begin{lemma} \label{lem:Bernoulli_rv}
Let $Y$ be a sum of independent Bernoulli random variables.
Then for any integer $b \geq 0$,
\[
\Ec{ \ind{Y-b \geq 1} (Y-b)}
\leq \Pp{Y-b \geq 1} \Ec{Y+1}
\]
\end{lemma}
\begin{proof} By assumption, $Y$ is of the form $\sum_{i=1}^n B_i$, where the $B_i$'s are independent Bernoulli r.v. Then let $T \coloneqq \inf \{ k \geq 0 : \sum_{i=1}^k B_i = b+1 \}$, where $\inf \emptyset = \infty$.
\begin{align*}
\Ec{ \ind{Y-b \geq 1} (Y-b)}
& = \Ec{ \ind{T \leq n} (Y-b)}
= \sum_{k=1}^n \Ec{ \ind{T = k} \left( 1 + \sum_{i=k+1}^n B_i \right)} \\
& = \sum_{k=1}^n \Pp{T = k} \Ec{1 + \sum_{i=k+1}^n B_i}
\leq \Pp{T \leq n} \Ec{1 + Y},
\end{align*}
and it proves the result.
\end{proof}
\begin{lemma} \label{lem:expectation_beginning_RW}
For any $\varepsilon > 0$, there exists $K_0 > 0$ that does not depend on $(\mathbf r,\mathbf j)$ such that, for $K \geq K_0$, for any $m \geq 0$, we have
\[
(1-\varepsilon) \rho (K-\Delta_m)
\leq \Ec{ \ind{\max_{j \leq m} S_j \leq K} \mathrm R(K-S_m)}
\leq (1+\varepsilon) \rho \left( K+2\Delta_m\right).
\]
\end{lemma}
\begin{proof}
Let $\varepsilon > 0$ be fixed.
For $K$ large enough, by \eqref{eq:equivalent_function_R}, we have for any $x \geq \sqrt{K}$,
\[
(1-\varepsilon) \rho x
\leq \mathrm R(x)
\leq (1+\varepsilon) \rho x.
\]
Then, distinguishing between the case $S_m > K-\sqrt{K}$ and $S_m \leq K-\sqrt{K}$, we get
\begin{align*}
\Ec{ \ind{\max_{j \leq m} S_j \leq K} \mathrm R(K-S_m)}
& \leq \mathrm R(\sqrt{K})
+ (1+\varepsilon) \rho \Ec{ \ind{\max_{j \leq m} S_j \leq K} (K-S_m) \ind{S_m \leq K-\sqrt{K}}} \\
& \leq \varepsilon K
+ (1+\varepsilon) \rho \Ec{ \ind{\max_{j \leq m} S_j \leq K}
(K-S_m)},
\end{align*}
for $K$ large enough using \eqref{eq:equivalent_function_R} again.
Proceeding similarly, we have
\begin{align*}
\Ec{ \ind{\max_{j \leq m} S_j \leq K} \mathrm R(K-S_m)}
&\geq \Ec{ \ind{\max_{j \leq m} S_j \leq K} \mathrm R(K-S_m) \ind{S_m\leq K-\sqrt{K}}}\\
&\geq (1-\epsilon) \rho \Ec{\ind{\max_{j \leq m} S_j \leq K} (K-S_m)\ind{S_m\leq K-\sqrt{K}}}\\
& \geq -\varepsilon K
+ (1-\varepsilon) \rho \Ec{ \ind{\max_{j \leq m} S_j \leq K} (K-S_m)}.
\end{align*}
Hence, it is now sufficient to prove the following bounds
\begin{align} \label{eq:encadrement_but}
K-\Delta_m \leq \Ec{ \ind{\max_{j \leq m} S_j \leq K} (K-S_m)}
\leq K + 2 + 2\Delta_m.
\end{align}
For this, we write
\begin{align*}
\Ec{ \ind{\max_{j \leq m} S_j \leq K} (K-S_m)}
&= - \mathbb{E}_{-K} \left[ \ind{\max_{j \leq m} S_j \leq 0} S_m \right]
= - \mathbb{E}_{-K} \left[ S_{\tau \wedge m} \right]
+ \mathbb{E}_{-K} \left[ \ind{\tau \leq m} S_{\tau} \right],
\end{align*}
where $\tau \coloneqq \inf \{ k \geq 0 : S_k > 0 \}$.
Recall that, for any $k \leq m$, $\abs{\mathbb{E}[S_k]} \leq \Delta_m$.
Hence, applying the optimal stopping theorem to the martingale $(S_k - \mathbb{E}[S_k])$ under $\P_{-K}$, we get that $-K-\Delta_m \leq \mathbb{E}_{-K} [S_{\tau \wedge m}] \leq -K+\Delta_m$.
Thus, \eqref{eq:encadrement_but} follows from the bounds
\begin{align} \label{eq:encadrement_but_2}
0 \leq \mathbb{E}_{-K} \left[ \ind{\tau \leq m} S_\tau \right] \leq 2 + \Delta_m.
\end{align}
The lower bound in \eqref{eq:encadrement_but_2} holds because $S_\tau \geq 0$.
For the upper bound, we distinguish according to the value of $\tau$:
\begin{align*}
\mathbb{E}_{-K} \left[ \ind{\tau \leq m} S_\tau \right]
& = \sum_{k=1}^m \mathbb{E}_{-K} \left[ \ind{S_1,\dots,S_{k-1} \leq 0} \ind{S_k \geq 1} S_k \right] \\
& = \sum_{k=1}^m \mathbb{E}_{-K} \left[ \ind{S_1,\dots,S_{k-1} \leq 0}
\Ecsq{ \ind{Y_k-1+S_{k-1} \geq 1} (Y_k-1+S_{k-1}) }{S_{k-1}}
\right] \\
& \leq \sum_{k=1}^m \mathbb{E}_{-K} \left[ \ind{S_1,\dots,S_{k-1} \leq 0}
\Ppsq{Y_k-1+S_{k-1} \geq 1}{S_{k-1}} \right]
(\Ec{Y_k}+1),
\end{align*}
applying Lemma~\ref{lem:Bernoulli_rv}. Writing $\Ec{Y_k} + 1 = 2 + \Ec{Y_k-1}$, we finally get
\begin{align*}
\mathbb{E}_{-K} \left[ \ind{\tau \leq m} S_\tau \right]
& \leq 2 \sum_{k=1}^m \P_{-K} \left( \tau=k \right)
+ \sum_{k=1}^m \Ec{Y_k-1}
\leq 2 + \Delta_m.
\end{align*}
This proves the upper bound in \eqref{eq:encadrement_but_2} and hence conclude the proof of the lemma.
\end{proof}
\begin{lemma} \label{lem:estimate_RW_double_barrier}
For any $\varepsilon > 0$ and $\lambda \in (0,1)$, there exist $K_0 > 0$ and $n_0 \geq 1$ that do not depend on $(\mathbf r,\mathbf j)$ such that, for any $n \geq n_0$, any $K \in \llbracket K_0, n^{1/4} \rrbracket$, any $L \in \llbracket -n^{1/4}, n^{1/4} \rrbracket$, and any $a \in \llbracket 0, n^{1/4} \rrbracket$, we have
\begin{align*}
(1-\varepsilon) \sqrt{\frac{2}{\pi}}
\left( K-\Delta_{\lfloor n^{1/4} \rfloor} \right)
\frac{\mathrm R^-(a)}{\rho^- n^{3/2}}
- \eta_n
& \leq \Pp{S_n = L-a,
\max_{k < \lambda n} S_k \leq K,
\max_{\lambda n \leq k \leq n} S_k \leq L} \\
& \leq (1+\varepsilon) \sqrt{\frac{2}{\pi}}
\left( K+2\Delta_{\lfloor n^{1/4} \rfloor} \right)
\frac{\mathrm R^-(a)}{\rho^- n^{3/2}}
+ \eta_n.
\end{align*}
\end{lemma}
\begin{proof}
We set $m \coloneqq \lfloor n^{1/4} \rfloor$.
We apply Markov's property at time $m$ and get
\begin{align} \label{eq:markov_at_m}
\Pp{S_n = L-a,\
\max_{k < \lambda n} S_k \leq K,\
\max_{\lambda n \leq k \leq n} S_k \leq L}
& = \Ec{\ind{\max_{j \leq m} S_j \leq K} \psi(S_m) },
\end{align}
where we set
\[
\psi(x) \coloneqq \P \Big( S_n - S_m = L-a-x,\
\max_{k\in < \lambda n-m} S_{m+k} - S_m \leq K-x,
\max_{\lambda n-m \leq k \leq n-m} S_{m+k} - S_m \leq L-x\Big).
\]
Applying Lemma~\ref{lem:comparison_S_Stilde}, we have
\[
\Pp{\exists k \in \llbracket 0,n-m \rrbracket : \widehat{S}_k \neq S_{m+k} - S_m}
\leq 2 \left( \sum_{j = j_m+1}^{j_n} r_j^2 \right) + 2 \left( \sum_{k=m}^n \delta_k \right)
= \eta_n.
\]
Hence, for any $x \geq 0$, we have $\widehat{\psi}(x) - \eta_n \leq \psi(x) \leq \widehat{\psi}(x) + \eta_n$, where we set
\begin{align*}
\widehat{\psi}(x)
& \coloneqq \Pp{ \widehat{S}_{n-m} = L-a-x,\
\max_{k < \lambda n-m} \widehat{S}_k \leq K-x,\
\max_{\lambda n-m \leq k \leq n-m]} \widehat{S}_k \leq L-x}.
\end{align*}
Applying \eqref{eq:estimate_RW_double_barrier}, there exists $n_0 \geq 1$, such that for any $n \geq n_0$, any $a,K \in \llbracket 0, n^{1/4} \rrbracket$, any $L \in \llbracket -n^{1/4}, n^{1/4} \rrbracket$ and any $x \in \llbracket -n^{1/4}, K \rrbracket$,
\begin{align*}
(1-\varepsilon) \sqrt{\frac{2}{\pi}} \frac{1}{\rho \rho^-}
\frac{\mathrm R(K-x) \mathrm R^-(a)}{n^{3/2}}
\leq \widehat{\psi}(x)
\leq (1+\varepsilon) \sqrt{\frac{2}{\pi}} \frac{1}{\rho \rho^-}
\frac{\mathrm R(K-x) \mathrm R^-(a)}{n^{3/2}}.
\end{align*}
Coming back to \eqref{eq:markov_at_m}, we can apply the above with $x = S_m$, because we are on the event $\{ S_m \leq K \}$ and the inequality $S_m \geq -m$ always holds by definition.
Hence, we get the upper bound
\begin{align*}
\Ec{\ind{\max_{j \leq m} S_j \leq K} \psi(S_m) }
\leq (1+\varepsilon) \sqrt{\frac{2}{\pi}} \frac{1}{\rho \rho^-}
\frac{\mathrm R^-(a)}{n^{3/2}}
\Ec{\ind{\max_{j \leq m} S_j \leq K} \mathrm R(K-S_m) }
+ \eta_n
\end{align*}
and a similar lower bound holds with $-\varepsilon$ and $-\eta_n$ instead of $\varepsilon$ and $\eta_n$. Applying Lemma~\ref{lem:expectation_beginning_RW} (which determines the choice of $K_0$), it concludes the proof.
\end{proof}
\begin{lemma} \label{lem:upper_bound_RW_double_barrier}
For any $\lambda \in (0,1)$, there exists $C > 0$ that does not depend on $(\mathbf r,\mathbf j)$ such that, for any $n \geq 0$, any $K,a \geq 0$ and any $L \in \ensemblenombre{R}$, we have
\[
\Pp{S_n = L-a,
\max_{k < \lambda n} S_k \leq K,
\max_{\lambda n \leq k \leq n} S_k \leq L}
\leq C \left( K+\Delta_{\lfloor n^{1/4} \rfloor} +1 \right) \frac{a+1}{n^{3/2}+1}
+ \eta_n.
\]
The constant $C$ can be chosen uniformly for $\lambda$ in a compact subset of $(0,1)$.
\end{lemma}
\begin{proof} This lemma is proved similarly as Lemma~\ref{lem:estimate_RW_double_barrier}, using \eqref{eq:upper_bound_RW_double_barrier} instead of \eqref{eq:estimate_RW_double_barrier} and the upper bound in \eqref{eq:encadrement_but} instead of Lemma~\ref{lem:expectation_beginning_RW}.
The fact that the constant $C$ can be chosen uniformly for $\lambda$ in a compact subset of $(0,1)$ follows from the observation that the considered probability is nondecreasing in $\lambda$ if $L \leq K$, and nonincreasing in $\lambda$ otherwise.
\end{proof}
\begin{lemma} \label{lem:exponential_RW_double_barrier}
For any $\lambda \in (0,1)$ and $z > 0$, there exists $C > 0$ that does not depend on $(\mathbf r,\mathbf j)$ such that, for any integers $n,K \geq 0$ and $L \in \ensemblenombre{Z}$, we have
\begin{align*}
\Ec{ \ind{\max_{k < \lambda n} S_k \leq K,\
\max_{\lambda n \leq k \leq n} S_k \leq L}
e^{z S_n} (L-S_n+1)^2 }
& \leq C e^{z L} \left(
\frac{K + \Delta_{\lfloor n^{1/4} \rfloor} +1}{n^{3/2}+1}
+ \eta_n \right).
\end{align*}
The constant $C$ can be chosen uniformly for $\lambda$ in a compact subset of $(0,1)$.
\end{lemma}
\begin{proof}
We distinguish according to the value of $S_n$:
\begin{align*}
& \Ec{ \ind{\max_{k\in[0,\lambda n)} S_k \leq K,
\max_{k\in[\lambda n,n]} S_k \leq L}
e^{z S_n} (L-S_n+1)^2} \\
& = \sum_{a = 0}^\infty (a+1)^2 e^{z (L-a)}
\Pp{\max_{k < \lambda n} S_k \leq K,
\max_{\lambda n \leq k \leq n} S_k \leq L,
S_n = L-a} \\
& \leq \sum_{a = 0}^\infty (a+1)^2 e^{z (L-a)}
\left( C \frac{(K+ \Delta_{\lfloor n^{1/4} \rfloor}+1)(a+1)}{n^{3/2}+1} + \eta_n \right),
\end{align*}
applying Lemma~\ref{lem:upper_bound_RW_double_barrier}.
The result follows.
\end{proof}
\section{Concerning assumptions for preferential attachment trees}
\label{section:PAT}
\begin{proof}[Proof of Lemma~\ref{lem:remainder sum p_i square for PAT}]
Recall the formulas for the $q$-th moment of a Beta distribution: if $\beta\sim \mathrm{Beta}(a,b)$ then
\begin{align*}
\Ec{\beta^q}=\prod_{k=0}^{q-1}\frac{a+k}{a+b+k}.
\end{align*}
Recall also that if $\beta\sim\mathrm{Beta}(a,b)$, then $(1-\beta)\sim \mathrm{Beta}(b,a)$.
For this proof, we write $Z_i \coloneqq (\frac{\mathsf{w}^\mathbf{a}_i}{\mathsf{W}^\mathbf{a}_i})^2$ for every $i\geq 2$.
Using the definition of the sequence $(\mathsf{w}^\mathbf{a}_n)_{n\geq 1}$, we can write for any $i\geq 1$,
\begin{align*}
Z_i=\left(\frac{\mathsf{w}^\mathbf{a}_{i}}{\mathsf{W}^\mathbf{a}_{i}}\right)^2= \left(\frac{\mathsf{W}^\mathbf{a}_{i}-\mathsf{W}^\mathbf{a}_{i-1}}{\mathsf{W}^\mathbf{a}_{i}}\right)^2=(1-\beta_{i-1})^2,
\end{align*}
so that the sequence $\left(Z_i\right)_{i\geq 2}$ is a sequence of independent random variables.
Note that since $(1-\beta_{i-1})\sim \mathrm{Beta}(a_{i},A_{i-1}+i-1)$, we have
\begin{align*}
\Ec{Z_i}
=\frac{a_{i}\cdot (a_{i}+1)}{(A_{i}+i-1)(A_{i}+i)}
\leq C\cdot \frac{a_i (a_{i}+1)}{i^2}.
\end{align*}
This entails using Assumption \eqref{eq:assumption_2 fitness sequence} that
\begin{align*}
\sum_{i=n}^{\infty} \Ec{Z_i}=\grandO{n^{-1}}.
\end{align*}
%
Then, for any $n\geq 0$, let $M_n \coloneqq \sum_{i=2}^n (Z_i-\Ec{Z_i})$, which is a martingale in its own filtration. We now prove that this martingale almost surely converges to a limit $M_\infty=\sum_{i=2}^\infty (Z_i-\Ec{Z_i})$ and that we almost surely have $\abs{M_n-M_\infty}=\grandO{n^{-1}}$.
Together with the above, this implies that almost surely
\begin{align*}
\sum_{i=n}^{\infty} Z_i = \sum_{i=n}^{\infty} \Ec{Z_i}+(M_\infty-M_{n-1})= \grandO{n^{-1}},
\end{align*}
which is what we want to prove.
%
For this, we use \cite[Lemma~A.3]{senizergues2021} with $q=2$ and $\alpha=-1$, for which we just need to verify that
\begin{align*}
\Ec{(M_{2n}-M_n)^2}\leq \grandO{n^{-2 - \delta}},
\end{align*}
for some $\delta>0$.
We have
\begin{align*}
\Ec{(M_{2n}-M_n)^2}=\sum_{i=n+1}^{2n}\Var(Z_i)
\end{align*}
and
\begin{align*}
\Var(Z_i)&=\Ec{(1-\beta_{i-1})^4}-\Ec{(1-\beta_{i-1})^2}^2\\
&=\frac{2 a_i (a_i + 1) (A_{i-1}+i-1) (2 a_i (A_i+i + 2) + 3 (A_i +i))}{(A_i+i-1)^2 (A_i+i)^2 (A_i+i+1) (A_i +i+ 2)}\\
&\leq C\frac{(a_i+2)^3}{i^4}.
\end{align*}
Hence,
\begin{align*}
\Ec{(M_{2n}-M_n)^2}\leq \sum_{i=n+1}^{2n}C\frac{(a_i+2)^3}{i^4} &\leq \frac{C}{n^4} \cdot \left(2+\max_{n+1\leq i \leq 2n}a_i\right)\cdot \sum_{i=n+1}^{2n} (a_i+2)^2\\
&= C \cdot n^{-4}\cdot n^{1-\delta} \cdot C\cdot n=\grandO{n^{-2-\delta}},
\end{align*}
using \eqref{eq:assumption_1 fitness sequence} and \eqref{eq:assumption_2 fitness sequence}.
This concludes the proof.
\end{proof}
\end{appendix}
\section*{Acknowledgements}
The authors would like to thank the anonymous referees for their careful reading, which helped improving the paper.
\addcontentsline{toc}{section}{References}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 2,884 |
\section{Introduction}
In recent years the interest in correlated quantum many-body systems has increased steadily due to the observation of correlation effects such as liquid and crystal formation, superfluidity of Bose systems or bound states. Examples of systems include nuclear matter \cite{danielewicz84,garny09}, solid state systems \cite{haug96} and dense astrophysical, laboratory dusty plasmas or the quark gluon plasma, for a recent overview see \cite{bonitz12,kremp05}. A quantity sensitive to spatial correlations is the pair distribution function (PDF) $h(r)$---the probability to find an arbitrary pair of particles at a distance $r$.
Of particular current interest is the short-time behavior of correlated systems following external perturbation such as excitation by intense radiation, e.g., \cite{krausz09,krasovskii07}. In quantum systems such as atoms or solids this is often connected with rapid electron thermalization coupled to the dynamics of electronic correlations. Time and space-resolved measurement techniques detecting chemical reaction products, nuclear collision fragments or electrons and ions produced by laser ionization, e.g., \cite{becker08}, are becoming increasingly powerful. This brings the direct measurement of time-dependent pair correlations described by the nonequilibrium generalization of the PDF, $h(r,t)$, within reach and increases the need for theoretical and computational tools that are able to predict $h(r,t)$.
From the theory side PDFs are routinely computed for nonideal classical systems using, e.g., Monte Carlo or molecular dynamics simulations, e.g., \cite{bonitz12}. Extensions to quantum systems in equilibrium are available, e.g., in the frame of quantum Monte Carlo methods. However, there is still a high demand for accurate nonequilibrium simulations. Theoretical access to nonequilibrium PDFs is straightforwardly reached within density operator theory, e.g., \cite{bonitz96,kremp97,bonitz98}.
An alternative approach to quantum many-body systems out of equilibrium is based on nonequilibrium Green's functions (NEGF). Apart from exact time-dependent numerical calculations, e.g., \cite{bauch08}, which are limited to a few particles, numerical results for the two-time NEGF are expected to be the most accurate ones for strongly correlated quantum systems in nonequilibrium. This concerns, in particular, full two-time calculations, i.e. direct solutions of the Keldysh/Kadanoff-Baym equations (KBE) which, after the pioneering work of Danielewicz \cite{danielewicz84}, has now become routine \cite{garny09,bonitz96j,bonitz97,kwong00,dahlen07,stan09,vonfriesen09}. They yield the single-particle Green's functions and all one-particle observables, including spectral function, as a function of time. A number of two-particle quantities can also be computed, taking advantage of the two-time structure of the equations, most importantly the interaction energy. However, in this approach the two-particle Green's function is eliminated by introduction of the selfenergy $\Sigma$ (the integration contour $\mathcal{C}$ and the arguments of the functions will be explained in \refsec{sec:bse}),
\begin{equation}
\label{eq:Selfenergy}
\pm \i\int_\mathcal{C}\mathrm{d}2\,V(1-2)G(12,1'2^+)=\int_\mathcal{C}\mathrm{d}2\,\Sigma(1,2)G(2,1')\,.
\end{equation}
This concept of the selfenergy has proven extremely successful for reducing the many-particle problem to an effective single-particle one (quasiparticle picture) which forms the basis of Green's function theory and the Feynman diagram technique. At the same time, the direct access to the pair distribution function---which contains important additional information beyond the one carried by the single-particle Green's function---is lost. Due to this reason, so far, no NEGF results for the full pair distribution function have been obtained which go beyond the computation of double occupancies, accessible from \refeqn{eq:Selfenergy} \cite{vonfriesen11}.
In this paper we solve this problem. Starting from the Bethe-Salpeter equation for the two-particle Green's function, we demonstrate in \refsec{sec:bse} how, from a given time-dependent solution for the single-particle Green's function in a chosen approximation for the selfenergy $\Sigma$, the PDF in the same approximation can be reconstructed. In this paper, we choose, as an example, the second order Born selfenergy approximation $\Sigma^\tn{2B}$ which includes the interaction up to second order ($\Sigma^\tn{2B}\propto V^2$). Our results include the standard PDF $h(r)$ in equilibrium, and its extension $h({\bf r}_1,{\bf r}_2)$ to inhomogeneous systems and to multicomponent systems where the PDF becomes a matrix $h^\tn{ab}({\bf r}_1,{\bf r}_2)$, $a,b$ labeling the particle species. Further, we obtain results for an arbitrary nonequilibrium system where the PDF becomes time-dependent, $h^\tn{ab} \rightarrow h^\tn{ab}(t)$. Finally, the results are directly generalized to two-time
PDF's, $h^\tn{ab}({\bf r}_1,{\bf r}_2) \rightarrow h^\tn{ab}({\bf r}_1,{\bf r}_2,t)$. Our results selfconsistently include the influence of a correlated initial state, and they describe the decay of initial correlations which is particularly important at the initial stage of the relaxation. This
problem was studied in detail for the single-time PDF within density operator theory \cite{bonitz96,kremp97,bonitz98,bonitz96p}, and these results are contained in our theory as a special case.
In \refsec{sec:bilayer} we discuss, as an illustration, the possible application of the PDF reconstruction algorithm to a two-component system of electrons and holes in a bilayer structure. This system has attracted substantial interest in recent years because it exhibits strong electron-electron and hole-hole correlations leading to spatial ordering and, at the same time, electron-hole bound states (excitons). There have been detailed investigations of the phase diagram \cite{depalo02,filinov03,hartmann05,schleede12}, of exciton and hole crystallization \cite{filinov03,filinov09, ludwig07}, of collective excitations \cite{ludwig08,kalman07} and of exciton Bose condensation and superfluidity, e.g., \cite{filinov09,boening11}. We conclude with a summary and discussion in \refsec{sec:discussion}.
\section{Bethe-Salpeter equation}\label{sec:bse}
In nonequilibrium Green's functions theory, the PDF of particle species ``a'' and ``b'' is obtained from the two-particle correlation function \cite{kremp05}
taken at four equal times $t_1=t_2=t'_1=t'_2=t$,
\begin{eqnarray}\label{eq:hab}
h^{\tn{ab}}({\bf r}_1,{\bf r}_2,{\bf r}_1,{\bf r}'_2,t) &=&
\i^2 g^{\tn{ab},<}(1,2,1',2')
\\
&=&
\langle \Psi_\tn{a}^{\dagger}(1')\Psi_\tn{b}^{\dagger}(2')\Psi_\tn{b}(2)\Psi_\tn{a}(1)\rangle\,,
\nonumber
\end{eqnarray}
where $\Psi_\tn{a}^{\dagger}$ and $\Psi_\tn{a}$ are fermionic or bosonic creation and annihiliation operators, and
we introduced the short-hand notation $1={\bf r}_1, s_{z1}, t_1$. To determine the two-particle correlation function $g^{\tn{ab},<}$ in nonequilibrium we start from the more general two-particle Green's function $g^{\tn{ab}}$ on the Schwinger-Keldysh contour ${\cal C}$ which consists of a Hartree-Fock and a correlation part
\begin{eqnarray}
\label{eq:g_ab}
g^{\tn{ab}}(12,1'2')&=&g_\tn{HF}^{\tn{ab}}(12,1'2')+g_\tn{corr}^{\tn{ab}}(12,1'2')\,, \\
g_\tn{HF}^{\tn{ab}}(12,1'2')&=& g^\tn{a}(1,1') g^\tn{b}(2,2') \pm \delta_{\tn{ab}} g^\tn{a}(1,2') g^\tn{b}(2,1')\,,
\end{eqnarray}
where we allow for four different time arguments, $t_1,t_2,t_1',t_2'$, all located on the contour $\mathcal{C}$. The correlation part, $g_\tn{corr}^{\tn{ab}}$, obeys the Bethe-Salpeter equation, e.g., \cite{bornath99},
\begin{equation}
\label{eq:bse}
g_\tn{corr}^{\tn{ab}}(12,1'2') = \i \int_{\cal C} \d {\bar 1}\d {\bar 2}\d {\tilde 1}\d {\tilde 2} \,
g^\tn{a}(1,{\bar 1}) g^\tn{b}(2,{\bar 2})
K^\tn{ab}({\bar 1} {\bar 2}, {\tilde 1}{\tilde 2})\,g^\tn{ab}({\tilde 1}{\tilde 2},1'2')\,,
\end{equation}
which presents a formal closure of the second equation of the Martin-Schwinger hierarchy for the two-particle Green's function. Compared to Ref.~\cite{bornath99} we also restored the exchange term where plus (minus) refers to bosons (fermions). In \refeqn{eq:bse} the function $K^\tn{ab}$ is a general dynamic interaction (for details see Ref.~\cite{kremp05}), which will be simplified in the following.
1.) The first simplification is to introduce the screened ladder approximation, $K^\tn{ab}({\bar 1} {\bar 2}, {\tilde 1}{\tilde 2}) \rightarrow
V^\tn{ab}({\bar 1} {\bar 2}) \delta({\bar 1}-{\tilde 1})\delta({\bar 2}-{\tilde 2})$. Suppressing for a moment the space integration and spin summation (they are implied by the repeated arguments ${\bar 1}$ and ${\bar 2}$ under the integral),
we obtain from \refeqn{eq:bse}
\begin{eqnarray}
g_\tn{corr}^\tn{ab}(1 2,1' 2') = \i \int_{\cal C} \d {\bar t}_1 \d {\bar t}_2 \,
g^\tn{a}(1,{\bar 1}) g^\tn{b}(2,{\bar 2})
V^\tn{ab}({\bar 1} {\bar 2})\,g^\tn{ab}({\bar 1} {\bar 2},1'2')\,.
\quad
\label{eq:bse_vs}
\end{eqnarray}
We mention that general nonequilibrium initial correlations can be included by the proper definition of the contour $\mathcal{C}$ or accounted for via additional contributions to the single particle selfenergy, e.g., \cite{bonitz97,semkat99,semkat00,semkat03}. Equation (\ref{eq:bse_vs}) contains strong coupling and dynamical screening effects leading to a complicated integro-differential equation.
2.) Our next simplification is to neglect dynamic effects in the potential (dynamical screening, related to the GW approximation) which leads to the replacement $V^\tn{ab}({\bar 1} {\bar 2}) \rightarrow V^\tn{ab}({\bar r}_{12})\delta({\bar t}_1-{\bar t}_2)$, where ${\bar r}_{12} = |{\bf r}_1-{\bf r}_2|$,
\begin{eqnarray}
g_\tn{corr}^\tn{ab}(1 2,1' 2') = \i \int_{\cal C} \d {\bar t} \,
g^\tn{a}(1,{\bar 1}) g^\tn{b}(2,{\bar 2})
V^\tn{ab}({\bar r}_{12})\,g^\tn{ab}({\bar 1} {\bar 2},1'2')\,,
\quad
\label{eq:bse_static}
\end{eqnarray}
and under the integral ${\bar t}_1={\bar t}_2={\bar t}$. This equation corresponds to a static T-matrix approximation for the two-particle Green's function and the pair correlations, i.e. to a complete summation of the Born series.
3.) Since our goal is to reconstruct the pair distributions from a solution of the two-time KBE for the single-particle Green's functions in second order Born approximation, we limit ourselves to the first iteration of the integral equation (\ref{eq:bse_static}), i.e. we replace, under the integral, the two-particle Green's function by the Hartree-Fock approximation:
\begin{equation}
g^\tn{ab}(1 2,1' 2') = \i \int_{\cal C} \d {\bar t} \,
g^\tn{a}(1,{\bar 1}) g^\tn{b}(2,{\bar 2})
V^\tn{ab}({\bar r}_{12})g_\tn{HF}^\tn{ab}(1 2,1' 2')\,,\quad \mbox {with}\quad {\bar t}_1={\bar t}_2={\bar t}\,.
\label{eq:bse_static_born}
\end{equation}
We can bring this equation to a more compact form by introducing the following
new functions
\begin{eqnarray}
\label{eq:G0ab}
G^\tn{ab}_0(1 2,1' 2') & = & g^\tn{a}(1,1') g^\tn{b}(2,2'),
\\[2ex]
\Sigma^\tn{ab}_0(1 2,1' 2') & = & V^\tn{ab}(r_{12})\left\{
G^\tn{ab}_0(1 2,1' 2') \pm \delta_\tn{ab} G^\tn{ab}_0(1 2,2' 1')
\right\}\,,
\label{eq:Sigma0ab}
\end{eqnarray}
where $G^\tn{ab}_0$ is the Hartree approximation for the two-particle Green's function ($g_\tn{HF}^\tn{ab}$ without exchange terms) and $\Sigma^\tn{ab}_0$ the first-order two-particle selfenergy. With these definitions \refeqn{eq:bse_static_born} becomes
\begin{equation}
g^{ab}_\tn{corr}(1 2,1' 2') = \i \int_{\cal C} \d {\bar t} \,
G^\tn{ab}_0(1 2,{\bar 1} {\bar 2})\Sigma^\tn{ab}_0({\bar 1} {\bar 2},1' 2')\,,\quad\mbox {with}\quad {\bar t}_1={\bar t}_2={\bar t}\,.
\label{eq:bse_static_born_short}
\end{equation}
We underline that all expressions, so far, are written on the Schwinger-Keldysh contour, i.e.
all single-particle Green's functions are $3\times 3$ matrices whereas the two-particle functions contain $3^4$ Keldysh matrix elements.
To obtain the nonequilibrium pair correlation function we now have to extract from \refeqn{eq:bse_static_born_short} functions depending on the real physical time. In particular, according to \refeqn{eq:hab}, we need only the two-particle correlation function $g^\tn{ab,<}$ which we consider in the following.
\section{Reduction of the time structure of the two-particle correlation function $g^\tn{ab,<}$}
In order to compute the pair distribution function, \refeqn{eq:hab}, the two-particle correlation function $g^\tn{ab,<}$ at four equal times is needed. To this end, we first determine the equation of motion for the two-time two-particle correlation function $g^\tn{ab,<}(t,t')$ and then specialize to the one-time two-particle correlation function $g^\tn{ab,<}(t)$.
\subsection{Two-time two-particle correlation function $g^\tn{ab,<}(t,t')$}
The problem of the large number of Keldysh matrix elements of $g^\tn{ab}$ can be simplified drastically in the static Born approximation. As a first step in simplifying the time dependencies we specialize to functions with pairwise equal time arguments, $t_1=t_2=t$, and $t'_1=t'_2=t'$. Then it is clear from \refeqn{eq:bse_static_born_short} that the functions $G_0^\tn{ab}$ and $\Sigma_0^\tn{ab}$ depend only on two times in the following way
\begin{eqnarray}
G^\tn{ab}_0({\bf r}_1{\bf r}_2;{\bf r}'_1{\bf r}'_2;tt') & = &
g^\tn{a}({\bf r}_1t;{\bf r}'_1t') g^\tn{b}({\bf r}_2t;{\bf r}'_2t')\,,
\\[2ex]
\Sigma^\tn{ab}_0({\bf r}_1{\bf r}_2;{\bf r}'_1{\bf r}'_2;tt') & = & V^\tn{ab}(r_{12})
\big\{G^\tn{ab}_0({\bf r}_1{\bf r}_2;{\bf r}'_1{\bf r}'_2;tt')
\pm \delta_\tn{ab} G^\tn{ab}_0({\bf r}_1{\bf r}_2;{\bf r}'_2{\bf r}'_1;tt')
\big\}\,,
\end{eqnarray}
where we also restored the coordinate arguments (spin variables are not written explicitly). Then \refeqn{eq:bse_static_born_short} turns into
\begin{eqnarray}
g^\tn{ab}_\tn{corr}({\bf r}_1{\bf r}_2;{\bf r}'_1{\bf r}'_2;tt') =
\i \int_{\cal C} \d {\bar t} \,
G^\tn{ab}_0({\bf r}_1{\bf r}_2;{\bar {\bf r}}_1 {\bar {\bf r}}_2,t{\bar t})
\Sigma^\tn{ab}_0({\bar {\bf r}}_1 {\bar {\bf r}}_2;{\bf r}'_1{\bf r}'_2;{\bar t} t')\,.
\label{eq:bse_static_born_short_1t}
\end{eqnarray}
With this result, \refeqn{eq:g_ab} for $g^\tn{ab}$ can be rewritten as
\begin{equation}
\label{eq:gabtt'}
g^{\tn{ab}}({\bf r}_1{\bf r}_2;{\bf r}'_1{\bf r}'_2;tt')=g_\tn{HF}^{\tn{ab}}({\bf r}_1{\bf r}_2;{\bf r}'_1{\bf r}'_2;tt')+g_\tn{corr}^{\tn{ab}}({\bf r}_1{\bf r}_2;{\bf r}'_1{\bf r}'_2;tt')\,,
\end{equation}
where $g^\tn{ab}_\tn{corr}$ is completed by the Hartree-Fock contribution which, in the new notation, acquires the form
\begin{eqnarray}
g^\tn{ab}_\tn{HF}({\bf r}_1{\bf r}_2;{\bf r}'_1{\bf r}'_2;tt')=G^\tn{ab}_0({\bf r}_1{\bf r}_2;{\bf r}'_1{\bf r}'_2;tt') \pm \delta_\tn{ab} G^\tn{ab}_0({\bf r}_1{\bf r}_2;{\bf r}'_2{\bf r}'_1;tt')\,.
\label{eq:gabHF}
\end{eqnarray}
According to \refeqn{eq:hab}, $g^{\tn{ab}}(tt')$ reads in terms of creation and annihilation operators (suppressing spatial arguments),
\begin{equation}
g^{\tn{ab}}(tt')=\i^2\langle \Psi_\tn{a}^{\dagger}(t')\Psi_\tn{b}^{\dagger}(t')\Psi_\tn{b}(t)\Psi_\tn{a}(t)\rangle\,.
\end{equation}
It is important to notice that this structure is different from a generalized density-density correlation function
\begin{equation}
c_\tn{n-n}^\tn{ab}(tt')=\i^2\langle n_\tn{b}(t')n_\tn{a}^{\dagger}(t)\rangle=\i^2\langle \Psi_\tn{b}^{\dagger}(t')\Psi_\tn{b}(t')\Psi_\tn{a}^\dagger(t)\Psi_\tn{a}(t)\rangle\neq g^{\tn{ab}}(tt')\,,
\end{equation}
since the order of the operators, in general, cannot be interchanged.
Now, to compute the pair distribution function from \refeqn{eq:gabtt'}, we have to extract $g^{\tn{ab},<}$ from the Keldysh matrix and, in particular, the ``$<$'' component from the contour integral in \refeqn{eq:bse_static_born_short_1t} . The solution of this problem is well known for one-particle functions, and for two-particle functions it has been solved in Ref.~\cite{bornath99}. However, the latter results are not needed here. Indeed, although we are dealing with two-particle functions $G_0^\tn{ab}$ and $\Sigma_0^\tn{ab}$, in the present approximation, they have the same time-dependence (they depend just on $t,t'$) as occurs in the case of single-particle functions in the integral term of the Keldysh
Kadanoff-Baym equations. As a consequence, both these functions are $3\times 3$ Keldysh matrices and, therefore, also
the two-particle Green's function $g^\tn{ab}$, \refeqn{eq:bse_static_born_short_1t}, is a $3\times 3$ Keldysh matrix.
The Keldysh components are classified by location of the two time-arguments on the contour $\mathcal{C}$. They include correlation functions, ``$>,<$'' with two real arguments, ``$\lceil,\rceil$'' having one real and one imaginary time argument and the Matsubara component, $\alpha=\tn{M}$, where both arguments lie on the imaginary track. Below we will need only the ``$<$'' component which determines the time-dependent nonequilibrium PDF and the Matsubara component which yields the PDF in thermodynamic equilibrium. We start the analysis with the former and consider the latter in \refsec{sec:eqpdf}.
Each of the nine components $G_0^{\tn{ab},\alpha}$ of the matrix $G_0^\tn{ab}$ is of the product form
\begin{eqnarray}
\label{eq:g0abalpha}
G^{\tn{ab},\alpha}_0({\bf r}_1{\bf r}_2;{\bf r}'_1{\bf r}'_2;tt') & = &
g^{\tn{a},\alpha}({\bf r}_1t;{\bf r}'_1t') g^{\tn{b},\alpha}({\bf r}_2t;{\bf r}'_2t')\,,
\end{eqnarray}
which allows for an easy matrix multiplication of $G_0^\tn{ab}$ and $\Sigma_0^\tn{ab}$ under the integral in \refeqn{eq:bse_static_born_short_1t}. Since each component $\alpha$ has the same dependence on the coordinates as in \refeqn{eq:bse_static_born_short_1t}, we will suppress the space arguments and integrations in the remainder of this section.
The result for the ``$<$'' component is well known (Langreth rules) and consists of an initial correlation and a collision term
\begin{equation}
\label{eq:gabcorrless}
g^{\tn{ab},<}_\tn{corr}(t,t') = g^{\tn{ab},<}_\tn{IC}(t,t') +g^{\tn{ab},<}_\tn{col}(t,t')\,,
\end{equation}
which arise, respectively, from the imaginary and real part of the contour $\mathcal{C}$,
\begin{eqnarray}
\label{eq:gablessIC}
g^{ab,<}_\tn{IC}(t,t')&=& -\i\int_0^\beta\d\tau\,G^{\tn{ab},\rceil}_0(t,\tau)\Sigma^{\tn{ab},\lceil}_0(\tau,t')\,, \\
g^{ab,<}_\tn{col}(t,t')&=&\int_0^\infty\d\bar{t}\left\{G^{\tn{ab},<}_0(t,\bar{t})\Sigma^{\tn{ab,A}}_0(\bar t,t')+G^{\tn{ab},R}_0(t,\bar{t})\Sigma^{\tn{ab,<}}_0(\bar t,t')\right\}\,.
\label{eq:gablesscol}
\end{eqnarray}
Here $G^{\tn{ab},<}_0$ denotes the product of two single-particle correlation functions $g^{\tn{a},<},g^{\tn{b},<}$, both having two real time arguments, whereas the components $\rceil$ and $\lceil$ describe products of functions depending on one real and one complex ($\tau$) time argument describing the propagation of initial correlations, for a detailed discussion, see, e.g., Refs.~\cite{bonitz98,stan09}. Further, we introduced retarded and advanced functions defined by
\begin{equation}
\label{eq:spec_id}
a^\tn{R/A}(t,t')=\pm\Theta\left[\pm(t-t')\right]\left\{a^>(t,t')-a^<(t,t')\right\}\,.
\end{equation}
\subsection{One-time two-particle correlation function $g^\tn{ab,<}(t)$}
We now perform the final step on the way to the nonequilibrium PDF---taking the time-diagonal limit, $t=t'$, in the above equations for $g^{\tn{ab},<}$ which has the general structure
\begin{equation}
\label{eq:gablesst}
g^{\tn{ab},<}(t)=g_\tn{HF}^{\tn{ab},<}(t)+g_\tn{IC}^{\tn{ab},<}(t)+g_\tn{col}^{\tn{ab},<}(t)\,.
\end{equation}
Expressing the time-diagonal part of the single-particle correlation function by the single-particle density matrix $\rho^\tn{a}(t)=\pm \i\, g^\tn{a}(t,t)$, where the upper (lower) sign refers to bosons (fermions), we obtain for the two-particle correlation function on the time-diagonal
\begin{equation}
G_0^{\tn{ab},<}(t,t)=-\rho^\tn{a}(t)\rho^\tn{b}(t)\,.
\end{equation}
With this relation and \refeqn{eq:gabHF} we first obtain the nonequilibrium Hartree-Fock pair distribution function
\begin{equation}
\label{eq:gabHFt}
g^{\tn{ab},<}_\tn{HF}({\bf r}_1{\bf r}_2;{\bf r}'_1{\bf r}'_2;t)=-\rho^\tn{a}({\bf r}_1{\bf r}'_1,t)\rho^\tn{b}({\bf r}_2{\bf r}'_2,t) \mp \delta_\tn{ab} \rho^\tn{a}({\bf r}_1{\bf r}'_2,t)\rho^\tn{b}({\bf r}_2{\bf r}'_1,t)\,.
\end{equation}
The second contribution to \refeqn{eq:gablesst} due to the initial correlations follows from \refeqn{eq:gablessIC} and is given by
\begin{eqnarray}
\label{eq:gablessICt}
g^{\tn{ab},<}_\tn{IC}({\bf r}_1{\bf r}_2;{\bf r}'_1{\bf r}'_2;t) &=
-\i&\int\limits^{\beta}_0 \d\tau \int \mathrm{d}^3{\bar r}_1 \mathrm{d}^3{\bar r}_2 V^\tn{ab}({\bar r}_{12}) g^{\tn{a},\rceil}({\bf r}_1t;{\bar {\bf r}}_1\tau) g^{\tn{b},\rceil}({\bf r}_2t;{\bar {\bf r}}_2\tau)
\\\nonumber
&&\times\bigg\{
g^{\tn{a},\lceil}({\bar {\bf r}}_1\tau,{\bf r}'_1,t) g^{\tn{b},\lceil}({\bar {\bf r}}_2\tau,{\bf r}'_2;t)
\pm \delta_\tn{ab}
g^{\tn{a},\lceil}({\bar {\bf r}}_1\tau,{\bf r}'_2,t) g^{\tn{b},\lceil}({\bar {\bf r}}_2\tau,{\bf r}'_1;t)
\bigg\}\,.
\end{eqnarray}
Finally, the scattering contribution (\ref{eq:gablesscol}) contains two real-time integrals extending to $t$ and $t'$, respectively. Since now both times are equal, a partial cancellation is possible. Indeed, taking advantage of relation (\ref{eq:spec_id}) allows to cancel all contributions with products of four ``$>$'' or four ``$<$'' functions, and we obtain
\begin{eqnarray}
\label{eq:gablesscolt}
g_\tn{col}^{\tn{ab},<}({\bf r}_1{\bf r}_2;{\bf r}'_1{\bf r}'_2;t) &=
\i&\int\limits^{t}_0 \d\bar t \int \d^3{\bar r}_1 \d^3{\bar r}_2 V^\tn{ab}({\bar r}_{12})
\bigg\{
g^{\tn{a},>}({\bf r}_1t;{\bar {\bf r}}_1 {\bar t}) g^{\tn{b},>}({\bf r}_2t;{\bar {\bf r}}_2 {\bar t})
\\\nonumber
&&\times\big[
g^{\tn{a},<}({\bar {\bf r}}_1{\bar t},{\bf r}'_1,t) g^{\tn{b},<}({\bar {\bf r}}_2 {\bar t},{\bf r}'_2;t)
\pm \delta_\tn{ab}
g^{\tn{a},<}({\bar {\bf r}}_1{\bar t},{\bf r}'_2,t) g^{\tn{b},<}({\bar {\bf r}}_2 {\bar t},{\bf r}'_1;t)
\big]\nonumber\\
&&- (> \leftrightarrow <)
\bigg\}\,.\nonumber
\end{eqnarray}
This expression is readily understood: the first term describes the correlation build-up due to scattering of a particle pair $a,b$ out of state $\ket{\bar {\bf r}_1}\ket{\bar {\bf r}_2}$ into state $\ket{{\bf r}_1}\ket{{\bf r}_2}$, whereas the second contribution which is obtained by interchanging functions with the indices ``$<$'' and ``$>$'' describes the opposite process. The integral has the familiar non-Markovian structure (``memory'') indicating that scattering processes from all times prior to the current one do contribute although their weight decreases since the single-particle Green's function decay with increasing difference of their time arguments.
Expression (\ref{eq:gablesscolt}) has exactly the same structure as known from density operator theory \cite{bonitz98}. The binary
density operator in Born approximation is recovered if the two-time correlation functions are eliminated using the generalized Kadanoff-Baym ansatz \cite{lipavsky86}, see also Ref.~\cite{hermanns12}. The present result is more general because this reconstruction ansatz, which is only valid approximately and becomes increasingly inaccurate with increasing correlation effects, is avoided.
\section{Nonequilibrium pair distribution function}
\label{sec:neqpdf}
The nonequilibrium pair distribution function $h^\tn{ab}(t)$ follows immediately from the two-particle correlation function according to \refeqn{eq:hab} and the results (\ref{eq:gablesst}), (\ref{eq:gabHFt}), (\ref{eq:gablessICt}) and (\ref{eq:gablesscolt}). Explicit results depend on the choice of a basis. We start from the coordinate representation.
\subsection{Coordinate representation}
\label{sec:NeqPDFcoord}
To obtain the standard pair distribution function which is defined in configuration space we set ${\bf r}_1={\bf r}'_1$
and ${\bf r}_2={\bf r}'_2$ in all expressions
\begin{equation}
\label{eq:habcoord}
\begin{split}
h^\tn{ab}({\bf r}_1,{\bf r}_2,t) =
&\rho^\tn{a}({\bf r}_1{\bf r}_1,t) \rho^\tn{b}({\bf r}_2{\bf r}_2,t)
\pm \delta_\tn{ab} \rho^\tn{a}({\bf r}_1 {\bf r}_2,t) \rho^\tn{b}({\bf r}_2 {\bf r}_1,t)\\
&-g^{\tn{ab},<}_\tn{IC}({\bf r}_1{\bf r}_2;{\bf r}_1{\bf r}_2;t)
-g^{\tn{ab},<}_\tn{col}({\bf r}_1{\bf r}_2;{\bf r}_1{\bf r}_2;t)\,.
\end{split}
\end{equation}
In a spatially inhomogeneous system it is advantageous to introduce center of mass and relative coordinates,
${\bf R}=({\bf r}_1+{\bf r}_2)/2$ and ${\bf r}={\bf r}_1-{\bf r}_2$, leading to the replacements
${\bf r}_{1,2}={\bf R}\pm {\bf r}/2$, on the right hand side. Then $h^\tn{ab}({\bf R},{\bf r})$ is understood
as the local probability to find a particle pair at distance ${\bf r}$ around space point ${\bf R}$.
If spatial inhomogeneities are not relevant or not of interest, a space integration leads to the space averaged nonequilibrium pair distribution
\begin{equation}
h^\tn{ab}(\b{r},t)=\int\d^dR\,h^\tn{ab}(\b{R},\b{r},t)\,,
\end{equation}
where $d$ is the dimensionality of the system. Note that $h^\tn{ab}$ is normalized to the total number of particles according to
\begin{equation}
\label{eq:pdf_int}
\int \d^d h^\tn{ab}(\b{r},t)=N_\tn{a}N_\tn{b}\,.
\end{equation}
Finally, in some cases just the dependence on the magnitude of the pair separation is of interest which is obtained by an angle integration. The result is called radial distribution function, $h^\tn{ab}(r,t)$, and follows from \refeqn{eq:pdf_int} according to (we consider a two-dimensional system and change to polar coordinates)
\begin{equation}
\label{eq:habrt}
h^\tn{ab}(r,t)=\int_0^{2\pi}\d\phi\, r h^\tn{ab}(r,\phi,t)\,,
\end{equation}
with the normalization
\begin{equation}
\int_0^\infty\d r h^\tn{ab}(r,t)=N_\tn{a}N_\tn{b}\,,
\end{equation}
and similarly in 3D.
\subsection{Arbitrary basis}
\label{sec:NeqPDFbasis}
Let us now consider the case of an arbitrary orthonormal stationary basis $\left\{\phi_i(\b{r})\right\}$ which is of relevance, in particular, for spatially inhomogenenous systems. Then the single-particle Green's functions become matrices according to
\begin{equation}
g^{\tn{b},\alpha}(1,1')=\sum_{ij}\phi_i(\b{r}_1)g_{ij}^{\tn{b},\alpha}(t_1,t_1')\phi_i^*(\b{r}_1')\,,
\end{equation}
which holds for any Keldysh component ``$\alpha$''. Analogously, the two-particle single-time correlation function is represented by a four-dimensional matrix
\begin{equation}
\label{eq:gablessbasis}
g^{\tn{ab},<}(\b{r}_1\b{r}_2;\b{r}_1'\b{r}_2';t)=\sum_{ijkl}\phi_i(\b{r}_1)\phi_j(\b{r}_2)g_{ijkl}^{\tn{ab},<}(t)\phi^*_k(\b{r}_1')\phi^*_l(\b{r}_2')\,.
\end{equation}
To compute the nonequilibrium PDF (\ref{eq:gablesst}) we have to expand the Hartree-Fock, the initial correlation and the scattering part in this basis. For the Hartree-Fock contribution we obtain, in analogy to (\ref{eq:gablessbasis}),
\begin{eqnarray}
\label{eq:gablessHFtbasis}
g_\tn{HF}^{\tn{ab},<}(\b{r}_1\b{r}_2;\b{r}_1'\b{r}_2';t)&=&\sum_{ijkl}\phi_i(\b{r}_1)\phi_j(\b{r}_2)g_{\tn{HF},ijkl}^{\tn{ab},<}(t)\phi^*_k(\b{r}_1')\phi^*_l(\b{r}_2')\,,\\
g_{\tn{HF},ijkl}^{\tn{ab},<}(t)&=&g_{ik}^{\tn{a},<}(t)g_{jl}^{\tn{b},<}(t)\pm\delta_\tn{ab}g_{il}^{\tn{a},<}(t)g_{jk}^{\tn{b},<}(t)\,.
\end{eqnarray}
Similarly, we obtain from \refeqn{eq:gablessICt} for the initial correlation contribution
\begin{eqnarray}
\label{eq:gablessICtbasis}
g_\tn{IC}^{\tn{ab},<}(\b{r}_1\b{r}_2;\b{r}_1'\b{r}_2';t)&=&\sum_{ijkl}\phi_i(\b{r}_1)\phi_j(\b{r}_2)g_{\tn{IC},ijkl}^{\tn{ab},<}(t)\phi^*_k(\b{r}_1')\phi^*_l(\b{r}_2')\,,\\
g_{\tn{IC},ijkl}^{\tn{ab},<}(t)&=&\int_0^\beta \d\tau \sum_{mnrs} V^\tn{ab}_{mnrs}\,
g^{\tn{a},\rceil}_{m,i} (t,\tau)g^{\tn{b},\rceil}_{n,j} (t,\tau)\, \times \\
&&\left\{
g^{\tn{a},\lceil}_{r,k} (\tau,t)g^{\tn{b},\lceil}_{s,l} (\tau,t)
\pm \delta_\tn{ab}\, g^{\tn{a},\lceil}_{r,l} (\tau,t)g^{\tn{b},\lceil}_{s,k} (\tau,t)
\right\}\nonumber\,,
\end{eqnarray}
and from \refeqn{eq:gablesscolt}
\begin{eqnarray}
\label{eq:gablesscoltbasis}
g_\tn{col}^{\tn{ab},<}(\b{r}_1\b{r}_2;\b{r}_1'\b{r}_2';t)&=&\sum_{ijkl}\phi_i(\b{r}_1)\phi_j(\b{r}_2)g_{\tn{col},ijkl}^{\tn{ab},<}(t)\phi^*_k(\b{r}_1')\phi^*_l(\b{r}_2')\,,\\
g_{\tn{col},ijkl}^{\tn{ab},<}(t)&=&\i \int\limits_0^t \d \bar t \sum_{mnrs} V^\tn{ab}_{mnrs}
\bigg\{g^{\tn{a},>}_{i,m}(t,\bar t)g^{\tn{b},>}_{j,n}(t,\bar t)\times \nonumber\\
&&\left[ g^{\tn{a},<}_{k,r}(\bar t, t)g^{\tn{b},<}_{l,s}(\bar t, t)
\pm \delta_\tn{ab}\, g^{\tn{a},<}_{l,r} (\bar t, t)g^{\tn{b},<}_{k,s} (\bar t, t) \right] \\
&&-(> \leftrightarrow < \textnormal{and}\; g_{1,2} \leftrightarrow g_{2,1})
\bigg\}\nonumber\,.
\end{eqnarray}
Basis expansions for inhomogeneous quantum many-body systems have been successfully applied to electrons in quantum dots (``artificial atoms''), e.g., \cite{balzer09}, and small atoms and molecules, e.g., \cite{dahlen07,balzer10}. For these systems, the Keldysh/Kadanoff-Baym equations are solved for the matrix function $g_{ij}^<(t,t')$. Using these results and formulas (\ref{eq:gablessHFtbasis}),(\ref{eq:gablessICtbasis}) and (\ref{eq:gablesscoltbasis}), the two-particle correlation function, $g^{\tn{ab},<}$ in configuration space, \refeqn{eq:gablessbasis}, can be reconstructed. Besides, also the matrix elements $g_{ijkl}^{\tn{ab},<}(t)$ themselves are of interest, as they carry extensive information on the many-body system. For example, the matrix components $g_{ijij}^{\tn{ab},<}(t)$ describe the correlation of two particles ``a,b'' occupying the orbitals i and j, respectively, at a given moment $t$.
\section{Equilibrium pair distribution function}
\label{sec:eqpdf}
To compute the pair distribution in thermodynamic equilibrium from the Matsubara Green's function we return to \refeqn{eq:bse_static_born_short_1t} for the Keldysh matrix and extract the Matsubara component. According to \refeqn{eq:g0abalpha} it is given by a product of one-particle Matsubara Green's functions,
\begin{equation}
\label{eq:g0abM}
G_0^\tn{ab,M}(\b{r}_1\b{r}_2;\b{r}_1'\b{r}_2';\tau)=g^\tn{a,M}(\b{r}_1\b{r}_1',\tau)g^\tn{b,M}(\b{r}_2\b{r}_2',\tau)\,,
\end{equation}
where $\tau=t-t'$. Similarly as in nonequilibrium, the two-particle Matsubara Green's function consists of a Hartree-Fock and correlation part,
\begin{equation}
\label{eq:gabM}
g^\tn{ab,M}(\tau)=g^\tn{ab,M}_\tn{HF}(\tau)+g^\tn{ab,M}_\tn{col}(\tau)\,
\end{equation}
where the latter is obtained from \refeqn{eq:g0abalpha} using the Langreth rules, in analogy to \refeqn{eq:gablessIC},
\begin{equation}
g^\tn{ab,M}_\tn{col}(\tau)=-\i\int_0^\beta\d\bar{\tau}\,G_0^\tn{ab,M}(\tau-\bar{\tau})\Sigma^\tn{ab,M}_0(\bar{\tau})\,.
\end{equation}
Restoring the coordinate arguments and using the definitions of $G_0^\tn{ab}$ and $\Sigma_0^\tn{ab}$, Eqs.~(\ref{eq:G0ab}) and (\ref{eq:Sigma0ab}), we obtain
\begin{eqnarray}
\label{eq:gabMHF}
g^{\tn{ab,M}}_\tn{HF}({\bf r}_1{\bf r}_2;{\bf r}'_1{\bf r}'_2)&=&-\rho^\tn{a}({\bf r}_1{\bf r}'_1)\rho^\tn{b}({\bf r}_2{\bf r}'_2) \mp \delta_\tn{ab} \rho^\tn{a}({\bf r}_1{\bf r}'_2)\rho^\tn{b}({\bf r}_2{\bf r}'_1)\,,\\
g^{\tn{ab,M}}_\tn{col}({\bf r}_1{\bf r}_2;{\bf r}'_1{\bf r}'_2,\tau)&=&-\i\int_0^\beta \d\bar \tau \int \d^3{\bar r}_1 \d^3{\bar r}_2 V^\tn{ab}({\bar r}_{12})\times
\nonumber\\
&&\bigg\{
g^{\tn{a,M}}({\bf r}_1{\bar {\bf r}}_1,{\tau-\bar \tau}) g^{\tn{b,M}}({\bf r}_2{\bar {\bf r}}_2,{\tau-\bar \tau}) \times
\\\nonumber
&&\big[
g^{\tn{a,M}}({\bar {\bf r}}_1{\bf r}'_1,\bar \tau) g^{\tn{b,M}}({\bar {\bf r}}_2{\bf r}'_2,\bar \tau)
\pm \delta_\tn{ab}
g^{\tn{a,M}}({\bar {\bf r}}_1{\bf r}'_2,\bar \tau) g^{\tn{b,M}}({\bar {\bf r}}_2{\bf r}'_1,\bar \tau)
\big]\nonumber\bigg\}\,.\nonumber
\label{eq:gabMcol}
\end{eqnarray}
From this the equilibrium PDF is obtained by introducing center of mass and relative coordinates as was done in the nonequilibrium situation, cf. \refsec{sec:NeqPDFcoord}.
\section{Numerical example: pair correlations in an electron-hole bilayer system}
\label{sec:bilayer}
To illustrate the results obtained so far we consider an example of a two-component system where strong correlations play a prominent role. The system of interest consists of two layers of zero thickness which contain an equal finite number $N$ of negative (electrons) and positive (holes) charged particles with a finite layer spacing $d$. In each plane, the particles are confined by a harmonic potential of frequency $\Omega$. Such electron-hole bilayers have been actively studied in recent years, e.g., \cite{depalo02,filinov03,hartmann05}, because they allow to study strongly correlated excitons which may exhibit Bose condensation and superfluidity, as well as liquid-like and crystal-like behavior. For more details, we refer to Refs.~\cite{ludwig07,boening11}.
\subsection{Model}
The Hamiltonian of the quasi-two-dimensional electron-hole bilayer is given by
\begin{eqnarray}
\label{eq:H}
H&=&H_\tn{e}+H_\tn{h}+H_\tn{eh} \\
H_\tn{e}&=&\sum_{i=1}^{N_\tn{e}}\frac{1}{2}\left(-\Delta_{i,\e} +{\bf r}_{i,\e}^2\right)+
\lambda\sum_{i<j=2}^{N_\e}\frac{1}{\sqrt{({\bf r}_{i,\e}-{\bf r}_{j,\e})^2}}\,,\\
H_\tn{h}&=&\sum_{i=1}^{N_\tn{h}}\frac{1}{2}\left(-\frac{m^*_\e}{m^*_\tn{h}}\Delta_{i,\tn{h}}+
\frac{m^*_\tn{h}}{m^*_\e}{\bf r}_{i,\tn{h}}^2\right)+
\lambda\sum_{i<j=2}^{N_\tn{h}}\frac{1}{\sqrt{({\bf r}_{i,\tn{h}}-{\bf r}_{j,\tn{h}})^2}}\,,\\
H_\tn{eh}&=&-\lambda\sum_{i=1}^{N_\e}\sum_{j=1}^{N_\tn{h}}\frac{1}{
\sqrt{({\bf r}_{i,\e}-{\bf r}_{j,\tn{h}})^2+d^{*2} } }\,,
\end{eqnarray}
where we introduced dimensionless variables by rescaling length and energy by the units,
\begin{equation}
r_0=\sqrt{\frac{\hbar}{m_\e\Omega}}\,,\qquad E_0=\hbar\Omega\,.
\end{equation}
The term $m_\tn{e/h}^*$ denotes the effective mass of electrons/holes and $d^*$ is the effective distance between the layers.
Further, we introduced the coupling parameter $\lambda$ measuring the strength of the Coulomb interaction relative to the confinement energy
\begin{equation}
\lambda=\frac{r_0}{a_\tn{B}}\,,\qquad a_\tn{B}=\frac{\hbar^2}{m_\e e^2}\,.
\end{equation}
Here $a_\tn{B}$ is the Bohr radius of a Hydrogen-like bound state---an exciton (we use the electron mass instead of the reduced mass).
The coupling parameter measures the strength of the Coulomb interaction among identical particles in each layer as well as the correlation between electron and holes. Generally, one may expect that for $\lambda \leq 1$, i.e. for very strong confinement, there is a strong wave function overlap, and the system approaches ideal gas like behavior. In the opposite case, $\lambda \gg 1$, the Coulomb interaction dominates, and particles will tend to become localized. Finally, variation of the layer separation gives an additional control of the many-particle state: for $d\rightarrow \infty$ both layers will be decoupled, containing independent electron and hole populations, whereas for decreasing $d$ Coulomb attraction plays an increasing role. This gives rise to formation of indirect excitons which behave (approximately) as bosons and exhibit dipole interaction, e.g., \cite{ludwig07,boening11}.
\subsection{Equilibrium PDF of the electron-hole bilayer---Comparison to Path Integral Monte-Carlo results}
Preliminary results for the equilibrium PDF of the electron-hole bilayer according to Sec.~\ref{sec:eqpdf} were obtained recently \cite{kobusch12}, however they still require further numerical tests. Therefore, to illustrate the physical content of the PDF, in this section, we show some results obtained from path integral Monte-Carlo (PIMC) calculations by \textit{Böning~et~al.} \cite{boening11}. Their approach to the description of the bilayer system is different to the one presented in \refsec{sec:bilayer}, as they assume beforehand, that the layer separation $d$ and the interaction strength $\lambda$ in \refeqn{eq:H} between the electrons and holes, respectively, induces the formation of indirect excitons, i.e. quasiparticles, comprised of strongly bound but spatially separated electron-hole pairs. The excitons exhibit an interaction, which for large distances is of dipole type and for small distances approaches a soft Coulomb potential, for details see Ref.~\cite{boening11}. With these assumptions \textit{Böning~et~al.} computed the equilibrium PDF $h^{\tn{X}_c\tn{X}}(\b{r})$ of one exciton $X$ relative to a fixed exciton $X_c$ in the center for different values of the exciton density $n$ in a ZnS$_x$Se$_{1-x}$/ZnSe quantum well with doping factor $x=0.3$. The density is measured in units of $a_\tn{B}^{*-2}=1.06\cdot 10^{17}\tn{m}^{-2}$, where $a_\tn{B}^{*}=\hbar^2\epsilon/(e^2m_e^*)$ is the electronic Bohr radius with the material constants $\epsilon=8.7$ and $m_e^*=0.15\,m_0$. The temperature is chosen to be $k_\tn{B}T=0.001\,\tn{Ha}^*$, where the energy unit is defined as $\tn{Ha}^*=e^2/(\epsilon a_\tn{B}^*)=53.93\,\tn{meV}$, resulting in a temperature of $T=0.63\,\tn{K}$. In \reffig{fig:XPDF}, $h^{\tn{X}_c\tn{X}}(\b{r})$ is shown for different densities.
\begin{figure}
\label{fig:XPDF}
\includegraphics[width=16cm]{Bilayer.jpeg}
\caption{Radial Exciton-Exciton PDF $h^{\tn{X}_c\tn{X}}(\b{r})$ in a ZnS$_{0.3}$Se$_{0.7}$/ZnSe quantum well at $T=0.63\,\tn{K}$ with layer separation $d=40.83\,\tn{nm}$. Densities in units of $1.06\cdot 10^{17}\tn{m}^{-2}$: (a) $0.84\cdot 10^{-3}$, (b) $1.3\cdot 10^{-3}$, (c) $1.7\cdot 10^{-3}$, (d) $3.2\cdot 10^{-3}$, (e) $3.6\cdot 10^{-3}$, (f) $4.0\cdot 10^{-3}$. The radial length is measured in units of the so called Brueckner parameter $r_\tn{s}=3.26\cdot 10^8\times a$, where $a$ is the mean interparticle distance. The illustration is taken from Ref.~\cite{boening11}.}
\end{figure}
One can see that for low densities, the excitons in the system are melted, showing no localization or radial ordering. If the density is increased, an exciton crystal starts to form, due to pressure crystallization. For further increased density this exciton crystal melts again, which is an effect of the Coulomb-like character of the exciton-exciton interaction at short distances, the excitons undergo quantum melting.
The advantage of the PDF is clear from this figure: different phases of the system can be clearly distinguished which is not possible on the basis of single-particle quantities such as the density.
PIMC is very efficient for computing the thermodynamic properties and also spectral properties \cite{filinov12} of bosons, such as excitons. However, at high densities, excitons break up and form an electron-hole plasma (Mott effect) consisting of fermions. PIMC simulations of fermions at low temperatures are still hampered by the notorious sign problem \cite{schoof11}. In contrast, with nonequilibrium Green's functions, this regime is easily accessible whereas limitations arise with increasing coupling strength. Therefore, PIMC and NEGF have complementary areas of applicability. Moreover, NEGF should allow one to access the time-evolution of the PDF, as demonstrated above.
\section{Discussion}
\label{sec:discussion}
In this paper we presented an approach to the pair distribution function of a quantum many-body system in the frame of the nonequilibrium real-time Green's functions. This problem is complicated due to the fact that the standard approach used in NEGFs uses a formal decoupling of the Martin-Schwinger hierarchy on the level of the first equation: the two-particle Green's function is eliminated by introduction of the single-particle selfenergy, cf. \refeqn{eq:Selfenergy}. With this elimination also direct access to the pair correlations is lost. Thus one has to reconstruct the pair correlations form the single-particle Green's function within a chosen approximation for the selfenergy.
To solve this reconstruction problem we started the analysis from the equation of motion of the two-particle Green's function---the Bethe-Salpeter equation and simplified it systematically. We concentrated on the case of the static second Born approximation because for it a large number of numerical solutions of the KBE exist, for which it would be desirable to evaluate the PDF. It was shown that in second Born approximation a closed expression for the nonequilibrium PDF can be derived which can be straightforwardly evaluated. The result involves combinations of four single-particle Green's functions and is computationally expensive. Numerical results will be presented in a forthcoming paper.
\ack
We thank Th. Bornath for stimulating discussions. This work is supported in part by the Deutsche Forschungsgemeinschaft via SFB-TR24 and project BO1366/9.
\section*{References}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 9,197 |
Combat Mission: Fortress Italy est un jeu vidéo de type wargame développé et édité par Battlefront.com, sorti en 2012 sur Windows et Mac.
Système de jeu
Accueil
Canard PC : 7/10
Notes et références
Jeu vidéo sorti en 2012
Jeu Windows
Jeu Mac
Wargame
Jeu vidéo développé aux États-Unis
Jeu Battlefront
Combat Mission | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 3,338 |
«Сорвиголова́» ( или просто ) — американский супергеройский телесериал, созданный Дрю Годдардом и основанный на одноимённом персонаже комиксов Marvel. Главную роль исполняет Чарли Кокс. Продюсированием занимаются студии Marvel Television и ABC Studios, а показ осуществляется через стриминговый сервис Netflix. «Сорвиголова», как и другие сериалы от Netflix, официально входит в медиафраншизу «Кинематографическая вселенная Marvel» (КВМ) и является первым из серии сериалов, которые объединятся в кроссоверный мини-сериал «Защитники» (2017). Шоураннером сериала выступает Стивен Денайт, а Годдард — консультантом. Премьера всех серий первого сезона состоялась 10 апреля 2015 года. 21 апреля стало известно, что сериал был продлён на второй сезон. В июле 2016 года сериал был продлён на третий сезон, он вышел 19 октября 2018 года.
«Сорвиголова» стал первым из серии таких телесериалов, как «Джессика Джонс» (2015), «Железный кулак» (2017), «Люк Кейдж» (2016) и «Каратель» (2017), которые объединились в кроссоверный мини-сериал «Защитники» (2017). При этом в «Защитниках» продолжается сквозной сюжет первых двух сезонов сериала «Сорвиголова» о могущественной международной организации «Рука», а действие третьего сезона «Сорвиголовы» хронологически следует сразу за последней серией «Защитников». В ноябре 2013 года глава Disney Боб Айгер сообщил, что если персонажи станут популярными на Netflix, не исключено, что они смогут превратиться в полнометражные фильмы. Netflix закрыл сериал 30 ноября 2018 года.
В фильме «Человек-паук: Нет пути домой» Мэтт Мёрдок появился в качестве камео. Его роль вновь исполнил Чарли Кокс.
В марте 2022 года Production Weekly включила перезагрузку Сорвиголовы в свой отчёт о предстоящих проектах, при этом Кевин Файги и Крис Грей были указаны в качестве продюсеров проекта.
Сюжет
Маленьким мальчиком Мэтт Мёрдок ослеп во время трагического дорожного происшествия. Вместе с тем после этого Мэтт обнаружил, что все остальные его чувства невероятно обострились. Став взрослым, Мёрдок поступил на юридический факультет, после окончания которого открыл юридическую фирму вместе со своим другом. Теперь он работает в своей родной Адской Кухне: днём защищает мирных жителей в роли адвоката, а ночью — под видом таинственного защитника в маске.
В ролях
= Главная роль в сезоне
= Второстепенная роль в сезоне
= Гостевая роль в сезоне
= Не появляется
Главные роли
Второстепенные роли
Эпизоды
Сезон 1 (2015)
Сезон 2 (2016)
Сезон 3 (2018)
Производство
Разработка
В своё время 20th Century Fox приобрела права на экранизации с участием персонажа комиксов Сорвиголова. В 2003 году был выпущен фильм «Сорвиголова». Долгое время разрабатывались различные проекты продолжения, которые в силу разных причин так и не были реализованы. По условиям контракта было оговорено, что если съёмки продолжения или перезапуска не начнутся 10 октября 2012 года, то права на экранизацию Сорвиголовы вернутся обратно к Marvel Studios. 23 апреля 2013 года Кевин Файги подтвердил, что права на Сорвиголову вернулись к Marvel и Disney, благодаря чему Сорвиголова может появиться в Кинематографической вселенной Marvel. В октябре 2013 года Deadline сообщил, что Marvel готовит четыре драматических сериала и один мини-сериал, совокупностью в 60 эпизодов, для показа на сервисах «Видео по запросу» (Video on demand) и кабельных каналах, которыми заинтересовались Netflix, Amazon и WGN America. Через несколько недель, Marvel и Disney анонсировали, что Netflix покажет игровые сериалы о Сорвиголове, Джессике Джонс, Железном кулаке и Люке Кейдже, и заканчивая общим мини-сериалом, основанном на комиксах о «Защитниках».
Исполнительным продюсером и шоураннером «Сорвиголовы» был выбран Дрю Годдард, который также должен написать и снять первый эпизод. В феврале 2014 года студия Marvel анонсировала, что сериал будет сниматься в Нью-Йорке. В апреле главный креативный директор Marvel Comics Джо Кесада уточнил, что съёмки будут вестись в районах Бруклина и Лонг-Айленд-Сити, которые до сих пор выглядят, как старая Адская Кухня, а также в оборудованном павильоне. Глава Marvel Television и исполнительный продюсер Джеф Лоуб сообщил, что съёмочный процесс «Сорвиголовы» начнётся в июле 2014 года. В мае 2014 года было объявлено, что Годдард ушёл с поста шоураннера, чтобы заняться постановкой художественного фильма, основанного на комиксах Marvel о «Зловещей шестёрке» для Sony Pictures Entertainment. Его место займёт Стивен Денайт. Годдард, написавший первые два эпизода, останется в проекте как консультант и исполнительный продюсер. Также было объявлено, что проект будет носить название «Сорвиголова» (Marvel's Daredevil). Сериал будет состоять из 13 серий длительностью в 60 минут.
В июле 2014 года Денайт подтвердил начало съёмок и рассказал о видении сериала: «Мы хотим грязи, Нью-Йорк 70-х для этого то, что надо. Нам нравится идея красоты и упадка города, и Адская Кухня является местом, сочетающим понятия красоты и грязи. Вот почему Мэтт Мёрдок любит его и хочет его защищать».
Съёмки второго сезона начались 7 июля 2015 года в Нью-Йорке. Его премьера состоялась 18 марта 2016 года. На сервисе Netflix были выложены все серии сразу, точно так же как это было с первым сезоном.
Кастинг
В конце мая 2014 года Чарли Кокс был утверждён на главную роль. 10 июня было объявлено, что Винсент Д'Онофрио сыграет Уилсона Фиска в сериале, а 20 июня к актёрскому составу присоединилась Розарио Доусон. Несколькими днями позже на роль Фогги Нельсона был утверждён Элден Хенсон. 16 июля был взят на роль второстепенного персонажа, а на следующий день Дебора Энн Уолл была утверждена на роль Карен Пейдж.
Релиз
«Сорвиголова» был выпущен 10 апреля 2015 года через потоковый видеосервис Netflix. Все 13 серий были выпущены мгновенно, в отличие от традиционного сериализованного формата, поддержав новую практику «просмотра всех серий залпом» (binge-watching), которая стала очень успешной для других проектов Netflix.
Критика
На сайте-агрегаторе Rotten Tomatoes первый сезон держит 99 % «свежести» на основе 69 отзывов со средним рейтингом 8,1/10. Критический консенсус сайта гласит: «Имея большую степень приверженности к исходному материалу, высокое качество съёмок и серьёзную драматическую составляющую, "Сорвиголова" выделяется эффектной историей становления супергероя, смелым процедуалом и захватывающим экшен-сценами». На Metacritic первый сезон получил 75 баллов из ста на основе 22-х «в целом благоприятных» отзывах критиков. На Rotten Tomatoes второй сезон держит 78 % «свежести» на основе 50 отзывов со средним рейтингом 7/10. Критический консенсус сайта гласит: «Подкреплённый несколькими впечатляющими экшен-сценами, "Сорвиголова" сохраняет свои позиции во втором сезоне, даже если его новые противники не могут полностью заполнить пустоту, оставленную Уилсоном Фиском». На Metacritic второй сезон получил 68 баллов из ста на основе 13-ти «в целом благоприятных» отзывах критиков. На Rotten Tomatoes третий сезон держит 92 % «свежести» на основе 34 отзывов со средним рейтингом 7,62/10. Критический консенсус сайта гласит: «Человек без страха возвращается в отличную форму с третьим сезоном, который хоть и начинается утомительно неторопливо, вскоре начинает демонстрировать напряжённые моменты из комиксов, чему в огромной степени способствует долгожданное возвращение Винсента Д'Онофрио в роли устрашающего Кингпина». На Metacritic третий сезон получил 71 балл из ста на основе шести отзывов критиков.
Награды и номинации
В декабре 2015 года IGN назвал «Сорвиголову» вторым лучшим оригинальным сериалом Netflix.
Будущее
Примечания
Ссылки
Официальный сайт
Телесериалы США 2010-х годов
Телесериалы США, запущенные в 2015 году
Телесериалы США, завершённые в 2018 году
Телесериалы на английском языке
Драматические телесериалы США
Криминальные телесериалы США
Телесериалы о юристах
Фильмы о слепых
Телесериалы, сюжет которых разворачивается в Нью-Йорке | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 9,973 |
{"url":"https:\/\/mathshistory.st-andrews.ac.uk\/Biographies\/Bouvelles\/","text":"# Charles de Bouvelles\n\n### Quick Info\n\nBorn\n1471\nSoyecourt, near Amiens, Picardy, France\nDied\n1553\nNoyon, Picardy, France\n\nSummary\nCharles de Bouvelles was a French priest who wrote works on geometry and philosophy.\n\n### Biography\n\nCharles de Bouvelles is also known as Carolus Bovillus. Charles' father was an aristocrat and Charles was born into the wealthy Bovelles family. However Soyecourt, the town of his birth, was in the Ponthieu region of Picardy and during Charles' childhood the region was being fought over. The dukes of Burgundy had acquired Ponthieu in 1435 under the Treaty of Arras which had been signed by Philip the Good of Burgundy and Charles VII of France. After much fighting the region was retaken by France under Louis XI in 1477. Picardy was for many years on the frontier and as a consequence subjected to frequent invasions.\n\nDe Bouvelles was educated in Paris. There he was a student of Jacques Lef\u00e8vre d'Etaples (1455-1536) who was a famous humanist, theologian, and translator. Ordained a priest, Lef\u00e8vre taught philosophy in Paris from about 1490 and it was about the time that de Bouvelles came to Paris. Lef\u00e8vre was, of course, from d'Etaples so like de Bouvelles he came from Picardy. While de Bouvelles was studying under him, Lef\u00e8vre began to produce student manuals on physics and mathematics and he began working on new annotated translations of Aristotle's works on ethics, metaphysics, and politics. Lef\u00e8vre had considerable influence on his student de Bouvelles, who went on to improve on the methods of his teacher.\n\nIn 1495 the plague hit Paris and de Bouvelles left without, it appears, taking a degree. In the following years he worked on mathematical topics, in particular trying to solve the classical Greek problem of squaring the circle. In 1501, while trying to solve this problem, he introduced the hypotrochoid (although he did not use this name) which is the curve traced by a point $P$ on a circle of radius $b$ which rolls round inside a fixed circle of radius $a$. Using this curve, de Bouvelles was able to give a mechanical means of squaring the circle.\n\nIn 1503 he published Geometricae introductionis in Latin. The book discussed the problem of squaring the circle and gave an account of his various attempts to solve the problem. It was after he completed work on his book that de Bouvelles set out travelling first to Switzerland, and Mainz in Germany. Later he travelled through Italy, Spain, and France. On his return he became a Catholic priest and then became a canon in the Gothic collegiate church at St Quentin back in his home region of Picardy.\n\nAfter being a canon at St Quentin, de Bouvelles became a canon at the Cathedral of Notre-Dame in Noyon, north-northeast of Paris and still in the Picardy region. The Cathedral there was a fine transitional late 12th century Romanesque-Gothic building in an important ecclesiastical centre. The Bishop of Noyon was Charles de Hangest and he was very pleased with his canon de Bouvelles, granting him much free time to undertake his studies of mathematics, philosophy and theology. In particular Bishop de Hangest had a country estate which provided the peace and quiet that de Bouvelles needed to concentrate on his studies.\n\nIn 1509 he published a philosophy book De Sapiente in which de Bouvelles presented a dualism between the observer and the observed. He saw human beings as:-\n... no longer part of the universe but as its eye and mirror; and indeed as a mirror that does not receive the images of things from outside but that rather forms and shapes them in itself.\nSo the human observer sees the world as something to dominate and exploit. This work would have considerable influence on Descartes who took de Bouvelles' ideas still further.\n\nIn 1510 de Bouvelles published another work on mathematics. This was Liber de XII numeris which studied perfect numbers. It is not a particularly deep work and some of the properties that de Bouvelles gives are left unjustified. Another work Geometrie en francoy has the distinction of being the first geometrical treatise printed in French. We noted that Geometricae introductionis was first published in Latin but the work proved quite popular and so translations were in order. A French translation was published in 1542 and, five years later, the work appeared in Dutch.\n\nDe Bouvelles remained in Noyon for the rest of his life, teaching philosophy but seldom celebrating mass.\n\n### References (show)\n\n1. H L L Busard, Biography in Dictionary of Scientific Biography (New York 1970-1990).","date":"2021-06-13 11:58:29","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 3, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.390743225812912, \"perplexity\": 3690.8616804996955}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2021-25\/segments\/1623487608702.10\/warc\/CC-MAIN-20210613100830-20210613130830-00276.warc.gz\"}"} | null | null |
Q: CPU Throttling on Opteron 6272 in Windows I'm in the process of attempting to benchmark a multithreaded application on my new HP Proliant Server which has an 2x Opteron 6272 and 64gb of ram.
When I run the application on a desktop machine (a range of i7s and a Xeon X5675 processors) the application will cause all cores to hit a near 100% utilization.
When I run the application on my server, no matter how many threads I run, the total cpu utilization of the application hovers around 20-25%. That is if I'm running with 32 threads, all 32 cores will hang at around 20%, if I run 16 threads they'll hang around 40%, and so on.
*
*At first I suspected this had to do with the operating system, so I
installed Windows 7 on the server so that the desktops and the
server had the same OS.
*Then I suspected it was the hardware, I changed the power management in the bios to High Performance. Even though this did increase the benchmark time, the same 20% utilization problem persists.
*I can get all 32 cores at 100% using the y-cruncher benchmark. My custom benchmark is written in .NET, could this possibly have anything to do with it?
I'm perplexed by this problem. Anyone have an idea of what could cause this?
A: If your app is processing a large amount of data, try following the data's path - if the input data is fed from the network, check for possible latencies, bandwidth limitations or transmission errors. You already checked disk I/O which otherwise would be a likely candidate for a bottleneck.
Last but not least, since it is a highly multithreaded .NET application, you should make sure that server garbage collection is used, otherwise you might see weird load characteristics as described in this post from stack overflow.
| {
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The Malta national under-21 football team is the under-21 football team of Malta and is controlled by the Malta Football Association.
The team is sponsored by Givova.
Competitive record
UEFA European Under-21 Championship
Current squad
The following players were called up for the friendly matches.
Match dates: 24 and 27 March 2023
Opposition:
Caps and goals correct as of:''' 24 September 2022, after the match against .
References
External links
Official page on Malta FA
European national under-21 association football teams
under-21
Youth football in Malta | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 4,375 |
Q: SQL Server query for related products I am trying to get related products but the issue which I'm facing is that there is product photos table which has one-to-many relationship with products table, so when I get products by matching category Id it also returns multiple product photos with that product which i do not want. I want only one product photo from product photos table of specific product. Is there any way to use distinct in joins or any other way? what I have done so far....
SELECT [Product].[ID],
,[Thumbnail]
,[ProductName]
,[Model]
,[SKU]
,[Price]
,[IsExclusive]
,[DiscountPercentage]
,[DiscountFixed]
,[NetPrice]
,[Url]
FROM [dbo].[Product]
INNER JOIN [ProductPhotos] ON [ProductPhotos].[ProductID]=[Product].[ID]
INNER JOIN [ProductCategories] ON [ProductCategories].[ProductID]=
[Product].[ID]
WHERE [ProductCategories].[CategoryID]=4
And the result I am getting is...
Product Photos table has
Is there any way to use distinct or group by on product Id column in product photos table to return only one row from photos table.
A: Instead of using inner join, use cross apply:
SELECT . . .
FROM dbo.Product p CROSS APPLY
(SELECT TOP (1) pp.*
FROM ProductPhotos pp
WHERE pp.ProductID = p.id
ORDER BY NEW_ID()
) pp INNER JOIN
ProductCategories pc
ON pc.ProductID = p.id
WHERE pc.CategoryID = 4;
Notes:
*
*The ORDER BY NEWID() chooses a random photo. You can order by specific columns to get the earliest, latest, biggest, or whatever.
*Note that I added table aliases. These make the query easier to write and to read.
*You should qualify all column names in your query, so it is clear which tables they come from.
*I removed the superfluous square braces. They just make the query harder to write and to read.
A: You can use ROW_NUMBER() to return one row for ProductID, like this:
JOIN (SELECT *,
ROW_NUMBER() OVER (PARTITION BY ProductID ORDER BY PhotoID) rn
FROM [ProductPhotos]) [ProductPhotos]
ON [ProductPhotos].[ProductID]=[Product].[ID] AND [ProductPhotos].rn = 1
Instead of this:
JOIN [ProductPhotos] ON [ProductPhotos].[ProductID]=[Product].[ID]
A: you can use sub query in join with distinct instead of joining table directly.
you can create alias and use that column as distinct in select statement, but it will create performance issues when having loads of data inside.
if you have 3 different photos for same product Id (like 2). you can use sub-query with top 1 order by PK desc to get latest picture.
| {
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Q: cannot change page in backbone app by typing address in browser I'm writing a Backbone app where I enabled push state in the router
Backbone.history.start({ pushState: true});
If I click a link get beer on the homepage to go to another page-- at localhost:8080/beer--, everything works as desired. However, if I type localhost:8080/beer in the browser, I don't get the Backbone page for the Beer route, but rather the template rendered by the server (in this case, a golang backend) or, if there isn't one, a 404 message. This makes the app basically useless as I can't count on users only clicking links and not typing addresses in the browser. Is it possible to navigate to different pages of a Backbone app that uses push state by typing the address in the browser and, if so, how?
A: You should configure your backend router to map all URLs that are mapped to in your Backbone router to the html page that renders your app
| {
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<?php
namespace BrandsSync\Models;
class Sync_Status {
const QUEUED = 'queued';
const IMPORTED = 'imported';
const NOT_AVAILABLE = 'not-available';
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 4,845 |
There are a lot of things to consider when picking a local or national dumpster rental company in Orange. Follow these guidelines to assist you choose which choice is better for you.
A local dumpster rental company in Orange may offer better customer services that help you finish your job while keeping costs low. Many of them, nonetheless, have a restricted variety of dumpsters to rent. Should you not schedule an appointment in advance, you may not have the choice you need.
A national dumpster rental company in Orange will typically have more sizes and designs to meet the exceptional needs of your job. National businesses are also a good choice for construction teams that work in a number of cities. Some people, however, complain that national businesses are not as adaptable as locally owned businesses.
When you rent a roll off dumpster, you will be tempted to throw anything and everything inside. Common items which people usually dispose of in a dumpster include solid waste material and most routine household and construction waste, together with tree limbs and landscaping debris. They could also be used for business and commercial cleanouts, house renovations, getting cleared of trash when you're moving to a new home, larger landscaping occupations and much more.
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Most individuals don't need to rent dumpsters unless they absolutely have to. At times, though, it becomes apparent that you must rent a dumpster in Orange for commercial and residential jobs.
Most cities don't haul away construction debris for you. It is your responsibility to ensure you have an appropriate container to collect discarded material from remodeling projects. Even though you just have a tiny project, municipal waste management is not likely to haul the debris away.
In case you have one of these projects in your mind, then you understand it's time to search for a dependable dumpster rental service in Orange.
Whether or not you require a permanent or roll off dumpster is dependent upon the kind of job and service you need. Long-Lasting dumpster service is for continuous demands that continue more than simply a couple of days. This includes things like day-to-day waste and recycling needs. Temporary service is precisely what the name implies; a one-time demand for job-specific waste removal.
Temporary roll off dumpsters are delivered on a truck and are rolled off where they will be properly used. All these are typically larger containers that can manage all the waste that comes with that specific job. Long-Lasting dumpsters are generally smaller containers as they are emptied on a regular basis and so do not need to hold as much at one time.
Should you request a permanent dumpster, some companies demand at least a one-year service agreement for this dumpster. Roll-off dumpsters just need a rental fee for the time that you just maintain the dumpster on the job.
Rubbish removal vs dumpster rental in Orange - Which is right for you?
When you have a job you are about to undertake at home, you might be wondering if it is better to hire someone to come haul off all your rubbish and crap for you, or if you need to only rent a dumpster in Orange and load it yourself.
Renting a container is a better solution if you want the flexibility to load it on your own time and you do not mind doing it yourself to save on labour. Dumpsters also work well in case you have at least seven cubic yards or more of debris. Roll-offs normally begin at 10 cubic yards, so should you only have 3-4 yards of waste, you are paying for a lot more dumpster than you desire.
Trash or junk removal makes more sense in case you want somebody else to load your old items. In addition, it works well should you want it to be taken away immediately so it is out of your own hair or in case you only have a few large things; this is likely cheaper than renting a whole dumpster.
Dumpster bags may offer an option to roll of dumpsters. Whether this choice works well for you, though, will depend on your own endeavor. Consider these pros and cons before you choose a disposal option that works for you.
It is difficult to overcome a roll off dumpster when you've got a big project that'll create a lot of debris. Most rental companies comprise dropping off and picking up the dumpster in the costs, so you could prevent additional fees. Roll off dumpsters usually have time restrictions because businesses need to get them back for other customers. This really is a potential disadvantage if you aren't great at meeting deadlines.
Dumpster bags in many cases are convenient for small jobs with loose deadlines. In case you don't need a lot of room for debris, then the bags could function well for you. Many companies are also happy to allow you to maintain the bags for as long as you need. That makes them useful for longer jobs.
Most dumpster rental firms in Orange have straightforward policies that will help you understand just how much it costs to rent gear. Following these tips can help you avoid hidden fees when renting a dumpster in Orange.
Many firms will charge you extra for keeping the dumpster more than concurred. Make sure you plan ahead so you can keep the dumpster for a suitable amount of time. You also ought to ask about additional fees so you will understand how much extra days cost.
What if I want my dumpster in Orange picked up early?
When you make arrangements to rent a dumpster in Orange, part of your rental agreement includes a given length of time you're permitted to use the container. You usually base this time on the length of time you think your project might take. The bigger the project, the more time you will need the dumpster. Most dumpster rental companies in Orange give you a rate for a specific amount of days. Should you surpass that quantity of days, you will pay an additional fee daily. In case the project goes more rapidly than expected, maybe you are ended with the dumpster sooner than you anticipated.
If that is the case, give the dumpster business a call and they will likely come pick your container up early; this will permit them to rent it to someone else more fast. You typically will not get a reduction on your own rate if you ask for early pickup. Your rental fee includes 7 days (or no matter your term is), whether you use them all or not. | {
"redpajama_set_name": "RedPajamaC4"
} | 3,128 |
class Hexpress
module Noncapture
OPEN = "(?:"
CLOSE = ")"
end
end
| {
"redpajama_set_name": "RedPajamaGithub"
} | 7,375 |
\section{Introduction}
One possible explanation for the existence of free-floating planets \citep{lucroc2000,zapetal2000,zapetal2002,bihetal2009,sumi11} is that they formed in protoplanetary disks around young stars, in systems of multiple planets. These planetary systems subsequently underwent large-scale dynamical instabilities involving close encounters between planets and strong planet-planet scattering events that ejected some planets and left the surviving planets on perturbed orbits~\citep{rasio96,weidenschilling96,linida97,papaloizou01,ford01,ford03,marzari02}. The planet-planet scattering model can reproduce a number of properties of the observed population of extra-solar planets: its broad eccentricity distribution~\citep{adams03,veras06,chatterjee08,juric08,ford08,raymond09b,raymond10}, the distribution of orbital separations between adjacent two-planet pairs~\citep{raymond09a}, and perhaps certain resonant systems~\citep{raymond08b}.
In order for planet-planet scattering to create the free-floating planet population, the following equation:
\begin{equation}
\frac{N_{free}}{N_{stars}} = f_{giant} \times f_{unstable} \times n_{ejec},
\label{eq1}
\end{equation}
\noindent{must} hold, where $N_{free}/N_{stars}$ is the observed frequency of free-floating giant planets of $1.8^{+1.7}_{-0.8}$ per main-sequence star~\citep{sumi11}, $f_{giant}$ is the fraction of stars with giant planets, $f_{unstable}$ is the fraction of giant planet systems that become unstable, and $n_{ejec}$ is the mean number of planets that are ejected during a dynamical instability. The terms on the right-hand side of Eq. (\ref{eq1}) are all dependent on stellar mass. We discuss these correlations extensively in Section 3; see also \cite{kenken2008}.
Exoplanet observations constrain the fraction of stars with gas giant planets to be larger than $\sim14$\%~\citep{cumming08,howard10,mayor11} and perhaps as high as 50\%~\citep{gould10}. The majority of giant planets are located beyond 1 AU~\citep{butler06,udry07}\footnote{See http://exoplanet.eu/ and http://exoplanets.org/}, and their abundance increases strongly with orbital distance within the observational capabilities ($\sim5$ AU) of radial velocity surveys \citep{mayor11}.
Given the difficulty of measuring eccentricities with radial velocity measurements~\citep{shen08,zakamska10}, the fraction of planetary systems that becomes unstable is modestly constrained by the eccentricities of surviving planets. In addition, there is a clear positive mass-eccentricity correlation: more massive exoplanets have higher eccentricities~\citep{ribas07,ford08,wright09}. The simplest way to reproduce the observed distributions is if a large fraction of systems -- at least 50\% but more probably 75\% or more -- become unstable, and if the giant planets' masses within systems with high-mass ($M \gtrsim M_J$) planets are roughly equal~\citep[][]{raymond10}. The typical number of planets ejected per unstable system, $n_{ejec}$, must be an increasing function of the number of planets that form in a given system. However, $n_{ejec}$ has been addressed only tangentially in previous studies, and we quantify this value in a consistent manner here.
Assuming observationally motivated constraints -- $N_{free}/N_{stars} = 1.8$, $f_{giant} = 0.2$, and $f_{unstable} = 0.75$ -- each instability must eject 12 Jupiter-mass planets (i.e., $n_{ejec}=12$). For the full range of plausible constraints -- $N_{free}/N_{stars} = 1-3.5$, $f_{giant} = 0.14-0.5$, and $f_{unstable} = 0.5-1$ -- the range of values for $n_{ejec}$ is between 2 and 50. At first glance, these values appear implausibly large. And as we will show, $n_{ejec}$ is indeed so large as to be inconsistent with observational constraints, which means that the planet-planet scattering model, at least in its simplest form, cannot explain the free-floating planet population.
Section 2 is dedicated to placing theoretical constraints on $n_{ejec}$ using N-body simulations of planet-planet scattering. We chose initial conditions that we expect to be the most efficient at ejecting planets and tested systems initialized with up to 50 planets. Section 3 incorporates this result into our main argument and discusses additional considerations, such as the contribution from previous generations of main sequence stars which are now stellar remnants, and other potential sources of free-floaters.
\begin{figure*}
\centerline{
\psfig{figure=EqualEscape.eps,height=6cm,width=8.5cm}
\psfig{figure=UnequalEscape.eps,height=6cm,width=8.5cm}
}
\caption{
Ejection fractions for planetary systems with different initial numbers of giant planets ($N_p$). The left panel shows the results for the {\tt equal} simulations, in which all planets have the same mass ($1$ Jupiter-mass). The right panel shows the results of the {\tt random} simulations, where the planetary masses were selected randomly and logarithmically between 1 Saturn-mass and $10$ Jupiter-masses. Vertical bars about the mean represent one standard deviation. The solid blue curves indicate the fraction of planets that is ejected, and the red dashed curve (which is slightly offset to the right from the blue curve in the right panel for clarity) represents the fraction of initial planetary mass that is lost. The four other segments in the right panel all represent different initial distributions for $N_p = 5$ (green: each planet has $e_0 = 0.5$; pink: each planet's initial eccentricity is assigned a random value; orange: $M_{\star} = 3 M_{\odot}$ and $a_{innermost} = 30$ AU; purple: $M_{\star} = (1/3) M_{\odot}$ and $a_{innermost} = 0.3$ AU). These plots provide relations between $N_p$ and $n_{ejec}$, the number of planets ejected; values from the unequal mass plot are used as coefficients in Eq. (\ref{eq2}).
}
\label{fig1}
\end{figure*}
\section{Scattering simulations}
The dynamical evolution of unstable multi-planet systems leads to planet-planet collisions, planet-star collisions, and/or the hyperbolic ejection of one or more planets. Previous work has shown that ejections comprise the most frequent outcome~\citep{weidenschilling96,papaloizou01,marzari02,adams03,juric08,veretal2009,raymond10}.
In an extensive investigation of planet-planet scattering in systems of 10 and 50 planets, ~\cite{juric08} found that $50\%-60\%$ of all planets were ejected from unstable systems with little dependence on the initial planetary distribution.
In addition, \cite{raymond10} showed that the number of ejected planets is larger in systems that start with unequal-mass planets and in systems with higher-mass planets.
In order to self-consistently assess $n_{\rm ejec}$ as a function of the number of planets which have formed in a planetary system, $N_p$, we performed a suite of planet-planet scattering simulations. Although the phase space of initial conditions is extensive, the results of the investigations referenced above (particularly from \citealt*{juric08}) demonstrate that $n_{\rm ejec}$ is largely insensitive to the initial distribution of planetary eccentricity or inclination. Therefore, we consider initially circular and nearly-coplanar ($i$ chosen randomly from $0^\circ-1^\circ$) sets of $N_p = 3-50$ planets. We tested two different planetary mass distributions: in the {\tt equal} simulations each planet was 1 Jupiter-mass, and in the {\tt random} simulations, the logarithm of the mass of each planet was chosen randomly such that the planet masses took values between 1 Saturn-mass and 10 Jupiter-masses. We assumed that giant planets tend to form at a few AU -- close to the ice line -- in marginally-unstable configurations. Thus, the innermost planet was placed at 3 AU and for $N_p =$ 3, 4, 5, 6, 8, and 10, additional planets were spread out radially with a separation of $K=4$ mutual Hill radii between adjacent planets~\citep[as $K$ determines the instability timescale;][]{marzari02,chatterjee08}. For $N_p =$ 20 and 50, $K$ was decreased to keep the outermost planet at $\lesssim 200$ AU (for $N_p =$ 20 and 50, $K$ = 2.56 and 0.99 for the {\tt equal} simulations, and $K$ = 2.00 and 0.70 for the {\tt random} simulations). Each system was integrated for 10 Myr using the Bulirsch-Stoer integrator in the {\it Mercury} integration package~\citep{chambers99}. Although slow, this integrator accurately models close encounters. The radius of each planet was taken to be Jupiter's current radius, and collisions were treated as inelastic mergers. A planet was considered to be ejected if its orbital distance exceeded $10^5$ AU, which represents a typical distance at which galactic tides can cause escape over a typical main sequence lifetime \citep{tremaine1993}. We ensured that each simulation conserved energy and angular momentum to one part in $10^4$ or better to avoid numerical artifacts~\citep{barnes04}.
We obtained a sufficiently large statistical measure of $n_{\rm ejec}$ by running ensembles of systems for each value of $N_p$. We integrated 100 sets of initial conditions for each of $N_p =$ 3, 4, 5, 6, 8, and 10, and assigned a random value to each planet's orbital angles in each instance. We did the same for $N_p =$ 20 and 50, but instead ran 40 and 10 simulations, respectively, for each due to the increased computational cost. Each simulation was run for $10^7$ yr. Our results are displayed in Fig. 1.
The figure demonstrates that between 20\% and 70\% of planets are ejected in each set of simulations. The vertical bars attached to the mean escape percentages for each bin represent $\pm 1$ standard deviation values from the mean. For the {\tt equal} simulations (left panel) this mean ejection fraction is roughly constant with $N_p$, and varies by at most 10\%. In contrast, the ejection rate in the {\tt random} simulations (right panel) increases monotonically with $N_p$. The mean ejection percentage for $N_p = 10$ is $50\%$-$60\%$, corroborating the results from the 10-planet simulations in \cite{juric08}. The red dashed lines represent the fraction of the initial planetary mass ejected for each value of $N_p$ (slightly offset to the right of the blue curves for clarity). This value is less than the percentage of planets ejected in all cases, demonstrating that the most massive planets tend to scatter out the smaller ones, corroborating previous results \citep[e.g.][]{ford03}.
The effect of varying the initial system configurations does not have a drastic effect on the outcome, as demonstrated in, e.g., \cite{juric08}. In order to sample this effect for our setup, we have performed 4 additional sets of simulations, all with $N_p = 5$, and have plotted the results on Fig. 1 to the immediate left of the $N_p = 5$ blue curves. The green curves demonstrate the ejection percentage when each planet is initialized with $e = 0.5$ and the pink curves for a randomized distribution of initial eccentricities. The orange and purple curves assume respectively different stellar masses ($3 M_{\odot}$ and $0.3 M_{\odot}$) and different innermost semimajor axes values ($0.3$ AU and $30$ AU) in order to account for the different approximate ice line boundaries. In all these cases, the fraction of mass ejected is less than the fraction of planets ejected, as in the nominal $N_p = 5$ cases, and the mean ejection fraction of planets varies by about $20\%$.
\section{Discussion}
We have related ${N_{free}}/{N_{stars}}$ to $n_{ejec}$ in Section 1, and have related $n_{ejec}$ to $N_p$ in Section 2 and Fig. 1. Now, we can link the two relations, and do so through a more precise formulation of Eq. (\ref{eq1}):
\begin{eqnarray}
&&\frac{N_{free}}{N_{stars}} = \sum_{N_p = 3}^{\infty} f_{giant}^{(N_p)} \times f_{unstable}^{(N_p)} \times n_{ejec}^{(N_p)}
\nonumber
\\
&& = 0.17 \cdot 3\cdot f_{giant}^{(3)} f_{unstable}^{(3)} + 0.37 \cdot 4\cdot f_{giant}^{(4)} f_{unstable}^{(4)}
\nonumber
\\
&&+ 0.43 \cdot 5\cdot f_{giant}^{(5)}f_{unstable}^{(5)} + 0.50 \cdot 6\cdot f_{giant}^{(6)}f_{unstable}^{(6)}
\nonumber
\\
&&+...
\label{eq2}
\end{eqnarray}
\noindent{where the} coefficients are taken from the mean ejection fractions of the {\tt random} simulations in Fig. 1. and which is subject to the constraint
\begin{equation}
\sum_{N_p = 3}^{\infty} f_{giant}^{(N_p)} \le 1.
\label{constraint}
\end{equation}
\noindent{Now} we can simply set ${N_{free}}/{N_{stars}} = 1.8$ and take a closer look at Eqs. (\ref{eq2})-(\ref{constraint}).
In order to satisfy the constraint in Eq. (\ref{constraint}), the vast majority of planetary systems must have $N_p \ge 5$. If we use the observationally determined {\it upper} bound of $0.5$ \citep{gould10} on the right-hand side of Eq. (\ref{constraint}), then the vast majority of planetary systems must have $N_p \ge 7$. If we use the lower bound of $0.14$ \citep{mayor11} -- which applies for Sun-like stars -- then the vast majority of planetary systems must have $N_p \ge 20$. These minimum values of $N_p$ would be even higher if we instead derived Eq. (\ref{eq2}) from the {\tt equal} simulation results. If, motivated by the monotonicity of the coefficients in Eq. (\ref{eq2}), we assume that all systems form a fixed number of planets, then we can calculate a critical giant planet frequency $f_{giant_{crit}}^{(N_p)}$ below which the free-floating population cannot be reproduced. We plot this quantity in Fig. \ref{fig3} for two different values of $f_{unstable}^{(N_p)}$. Here, coefficients for values of $N_p$ that were not sampled in our simulations were conservatively fixed at the coefficient of the next highest value of $N_p$ that was sampled. For example, the coefficients of $f_{giant}^{(20)}$ and $f_{giant}^{(50)}$ are $0.65$ and $0.70$; hence, the coefficient of $f_{giant}^{(21)}$ is taken to be $0.70$.
\begin{figure}
\centerline{
\psfig{figure=Simplef.eps,height=6cm,width=8.5cm}
}
\caption{
The critical fraction of stellar systems that must initially contain at least $N_p$ giant planets in order to produce the free-floating planet population. The curves were obtained from Eq. (\ref{eq2}) assuming ${N_{free}}/{N_{stars}} = 1.8^{+1.7}_{-0.8}$; the solid curves with symbols assume the nominal value of $1.8$, and the dashed curves without the symbols assume values of $1.0$ and $3.5$. All three blue curves assume every system became unstable, and the three red curves assume that half of all systems became unstable. Current observational limits for systems which contain {\it any} number of detected planets are given by the horizontal black lines. This plot illustrates that an unrealistically large number of giant planets must form per star if planet-planet scattering represents the sole source of the free-floating planet population.
}
\label{fig3}
\end{figure}
Now that we have determined the relation between $N_p$ and $f_{giant_{crit}}^{(N_p)}$, we can assess the constraints on forming $N_p$ giant planets in a single system. A simple first consideration is the outermost planet's semimajor axis before any scattering occurs. For simplicity, assume $N_p$ 1-Jupiter-mass planets all orbit a $1 M_{\star}$ star, and that the planets are formed close enough to be on the verge of instability ($K=4$). Then, with an adopted innermost semimajor axis of $3$ AU, $a_{outermost} = 3$~AU $\cdot (1.415)^{N_p-1}$. Therefore, for $N_p > 13$, $a_{outermost} > 200$ AU. Core accretion cannot form planets beyond $\approx 35$ AU \citep{dodetal2009}, gravitational instability has not yet been demonstrated to produce planets beyond $200$ AU \citep{boss2006}, and only in the most extreme cases may planet-disc interactions cause planets to migrate outward beyond 200 AU \citep{crietal2009}. If giant planets were all formed by core accretion, then the $a < 35$ AU restriction implies $N_p \le 8$, implying that at least $40\%$ of systems, all with 8 giant planets, all must have become unstable in order to produce the free-floating planet population by planet-planet scattering alone. Alternatively, if giant planets were all formed by gravitational instability, even in extended ``maximum-mass'' discs \citep{dodetal2009}, then not more than a few giant-planet-mass clumps form \citep{boley2009,boletal2010}.
Radial velocity observations suggest that, within a few AU, giant planets are far more common around higher-mass stars \citep{johetal2007,lovmay2007,bowetal2010,johetal2010}. However, low-mass stars outnumber higher-mass stars by a large factor \citep[][and references therein]{paretal2011}. If $f_{giant}$ does indeed decrease as $M_{\star}$ decreases, then explaining free-floaters via planet-planet scattering proves to be more difficult simply because fewer total stars would form giant planets. Consider, for example, the observed lower-bound frequencies of giant planets for different stellar masses deduced from radial velocity surveys for three categories of stars: M dwarfs \citep[3\%,][]{bonetal2011}, Solar-like stars: \citep[14\%,][]{mayor11}, and A-type stars \citep[20\%,][]{johetal2010}. The total integrated value of $f_{giant}$ depends on the mass ranges adopted for these stellar types and the particular initial mass function assumed. At minimum, the relative frequency of stars in these three bins should differ by a factor of a few (e.g., in the ratio $4$:$2$:$1$), which yields an integrated $f_{giant}$ of $\lesssim 8.5\%$. If, however, there exists at least one order of magnitude more M dwarfs than Solar-type stars, then the integrated $f_{giant}$ must be $\lesssim 4.5\%$. If this value is adopted as the true value of $f_{giant}$, then Fig. 2 demonstrates that giant planet systems must be extremely crowded, with at minimum 25 giant planets per system. This value is almost certainly unrealistic given the arguments presented above and current observational constraints. However, we note that microlensing surveys suggest that giant planets on more distant orbits may actually be very common around low-mass stars \citep{gould10}, in which case a typical giant planet system need only contain 4-10 planets (Fig. 2).
To what degree do stars that have already evolved off the main sequence contribute to the free-floating planet population? In order to estimate this contribution, we need only count the current population of white dwarfs, as stars that underwent supernovae or/and formed a black hole comprise a negligible fraction ($< 1\%$) of the total stellar population \citep{paretal2011}. One of the most complete and least-biased samples of white dwarfs represents the local population (within 20 pc of the Sun), which is estimated to have a space density of $4.8 \pm 0.5 \times 10^{-3}$ pc$^{-3}$ \citep{holetal2008}. The space density of stars in the Galactic Disc is $\approx 6 \times 10^{-1}$ pc$^{-3}$ \citep[][Pg. 3]{bintre2008}, implying that the fraction of the free-floating population which has arisen from dynamical instability soon after formation in already-dead stars is on the order of $1\%$. This value is not great enough to change the results here unless $N_p$ is orders of magnitude higher for high-mass stars than for the lower-mass stars that dominate the current galactic population.
If the planet-planet scattering model can reproduce the free-floating planet population in a realistic framework, then the following observational predictions must hold. First, the frequency of giant planets around low-mass stars must be high ($\sim 50\%$), in agreement with microlensing results \citep{gould10} and in disagreement with radial velocity surveys \citep{johetal2007,lovmay2007,bowetal2010,johetal2010,bonetal2011}. This scenario could be explained if giant planets around M dwarfs are simply too distant to be sampled by current radial velocity surveys, further implying that giant planets are found at larger orbital separations around low-mass stars than Sun-like stars. Second, systems containing a large number of giant planets and extending to large orbital radii must be abundant, at least at early times before they become unstable. Such systems may be detectable by direct imaging of young stars \cite[e.g. HR 8799,][see also \citealt*{deletal2011}]{maretal2008,maretal2010}. Third, the free-floating planet population of $N_{free}/N_{stars} = 1.8$ reported by \cite{sumi11} must be somewhat overestimated. Fig. 2 shows that observations are far easier to reproduce if this value is closer to 1. Finally, the vast majority of giant planet systems must go unstable. This statement, in turn, implies that giant planets on highly-eccentric orbits should continue to be common and that both terrestrial planets and debris disks should be anti-correlated with eccentric giant planets \citep{veras06,raymond11}.
Other potential sources of free-floating planets exist. One such source is dynamical ejection from multiple-star systems; only about two-thirds of all stars are single stars \citep{lada2006} so multiple-star systems may provide a comparable contribution to free-floaters. Another potential source arises from external forces such as passing stars, galactic tides, or -- most relevant for close ($\lesssim 100$ AU) planets -- perturbations while stars are still in their birth clusters. Indeed, studies of flybys on planetary systems \citep{malmberg07,malmberg11} indicate these perturbations may eject planets. Recent cluster simulations have shown that planets with orbital radii of 5-30 AU are likely to disrupted by close stellar passages within their birth clusters at a rate of up to $\sim 10\%$~\citep{parqua2011}. The cluster disruption rate is much higher than the the long-term effects from passing stars \citep[e.g.][]{weietal1987} or galactic tides \citep[e.g.][]{tremaine1993}, which are thought to cause disruption for semimajor axes of $\sim 10^5$ AU. Free-floating Jupiter-mass objects can also be formed by collisions between high-mass protoplanetary discs \citep{linetal1998}, but extremely dense stellar conditions are needed to cause such collisions. Other potential sources of free-floaters may arise from dynamical ejection prompted by mass loss during post-main sequence evolution. \cite{veretal2011} show that planets at several hundred AU can be dynamically ejected due to mass loss from stars with progenitor masses greater than $\sim 2 M_{\odot}$; these planets may reach such wide distances through scattering over the main sequence lifetime of the system. The interaction of planetary systems with localized Galactic phenomena such as the tidal streams, passage into and out of spiral arms from radial stellar migration, Lindblad resonances with the bar, and passing molecular clouds represent other, largely unexplored, potential causes for ejection. Also, we cannot rule out the possibility that Jupiter-mass objects could simply represent the low-mass tail of the stellar initial mass function, and that free-floaters could help constrain the presence or extent of a planet-star gap in the initial mass function \citep[e.g.][]{chabrier2003,paretal2011}.
\section*{Acknowledgments}
We thank the referee for helpful comments. S.N.R. is grateful to the IoA and DAMTP for their hospitality during his visit to Cambridge in November 2011, and acknowledges support from the CNRS's PNP and EPOV programs and the NASA Astrobiology Institute's VPL lead team.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 7,452 |
Q: Make Symfony forms use simple GET names I am currenly creating a simple search form, using Symfony 4.1's form builder. Rendering works great, but I lack a bit of control on the way the request is formed.
The generated request looks like:
http://localhost:8000/fr/search?advanced_search%5Bquery%5D=test&advanced_search%5Bcategory%5D=1&advanced_search%5BverifiedOnly%5D=&advanced_search%5Bsave%5D=
And I want it to look like:
http://localhost:8000/fr/search?query=test&category=1&verifiedOnly=
The code I'm using:
$this->ff->create(
AdvancedSearchType::class,
null,
['csrf_protection' => false]
)->createView()
And
public function buildForm(FormBuilderInterface $builder, array $options)
{
$builder
->setMethod('GET')
->add('query', SearchType::class,
[
'attr'=> [
'placeholder' => 'search.query'
]
]
)
->add('category', EntityType::class,
[
'class' => Category::class,
'label' => 'search.category',
'group_by' => function(Category $category, $key, $value) {
// Code...
return $category->getName();
}
]
)
->add('verifiedOnly', CheckboxType::class,
[
'label' => 'search.verifiedOnly',
'required' => false
]
)
->add('save', SubmitType::class,
[
'label' => 'search.submitButton'
]
);
}
The reason behind this is because it generates widgets like this
<input .. name="advanced_search[query]" ..>
When I want them like this
<input .. name="query" ..>
Is there any way to change this? Thank you!
A: When you are using the shortcut method provided by Symfony's ControllerTrait, the name of the generated form will be automatically derived from the form type's block prefix.
You can change the implicit name for all forms based on this type by overriding the getBlockPrefix() method in your form type:
public function getBlockPrefix()
{
return '';
}
Or you decide to change the name for just one particular form by giving its name explicitly making use of the form factory that is used under the hood by the controller trait's shortcut methods like this:
$form = $this->get('form.factory')
->createNamedBuilder('', AdvancedSearchType::class, null, [
'csrf_protection' => false,
])
->getForm();
But you need to be careful now. If there is more than one form without a name handled during the same request, the component is not able to decide which of these forms has been submitted and will act as if both had been so.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 6,708 |
<!DOCTYPE html>
<html>
<head>
<meta http-equiv="content-type" content="text/html; charset=utf-8"/>
<title></title>
<link rel="Stylesheet" href="../css/analysis.css" />
<script type="text/javascript">
function init() {
if (window.location.hash) {
var parentDiv, nodes, i, helpInfo, helpId, helpInfoArr, helpEnvFilter, envContent, hideEnvClass, hideNodes;
helpInfo = window.location.hash.substring(1);
if(helpInfo.indexOf("-")) {
helpInfoArr = helpInfo.split("-");
helpId = helpInfoArr[0];
helpEnvFilter = helpInfoArr[1];
}
else {
helpId = helpInfo;
}
parentDiv = document.getElementById("topics");
nodes = parentDiv.children;
hideEnvClass = (helpEnvFilter === "OnlineOnly"? "PortalOnly": "OnlineOnly");
if(document.getElementsByClassName) {
hideNodes = document.getElementsByClassName(hideEnvClass);
}
else {
hideNodes = document.querySelectorAll(hideEnvClass);
}
for(i=0; i < nodes.length; i++) {
if(nodes[i].id !== helpId) {
nodes[i].style.display ="none";
}
}
for(i=0; i < hideNodes.length; i++) {
hideNodes[i].style.display ="none";
}
}
}
</script>
</head>
<body onload="init()">
<div id="topics">
<div id="toolDescription" class="smallsize">
<h2>Pārraudzīt veģetāciju</h2><p/>
<h2><img src="../images/GUID-7763FCC0-2EA1-463B-98D0-4EBDF6150907-web.png" alt="Portāla veģetācijas pārraudzības rīks"></h2>
<hr/>
<p>Šis rīks veic aritmētisku darbību vairākjoslu rastra slāņa joslās, lai atklātu pētījumu teritorijas veģetācijas seguma informāciju.
</p>
</div>
<!--Parameter divs for each param-->
<div id="inputLayer">
<div><h2>Izvēlēties ievades datus</h2></div>
<hr/>
<div>
<p>Izvēlieties vairākjoslu rastra slāni. Pārliecinieties, vai ievades rastram ir pieejamas atbilstošas joslas.
</p>
</div>
</div>
<div id="vegetationIndexType">
<div><h2>Izvēlēties veģetācijas pārraudzības metodi</h2></div>
<hr/>
<div>
<p>Izvēlieties metodi, kas tiek izmantota veģetācijas indeksa slāņa izveidei. Dažādie veģetācijas indeksi var palīdzēt izcelt noteiktus elementus vai palīdzēt samazināt dažādus trokšņus.
</p>
<ul>
<li>Global Environmental Monitoring Index —
GEMI ir nelineārs veģetācijas indekss globālai vides pārraudzībai, izmantojot satelīta attēlus. Tas ir līdzīgs NDVI, bet to mazāk ietekmē atmosfēras iedarbība. To ietekmē atklāta augsne, tādēļ to nav ieteicams izmantot teritorijās ar retu vai vidēji blīvu veģetāciju.
</li>
<li>Green Vegetation Index - Landsat TM —
GVI tika sākotnēji izstrādāts no Landsat MSS attēliem, bet ir modificēts lietošanai ar Landsat TM attēliem. Tas tiek dēvēts arī par Landsat TM Tasseled Cap zaļās veģetācijas indeksu. Šo pārraudzības indeksu var lietot ar attēliem, kuru joslām ir tādi paši spektrālie parametri.
</li>
<li>Modified Soil Adjusted Vegetation Index —
MSAVI2 ir veģetācijas indekss, kas mēģina samazināt SAVI metodes atklātas augsnes ietekmi.
</li>
<li>Normalized Difference Vegetation Index —
NDVI ir standartizēts indekss, kas ļauj ģenerēt attēlu, kurā tiek rādīts zaļums, relatīvā biomasa. Šis indekss izmanto vairākspektru rastra datu kopas divu joslu parametru kontrastu, hlorofila pigmenta absorbciju sarkanajā joslā un augu materiālu augsto atstarošanu infrasarkanajā (NIR) joslā.
</li>
<li>Perpendicular Vegetation Index —
PVI ir līdzīgs starpības veģetācijas indeksam, taču to ietekmē atmosfēras svārstības. Izmantojot šo metodi, lai salīdzinātu dažādus attēlus, tā ir izmantojama tikai attēliem, kam veikta atmosfēriskā korekcija. Šo informāciju var sniegt datu pakalpojumu sniedzējs.
</li>
<li>Soil-Adjusted Vegetation Index —
SAVI ir veģetācijas indekss, kas mēģina samazināt augsnes spilgtuma ietekmi, izmantojot augsnes spilgtuma korekcijas koeficientu. Tas bieži tiek izmantots sausos reģionos, kuros ir rets veģetatīvais segums.
</li>
<li>Sultan's Formula —
Process Sultan's Formula sešu joslu 8 bitu attēlam pielieto noteiktu algoritmu, lai izveidotu trīs joslu 8 bitu attēlu. Rezultāta attēls piekrastes zonās izceļ iežu veidojumus, tā dēvētos ofiolītus. Šī formula tika izstrādāta, pamatojoties uz Landsat 5 vai 7 scēnas TM un ETM joslām.
</li>
<li>Transformed Soil-Adjusted Vegetation Index —
Pārveidotais SAVI ir veģetācijas indekss, kas mēģina samazināt augsnes spilgtuma ietekmi, pieņemot, ka augsnes līnijai ir brīvi noteikts slīpums, un pārtvert.
</li>
</ul>
</div>
</div>
<div id="bandIndexes">
<div><h2>Norādīt NIR joslas un sarkanās joslas indeksus</h2></div>
<hr/>
<div>
<p>Ievadiet infrasarkanās (NIR) un sarkanās joslas indeksus.
</p>
<p>Katrs satelīta sensors un lidojuma kamera tver informāciju, kas ir sadalīta joslu indeksos. Katrs joslas indekss ietver noteiktas elektromagnētiskā spektra daļas informāciju. Šai veģetācijas pārraudzības metodei nepieciešams norādīt joslas indeksu, kas uztvēra NIR un sarkanos viļņu garumus.
</p>
</div>
</div>
<div id="slopeOfSoilLine">
<div><h2>Augsnes līnijas slīpums</h2></div>
<hr/>
<div>
<p>Augsnes līnijas slīpums. Slīpums ir aptuvenā izkliedes diagrammas NIR un sarkano joslu lineārā attiecība.
</p>
<p>Šis parametrs ir derīgs tikai pārveidotajam, augsnei pielāgotajam veģetācijas indeksam.
</p>
</div>
</div>
<div id="interceptOfSoilLine">
<div><h2>Pārtveršana</h2></div>
<hr/>
<div>
<p>Šī ir infrasarkanā (NIR) vērtība, kurā noteikto augsnes līniju sarkanās joslas atstarošanas vērtība ir 0.
</p>
<p> <code>(a = NIR - sRed)</code> , ja sarkanā ir 0.
</p>
<p>Šis parametrs ir derīgs tikai pārveidotajam, augsnei pielāgotajam veģetācijas indeksam.
</p>
</div>
</div>
<div id="greenVegetativeCover">
<div><h2>Zaļās veģetācijas seguma apjoms</h2></div>
<hr/>
<div>
<p>SAVI metodei nepieciešams norādīt veģetācijas seguma daudzumu.
</p>
<p>Ievadiet vērtību starp 0.0 un 1.0, kur
<ul>
<li>1 = teritorijas bez zaļās veģetācijas seguma
</li>
<li>0,5 = teritorijas ar vidēju zaļās veģetācijas segumu
</li>
<li>0 = teritorijas ar augstu zaļās veģetācijas segumu
</li>
</ul>
</p>
</div>
</div>
<div id="adjustmentFactor">
<div><h2>Korekcijas koeficients</h2></div>
<hr/>
<div>
<p>Pārveidotā, augsnei pielāgotā veģetācijas indeksa metodei nepieciešams iestatīt korekcijas koeficientu, lai palīdzētu samazināt augsnes ietekmi. Noklusējuma vērtība ir 0.08.
</p>
<p>Zemāka vērtība nozīmē, ka tiek ignorēta augsnes ietekme. Augsta vērtība nozīmē, ka augsne ietekmē rezultātu.
</p>
</div>
</div>
<div id="outputLayer">
<div><h2>Rezultātu slāņa nosaukums</h2></div>
<hr/>
<div>
<p>Slāņa nosaukums, kas tiks izveidots sadaļā <b>Mans saturs</b> un pievienots kartei. Noklusējuma nosaukums ir balstīts uz rīka nosaukumu un ievades slāņa nosaukumu. Ja slānis jau pastāv, jums tiks lūgts norādīt citu nosaukumu.
</p>
<p>Lietojot <b>Saglabāt rezultātus</b> nolaižamajā sarakstlodziņā, jūs varat norādīt nosaukumu mapē <b>Mans saturs</b>, kur tiks saglabāti rezultāti.
</p>
</div>
</div>
</div>
</html>
| {
"redpajama_set_name": "RedPajamaGithub"
} | 4,246 |
Q: Let $z = x + iy$ be a fifth root of unity. Show that the quotient y/x can only take on five distinct values, and determine those five values. It's easy to prove that y/x can only take on 5 different values through the use of the exponential form of z. However that doesn't allow us to give a precise value. For example, for k=1, $z = e^{i\frac{2\pi}{5}} $, so $x/y = \tan(\frac{2\pi}{5}) $.
What I think we need to do is find the cartesian form of those numbers and I have no idea how to go about that.
I could take the route mentioned by this question, but that seems like too much work, which will amount to finding tan of all of those angles:
Find exact value of $\cos (\frac{2\pi}{5})$ using complex numbers.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 2,149 |
"Tools and utilities for talking to the stitching computation service."
from __future__ import absolute_import
import json
import os.path
import pprint
import sys
import urllib
import xmlrpclib
try:
from .utils import StitchingError, StitchingServiceFailedError
from ..xmlrpc.client import make_client
from ..util.json_encoding import DateTimeAwareJSONDecoder
except:
from gcf.omnilib.stitch.utils import StitchingError, StitchingServiceFailedError
from gcf.omnilib.xmlrpc.client import make_client
from gcf.omnilib.util.json_encoding import DateTimeAwareJSONDecoder
# Tags used in the options to the SCS
HOP_EXCLUSION_TAG = 'hop_exclusion_list'
HOP_INCLUSION_TAG = 'hop_inclusion_list'
GENI_PROFILE_TAG = 'geni_routing_profile'
GENI_PATHS_MERGED_TAG = 'geni_workflow_paths_merged'
ATTEMPT_PATH_FINDING_TAG = 'attempt_path_finding'
class Result(object):
'''Hold and parse the raw result from the SCS'''
CODE = 'code'
VALUE = 'value'
GENI_CODE = 'geni_code'
OUTPUT = 'output'
def __init__(self, xmlrpc_result):
self.result = xmlrpc_result
def isSuccess(self):
return (self.CODE in self.result
and self.GENI_CODE in self.result[self.CODE]
and int(self.result[self.CODE][self.GENI_CODE]) == 0)
def value(self):
if self.VALUE in self.result:
return self.result[self.VALUE]
else:
raise StitchingError("No value in result")
def errorString(self):
ret = ""
if self.CODE in self.result:
ret = str(self.result[self.CODE])
if self.OUTPUT in self.result:
ret +=" %s" % self.result[self.OUTPUT]
return ret
class Service(object):
def __init__(self, url, key=None, cert=None, timeout=None, verbose=False):
self.url = url
self.timeout=timeout
self.verbose=verbose
if isinstance(url, unicode):
url2 = url.encode('ISO-8859-1')
else:
url2 = url
type, uri = urllib.splittype(url2.lower())
if type == "https":
self.key=key
self.cert=cert
else:
self.key=None
self.cert=None
def GetVersion(self, printResult=True):
server = make_client(self.url, keyfile=self.key, certfile=self.cert, verbose=self.verbose, timeout=self.timeout)
# As a sample of how to do make_client specifying the SSL version / ciphers (these are the defaults though):
# import ssl
# server = make_client(self.url, keyfile=self.key, certfile=self.cert, verbose=self.verbose, timeout=self.timeout, ssl_version=ssl.PROTOCOL_TLSv1, ciphers="HIGH:MEDIUM:!ADH:!SSLv2:!MD5:!RC4:@STRENGTH")
try:
result = server.GetVersion()
except xmlrpclib.Error as v:
if printResult:
print "ERROR", v
raise
except Exception, e:
if printResult:
import traceback
print "ERROR: %s" % traceback.format_exc()
raise
if printResult:
print "GetVersion said:"
pp = pprint.PrettyPrinter(indent=4)
print pp.pformat(result)
return result
def ListAggregates(self, printResult=True):
server = make_client(self.url, keyfile=self.key, certfile=self.cert, verbose=self.verbose, timeout=self.timeout)
try:
result = server.ListAggregates()
except xmlrpclib.Error as v:
if printResult:
print "ERROR", v
raise
if printResult:
print "ListAggregates said:"
pp = pprint.PrettyPrinter(indent=4)
print pp.pformat(result)
return result
def ComputePath(self, slice_urn, request_rspec, options, savedFile=None):
"""Invoke the XML-RPC service with the request rspec.
Create an SCS PathInfo from the result.
"""
result = None
if savedFile and os.path.exists(savedFile) and os.path.getsize(savedFile) > 0:
# read it in
try:
savedSCSResults = None
with open(savedFile, 'r') as sfP:
savedStr = str(sfP.read())
result = json.loads(savedStr, encoding='ascii', cls=DateTimeAwareJSONDecoder)
except Exception, e:
import traceback
print "ERROR", e, traceback.format_exc()
raise
if result is None:
server = make_client(self.url, keyfile=self.key, certfile=self.cert, verbose=self.verbose, timeout=self.timeout)
arg = dict(slice_urn=slice_urn, request_rspec=request_rspec,
request_options=options)
# import json
# print "Calling SCS with arg: %s" % (json.dumps(arg,
# ensure_ascii=True,
# indent=2))
try:
result = server.ComputePath(arg)
except xmlrpclib.Error as v:
print "ERROR", v
raise
self.result = result # save the raw result for stitchhandler to print
geni_result = Result(result) # parse result
if geni_result.isSuccess():
return PathInfo(geni_result.value())
else:
# when there is no route I seem to get:
#{'geni_code': 3} MxTCE ComputeWorker return error message ' Action_ProcessRequestTopology_MP2P::Finish() Cannot find the set of paths for the RequestTopology. '.
if self.result:
raise StitchingServiceFailedError(None, self.result)
else:
raise StitchingServiceFailedError("ComputePath invocation failed: %s" % geni_result.errorString(), self.result)
class PathInfo(object):
'''Hold the SCS expanded RSpec and workflow data'''
SERVICE_RSPEC = 'service_rspec'
WORKFLOW_DATA = 'workflow_data'
DEPS = 'dependencies'
def __init__(self, raw_result):
self.raw = raw_result
self.links = list()
wd = raw_result[self.WORKFLOW_DATA]
for link_name in wd:
link = Link(link_name)
link.parse_dependencies(wd[link_name][self.DEPS])
self.links.append(link)
def rspec(self):
return self.raw[self.SERVICE_RSPEC]
def workflow_data(self):
return self.raw[self.WORKFLOW_DATA]
def dump_workflow_data(self):
"""Print out the raw workflow data for debugging."""
wd = self.raw[self.WORKFLOW_DATA]
for link_name in wd:
print "Link %r:" % (link_name)
self.dump_link_data(wd[link_name], " ")
def dump_link_data(self, link_data, indent=""):
print "%sDepends on:" % (indent)
for d in link_data[self.DEPS]:
self.dump_dependency(d, indent + " ")
def dump_dependency(self, dep_data, indent=""):
keys = sorted(dep_data.keys())
deps = []
if self.DEPS in keys:
deps = dep_data[self.DEPS]
keys.remove(self.DEPS)
for k in keys:
print "%s%r: %r" % (indent, k, dep_data[k])
if deps:
print "%sDepends on:" % (indent)
for d in deps:
self.dump_dependency(d, indent + " ")
class Dependency(object):
'''A dependency of a stitching path (aka Link) from the workflow_data'''
AGG_URN = 'aggregate_urn'
AGG_URL = 'aggregate_url'
DEPS = 'dependencies'
IMPORT_VLANS = 'import_vlans'
HOP_URN = 'hop_urn'
def __init__(self, data):
for k in (self.AGG_URN, self.AGG_URL, self.IMPORT_VLANS, self.HOP_URN):
object.__setattr__(self, k, data[k])
self.dependencies = list()
if self.DEPS in data:
for d in data[self.DEPS]:
self.dependencies.append(Dependency(d))
class Link(object):
'''A stitching path's entry in the workflow_data'''
def __init__(self, name):
self.name = name
self.dependencies = list()
def parse_dependencies(self, data):
for d in data:
self.dependencies.append(Dependency(d))
def main(argv=None):
if argv is None:
argv = sys.argv[1:]
# I2 SSL
SCS_URL = "https://geni-scs.net.internet2.edu:8443/geni/xmlrpc"
# I2 non SSL (deprecated) SCS_URL = "http://geni-scs.net.internet2.edu:8081/geni/xmlrpc"
# MAX SCS_URL (will go away) = "https://oingo.dragon.maxgigapop.net:8443/geni/xmlrpc"
# Non SSL MAX SCS_URL (deprecated, will go away) = "http://oingo.dragon.maxgigapop.net:8081/geni/xmlrpc"
# Test SCS (for untested AMs): https://nutshell.maxgigapop.net:8443/geni/xmlrpc
# Non SSL Test SCS (deprecated): http://nutshell.maxgigapop.net:8081/geni/xmlrpc
# Dev (usually down) SCS: http://geni.maxgigapop.net:8081/geni/xmlrpc
# FIXME: Ideally we'd support loading your omni_config and finding the cert/key that way
ind = -1
printR = True
listAMs = False
keyfile=None
certfile=None
verbose = False
timeout = None
if "-h" in argv or "-?" in argv:
print "Usage: scs.py [--scs_url <URL of SCS server if not standard (%s)] [--monitoring to suppress printouts] [--timeout SSL timeout in seconds] --key <path-to-trusted-key> --cert <path-to-trusted-client-cert>" % SCS_URL
print " Key and cert are not required for an SCS not running at an https URL."
print " Supply --listaggregates to list known AMs at the SCS instead of running GetVersion"
print " Supply --verbosessl to turn on detailed SSL logging"
return 0
for arg in argv:
ind = ind + 1
if ("--scs_url" == arg or "--scsURL" == arg) and (ind+1) < len(argv):
SCS_URL = argv[ind+1]
if "--monitoring" == arg:
printR = False
if arg.lower() == "--listaggregates":
listAMs = True
if ("--key" == arg or "--keyfile" == arg) and (ind+1) < len(argv):
keyfile = argv[ind+1]
if ("--cert" == arg or "--certfile" == arg) and (ind+1) < len(argv):
certfile = argv[ind+1]
if arg.lower() == "--verbosessl":
verbose = True
if arg.lower() == "--timeout" and (ind+1) < len(argv):
timeout = float(argv[ind+1])
if SCS_URL.lower().strip().startswith('https') and (keyfile is None or certfile is None):
print "ERROR: When using an SCS with an https URL, you must supply the --key and --cert arguments to provide the paths to your key file and certificate"
return 1
if keyfile is not None:
# Ensure have a good path for it
if not os.path.exists(keyfile) or not os.path.getsize(keyfile) > 0:
print "ERROR: Key file %s doesn't exist or is empty" % keyfile
return 1
keyfile = os.path.expanduser(keyfile)
if certfile is not None:
# Ensure have a good path for it
if not os.path.exists(certfile) or not os.path.getsize(certfile) > 0:
print "ERROR: Cert file %s doesn't exist or is empty" % certfile
return 1
certfile = os.path.expanduser(certfile)
try:
scsI = Service(SCS_URL, key=keyfile, cert=certfile, timeout=timeout, verbose=verbose)
if listAMs:
result = scsI.ListAggregates(printR)
else:
result = scsI.GetVersion(printR)
tag = ""
try:
verStruct = result
if verStruct and verStruct.has_key("value") and verStruct["value"].has_key("code_tag"):
tag = verStruct["value"]["code_tag"]
except:
print "ERROR: SCS return not parsable"
raise
print "SUCCESS: SCS at ",SCS_URL, " is running version: ",tag
return 0
except Exception, e:
print "ERROR: SCS at ",SCS_URL, " is down: ",e
return 1
# To run this main, be sure to do:
# export PYTHONPATH=$PYTHONPATH:/path/to/gcf/src
if __name__ == "__main__":
sys.exit(main())
| {
"redpajama_set_name": "RedPajamaGithub"
} | 3,284 |
Айн-Газаль () — поселення культури докерамічного неоліту B в передмісті Амману, Йорданія. Відповідно до старого датування, було населене в період 7250 — 5000 років до н. е.; більш сучасне каліброване датування удревляє цей період до 8440 — 6500 рр. до н. е.. Площа — 15 га, одне з найбільших поселень епохи неоліту. Іноді пізній етап розвитку Айн-Газаля класифікують як докерамічний неоліт C.
Поселення
За часів свого розквіту (кінець 8-го тисячоліття до н. е.) населення становило близько 3000 осіб (більше, ніж у місті Єрихон в ту саму епоху). Після 6500 року до н. е. протягом декількох поколінь населення скоротилося в кілька разів, ймовірно, через погіршення клімату.
Складається з великої кількості будівель, які діляться на три різних райони. Прямокутні споруди з сирцевої цегли складалися з двох і більше неоднакових кімнат. Стіни іззовні обмазували глиною, а зсередини — алебастром, яким покривали і підлогу. Покриття оновлювали раз у декілька років.
На розташованих поблизу полях розводили пшеницю, ячмінь, бобові, а також пасли кіз. До того ж, мешканці полювали на диких оленів, газелей, ослів, кабанів, лисиць, зайців тощо.
Культура
Частину мерців ховали у фундаменті будівель, інших — в полях. Черепа мерців, похованих у будинках, зберігали окремо. Археологи виявили такі черепа в декількох місцях Палестини, Сирії та Йорданії, в тому числі в Айн-Газалі. Вони були покриті алебастром, очниці були залиті бітумом, що свідчить про своєрідний культ предків у цих місцях. Деякі мерці взагалі не були поховані і потрапляли до сміттєвих куп.
Крім решток людей ховали антропоморфні алебастрові статуї, які були покладені біля особливих будівель, ймовірно, мали ритуальне значення. На голові статуй були зображені очі і волосся, на тілі — татуювання у вигляді орнаменту або одяг. Для зображення очей використовували раковини, а зіниць — бітум. У селищі знайдено 32 таких статуї, з яких 15 в повний зріст, ще 15 — бюсти і дві фрагментарно збережені голови. Три бюста мали по дві голови. Одна зі статуй, приблизно VI тисячоліття до н. е., зображує жінку з великими очима, тонкими руками, виступаючими колінами і ретельно виліпленими пальцями ніг.
Археологічні дослідження
Давнє поселення було відкрито випадково при будівництві дороги в 1974 році. Розкопки почалися в 1982 році і тривали до 1989 року. На початку 1990-х років була проведена ще одна серія досліджень.
Палеогенетика
У мешканців Айн-Газалю були виявлені Y-хромосомні гаплогрупи CT, E, E1b1b1, T (xT1a1, T1a2a) і мітохондріальні гаплогрупи R0a, R0a2, T1a, T1a2.
Джерела
Ресурси Інтернету
Scarre Chris (ed.): The Human Past, Thames & Hudson 2005, p.222
'Ain Ghazal statues at Smithsonian Institution
'Ain Ghazal Excavation Reports (menic.utexas.edu)
Institut du Monde Arabe
The 'Ain Ghazal Statue Project
The Joukowsky Institute of Archaeology
Примітки
Близькосхідний неоліт
Археологічні культури Азії
Натуфійська культура
Археологічні пам'ятки Йорданії | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 1,087 |
describe('mocha_sample', function () {
describe('#indexOf()', function () {
it('should return -1 when the value is not present', function () {
[1, 2, 3].indexOf(5).should.equal(-1);
[1, 2, 3].indexOf(0).should.equal(-1);
});
it('should return the position of the value (with first element position is 0) in the array when it is present', function () {
[1, 2, 3].indexOf(1).should.equal(0);
[1, 2, 3].indexOf(2).should.equal(1);
[1, 2, 3].indexOf(3).should.equal(2);
});
});
}); | {
"redpajama_set_name": "RedPajamaGithub"
} | 3,772 |
Rebecca McLeod on Farewell for now
Rebecca McLeod on Otago Harbour in a red frenzy
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Stick 222
Suffrage 125 14
The Dismal Science 1657
The Psychology Report 23
Up and Atom 6
Wild Science 10
Search within Science Life
Back to Vantage Point
Southern right whale population on the rebound
By Rebecca McLeod • 14/10/2009 • 3
Southern right whales, hunted perilously close to extinction last century, appear to be making a remarkable recovery in New Zealand according to recent research. For the past four years a group of scientists from Auckland and Otago Universities, the Department of Conservation and the Australian Antarctic Division have been sailing south to the Auckland Islands to count and identify individual whales that go there to breed and calve. Recent DNA matches of whales recorded in both the Auckland Islands and mainland New Zealand have shown that the animals migrate between these two areas and likely form one intermingling population. Certain individuals have also been seen at the Auckland Islands, Campbell Island, mainland New Zealand and South Australia — these animals certainly get around!
The research group sails to the Auckland Islands on the R.V. Evohe, and then conducts surveys from small boats. Here they are in Port Ross.
Individual whales are able to be identified by unique markings on their skin. These white patches are aggregations of crustaceans, called cyamids, which cluster around skin calluses.
These patches of cyamids remain remarkably consistent year on year.
Results of genetic analyses by Professor Scott Baker and his team at Auckland and Oregon State Universities indicate that the New Zealand population of southern rights was reduced to as few as 50 reproductive females following years of hunting in the 1800s and early 1900s, and further illegal whaling of the species by the Soviet Union in the 1950s and 60s. Since the 1960s the population appears to have been steadily increasing. Ten years ago the population was estimated to include about 900 whales, and the preliminary findings of the latest surveys, indicate that numbers have likely doubled since then. According to Dr Simon Childerhouse, the leader of the most recent expeditions, the rate of recovery of New Zealand southern right whales appears to be at least as high as that seen for populations in Australia and South Africa. In contrast, populations of northern right whales are incredibly depleted, and do not appear to be recovering. Despite right whales being protected in the northern hemisphere, mortality from ship strike and entanglement in fishing gear appears to be outweighing natural population increase. In this sense, southern right whales are fortunate — their natural home range around the Southern Ocean and coastal and offshore New Zealand, has relatively low volumes of shipping traffic.
Southern rights are baleen whales, and feed upon zooplankton such as copepods and euphausids.
Although, as Dr Will Rayment from the University of Otago explains, as the species starts to recolonise mainland New Zealand, it is possible that they will be more at risk of such threats. 'Historically, southern right whales have aggregated in sheltered bays, including Otago and Wellington Harbours, to breed and calve. As this species makes a resurgence around the mainland, it is expected that they will again tend to spend time in these areas – although of course since they were last here the intensity of human use of harbours has changed somewhat. Their tendency to spend time in coastal areas means that they could possibly be affected by human activities such as shipping, fishing, aquaculture, and even tidal power generation. It will be interesting to see how the species and human activity interact in coming years. Here we have a unique opportunity for proactive management of an endangered species — as opposed to reactive management, which is more often the case.'
Two southern right whales, with the R.V. Evohe anchored in the background.
These days, Port Ross at the northern end of the Auckland Islands, is the main breeding area for New Zealand southern rights. The whales congregate there in large numbers throughout the winter months. Dr Rayment says that there may be up to 200 individuals in the harbour at any one time, and all evidence points towards the species being highly promiscuous. During the latest trip to the Auckland Islands, it was common to see several males pursuing a female, with the female often rolling on her back in an effort to stop males from mating with her. Following a one year gestation period, females tend to return to the harbour to calve, and then spend a year nursing their calf before conceiving again — resulting in most females producing one calf every three or four years. The increase in whale numbers appears to be following a typical exponential population growth often seen in recovering populations. And the increase is starting to be noticeable in mainland New Zealand — numbers of annual whale sightings recorded by the Department of Conservation are trending upwards around Otago. The current population is estimated to be only 10% of the pre-whaling numbers, suggesting that we may well be visited by a lot more southern rights in the future. In these times of doom and gloom for the marine environment (think depleted fish stocks, marine pollution, ocean acidification…), it is uplifting to see a species making a comeback.
Southern right whales often approached the research vessels during surveys.
Last year the expedition was joined by a journalist and a photographer from National Geographic — the resulting underwater photographs are truly awesome.
population recovery
Southern right whale
About Vantage Point
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"redpajama_set_name": "RedPajamaCommonCrawl"
} | 9,198 |
/* Hans Pabst (Intel Corp.)
******************************************************************************/
#ifndef LIBXSMM_TIMER_H
#define LIBXSMM_TIMER_H
#include "libxsmm_macros.h"
typedef unsigned long long libxsmm_timer_tickint;
LIBXSMM_EXTERN_C typedef struct LIBXSMM_RETARGETABLE libxsmm_timer_info {
int tsc;
} libxsmm_timer_info;
/** Query timer properties. */
LIBXSMM_API int libxsmm_get_timer_info(libxsmm_timer_info* info);
/**
* Returns the current clock tick of a monotonic timer source with
* platform-specific resolution (not necessarily CPU cycles).
*/
LIBXSMM_API libxsmm_timer_tickint libxsmm_timer_tick(void);
/** Returns the difference between two timer ticks (cycles); avoids potential side-effects/assumptions of LIBXSMM_DIFF. */
LIBXSMM_API_INLINE libxsmm_timer_tickint libxsmm_timer_ncycles(libxsmm_timer_tickint tick0, libxsmm_timer_tickint tick1) {
return LIBXSMM_DELTA(tick0, tick1);
}
/** Returns the duration (in seconds) between two values received by libxsmm_timer_tick. */
LIBXSMM_API double libxsmm_timer_duration(libxsmm_timer_tickint tick0, libxsmm_timer_tickint tick1);
#endif /*LIBXSMM_TIMER_H*/
| {
"redpajama_set_name": "RedPajamaGithub"
} | 7,372 |
///<reference path='refs.ts'/>
module TDev
{
export class DeclEntry
{
public icon = "svg:hammer,white,clip=50";
public iconArtId: string;
public color = "blue";
public description = "";
public classAdd = "";
constructor(public name:string) {
}
private getName() { return this.name; }
private getDescription() { return this.description; }
private nodeType() { return "declEntry"; }
public mkBox():HTMLElement
{
var r = DeclRender.mkBoxEx(this, this.nodeType());
r.className += this.classAdd;
return r;
}
public getIconArtId() { return this.iconArtId; }
public makeIntoAddButton()
{
this.icon = "svg:circlePlus,black";
this.color = "transparent";
this.classAdd += " navRound";
}
static mkSeeMore(lbl:string)
{
var d = new DeclEntry(lf("see more options"));
d.description = lbl
return d.mkBox()
}
}
export module DeclRender
{
//var libsIcon = ScriptIcon("Book");
//var libsBrush = new SolidColorBrush(Colors.Magenta); // TODO find good color
var artColor = "#ff0038";
var dataColor = "#ff7518";
var actionColor = "#E72A59";
var recordColor = "#800080";
var userDefinedColor = "#1B91E0";
export var declColor:any =
{
globalDef: (d:AST.GlobalDef) => {
var c = DeclRender.propColor(d);
if (c) return c;
return d.isResource ? artColor : dataColor;
},
recordDef: () => recordColor,
action: function (a: AST.Action) {
if (a.isEvent()) return "#007fff";
if (a.isPage()) return "#00008B";
if (a.isActionTypeDef()) return recordColor;
return actionColor;
},
libraryRef: (l:AST.LibraryRef) =>
l.resolved ? l.resolved.htmlColor() : "#48A300",
/*
globalDef: (d:AST.GlobalDef) => d.isResource ? "#A4500F" : "#FD882E",
tableDef: () => "#E72A59",
action: (a:AST.Action) => a.isEvent() ? "#41900D" : "#70DE29",
*/
app: (a:AST.App) => a.htmlColor(),
localDef: () => "#E72A59",
kind: (k:Kind) =>
k.isAction ? "#007fff" : k.isUserDefined() ? recordColor : k.getParameterCount() > 0 ? "#c22" : "#40B619",
singletonDef: function(s:AST.SingletonDef) {
if (s.getKind() instanceof ThingSetKind)
return userDefinedColor;
return "#40B619";
/*
switch (s.getName()) {
case "data": return dataColor;
case "art": return artColor;
case "code": return actionColor;
default: return "#40B619";
}
*/
},
recordField: () => "#0d2",
property: function(p:IProperty) {
var c = DeclRender.propColor(p);
if (c)
return c;
else if (p.forwardsToStmt() instanceof AST.RecordField)
return "#0d2";
else if (p.parentKind.isData)
return dataColor;
else if (p instanceof MultiplexProperty)
return declColor.kind((<MultiplexProperty> p).forKind);
else
return declColor.kind(p.getResult().getKind());
/*
if (p.getResult().getKind() == api.core.Nothing)
return actionColor;
else {
return artColor;
var pp = p.getParameters();
var len = pp.length;
if (!pp[0].getKind().isData) len--;
if (len == 0) return artColor;
else if (len == 1) return dataColor;
else return "#800080";
}
*/
},
declEntry: (d:DeclEntry) => d.color,
codeLocation: () => "#1B91E0",
codeLocationCurr: () => "#E31B78",
codeLocationLib: () => "#48A300",
};
export function propColor(p:IProperty)
{
if (p && p.getResult().getKind() == api.core.Color) {
var m = /#([a-fA-F0-9]+)/.exec(p.getDescription());
if (m && m[1].length >= 6) {
return "#" + m[1].slice(-6);
}
}
return null;
}
export function colorByPersistence(icon: string, pers: AST.RecordPersistence): string {
return AST.RecordDef.colorByPersistence(icon, pers);
}
function appCloudColor(app:AST.App, icon:string)
{
if (!app) return icon
if (!icon) icon = Cloud.artUrl(app.iconArtId, true) || app.iconPath()
if (app.isCloud) // TODO: wrong color
icon = icon.replace(/,white/, ",cyan")
return icon
}
var declIcon:any =
{
globalDef: (d: AST.GlobalDef) =>
colorByPersistence(d.getKind().icon() || "svg:Document,white", d.getRecordPersistence()),
recordDef: (r: AST.RecordDef) =>
colorByPersistence(AST.RecordDef.GetIcon(r.recordType), r.getRecordPersistence()),
recordField: (r: AST.RecordField) =>
declIcon["kind"](r.dataKind),
action: (a:AST.Action) =>
// a.isMainAction() ? "svg:actionMain,white" :
a.isActionTypeDef() ? "svg:Bolt,white" :
a.isPage() ? "svg:Book,white" :
a.isEvent() ? "svg:actionEvent,white" :
a.isPrivate ? "svg:Lock,white" :
a.isOffline ? "svg:SignalAlt,white" :
a.parent && a.parent.isCloud ? "svg:Signal,white" :
"svg:emptyplay,white",
app: (a:AST.App) => appCloudColor(a, null),
localDef: (d:AST.LocalDef) =>
d.getKind().icon() || "svg:Document,white",
singletonDef: () => "svg:touchDevelop,white",
property: (p:IProperty) =>
p.getResult().getKind().icon() || "svg:touchDevelop,white",
declEntry: (d:DeclEntry) => d.icon,
kind: (k:Kind) => k.icon() || "svg:Document,white",
codeLocation: () => "svg:actionLocation,white",
codeLocationCurr: () => "svg:actionLocation,white",
codeLocationLib: () => "svg:actionLocation,white",
libraryRef: (l:AST.LibraryRef) =>
appCloudColor(l.resolved,
l.resolved && l.resolved.icon ? l.resolved.iconPath() : "svg:recycleLib,white"),
};
export function mkPropBox(p:IProperty)
{
var f = p.forwardsTo();
if (f != null)
return mkBox(f);
else
return mkBoxEx(p, "property");
}
export function mkKindBox(p:Kind)
{
return mkBoxEx(p, "kind");
}
export function mkBox(decl: AST.Decl) { return mkBoxEx(decl, decl.nodeType()); }
export function mkNameSpaceDecl(decl: any) {
var ns = null;
if (decl.getNamespace) {
ns = span("navSig symbol", decl.getNamespace());
}
var name = decl.getName();
return [ns,name];
}
function iconFromDecl(decl: AST.Decl, tp: string) {
var img;
var iconArtId = decl.getIconArtId ? decl.getIconArtId() : undefined;
if (iconArtId) img = ArtUtil.artImg(iconArtId, true);
else {
var iconPath = declIcon[tp](decl);
img = !iconPath ? <any> text("") : HTML.mkImg(iconPath);
}
var icon = div("navImg", img);
icon.style.backgroundColor = declColor[tp](decl);
return icon;
}
var mdCmt:MdComments;
export function mkBoxEx(decl:any, tp:string):HTMLElement
{
if (!mdCmt) mdCmt = new MdComments();
var icon = iconFromDecl(decl, tp);
var innerElt = div("navItemInner");
var elt= HTML.mkButtonElt("navItem", innerElt);
var sig = null;
var ns = null;
var desc = decl.getBoxInfo ? Util.htmlEscape(decl.getBoxInfo()) : mdCmt.formatInline(decl.getDescription());
var name = decl.getName();
var sigText = decl.getSignature && decl.getSignature();
if (sigText) {
var limit = 18;
if (decl instanceof Kind) limit = 40;
if ((name + sigText).length > limit && sigText != "()") {
if (desc)
desc = Util.htmlEscape(sigText) + " :: " + desc;
else
desc = Util.htmlEscape(sigText);
} else {
sig = span("navSig", decl.getSignature());
}
}
if (decl.getNamespaces) {
var namespaces : string[] = <string[]>decl.getNamespaces();
if (namespaces && namespaces[0]) ns = span("navSig", namespaces[0] + " → ");
}
if (!ns && decl.getNamespace) {
ns = span("navSig symbol", decl.getNamespace());
}
var descDiv = div("navDescription md-inline")
if (decl instanceof AST.Action && !decl.isAtomic)
desc = "<span class='actionAwait'>" + SVG.getIconSVGCore("clock2,#666,clip=60") + "</span>" + desc;
Browser.setInnerHTML(descDiv, desc)
var suff = null
if (decl instanceof Kind) {
if ((<Kind>decl).isImmutable())
suff = div("navDiamond", SVG.getIconSVG("diamond,#00f,clip=60"))
}
var nameDiv = div("navName", ns, name, sig);
innerElt.setChildren([icon, div("navContent", [nameDiv, descDiv]), suff]);
if (decl.debuggingData && decl.debuggingData.critical && decl.debuggingData.max) {
var scorePartial = decl.debuggingData.critical / decl.debuggingData.max.critical;
var score = Math.floor(scorePartial * 27); // there are 28 colors, first of them is white
var color: string = AST.ExprHolder.heatmapColors[score];
innerElt.style.backgroundColor = color;
}
(<any> elt).theDesc = descDiv;
(<any> elt).theName = nameDiv;
(<any> elt).theNode = decl;
return elt;
}
export function mkKindList(ctx:KindContext, curr:Kind, selected:(k:Kind)=>void)
{
var profile = TheEditor.intelliProfile;
var kinds = Script.getKinds().filter((k:Kind) =>
k.isData && k.hasContext(ctx) && Script.canUseCapability(k.generalCapabilities) && k != api.core.Unknown &&
k.getParameterCount() <= 1 &&
(!profile || profile.hasKind(k))
);
function cmp(a:Kind, b:Kind) {
var d = b.listPriority() - a.listPriority();
if (d) return d;
else return a.toString().localeCompare(b.toString());
}
kinds.sort(cmp);
return kinds.map(function (k:Kind) {
var kk = DeclRender.mkKindBox(k);
if (k == curr)
kk.setFlag("selected", true);
Util.clickHandler(kk, function() { selected(k) });
return kk;
});
}
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 7,684 |
package com.netflix.conductor.core.event;
import java.io.Serializable;
import com.netflix.conductor.model.WorkflowModel;
public final class WorkflowEvaluationEvent implements Serializable {
private final WorkflowModel workflowModel;
public WorkflowEvaluationEvent(WorkflowModel workflowModel) {
this.workflowModel = workflowModel;
}
public WorkflowModel getWorkflowModel() {
return workflowModel;
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 6,978 |
package operators
import (
"vitess.io/vitess/go/vt/sqlparser"
"vitess.io/vitess/go/vt/vtgate/planbuilder/operators/ops"
"vitess.io/vitess/go/vt/vtgate/planbuilder/operators/rewrite"
"vitess.io/vitess/go/vt/vtgate/planbuilder/plancontext"
"vitess.io/vitess/go/vt/vtgate/semantics"
)
type Filter struct {
Source ops.Operator
Predicates []sqlparser.Expr
}
var _ ops.PhysicalOperator = (*Filter)(nil)
func newFilter(op ops.Operator, expr sqlparser.Expr) ops.Operator {
return &Filter{
Source: op, Predicates: []sqlparser.Expr{expr},
}
}
// IPhysical implements the PhysicalOperator interface
func (f *Filter) IPhysical() {}
// Clone implements the Operator interface
func (f *Filter) Clone(inputs []ops.Operator) ops.Operator {
predicatesClone := make([]sqlparser.Expr, len(f.Predicates))
copy(predicatesClone, f.Predicates)
return &Filter{
Source: inputs[0],
Predicates: predicatesClone,
}
}
// Inputs implements the Operator interface
func (f *Filter) Inputs() []ops.Operator {
return []ops.Operator{f.Source}
}
// UnsolvedPredicates implements the unresolved interface
func (f *Filter) UnsolvedPredicates(st *semantics.SemTable) []sqlparser.Expr {
var result []sqlparser.Expr
id := TableID(f)
for _, p := range f.Predicates {
deps := st.RecursiveDeps(p)
if !deps.IsSolvedBy(id) {
result = append(result, p)
}
}
return result
}
func (f *Filter) AddPredicate(ctx *plancontext.PlanningContext, expr sqlparser.Expr) (ops.Operator, error) {
newSrc, err := f.Source.AddPredicate(ctx, expr)
if err != nil {
return nil, err
}
f.Source = newSrc
return f, nil
}
func (f *Filter) AddColumn(ctx *plancontext.PlanningContext, expr sqlparser.Expr) (int, error) {
return f.Source.AddColumn(ctx, expr)
}
func (f *Filter) Compact(*plancontext.PlanningContext) (ops.Operator, rewrite.TreeIdentity, error) {
if len(f.Predicates) == 0 {
return f.Source, rewrite.NewTree, nil
}
other, isFilter := f.Source.(*Filter)
if !isFilter {
return f, rewrite.SameTree, nil
}
f.Source = other.Source
f.Predicates = append(f.Predicates, other.Predicates...)
return f, rewrite.NewTree, nil
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 7,884 |
<?xml version="1.0" encoding="utf-8"?>
<manifest xmlns:android="http://schemas.android.com/apk/res/android"
package="no.finn.rxactivityresponse"
android:versionCode="1"
android:versionName="1.0">
</manifest>
| {
"redpajama_set_name": "RedPajamaGithub"
} | 5,837 |
{"url":"https:\/\/www.physicsforums.com\/threads\/i-dont-understand-how-to-find-acceleration-for-the-second-part.672016\/","text":"# I dont understand how to find acceleration for the second part\n\n1. Feb 15, 2013\n\n### Sneakatone\n\nfor the first two I used the equation a=v^2\/r\nbut for the second part I dont know what it is asking for or how to approach it. is there an equation that goes with it?\n\n#### Attached Files:\n\n\u2022 ###### Screen shot 2013-02-15 at 3.54.44 PM.png\nFile size:\n32.2 KB\nViews:\n135\n2. Feb 15, 2013\n\n### Sneakatone\n\nthe 1st two are wrong when I use a=v\/r it is also wrong, and I converted km\/h to m\/s\n\n3. Feb 15, 2013\n\n### tiny-tim\n\nHi Sneakatone!\n\na = v2\/r should be correct.\n\nHow exactly did you get 74.3 and 197.7 ?\n\n4. Feb 15, 2013\n\n### HallsofIvy\n\n$$a= v^2\/r$$ will give the acceleration due to the motion around the circle. The actual force the pilot experiences will be those plus or minus the weight of the pilot.\n\n5. Feb 15, 2013\n\n### Sneakatone\n\n105.5^2\/150=74.2 m\/s\n172.22^2\/150= 197.7 ms\n\n6. Feb 15, 2013\n\n### tiny-tim\n\nerm\n\nit's not 150 !\n\n7. Feb 15, 2013\n\n### Sneakatone\n\nthe diameter is 300 so 1\/2 of it is 150 , thats where I got it. and then I tried using the whole diameter ans that is not right\n\n8. Feb 15, 2013\n\n### tiny-tim\n\nno, the diameter is 1000\n\n9. Feb 15, 2013\n\n### Sneakatone\n\nwell sonb , I cant believe I didnt see that thanks!\nnow that we have that I still dont know how to do the second part.\n\n10. Feb 15, 2013\n\n### tiny-tim\n\nyou mean the centripetal acceleration at the bottom?\n\nsame method\n\n11. Feb 15, 2013\n\n### Sneakatone\n\nwould i use gravity and the magnitude?\n\n12. Feb 15, 2013\n\n### tiny-tim\n\ndo you mean the third part?\n\nyes, you have to take gravity into account\n\n13. Feb 15, 2013\n\n### Sneakatone\n\nIm thinking it would be something like 22.1-(1\/2*9.82) because gravity is downward on a horizontal acceleration.?\n\n14. Feb 15, 2013\n\n### tiny-tim\n\nyou're doing it again!\n\nwhere do those figures come from?\n\n15. Feb 15, 2013\n\n### Sneakatone\n\nthe way im thinkg of it is that the found acceleration which is 22.1 is being acted upon a down ward acceleration of gravity.\n\nhow would you do this?\n\n16. Feb 15, 2013\n\n### tiny-tim\n\n(i don't make it exactly 22.1)\n\nwhere did the 1\/2 come from?\n\nhas your professor taught you about rotating frames of reference, and centrifugal force? what do you know about them?\n\n(i'm off to bed now :zzz:)\n\n17. Feb 15, 2013\n\n### Sneakatone\n\nI believe not , i dont even know which equation I should appy\n\n18. Feb 15, 2013\n\n### Sneakatone\n\nI belive not , I ont even know which equaton to apply.\nit seems like w^2r is a possibility.\n\n19. Feb 16, 2013\n\n### tiny-tim\n\n(just got up :zzz:)\n\nhas your professor taught you about rotating frames of reference, and centrifugal force? what do you know about them?\n\n2r and v2\/r are the same, since v = \u03c9r, even when \u03c9 isn't constant)","date":"2018-02-25 20:41:41","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.4616413116455078, \"perplexity\": 4062.712652612426}, \"config\": {\"markdown_headings\": true, \"markdown_code\": false, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2018-09\/segments\/1518891816912.94\/warc\/CC-MAIN-20180225190023-20180225210023-00770.warc.gz\"}"} | null | null |
Swift codes, also called BIC Codes, allow you to make an international wire transfer. Unlike routing numbers used for domestic wire transfers, Swift codes are only used for making international transfers. In order to make or receive an international wire transfer to ARIAL ASSURANCE, you'll need the appropriate Swift code..
Notice: Swift codes for ARIAL ASSURANCE are used ONLY for International Wire Transfers. | {
"redpajama_set_name": "RedPajamaC4"
} | 1,606 |
Guillaume Anger (mort le ) est un ecclésiastique breton qui fut évêque de Saint-Brieuc de 1385 à 1404.
Biographie
Guillaume dit Anger ou Angier est le fils de Thibault, seigneur du Plessis-Anger, et de Marguerite de Châteaubriant. Il nommé évêque de Saint-Brieuc par Clément VII le et devient conseiller du duc Jean IV de Bretagne. Il meurt en 1404 après un épiscopat de 20 années.
Héraldique
Ses armoiries portaient: de vair au bâton de gueules brochant le tout.
Notes et références
Évêque de Saint-Brieuc
Évêque catholique du XIVe siècle
Décès en 1404 | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 8,143 |
Orawica (słow. Oravica) – dopływ Orawy
Cicha Woda Orawska (słow. Oravica, Tichá voda) – źródłowy odcinek Orawicy | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 4,918 |
Q: Is the following function a metric on $\Bbb R^2$? Is the following function a metric on $\Bbb R^2$?
$d((x_1,x_2),(y_1,y_2))=|x_1|+|x_2|+|y_1|+|y_2|$
Now $d((x_1,x_2),(y_1,y_2))=0\iff (x_1,x_2)=(y_1,y_2)=0$
Also the other conditions are satisfied.Hence it is a metric.
But the answer is given that it is not a metric.Where am I wrong?Please help.
A: Note that, for instance, $d((1,2),(1,2))=6 \neq 0.$
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 23 |
Q: How I can fix "iio-sensor-proxy" detect orientation problem? I am a Arch Linux user and I have a Laptop that has a built in sensor to detect orientation .and according this sensor the screen will be rotate. but the main problem here is that this sensor detect wrongly. this mean when I turn on my Laptop the screen has been rotated to right 90 deg. How I can solve this problem?
A: You can change the way orientation is detected by using a matrix to switch axes and orientations with systemd. You will find a really good documentation at systemd github project.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 3,383 |
Q: How can I fix this error from pygame I think I have downloaded pygame wrong. Whenever I try to import and initialize it I always get this error:
ImportError: dlopen(/Library/Frameworks/Python.framework/Versions/2.7/lib/python2.7/site-packages/pygame/base.so, 2): no suitable image found. Did find:
/Library/Frameworks/Python.framework/Versions/2.7/lib/python2.7/site-packages/pygame/base.so: no matching architecture in universal wrapper
Can someone explain what this is?
A: It looks like you are trying to install Pygame against the OS X included version of Python. This is a bad idea for several reasons:
*
*It's old - the version that ships with OS X is an older 2.7 release.
*It's non-standard - Apple has modified it in un-obvious ways.
*You can't mess with it - you can break your OS X installation if you tinker with it.
For this reason, it is highly recommended that you set up a development environment with a separate, fresh install of Python. The easiest way to do this is with Homebrew, although you can download the installer from http://python.org as well.
While you're at it, I strongly recommend you use Python 3 (the current version is 3.6). There is no reason for a beginner to be using 2.7.
Once you have Python installed correctly, installing Pygame is as simple as:
$ pip3 install pygame
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 2,358 |
//
// ZHAllMusicVC.m
// zhMusic
//
// Created by 张淏 on 16/12/27.
// Copyright © 2016年 张淏. All rights reserved.
//
#import "ZHAllMusicVC.h"
#import <MediaPlayer/MediaPlayer.h>
#import "Header.h"
#import "ZHMusicInfo.h"
#import "ZHAllMusicCell.h"
#import "ZHPlayMusicListManager.h"
#import "ZHPlayMusicManager.h"
#import "ZHTableView.h"
#import "ZHMiniPlayView.h"
#import "UIImage+Extension.h"
#define HeaderHeight 25
#define ShuffleAllHeaderH 40
@interface ZHAllMusicVC ()<UITableViewDelegate, UITableViewDataSource>
@property (nonatomic, strong) ZHTableView *tableView;
@property (nonatomic, strong) NSDictionary *allMusic; // 数据源
@property (nonatomic, strong) NSArray *headerArr; // header 数据源
@end
@implementation ZHAllMusicVC {
UIView *_headerView;
}
- (void)viewDidLoad {
[super viewDidLoad];
// Do any additional setup after loading the view.
self.view.backgroundColor = [UIColor whiteColor];
self.title = @"歌曲";
[self configureTableView];
[[ZHPlayMusicListManager defaultManager] loadAllMusicComplation:^(NSArray *header, NSDictionary *allMusic) {
_headerArr = header;
_allMusic = allMusic;
[_tableView reloadData];
}];
}
- (void)configureTableView {
[self prepareHeaderView];
_tableView = [[ZHTableView alloc] initWithFrame:CGRectMake(0, ShuffleAllHeaderH, self.view.width, self.view.height - ShuffleAllHeaderH - 64) style:UITableViewStylePlain];
_tableView.delegate = self;
_tableView.dataSource = self;
[_tableView setRowHeight:55.5];
[_tableView setSectionHeaderHeight:HeaderHeight];
[_tableView setSectionIndexColor:ZHRedColor];
_tableView.tableFooterView = [UIView new];
[self.view addSubview:_tableView];
[self.view bringSubviewToFront:_headerView];
}
- (void)prepareHeaderView {
_headerView = [self createHeaderWithFrame:CGRectMake(0, 0, self.view.width, ShuffleAllHeaderH)];
_headerView.backgroundColor = ZHNavColor;
[self.view addSubview:_headerView];
}
- (UIView *)createHeaderWithFrame:(CGRect)frame {
UIView *header = [[UIView alloc] initWithFrame:frame];
header.backgroundColor = _tableView.backgroundColor;
UILabel *shuffleAll = [UILabel new];
shuffleAll.text = @"随机播放";
shuffleAll.font = [UIFont systemFontOfSize:12];
shuffleAll.textColor = ZHRedColor;
[shuffleAll sizeToFit];
shuffleAll.origin = CGPointMake(20, header.height * 0.5 - shuffleAll.height * 0.5);
[header addSubview:shuffleAll];
UIImageView *shuffleAllImg = [[UIImageView alloc] initWithImage:[[UIImage imageNamed:@"NowPlaying-Shuffle_31x20_"] imageWithRenderingMode:UIImageRenderingModeAlwaysTemplate]];
shuffleAllImg.tintColor = ZHRedColor;
[shuffleAllImg sizeToFit];
shuffleAllImg.origin = CGPointMake(header.width - shuffleAllImg.width - 20, header.height * 0.5 - shuffleAllImg.height * 0.5);
[header addSubview:shuffleAllImg];
UIView *line1 = [[UIView alloc] initWithFrame:CGRectMake(15, 0, header.width - 15 - 15, 0.5)];
line1.backgroundColor = ZHRGBColor(200, 200, 200);
[header addSubview:line1];
UIView *line2 = [[UIView alloc] initWithFrame:CGRectMake(15, header.height - 0.5, header.width - 15 - 15, 0.5)];
line2.backgroundColor = ZHRGBColor(200, 200, 200);
[header addSubview:line2];
UITapGestureRecognizer *tap = [[UITapGestureRecognizer alloc] initWithTarget:self action:@selector(shufflePlay:)];
[header addGestureRecognizer:tap];
return header;
}
#pragma mark - 随机播放
- (void)shufflePlay:(UITapGestureRecognizer *)tap {
NSLog(@"%s", __func__);
[UIView animateWithDuration:0.25 animations:^{
tap.view.backgroundColor = ZHRGBColor(217, 217, 217);
} completion:^(BOOL finished) {
[UIView animateWithDuration:0.25 animations:^{
tap.view.backgroundColor = ZHNavColor;
}];
}];
}
#pragma mark - tableViewDataSource
- (NSInteger)numberOfSectionsInTableView:(UITableView *)tableView {
return _headerArr.count;
}
- (NSInteger)tableView:(UITableView *)tableView numberOfRowsInSection:(NSInteger)section {
NSString *key = _headerArr[section];
NSArray *arr = _allMusic[key];
return arr.count;
}
static NSString *ZHAllMusicCellID = @"ZHAllMusicCellID";
- (UITableViewCell *)tableView:(UITableView *)tableView cellForRowAtIndexPath:(NSIndexPath *)indexPath {
ZHAllMusicCell *cell = [ZHAllMusicCell allMusicCellWithTableView:tableView identifier:ZHAllMusicCellID indexPath:indexPath rowHeight:tableView.rowHeight];
NSString *key = _headerArr[indexPath.section];
NSArray *arr = _allMusic[key];
MPMediaItem *song = arr[indexPath.row];
cell.image = [UIImage defaultImageWithSongItem:song size:CGSizeMake(48, 48)];
cell.songNameLbl.text = [song valueForProperty: MPMediaItemPropertyTitle];
cell.singerLbl.text = [song valueForProperty:MPMediaItemPropertyArtist];
return cell;
}
- (UIView *)tableView:(UITableView *)tableView viewForHeaderInSection:(NSInteger)section {
UIView *header = [[UIView alloc] initWithFrame:CGRectMake(0, 0, self.view.width, HeaderHeight)];
header.backgroundColor = ZHNavColor;
UILabel *title = [UILabel new];
title.text = _headerArr[section];
title.font = [UIFont boldSystemFontOfSize:12];
[title sizeToFit];
title.origin = CGPointMake(20, HeaderHeight * 0.5 - title.height * 0.5);
[header addSubview:title];
return header;
}
#pragma mark - tableViewDelegate
#pragma mark - 实现右侧索引
- (NSArray *)sectionIndexTitlesForTableView:(UITableView *)tableView {
return _headerArr;
}
#pragma mark - 下拉跟随
- (void)scrollViewDidScroll:(UIScrollView *)scrollView {
CGFloat offset = scrollView.contentOffset.y + scrollView.contentInset.top;
// NSLog(@"%f", offset);
// 放大
if (offset <= 0) {
// 调整 headView
_headerView.y = offset == 0 ? offset : -offset;
} else {
// 整体移动
_headerView.y = 0;
// headerView 最小 y 值
// CGFloat min = fabs(ShuffleAllHeaderH - 64.0) + 24;
// _headerView.y = -MIN(min, offset);
// NSLog(@"%f, %f, %f", _headerView.y, min, offset);
// _tableView.y = _headerView.y + ShuffleAllHeaderH;
// 设置透明度
// NSLog(@"%f", offset / min);
// 根据输出可以知道 offset / min == 1 的不可见
// CGFloat progress = 1 - (offset / min);
// 根据透明度,来修改状态栏的颜色
// _statusBarStyle = (progress < 0.5) ? UIStatusBarStyleDefault : UIStatusBarStyleLightContent;
// 主动更新状态栏
// [self.navigationController setNeedsStatusBarAppearanceUpdate];
}
}
#pragma mark - 播放音乐
- (void)tableView:(UITableView *)tableView didSelectRowAtIndexPath:(NSIndexPath *)indexPath {
[[ZHMiniPlayView defaultView] setPuserBtnSelect];
UITableViewCell *cell = [tableView cellForRowAtIndexPath:indexPath];
UIColor *color = cell.backgroundColor;
[UIView animateWithDuration:0.25 animations:^{
cell.backgroundColor = ZHRGBColor(217, 217, 217);
} completion:^(BOOL finished) {
[UIView animateWithDuration:0.25 animations:^{
cell.backgroundColor = color;
}];
}];
NSString *key = _headerArr[indexPath.section];
NSArray *arr = _allMusic[key];
MPMediaItem *song = arr[indexPath.row];
[[ZHMiniPlayView defaultView] showWithItem:song];
[[ZHPlayMusicManager defaultManager] playMusicWithSongUrl:[song valueForProperty:MPMediaItemPropertyAssetURL] didComplete:^{
}];
}
- (void)dealloc {
NSLog(@"%s", __func__);
}
/*
#pragma mark - Navigation
// In a storyboard-based application, you will often want to do a little preparation before navigation
- (void)prepareForSegue:(UIStoryboardSegue *)segue sender:(id)sender {
// Get the new view controller using [segue destinationViewController].
// Pass the selected object to the new view controller.
}
*/
@end
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{"url":"https:\/\/mathoverflow.net\/questions\/346153\/surmounting-set-theoretical-difficulties-in-algebraic-geometry","text":"# Surmounting set-theoretical difficulties in algebraic geometry\n\nThe category $$\\text{AffSch}_S$$ of affine schemes over some base affine scheme $$S$$ is not essentially small. This lends itself to certain set-theoretical difficulties when working with a category $$Sh(\\text{AffSch}_S)$$ of abelian sheaves on $$\\text{AffSch}_S$$ with respect to some Grothendieck topology. In fact, many definitions of the notion of category would not consider this a category at all.\n\nNevertheless, in some sense, such a category of sheaves should be somewhat like a presentable category; it should have a collection of generators indexed by $$\\text{AffSch}_S$$. As such, I would like to be able to use arguments involving theorems like the adjoint functor theorem. For example, I would like to show that for an affine scheme $$c$$, the evaluation functor $$\\mathcal{F}_c: Sh(\\text{AffSch}_S) \\to Ab$$ given by $$\\mathcal{F}_c(F)=F(c)$$ has a left-adjoint. If $$Sh(\\text{AffSch}_S)$$ were presentable, this would follow from the adjoint functor theorem for presentable categories.\n\nEven though $$\\text{AffSch}_S$$ is not essentially small, can we still expect statements such as the adjoint functor theorem to hold for $$Sh(\\text{AffSch}_S)$$? I know that in many cases, one is able to restrict to some sufficiently large small subcategory of the category of affine schemes, but I'm not sure how to do it in this case. To make matters worse, certain \"small\" sites such as the small $$\\text{fpqc}$$ site over a scheme are not even essentially small, so when working with an arbitrary topos associated to $$\\text{AffSch}_S$$ it seems difficult to restrict to small subcategories for many purposes.\n\n\u2022 If we amend the category Sh (AffSch_S), considering only its subcategory of functors which are accessible, would not we get a presentable category? If so, I would think this amended version is the \"correct\" version to work with always. Nov 16 '19 at 13:31\n\u2022 @Sasha Do you have a reference for that statement? The last time I looked into it I only found that the subcategory of $\\kappa$-accessible functors for a fixed $\\kappa$, is accessible, but that's equivalent to just working with universes. Nov 16 '19 at 15:13\n\u2022 I don't know algebraic geometry, but do you think it suffices if you have a higher-order set theory (i.e. all finite-order sorts of sets, classes of sets, collections of classes of sets and so on)? If you do not need to mix sorts, then you can easily get away with this. Note that MK set theory is like second-order ZFC, and you can go all the way up without much concern, since (I think) ZFC proves that existence of a transitive set model of ZFC (which is not that strong) implies existence of a set model for higher-order ZFC. Nov 16 '19 at 18:10\n\u2022 @Sasha What would the generators be? Nov 16 '19 at 23:53\n\u2022 @user21820 How would higher-order set theory solve this issue? I have almost zero experience with anything beyond first-order things Nov 16 '19 at 23:53\n\nLet me start by discussing a bit the option of having a large class of generators. You might be interested in the notion of locally class-presentable.\n\nTo be precise here, I need to be a bit set-theoretical, thus, let me start with an informal comment.\n\nInformal comment. Indeed your category is locally class-presentable, class-accessibility is a very strong weakening of the notion of accessibility. On one hand, it escapes the world of categories with a dense (small) generator, on the other, it still allows to build on the technical power of the small object argument via a large class of generators.\n\nLocally class-presentable and class-accessible categories, B. Chorny and J. Rosick\u00fd, J. Pure Appl. Alg. 216 (2012), 2113-2125.\n\ndiscusses a part of the general theory of class-accessibility and class-local presentability. Unfortunately, the paper is designed towards a homotopical treatment and thus insists on weak factorization systems and injectivity but a lot of techniques coming from the classical theory can be recast in this setting.\n\nFormal comment. To be mathematically precise, your category is locally large, while locally class-presentable categories will be locally small. Here there are two options, the first one is to study small sheaves $$\\mathsf{Shv}_{\\text{small}}(\\text{AffSch})$$, this is a full subcategory of the category of sheaves and contains many relevant sheaves you want to study. In the informal comment, this is the locally class-presentable one. Two relevant paper to mention on this topic are:\n\n\u2022 Exact completions and small sheaves, M. Shulman, Theory and Applications of Categories, Vol. 27, 2012, No. 7, pp 97-173.\n\u2022 Limits of small functors, B. J. Day and S. Lack, Journal of Pure and Applied Algebra, 210(3):651-683, 2007.\n\nThe other option is the one of being very careful with universes, in fact restricting to small presheaves might destroy sometimes your only chance of having a right adjoint. It would be too long to elaborate on this last observation here. As a general remark, small presheaves will give you the free completion under small colimits, while all presheaves will give you the free completion under large colimits, how big you need to go depends on the type of constructions that you need to perform.\n\nComing to the adjoint functor theorem, let me state the most general version that I know of. Since it is an if and only if, I hope it provides you with a good intuition on when one can expect a right adjoint to exists. The dual version is true for functors preserving limits.\n\nThm. (AFT) Let $$f: \\mathsf{A} \\to \\mathsf{B}$$ be a functor preserving colimits from a cocomplete category. The following are equivalent:\n\n\u2022 For every $$b \\in \\mathsf{B}$$, $$\\mathsf{B}(f\\_,b): \\mathsf{A}^\\circ \\to \\mathsf{Set}$$ is a small presheaf.\n\u2022 $$f$$ has a right adjoint.\n\nThis version of the AFT is designed for locally small categories and can be made enrichment sensitive - and thus work also for locally large categories - using the proper notion of smallness, or equivalently choosing the correct universe.\n\nUnfortunately, I do not know a reference for this version of the AFT. Indeed it can be deduced by the too general Thm 3.25 in On the unicity of formal category theories by Loregian and myself, where it appears as a version of the very formal adjoint functor theorem by Street and Walters in the language of the preprint.\n\nFinally, about to the evaluation functor, I am not an expert of the abelian world, but it looks to me that one can mimic the argument presented in the accepted answer to this question (at least if the topology is subcanonical). Thus, the left adjoint should indeed exist.\n\n\u2022 I like this. So by your version of the AFT it seems obvious that $\\mathcal{F}_c$ should have a left adjoint when we restrict to the category of small sheaves at least Nov 16 '19 at 23:51","date":"2021-12-01 19:32:52","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 18, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.8968173265457153, \"perplexity\": 210.1273524528941}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 20, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2021-49\/segments\/1637964360881.12\/warc\/CC-MAIN-20211201173718-20211201203718-00386.warc.gz\"}"} | null | null |
{"url":"https:\/\/www.iacr.org\/cryptodb\/data\/paper.php?pubkey=32250","text":"## CryptoDB\n\n### Paper: Provably Secure Reflection Ciphers\n\nAuthors: Tim Beyne , KU Leuven Yu Long Chen , KU Leuven Search ePrint Search Google Slides CRYPTO 2022 This paper provides the first analysis of reflection ciphers such as PRINCE from a provable security viewpoint. As a first contribution, we initiate the study of key-alternating reflection ciphers in the ideal permutation model. Specifically, we prove the security of the two-round case and give matching attacks. The resulting security bound takes form $O(qp^2\/2^{2n}+q^2\/2^n)$, where q is the number of construction evaluations and p is the number of direct adversarial queries to the underlying permutation. Since the two-round construction already achieves an interesting security lower bound, this result can also be of interest for the construction of reflection ciphers based on a single public permutation. Our second contribution is a generic key-length extension method for reflection ciphers. It provides an attractive alternative to the FX construction, which is used by PRINCE and other concrete key-alternating reflection ciphers. We show that our construction leads to better security with minimal changes to existing designs. The security proof is in the ideal cipher model and relies on a reduction to the two-round Even-Mansour cipher with a single round key. In order to obtain the desired result, we sharpen the bad-transcript analysis and consequently improve the best-known bounds for the single-key Even-Mansour cipher with two rounds. This improvement is enabled by a new sum-capture theorem that is of independent interest.\n##### BibTeX\n@inproceedings{crypto-2022-32250,\ntitle={Provably Secure Reflection Ciphers},\npublisher={Springer-Verlag},\nauthor={Tim Beyne and Yu Long Chen},\nyear=2022\n}","date":"2022-09-28 20:05:32","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.5394271612167358, \"perplexity\": 1689.2221503203293}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2022-40\/segments\/1664030335276.85\/warc\/CC-MAIN-20220928180732-20220928210732-00156.warc.gz\"}"} | null | null |
Mourinho deserves credit for how he's handling Luke Shaw
Zaid Khan
Luke Shaw's prolonged period in the wilderness has caused a bit of a stir amongst the Manchester United faithful, who are slightly fearful of Jose Mourinho losing his patience with the former Southampton defender.
Perhaps the biggest shock when the Red Devils' team was announced against Ewood Park, was the absence of Shaw's name from the starting XI for the sixth consecutive line-up – Shaw's last appearance in a United shirt coming in the club's 4-0 pistol-whipping of Wigan Athletic at Old Trafford.
The former Saints man was widely expected to be given a much-fancied crack of the whip by Jose Mourinho against a Blackburn side languishing just one point above the foot of the Championship table. To their disappointment and surprise, Mourinho persevered with Matteo Darmian at left-back (of all people), with Ashley Young (yes, you read that right) occupying the right-back spot. He has also been left out of United's Europa League squad to face Saint Etienne.
Whatever Mourinho doesn't see in Luke Shaw, he is a better left-back than Darmian..
— Mark Ogden (@MarkOgden_) February 19, 2017
SEE ALSO: Why Monaco are getting the best out of El Tigre
Many fans have been left scratching their heads in an attempt to figure out what really is the reason behind Shaw being continuously overlooked. While some are of the opinion that the 21-year-old may not be showing the kind of hunger and desire in training that Mourinho might want him to exhibit, certain members of the press argue that Shaw is yet to get to grips with the tactical nuances that the typical Mourinho full-back needs to master. When grilled about why Shaw has been missing from United's match day squads in spite of being fit, this is what Mourinho had to say:
"At the moment he is behind the others. Potentially he has many things that I like but potential is different to the pitch. He has to work hard like Mkhitaryan did for an extended period of time."
Quite evidently, looks like a masterplan that Mourinho has in place for reinvigorating the Englishman like he's done with teammates Henrikh Mkhitaryan and Anthony Martial.
Everyone knows that since his arrival at the club, Mourinho has been testing the character and mettle of all his squad members – be it publicly or privately, in an attempt to establish an unshakeable faith in his methods.
As many players who have previously played under him would testify – you either get on the bus with him, or you're off.
The first beneficiary of Mourinho's tough-love approach was Mkhitaryan. The Armenian international disappeared from the first-team fold for about three months after a detestable half of football in the Manchester derby. On being asked as to why the former Borussia Dortmund man had been missing from the team, Mourinho said that Mkhitaryan needed time to adapt to the pace of the English game and get more acquainted with the tactical side of what he requires from him. The results, quite apparently, are there for all to see.
However, since his reinstatement into the starting eleven, Mkhitaryan has arguably been one of United's most supreme attackers, causing opposition's defences problems with his immense dribbling skills and impeccable eye for an incisive pass.
How Mourinho has managed Mata, Mkhi, Martial,
Shaw should return the next Roberto Carlos & Rooney the next..Wayne Rooney#Mufc#MUFC_FAMILY
— EC7® (@cantonesque7) February 12, 2017
SEE ALSO: The Premier League would be a better place without Jesse Lingard
Something similar happened with Martial, wherein he was rotated in and out of the team in order to fully understand what his manager wants from him. Like Mkhitaryan, Martial too has returned a better player and has been in scintillating form ever since.
As logic suggests, Mourinho is probably trying to do something similar with Shaw, given that he's publicly stated that the full-back's long term future is with United.
By keeping him out of the team and making him fight tooth-and-nail for his place in the starting eleven, Mourinho is remoulding Shaw's character and making sure that he regains his lost mental strength, determination and self-belief. The double leg-break which he suffered against PSV Eindhoven in the Champions League took a lot out of the left-back.
His confidence had been shattered, mental strength ravaged and self-belief was nethermost. The amount of emotional trauma that this kind of injury causes is almost unimaginable to outsiders. Imagine the prospect of having a ridiculously promising career at one of the biggest clubs in world football being snatched away from you for no fault of yours.
As someone who has coached exceptional teams in multiple countries and won titles everywhere he's been, Mourinho understands Shaw's situation better than anybody else can. He knows for a fact that the Englishman needs to have his confidence and mental strength re-established. It is something Mourinho has been known for throughout his career – dismantling a player completely and then calmly fostering him into something stronger than anybody could've envisaged – both mentally and physically.
At only 21 years of age, Shaw has a decade or so of his best football ahead of him. In such a situation, going through a mental and physical rehabilitation for one season under a coach like Mourinho, who is known for how well he grooms defenders to be the best in the business will only benefit him in the long run. All he needs to do is push harder and most importantly, remain patient and believe in his intrinsic abilities.
Is Luke Shaw on his way to joining the list of the worst players that Jose Mourinho has ever managed?
Winston Bogarde – Barcelona
Whilst Assistant Manager at Barca, Mourinho had the pleasure of dealing with the bloke who would go on to be dubbed the worst Premier League signing ever. Image Source: Twitter
Hugo Almeida – Porto
Like a lot of strikers on the European mainland, we have been told Almeida is great, for years. He's not. Image Source: Twitter
Alexei Smertin – Chelsea
Looks like he should be in the top 10 of female tennis players. Image Source: Twitter
Asier Del-Horno – Chelsea
Why does the Spaniard look like Wayne Bridge, here? Image Source: Twitter
Ben Sahar – Chelsea
Chelsea had actually convinced themselves that the Israeli and Scott Sinclair were the future of the club. Image Source: Twitter
Scott Sinclair – Chelsea
Part of me just knows that Sinclair still believes he's good enough for Man City. Image Source: chelseanews24
Carlton Cole – Chelsea
Cole is legit deemed one of West Ham's greatest ever strikers! Image Source: Twitter
Jiri Jarosik – Chelsea
Useful in Scrabble. Rubbish at football. Image Source: Twitter
Khalid Boulahrouz – Chelsea
One of those names that sounds like you've been told to work out your 'porn name' from the name of your first pet and place of birth. Image Source: Twitter
Mikael Forssell – Chelsea
No, honestly, he genuinely existed. Image Source: Twitter
Victor Obinna – Inter Milan
With one t-shirt, the striker has managed to support a great cause and more-or-less summed up his strike rate. Image Source: Join1Gol
Joselu – Real Madrid
As bad as you'd expect a bloke that now can't get into Stoke's first-team. Image Source: Twitter
Marouane Fellaini
Best part about the Belgian being at United, is Mourinho - in true Mourinho style - is trying to prove a point by playing him; trying to show that he knows better than most. Long may that continue. Liability. Image Source: Twitter
Jesse Lingard – Manchester United
Fun fact for you: there's actually Red Devils fans, out there, that can keep a straight face when saying that Lingard is good. Image Source: Twitter
Zaid Khan | {
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Q: libstdc++ is deprecated; move to libc++ when installing Babel using npm on Catalina my error output looks like this:
> node-gyp rebuild
SOLINK_MODULE(target) Release/.node
clang: warning: libstdc++ is deprecated; move to libc++ with a minimum deployment target of OS X 10.9 [-Wdeprecated]
ld: library not found for -lstdc++
clang: error: linker command failed with exit code 1 (use -v to see invocation)
make: *** [Release/.node] Error 1
gyp ERR! build error
gyp ERR! stack Error: `make` failed with exit code: 2
gyp ERR! stack at ChildProcess.onExit (/usr/local/lib/node_modules/npm/node_modules/node-gyp/lib/build.js:276:23)
gyp ERR! stack at emitTwo (events.js:106:13)
gyp ERR! stack at ChildProcess.emit (events.js:191:7)
gyp ERR! stack at Process.ChildProcess._handle.onexit (internal/child_process.js:219:12)
gyp ERR! System Darwin 19.4.0
gyp ERR! command "/usr/local/bin/node" "/usr/local/lib/node_modules/npm/node_modules/node-gyp/bin/node-gyp.js" "rebuild"
gyp ERR! cwd /Users/simonhurst/PycharmProjects/supervalet/node_modules/fsevents
gyp ERR! node -v v6.17.1
gyp ERR! node-gyp -v v3.4.0
gyp ERR! not ok
When running
npm i -D @babel/core babel-loader @babel/preset-env @babel/preset-react babel-plugin-transform-class-properties
Now I can see the issue is here :
library not found for -lstdc++
However have zero idea how to resolve it.
Been searching the web and stackoverflow - messing around with uninstalling Xcode reinstalling exode looking hombrew... etc but as of yet absolutely no joy.
I'm Python dev by trade so node is most certainly not my expertise. If someone could shed some light on how to resolve this issue that would be wonderful. I can't believe I'm the only one having it.
Thanks
A: Wow after reading many posts and many issues on GitHub... the solution in my case wasn't making sure I had Xcode installed, and the corresponding command line tools installed and making sure I'd accepted the Apple Licence agreement. It was simply a question of updating the version of node that I was using. In my case I was using version 6.x this was the version that came pre-installed on my brand new mac. Annoying. Visit https://nodejs.org/en/ to upgrade your node version. At the time of writing this the versions I upgraded to was 12.16.1 - in the event that's helpful to a future reader of this question 'n answer session :)
Really feel the error message could have been way more helpful here, but hey that's how things are some times.
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\section{Introduction}
Let $X$ be a Fano variety, i.e. $X$ is a normal projective complex variety such that the anticanonical
divisor $-K_X$ is Cartier and ample.
While Fano varieties with mild singularities (terminal or canonical)
have been studied by many authors, the goal of this paper is to study Fano varieties whose
non-klt locus $\Nklt(X)$ is not empty.
A cone over a smooth variety $Y$ with trivial anticanonical
divisor provides a simple example of such a variety.
Using methods from the minimal model program, Ishii \cite{Ish91, Ish94} characterised
cones as the only Fano varieties having a {\em finite} non-klt locus:
\begin{theorem} \cite{Ish91} \label{theoremishii}
Let $X$ be a Fano variety of dimension $n$ such that $\Nklt(X)$ is not empty and finite.
Then $X$ is a cone over a variety $Y$ of dimension $n-1$ such that $Y$ has canonical singularities and $K_Y$ is trivial.
\end{theorem}
Recall now that the index of a Fano variety $X$ is defined as
$$
\sup \{
m \in \ensuremath{\mathbb{N}} \ | \ \exists \ H \in \pic(X) \ \mbox{s.t.} -K_X \simeq m H
\}.
$$
Making stronger assumptions on the singularities of $X$, the first-named author and Sommese
established a basic relation between the index and the dimension of the non-klt locus:
\begin{theorem} \cite{BS87} \label{theoremBS}
Let $X$ be a Fano variety of index $k$ that is Cohen--Macaulay and
such that $-K_X \simeq k H$, with $H$ a very ample Cartier divisor on~$X$.
Suppose that the non-klt locus $\Nklt(X)$ is not empty. Then we have
$$
\dim \Nklt(X) \geq k-1,
$$
and equality holds if and only if $\Nklt(X)$ is a linear $\ensuremath{\mathbb{P}}^{k-1}$ and $X$ is a generalised cone with $\Nklt(X)$ as vertex.
\end{theorem}
Unfortunately the Cohen--Macaulay condition excludes an important number of examples: cones
over Calabi--Yau manifolds are Cohen--Macaulay, but a cone over an abelian variety is not.
Our first result generalises Theorem \ref{theoremishii}
and Theorem \ref{theoremBS}:
\begin{theorem} \label{theorembasicestimate}
Let $X$ be a Fano variety of index $k$ and such that $-K_X \simeq k H$, with $H$ a Cartier divisor on~$X$.
Suppose that the non-klt locus $\Nklt(X)$ is not empty. Then we have
$$\dim \Nklt(X) \geq k-1,$$ and equality holds if and only if
$
(\Nklt(X),\sO_{\Nklt(X)}(H)) \cong (\ensuremath{\mathbb{P}}^{k-1},\sO_{\ensuremath{\mathbb{P}}^{k-1}}(1))
$.
In this case $X$ has lc singularities and is a generalised cone
with $\Nklt(X)$ as vertex.
\end{theorem}
A remarkable feature that is common to the Theorems \ref{theoremishii}, \ref{theoremBS} and \ref{theorembasicestimate}
is that the property $\dim \Nklt(X) = k-1$ implies that the singularities of $X$ are log-canonical.
If $\dim \Nklt(X) = k$ this is no longer the case (cf. Example \ref{examplenonlc}),
so for the rest of the paper we will make the additional assumption that $X$ is a Fano variety
with lc singularities.
Since we assume $K_X$ to be Cartier the non-klt locus
coincides with the locus of irrational singularities \cite[Cor.5.24]{KM98}, so we can study $\Nklt(X)$ both in terms of
discrepancies and using cohomological methods.
Note also that Theorem \ref{theorembasicestimate} naturally separates into
a local part, i.e. the description of the non-klt locus $\Nklt(X)$, and a global part, i.e. the description
of the geometry of $X$.
For the local part we use a subadjunction argument to describe the low-dimensional
lc centres:
\begin{theorem} \label{theoremnkltlocus}
Let $X$ be a Fano variety of index $k$ with lc singularities and such that $-K_X \simeq k H$, with $H$ a Cartier divisor on~$X$.
If $\dim \Nklt(X) = k$ we have
$$
(\Nklt(X),\sO_{\Nklt(X)}(H)) \cong (\ensuremath{\mathbb{P}}^{k},\sO_{\ensuremath{\mathbb{P}}^{k}}(1))
$$
or
$$
(\Nklt(X),\sO_{\Nklt(X)}(H)) \cong (Q^{k},\sO_{Q^{k}}(1)),
$$
where $Q^k \subset \ensuremath{\mathbb{P}}^{k+1}$ is a (possibly reducible) hyperquadric.
\end{theorem}
This local result gives some interesting global information:
\begin{corollary}
Let $X$ be a Fano variety of index $k$ with lc singularities and such that $\dim \Nklt(X) = k$. Then $X$ is rationally chain-connected.
\end{corollary}
Indeed by a result of Broustet and Pacienza \cite[Thm.1.2]{BP11} the variety $X$ is rationally chain-connected modulo
the non-klt locus. Since $\Nklt(X)$ is rationally chain-connected the statement follows.
We continue the study of the case $\dim \Nklt(X)=k$ by considering a terminal modification $X' \rightarrow
X$ (cf. Definition \ref{definitionterminal}).
If $\Nklt(X)$ is a linear $\ensuremath{\mathbb{P}}^{1}$ the variety $X'$ can be rationally connected and have a very rich birational
geometry, cf. \cite{Ish91, Ish94}. If $\Nklt(X)$ is a conic the variety $X'$ is never rationally connected and
we obtain a precise classification:
\begin{theorem} \label{theoremkone}
Let $X$ be a Fano variety (of index $1$) and dimension $n \geq 3$ with lc singularities. Suppose that $\Nklt(X)$ is a curve
and $-K_X \cdot \Nklt(X)=2$. Let $\mu: X' \rightarrow X$ be a terminal modification.
Then the base of the MRC-fibration $X' \dashrightarrow Z$ has dimension $n-2$ and the general fibre
$F$ polarised by $\sO_F(- \mu^* K_X)$ is a linear $\ensuremath{\mathbb{P}}^2$, a quadric, a Veronese surface or a ruled surface.
\end{theorem}
In fact we know much more. The base $Z$ has an effective canonical divisor, moreover we can construct
birational models of $X$ which have a very simple fibre space structure:
\begin{proposition} \label{propositionfibrespace}
Let $X$ be a Fano variety of dimension $n$ and index $k$ with lc singularities such that $\dim \Nklt(X) = k$. Suppose that the base of the MRC-fibration $X' \dashrightarrow Z$ has dimension $n-k-1$. Then there exists
a normal projective variety $\Gamma$ admitting a birational morphism
\holom{p}{\Gamma}{X} and an equidimensional fibration \holom{q}{\Gamma}{\ensuremath{\mathcal{H}}} onto a projective manifold ${\mathcal H}$ such that one of the following holds:
\begin{enumerate}
\item the fibration $q$ is a projective bundle;
\item the fibration $q$ is a quadric fibration;
\item the general $q$-fibre is a Veronese surface.
\end{enumerate}
\end{proposition}
In Section \ref{sectionexamples} we show that all the classification results in this paper
are effective, i.e. there exist examples realising all the cases in Theorem \ref{theoremkone} and Proposition \ref{propositionfibrespace}.
The condition $\dim Z=n-k-1$ may seem rather ad-hoc, but we prove that it is satisfied if $\Nklt(X)$ is a
quadric and $k=1$ or $k \geq n-3$ (cf. Proposition \ref{propositionladder}).
Actually we prove that if $X$ admits a ladder (in the sense of Fujita, cf. Definition \ref{definitionladder}), then $H^{n-k-1}(X', \sO_{X'}) \neq 0$. We expect that any Fano variety with lc singularities admits a ladder, but this depends on the
difficult non-vanishing conjecture \cite[Conj.2.1]{Kaw00}.
{\bf Acknowledgements.} The first and the third authors thank the Research Network Program ``GDRE-GRIFGA'' for partial support.
The second-named author was partially supported by the A.N.R. project ``CLASS''.
\begin{center}
{\bf Notation}
\end{center}
We work over the complex numbers, topological notions always refer to the Zariski topology.
For general definitions we refer to \cite{Har77}.
The dimension of an algebraic variety is defined as the maximum of the dimension of its irreducible components.
On a normal variety we will denote by $\simeq$ the linear equivalence of {\em Cartier} divisors,
while $\sim_\ensuremath{\mathbb{Q}}$ (resp. $\equiv$) will be used for the $\ensuremath{\mathbb{Q}}$-linear (resp. numerical) equivalence
of $\ensuremath{\mathbb{Q}}$-Cartier $\ensuremath{\mathbb{Q}}$-divisors.
We will frequently use the terminology and results
of the minimal model program (MMP) as explained in \cite{KM98, Deb01, Kol13}. In particular klt stands for ``Kawamata log terminal",
dlt for ``divisorial log terminal", plt for ``purely log terminal", and lc for ``log canonical'' singularities.
\begin{definition} \label{definitioncanonical}
Let $X$ be a normal variety. The {\rm canonical modification} of $X$
is the unique projective birational morphism \holom{\mu}{X'}{X} from a normal
variety $X'$ with canonical singularities such that $K_{X'}$ is $\mu$-ample.
\end{definition}
\begin{remarks} \label{remarkscanonical}
The existence of the canonical modification is a consequence
of \cite{BCHM10}, cf. the forthcoming book \cite{Kol13}. If $K_X$ is $\ensuremath{\mathbb{Q}}$-Cartier we have
$$
K_{X'} \sim_\ensuremath{\mathbb{Q}} \mu^* K_X - E,
$$
where $E$ is an effective $\ensuremath{\mathbb{Q}}$-divisor whose support is the exceptional locus of $\mu$.
Let us recall that a normal variety is Gorenstein if it is Cohen--Macaulay and the canonical divisor is Cartier.
Since canonical singularities are Cohen--Macaulay the first condition is empty for $X'$, so the Gorenstein
locus of $X'$ is the open subset where $K_{X'}$ is Cartier.
\end{remarks}
An important advantage of canonical models is their uniqueness, but their singularities can be rather complicated.
One can improve the singularities by losing uniqueness:
\begin{definition} \label{definitionterminal}\cite{Kol13}
Let $X$ be a normal variety. A {\rm terminal modification} of $X$
is a projective birational morphism \holom{\mu}{X'}{X} from a normal
variety $X'$ with terminal singularities such that $K_{X'}$ is $\mu$-nef.
\end{definition}
We will use the standard definitions and results of adjunction theory from \cite{Fuj90, BS95},
except the following generalised version of the nefvalue of a Mori contraction:
\begin{definition} \label{definitionnefvalue}
Let $X$ be a normal quasi-projective variety with lc singularities, and
let $H$ be a nef and big Cartier divisor on $X$.
Let $\holom{\varphi}{X}{Y}$ be the contraction of a $K_X$-negative extremal
ray $R$ such that $H \cdot R>0$. The {\rm nefvalue} $r := r(\varphi, H)$
is the positive number such that
$(K_X+r H) \cdot R=0$.
\end{definition}
Let us recall a well-known consequence of the cone theorem:
\begin{lemma} \label{lemmacontraction}
Let $X$ be a normal projective variety
with klt singularities such that
$$
-K_X \sim_\ensuremath{\mathbb{Q}} N + E,
$$
where $N$ is a nef $\ensuremath{\mathbb{Q}}$-Cartier $\ensuremath{\mathbb{Q}}$-divisor and $E$ is a non-zero effective $\ensuremath{\mathbb{Q}}$-divisor. Suppose also that for every curve $C \subset X$ such that $N \cdot C=0$ we have $K_X \cdot C \geq 0$.
Then there exists a $K_X$-negative extremal ray $R$ such that $E \cdot R>0$ and $N \cdot R>0$.
\end{lemma}
\begin{proof}
Arguing by contradiction we suppose that $-E \cdot R \geq 0$ for all $K_X$-negative extremal rays. If $C \subset X$
is a curve such that $K_X \cdot C \geq 0$, then
$$
-E \cdot C = K_X \cdot C + N \cdot C \geq 0.
$$
By the cone theorem
this implies that the antieffective divisor $-E$ is nef, a contradiction. The property $N \cdot R>0$ is trivial since
$N$ is positive on all $K_X$-negative curves.
\end{proof}
\section{Proof of Theorem \ref{theorembasicestimate}}
Before we can prove Theorem \ref{theorembasicestimate} we need a technical lemma which
replaces an inaccurate statement\footnote{The statement is $\dim F \geq r$, but the proof only yields $\dim F \geq \lfloor r \rfloor$.} in \cite[Thm.2.1(II,i)]{And95}.
\begin{lemma} \label{lemmarounddown}
Let $X$ be a normal quasi-projective variety with canonical singularities,
and let $H$ be a nef and big Cartier divisor on $X$.
Let $\holom{\varphi}{X}{Y}$ be a birational projective morphism with connected fibres
onto a normal variety $Y$ such that $H$ is $\varphi$-ample and
$K_X+rH$ is $\varphi$-numerically trivial for some $r>0$.
Fix a point $y \in Y$ and suppose that all the irreducible components
of $\fibre{\varphi}{y}$ have dimension at most $\lfloor r \rfloor$.
Suppose that there exists an irreducible component $F \subset \fibre{\varphi}{y}$
that meets the Gorenstein locus of $X$.
Then we have $\lfloor r \rfloor=r$.
\end{lemma}
\begin{proof}
The statement is local on the base, so we can assume that $Y$ is affine. In particular
every $\varphi$-generated line bundle is globally generated.
By \cite[Thm.,p.740]{AW93} we know that $H$ is $\varphi$-globally generated, moreover by
\cite[Thm.2.1(II,ii)]{And95} all the irreducible components of $\fibre{\varphi}{y}$
are isomorphic to $\ensuremath{\mathbb{P}}^{\lfloor r \rfloor}$ and $H|_F$ is a hyperplane divisor.
We will proceed by induction on $\lfloor r \rfloor$.
For the case $\lfloor r \rfloor=1$ note that by \cite[Lemma 1]{Ish91}
we have $K_X \cdot F \geq -1$. Since $H \cdot F=1$ we obtain that $r \leq 1$.
For the induction step choose $X' \in |H|$ a general divisor,
and consider the induced birational morphism $\holom{\varphi|_{X'}}{X'}{\varphi(X')}$.
Since $H$ is $\varphi$-globally generated the variety $X'$ is normal with
canonical singularities, moreover the fibre \fibre{\varphi|_{X'}}{y}
has pure dimension $\lfloor r \rfloor - 1$ and $F \cap X'$ meets the Gorenstein
locus of $X'$. By adjunction we know that $K_{X'}+(r-1) H|_{X'}$ is $\varphi|_{X'}$-numerically trivial,
so by the induction hypothesis we have $\lfloor r - 1 \rfloor = r - 1$.
\end{proof}
\begin{proof}[Proof of Theorem \ref{theorembasicestimate}]
Let $\holom{\mu}{X'}{X}$ be the canonical modification of $X$ (cf. Definition \ref{definitioncanonical}). Then we have
$$
K_{X'} = \mu^* K_X + \sum_{E_i \ \mbox{\tiny $\mu$-exc.}} a_i E_i,
$$
and $a_i \leq -1$ for all $i$.
Set $E:=- \sum_{E_i \ \mbox{\tiny $\mu$-exc.}} a_i E_i$, then $E$ is an effective divisor mapping onto $\Nklt(X)$. Since $K_X$ is Cartier, the non-Gorenstein locus of $X'$ is contained in $E$.
By Lemma \ref{lemmacontraction} there exists a $K_{X'}$-negative extremal ray $R$ on $X'$ such that
$E \cdot R>0$ and $\mu^* H \cdot R>0$. Let $\holom{\varphi}{X'}{Y}$ be the corresponding Mori contraction, and
let $F$ be an irreducible component of a positive-dimensional $\varphi$-fibre.
Since $E$ is $\varphi$-ample, the intersection $E \cap F$ is non-trivial.
Since $E$ is $\ensuremath{\mathbb{Q}}$-Cartier we have
$$
\dim (F \cap E) \geq \dim F - 1,
$$
and equality holds if and only if $F \not\subset E$.
Since $K_X$ is $\mu$-ample and $\varphi$-antiample the morphism
$$
(F \cap E) \rightarrow \mu(F \cap E)
$$
is finite, thus we have
\begin{equation} \label{eqndimfibres}
\dim \Nklt(X) = \dim \mu(E) \geq \dim \mu(F \cap E) = \dim (F \cap E) \geq \dim F -1,
\end{equation}
and equality holds if and only if $\dim F= \dim \Nklt(X) +1$ and $F \not\subset E$.
Since $-K_{X'} \sim_\ensuremath{\mathbb{Q}} k \mu^* H + E$ we see that the nefvalue $r:=r(\varphi, H)$ (cf. Definition \ref{definitionnefvalue})
is strictly larger than $k$. By \cite[Thm.2.1(I,i)]{And95} this implies that $\dim F \geq r-1>k-1$.
By \eqref{eqndimfibres} we get $\dim \Nklt(X) > k-2$. Since $\dim \Nklt(X)$ is an integer the inequality in the statement
follows.
Suppose now that we are in the boundary case $\dim \Nklt(X)=k-1$. Arguing by contradiction
we suppose that the extremal contraction $\varphi$ is birational.
By \cite[Thm.2.1(II,i)]{And95} we then have $\dim F \geq \lfloor r \rfloor \geq k$.
Thus equality holds in \eqref{eqndimfibres} and the variety $F$ is not contained in $E$.
Therefore we satisfy
the conditions of Lemma \ref{lemmarounddown} and get $\lfloor r \rfloor = r$, so $r=k$ by (\ref{eqndimfibres}).
However by construction we have $r>k$, a contradiction.
Thus the contraction $\varphi$ is of fibre type; moreover all the irreducible components of each $\varphi$-fibre have dimension exactly $k$. By \cite[Thm.2.1(I,ii)]{And95} this implies that
$X' \rightarrow Y$ is a $\ensuremath{\mathbb{P}}^k$-bundle. Let now $F \cong \ensuremath{\mathbb{P}}^k$ be a general $\varphi$-fibre. Then $F$ is contained
in the smooth locus of $X'$, in particular all the divisors $E_i$ are Cartier in a neighborhood of $F$. By adjunction we see that
$$
\sO_F\big(\sum a_i E_i\big) \simeq \sO_{\ensuremath{\mathbb{P}}^k}(-1).
$$
Since the left hand side is a sum of antieffective Cartier divisors, we see that (up to renumbering) we have $a_1=-1$ and $E_1 \cap F$ is a hyperplane. Moreover we have $E_i \cap F= \emptyset$ for all $i \geq 2$. In particular for every $i \geq 2$ we have
$E_i \simeq \varphi^* D_i$ with $D_i$ a Weil divisor on $Y$. However if we take $y \in D_i$ a point,
then $\fibre{\varphi}{y} \subset E_i$ and $-K_{X'}|_F$ is ample, so $F \rightarrow \mu(F) \subset \mu(E_i)$ is finite.
Since we assumed that $\dim \Nklt(X)= \dim \mu(E) =k-1$ this yields $E_i=0$ for all $i \geq 2$. Thus we have
$$
K_{X'} = \mu^* K_X - E_1.
$$
One easily sees that the pair $(X', E_1)$ is lc, so $X$ has lc singularities. The generalised cone structure is given
by the maps $\mu$ and $\varphi$.
\end{proof}
\begin{example} \label{examplenonlc}
Let $Y \subset \ensuremath{\mathbb{P}}^3$ be a cone over a smooth quartic curve in $\ensuremath{\mathbb{P}}^2$, then
$K_Y$ is trivial and the vertex is the unique irrational point on $Y$. Clearly
$Y$ does not have lc singularities, so if $X$ is the cone over $Y$,
then $X$ is a Fano variety of index one such that $\Nklt(X)$ has dimension one
and $X$ is not lc.
\end{example}
\section{Description of the non-klt locus}
Let $X$ be a normal quasi-projective variety, and let $\Delta$ be an effective boundary divisor on $X$
such that $K_X+\Delta$ is $\ensuremath{\mathbb{Q}}$-Cartier and the pair $(X, \Delta)$ is lc. Let $\Nklt(X, \Delta)$ be the non-klt locus.
Recall that a subvariety $W \subset X$ is an lc centre
of the pair $(X, \Delta)$ if there exists a birational morphism $\holom{\mu}{X'}{X}$
and an effective divisor $E \subset X'$ of discrepancy $-1$ such that $\mu(E)=W$.
Recall also that the intersection $W_1 \cap W_2$ of two lc centres $W_i$ is a union
of lc centres \cite[Prop.1.5]{Kaw97}. In particular, given a point $x \in \Nklt(X, \Delta)$, there
exists a unique lc centre $W$ passing through $x$ that is minimal with respect to the inclusion.
By \cite[Thm.1.6]{Kaw97} the lc centre $W$ is normal in the point $x$. If $W$ is minimal (in every
point $x \in W$), the Kawamata subadjunction formula holds \cite{Kaw98, FG12}:
there exists an effective $\ensuremath{\mathbb{Q}}$-divisor $\Delta_W$ on $W$ such that the pair $(W, \Delta_W)$
is klt and
\begin{equation} \label{subadjunction}
K_{W}+\Delta_{W} \sim_\ensuremath{\mathbb{Q}} (K_X+\Delta)|_W.
\end{equation}
The following weak form of the subadjunction formula for non-minimal lc centres
is well-known to experts, we nevertheless include a proof for lack of reference:
\begin{lemma} \label{lemmasubadjunction}
Let $(X, \Delta)$ be a projective lc pair, and let $W \subset X$ be an lc centre.
Let $\holom{\nu}{W^n}{W}$ be the normalisation. Then there exists an effective divisor $\Delta_{W^n}$ on $W^n$
such that
$$
K_{W^n}+\Delta_{W^n} \sim_\ensuremath{\mathbb{Q}} \nu^* (K_X+\Delta)|_W.
$$
Suppose that $Z \subset W$ is an lc centre such that $\dim Z=\dim W-1$.
Then we have a set-theoretical inclusion
$$
\fibre{\nu}{Z} \subset \Delta_{W^n}.
$$
\end{lemma}
\begin{proof}
Let $\holom{\mu}{(X^m, \Delta^m)}{(X, \Delta)}$ be a dlt-model, i.e. $\mu$ is birational, the pair $(X^m, \Delta^m)$ is dlt and
$K_{X^m}+\Delta^m \sim_\ensuremath{\mathbb{Q}} \mu^*(K_X+\Delta)$ \cite[Thm.3.1]{KK10}. Let $S \subset X^m$
be an lc centre of $(X^m, \Delta^m)$ that dominates $W$ and that is minimal with respect to the inclusion.
By \cite[Thm.1]{Kol11} there exists an effective divisor $\Delta_S$ such that $(S, \Delta_S)$ is dlt and
$K_S+\Delta_S \sim_\ensuremath{\mathbb{Q}} \mu_S^* (K_X+\Delta)|_W$, where $\holom{\mu_S}{S}{W}$ is the restriction
of $\mu$ to $S$. Moreover $(S, \Delta_S)$ is klt on the generic fibre of $\mu_S$.
The variety $S$ being normal, the morphism $\mu_S$ factors through the normalisation $\nu$, and we denote by
$\holom{\mu_S^n}{S}{W'}$ and $\holom{\tau}{W'}{W^n}$ the Stein factorisation.
Moreover,
\begin{equation}\label{firstformula}
K_S+\Delta_S \sim_\ensuremath{\mathbb{Q}} (\mu^n_S)^* \circ \tau^* \circ \nu^* (K_X+\Delta)|_W
\end{equation}
implies that $\mu_S^n$ is an lc-trivial fibration in the sense of \cite[Defn.2.1]{Amb04}
and we denote by $\Delta_{W'}$ the discriminant divisor. Up to replacing $\mu_S^n$
by a birationally equivalent fibration we know by inversion of adjunction \cite[Thm.3.1]{Amb04}
that the pair $(W', \Delta_{W'})$ is lc.
Using the terminology of \cite{Amb05} (see in particular Definition 3.2 and Theorem 3.3) the moduli b-divisor
of the lc-trivial fibration is $b$-nef and good, in particular
it has non-negative Kodaira dimension. Thus there exists an effective divisor $E$ such that
$$
K_S+\Delta_S \sim_\ensuremath{\mathbb{Q}} (\mu_S^n)^* (K_{W'} + \Delta_{W'} + E).
$$
By the proof of \cite[Lemma 1.1]{FG12} there exists an effective divisor $\Delta_{W^n}$ such that
$$
K_{W'} + \Delta_{W'} + E \sim_\ensuremath{\mathbb{Q}} \tau^* (K_{W^n}+\Delta_{W^n}).
$$
Recalling \eqref{firstformula} we derive
$$
K_{W^n}+\Delta_{W^n} \sim_\ensuremath{\mathbb{Q}} \nu^* (K_X+\Delta)|_W.
$$
Suppose now that $Z \subset W$ is an lc centre such that $\dim Z=\dim W-1$.
Then we know by \cite[Cor.11]{Kol11} that
every irreducible component of
$\fibre{(\nu \circ \tau)}{Z}$ is an lc centre of the pair $(W', \Delta_{W'})$. Since $\fibre{(\nu \circ \tau)}{Z}$ is a divisor
in $W'$ we have a set-theoretical inclusion
\begin{equation} \label{inclusionupstairs}
\fibre{(\nu \circ \tau)}{Z} \subset \Delta_{W'}.
\end{equation}
Since the pair $(W^n, \Delta_{W^n})$ is not klt in the points where the pair $(W', \Delta_{W'}+E)$ is not klt (cf. \cite[Prop.20.3]{Uta92}),
the inclusion \eqref{inclusionupstairs} implies a set-theoretical inclusion
$\fibre{\nu}{Z} \subset \Delta_{W^n}$.
\end{proof}
For the description of the non-klt locus
we start with a refinement of the local part of Theorem \ref{theorembasicestimate}
in the log-canonical case:
\begin{lemma} \label{lemmaestimate}
Let $(X, \Delta)$ be a projective lc pair such that $-(K_X+\Delta) \sim_\ensuremath{\mathbb{Q}} k H$, with $H$ an ample Cartier divisor
and $k \geq 1$.
Let $W \subset X$ be an lc centre. Then we have
$$
\dim W \geq k-1,
$$
and equality holds if and only if $\lfloor k \rfloor = k$ and $(W,H|_W) \cong (\ensuremath{\mathbb{P}}^{k-1},\sO_{\ensuremath{\mathbb{P}}^{k-1}}(1))$.
\end{lemma}
\begin{proof}
The statement is trivial if $k=1$, so suppose $k>1$.
It is sufficient to prove the statement for $W \subset X$ a minimal centre.
By the subadjunction formula \eqref{subadjunction} there exists a divisor $\Delta_W$ on $W$ such that $(W, \Delta_W)$ is klt
and
$$
K_W + \Delta_W \sim_\ensuremath{\mathbb{Q}} (K_X+\Delta)|_W \sim_\ensuremath{\mathbb{Q}} -k H|_W.
$$
If $\dim W>0$ we can apply \cite[Thm.2.5]{AD12}
to see that the log Fano variety $(W, \Delta_{W})$ has dimension at least $k-1$ and
equality holds if and only if $(W,H|_W) \cong (\ensuremath{\mathbb{P}}^{k-1},\sO_{\ensuremath{\mathbb{P}}^{k-1}}(1))$.
Thus we are left to exclude the possibility that $\dim W=0$:
since $-H-(K_X+\Delta) \sim_\ensuremath{\mathbb{Q}} (k-1) H$ is ample, the restriction map
$$
H^0(X, \mathcal O_X(-H)) \to H^0(W, \mathcal O_W(-H))
$$
is surjective by \cite[Thm.2.2]{Fuj11}. If $W$ is a point, the space $H^0(W, \mathcal O_W(-H))$ is not zero,
which is impossible since the antiample divisor $-H$ has no global sections on $X$.
\end{proof}
The following proposition is the key step in the proof of Theorem \ref{theoremnkltlocus}:
\begin{proposition} \label{propositioncentrek}
Let $(X, \Delta)$ be a projective lc pair of dimension $n \geq 3$ such that $-(K_X+\Delta) \sim_\ensuremath{\mathbb{Q}} k H$, with $H$ an ample Cartier divisor
and $k \in \ensuremath{\mathbb{N}}$. Let $W$ be an lc centre of $(X, \Delta)$ of dimension $k$.
If $W$ is minimal, then $(W,H|_W) \cong (\ensuremath{\mathbb{P}}^{k},\sO_{\ensuremath{\mathbb{P}}^{k}}(1))$ or
$(W,H|_W) \cong (Q^{k},\sO_Q(1))$, with $Q^k \subset \ensuremath{\mathbb{P}}^{k+1}$ an integral quadric.
If $W$ is not minimal, then $(W,H|_W) \cong (\ensuremath{\mathbb{P}}^{k},\sO_{\ensuremath{\mathbb{P}}^{k}}(1))$
and $W$ contains exactly one lc centre $Z \subsetneq W$.
\end{proposition}
\begin{proof}
If $W$ is minimal we know by the subadjunction formula \eqref{subadjunction}
that there exists an effective divisor $\Delta_{W}$ on $W$
such that $(W, \Delta_{W})$ is log Fano of index $k$ and dimension $k$.
The statement then follows from \cite[Thm.2.5]{AD12}.
Suppose now that $W$ is not minimal. Then $W$ contains another lc centre $Z \subsetneq W$
and by Lemma \ref{lemmaestimate} we know that $Z$ has dimension $k-1$.
Denote by $\holom{\nu}{W^n}{W}$ the normalisation.
By Lemma \ref{lemmasubadjunction}
there exists an effective divisor $\Delta_{W^n}$
such that
\begin{equation} \label{help1}
K_{W^n}+\Delta_{W^n} \sim_\ensuremath{\mathbb{Q}} \nu^* (K_X+\Delta)|_W \sim_\ensuremath{\mathbb{Q}} -k \nu^* H|_W.
\end{equation}
Thus the pair $(W^n, \Delta_{W^n})$ is log Fano of dimension $k$ and index $k$,
moreover by the last part of Lemma \ref{lemmasubadjunction}
we have a set-theoretical inclusion
$$
\fibre{\nu}{Z} \subset \Delta_{W^n}.
$$
In particular $\Delta_{W^n}$ is not empty, so by
\cite[Thm.2.5]{AD12} we obtain
$W^n \cong \ensuremath{\mathbb{P}}^{k}$ and $\sO_{W^n}(\nu^* H) \simeq \sO_{\ensuremath{\mathbb{P}}^{k}}(1)$.
By \eqref{help1} this implies $\sO_{W^n}(\Delta_{W^n}) \simeq \sO_{\ensuremath{\mathbb{P}}^{k}}(1)$,
so we see that $\fibre{\nu}{Z}=\Delta_{W^n}$ and $\fibre{\nu}{Z}$ is a hyperplane.
Note that this already implies that $Z$ is unique.
Therefore it remains to prove that $W$ is normal. Note
first that $W$ is minimal, hence normal, in the complement of $Z$. Thus it is sufficient to prove that $W$ is normal
in every point $x \in Z$.
By Lemma \ref{lemmaestimate} we have $Z \cong \ensuremath{\mathbb{P}}^{k-1}$, so we get
a finite map
$$
\holom{\nu|_{\fibre{\nu}{Z}}}{\fibre{\nu}{Z} \cong \ensuremath{\mathbb{P}}^{k-1}}{Z \cong \ensuremath{\mathbb{P}}^{k-1}}.
$$
Since $\sO_{\fibre{\nu}{Z}}(\nu^* H) \simeq \sO_{\ensuremath{\mathbb{P}}^{k-1}}(1)$ this map has degree one, so it is an isomorphism. This proves that the normalisation $\nu$ is an injection on points.
By a result of Ambro \cite[Thm.1.1]{Amb11} we know that $W$ is semi-normal, so $\nu$ is an isomorphism.
\end{proof}
\begin{proof}[Proof of Theorem \ref{theoremnkltlocus}]
By Nadel's vanishing theorem (see e.g. \cite[Thm.3.2]{Fuj11}) we have $H^1(X, \sI_{\Nklt(X)})=0$, so
the map
$$
H^0(X, \sO_X) \rightarrow H^0(\Nklt(X), \sO_{\Nklt(X)})
$$
is surjective. In particular the non-klt locus $\Nklt(X)$ is connected.
If $\Nklt(X)$ is irreducible we conclude by Proposition \ref{propositioncentrek}.
Suppose from now on that $\Nklt(X)$ is reducible. If $W_1$ (resp. $W_2$) is an irreducible component
of $\Nklt(X)$, hence an lc centre, of dimension $r_1$ (resp. $r_2$), the intersection
$W_1 \cap W_2$ is either empty or a union of lc centres of dimension at most
$\min(r_1, r_2)-1$. By the connectedness of $\Nklt(X)$ we can reduce to consider the second case. Then Lemma \ref{lemmaestimate} implies that every irreducible component
of $\Nklt(X)$ has dimension $k$; moreover two components meet along a set of dimension $k-1$.
By Lemma \ref{propositioncentrek} every irreducible component $W_i$ is isomorphic to $\ensuremath{\mathbb{P}}^k$
and contains exactly one lc centre, so we see that $\Nklt(X)$ has exactly two irreducible components.
These two irreducible components meet along an lc centre of dimension $k-1$,
so by Lemma \ref{lemmaestimate} the intersection $W_1 \cap W_2$ is a linear $\ensuremath{\mathbb{P}}^{k-1}$.
Thus $\Nklt(X)=W_1 \cup W_2$ is a reducible quadric of dimension $k$.
\end{proof}
\section{Description of the geometry of the Fano variety}
\label{sectiondescriptionX}
We start by classifying certain weak log Fano varieties that will appear as the fibres
of the MRC-fibration:
\begin{proposition} \label{propositionindexk}
Let $X$ be a normal projective variety of dimension $k+1 \geq 2$ with terminal singularities,
and let $\Delta$ be a non-zero effective Weil $\ensuremath{\mathbb{Q}}$-Cartier divisor on $X$ such that the pair $(X, \Delta)$ is lc, and
$$
-(K_X+\Delta) \sim_\ensuremath{\mathbb{Q}} k H
$$
with $H$ a nef and big Cartier divisor on $X$. Suppose also that for every curve $C \subset X$
such that $H \cdot C=0$ we have $K_X \cdot C \geq 0$. Then $(X, \sO_X(H))$ is one of the following quasi-polarised varieties:
\begin{enumerate}
\item $(\mathbb P^{k+1}, \mathcal O_{\mathbb P^{k+1}}(1))$ and $\Delta$ is a quadric; or
\item $(Q^{k+1}, \mathcal O_{Q^{k+1}}(1))$ and $\Delta$ is a quadric; or
\item a generalised cone of dimension $k+1$ over the Veronese surface $(\mathbb P^2, \mathcal O_{\mathbb P^2}(2))$ and $\Delta$
is the generalised cone of dimension $k$ over $(\mathbb P^1, \mathcal O_{\mathbb P^1}(2))$; or
\item a scroll $\ensuremath{\mathbb{P}}(\sO_{\ensuremath{\mathbb{P}}^1}(a) \oplus \sO_{\ensuremath{\mathbb{P}}^1}(1) \oplus \sO_{\ensuremath{\mathbb{P}}^1}^{\oplus k-1})$ where $a \in \ensuremath{\mathbb{N}}_{>0}$
and $\Delta$ is the union of $\ensuremath{\mathbb{P}}(\sO_{\ensuremath{\mathbb{P}}^1}(1) \oplus \sO_{\ensuremath{\mathbb{P}}^1}^{\oplus k-1})$ and a $\ensuremath{\mathbb{P}}^k$; or
\item a scroll $\ensuremath{\mathbb{P}}(\sO_{\ensuremath{\mathbb{P}}^1}(a) \oplus \sO_{\ensuremath{\mathbb{P}}^1}(1)^{\oplus 2} \oplus \sO_{\ensuremath{\mathbb{P}}^1}^{\oplus k-2})$ where $a \in \ensuremath{\mathbb{N}}_{>0}$ and $\Delta=\ensuremath{\mathbb{P}}(\sO_{\ensuremath{\mathbb{P}}^1}(1)^{\oplus 2} \oplus \sO_{\ensuremath{\mathbb{P}}^1}^{\oplus k-2})$; or
\item a scroll $\ensuremath{\mathbb{P}}(\sO_{\ensuremath{\mathbb{P}}^1}(a) \oplus \sO_{\ensuremath{\mathbb{P}}^1}(2) \oplus \sO_{\ensuremath{\mathbb{P}}^1}^{\oplus k-1})$ where $a \in \ensuremath{\mathbb{N}}_{>0}$
and $\Delta=\ensuremath{\mathbb{P}}(\sO_{\ensuremath{\mathbb{P}}^1}(2) \oplus \sO_{\ensuremath{\mathbb{P}}^1}^{\oplus k-1})$; or
\item a scroll $\ensuremath{\mathbb{P}}(V)$ over an elliptic curve and $\Delta = \ensuremath{\mathbb{P}}(W)$ where $V \rightarrow W$
is a quotient bundle of rank $k$ such that $\det W \simeq \mathcal O_W$.
\end{enumerate}
\end{proposition}
\begin{proof}
By Lemma \ref{lemmacontraction} there exists a $K_X$-negative extremal ray $R$
such that $\Delta \cdot R>0$ and $H \cdot R>0$. Thus if \holom{\varphi}{X}{Y} denotes the contraction of this extremal ray,
the nefvalue $r:= r(\varphi, H)$ (cf. Definition \ref{definitionnefvalue}) is strictly larger than $k$.
Arguing by contradiction
we suppose that the extremal contraction $\varphi$ is birational.
Let $F$ be a non-trivial $\varphi$-fibre, then by \cite[Thm.2.1(II,i)]{And95} we have $\dim F \geq \lfloor r \rfloor \geq k= \dim X-1$. Thus $\varphi$ contracts the divisor $F$ onto a point, in particular $F$ meets the Gorenstein locus
of $X$. By Lemma \ref{lemmarounddown} this implies that $r = \lfloor r \rfloor= k$, a contradiction.
Thus $\varphi$ is of fibre type and we can apply \cite[Sect.7.2, 7.3]{BS95} to see that
$X$ is isomorphic to one of the following varieties:
\begin{enumerate}
\item $(\mathbb P^{k+1}, \mathcal O_{\mathbb P^{k+1}}(1))$; or
\item $(Q^{k+1}, \mathcal O_{Q^{k+1}}(1))$; or
\item a generalised cone over $(\mathbb P^2, \mathcal O_{\mathbb P^2}(2))$; or
\item a scroll over a curve $C$.
\end{enumerate}
In the cases a)-c) we are obviously finished, so suppose that $X \cong \ensuremath{\mathbb{P}}(V)$
with $V$ a vector bundle of rank $k+1$. Note that $\Delta$ has exactly one irreducible component $\Delta_1$ that surjects onto $C$. Since $\Delta_1 \rightarrow C$ is flat and every fibre is a hyperplane in $\ensuremath{\mathbb{P}}^k$, we see that
$\Delta_1 \cong \ensuremath{\mathbb{P}}(W)$ with $V \rightarrow W$ a quotient bundle of rank $k$. Set $\Delta':=\Delta-\Delta_1$.
By the adjunction formula
$$
-(K_{\Delta_1}+(\Delta_1 \cap \Delta')) \simeq - k H|_{\Delta_1}
$$
and by the canonical bundle formula
$$
K_{\Delta_1} = \varphi|_{\Delta_1}^*(K_C+\det W) - k H|_{\Delta_1}
$$
thus we obtain $-(\Delta_1 \cap \Delta')= \varphi|_{\Delta_1}^*(K_C+\det W)$. Since $\det W$ is nef, this implies
that $K_C$ is antinef. If $C$ is a rational curve we obtain the cases d)-f).
If $C$ is an elliptic curve, the divisors $-(\Delta_1 \cap \Delta')$ and $\det W$ must be trivial.
Thus we obtain the case g).
\end{proof}
\begin{proposition} \label{propositionMRC}
Let $X$ be a Fano variety of dimension $n$ and index $k$ with lc singularities such that $-K_X \simeq kH$, with $H$ an ample Cartier divisor on $X$.
Assume that $\dim \Nklt(X) = k$.
Let \holom{\mu}{X'}{X} be a terminal modification of $X$, and write
$$
K_{X'} \simeq \mu^* K_X - E,
$$
where $E$ is an effective, reduced, $\mu$-exceptional Weil divisor.
Suppose that the base of the MRC-fibration $X' \dashrightarrow Z$ has dimension $n-k-1$, and let $F$ be a general fibre.
Then the log-pair $(F, F \cap E)$ quasi-polarised by the nef and big divisor $(\mu^* H)|_F$
is isomorphic to one of the varieties {\rm a)-f)} in Proposition \ref{propositionindexk}.
Moreover this statement is effective, i.e. there exist examples realising all these cases.
\end{proposition}
\begin{proof}
Since $X$ has lc singularities
and $K_{X'}+E \sim_\ensuremath{\mathbb{Q}} \mu^* K_X$, the pair $(X', E)$ is lc. By hypothesis $\dim Z=n-k-1$,
so the general fibre $F$ is a $(k+1)$-dimensional variety with terminal singularities.
Moreover the pair
$(F, E|_F)$ is lc and $E|_F \neq 0$ since otherwise $X$
is not rationally connected modulo the non-klt locus, in contradiction to \cite[Thm.1.2]{BP11}.
By adjunction we have $K_F+E|_F \sim_\ensuremath{\mathbb{Q}} -k (\mu^* H)|_F$, moreover any curve $C \subset F$
such that $(\mu^* H)|_F \cdot C=0$ is $\mu$-exceptional, so $K_F \cdot C=K_{X'} \cdot C \geq 0$.
Thus Proposition \ref{propositionindexk} applies. Case g) is excluded since $F$ is rationally connected.
The statement is effective, the examples corresponding to the varieties a)-f) are:
Examples \ref{exampledimk}, \ref{exampledimkquadric}, \ref{exampleveronese}, \ref{examplereduciblequadric}
and \ref{exampleprojectivebundles} (twice).
\end{proof}
\begin{remark*}
An analogous statement of Proposition \ref{propositionMRC} should hold
if we replace a terminal modification by the canonical modification. However this would make
it necessary to prove Proposition \ref{propositionindexk} and thus \cite[Sect.7.2, 7.3]{BS95} for varieties with canonical singularities,
a rather tedious exercise.
\end{remark*}
The following lemma is an analogue of classical descriptions of projective bundles
as in \cite[Prop.3.2.1]{BS95}:
\begin{lemma} \label{lemmaquadricbundle}
Let $Z$ be a projective manifold, and let $X$ be a normal projective variety
admitting an equidimensional fibration \holom{\varphi}{X}{Z} of relative dimension $k$. Assume that
there exists an ample Cartier divisor $H$ on $X$ such that the general
polarised fibre $(F, \sO_F(H))$ is isomorphic to the quadric $(Q^k, \sO_{Q^k}(1))$.
Then $X \rightarrow Z$ is a quadric fibration\footnote{We use the definition of an
adjunction theoretic quadric fibration \cite[3.3.1]{BS95} which is a-priori weaker
than supposing that all the fibres are quadrics.}, i.e. there exists a Cartier divisor $M$ on $Z$ such that
$K_X+k H \sim_\ensuremath{\mathbb{Q}} \varphi^* M$.
\end{lemma}
\begin{proof}
Let $C \subset Z$ be a complete intersection of $\dim Z-1$ general hyperplane sections. The preimage
$X_C := \fibre{\varphi}{C}$ is a normal projective variety and the fibration $\varphi_C \colon X_C \rightarrow C$
satisfies the conditions of \cite[Lemma 2.6]{a23}. Thus we know that $X_C$
has canonical singularities, and there exists a Cartier divisor $M_C$ on $C$ such that
$$
K_{X_C}+k H|_{X_C} \sim_\ensuremath{\mathbb{Q}} \varphi_C^* M_C.
$$
Using the canonical modification of $X$ we see that there exists
a closed (maybe empty) subset $Z' \subset Z$ of codimension at least two in $Z$ such that $X_0:= \fibre{\varphi}{Z \setminus Z'}$ has
canonical singularities, and $(K_{X}- k H)|_{X_0}$ is nef with respect to the equidimensional fibration
$\varphi_0\colon X_0 \rightarrow Z_0:=Z \setminus Z'$. It follows from Zariski's lemma \cite[Lemma 8.2]{BHPV04} that
$$
(K_{X}+k H)|_{X_0} \sim_\ensuremath{\mathbb{Q}} \varphi_0^* M_0
$$
where $M_0$ is a Cartier divisor on $Z_0$. Since $Z$ is smooth the divisor $M_0$ extends to a Cartier divisor $M$ on $Z$. Since $X \setminus X_0$ has codimension at least two in $X$, the isomorphism above extends to
$K_X+k H \sim_\ensuremath{\mathbb{Q}} \varphi^* M$.
\end{proof}
\begin{proof}[Proof of Proposition \ref{propositionfibrespace}]
By hypothesis the
base of the MRC-fibration $X' \dashrightarrow Z$ has dimension $n-k-1$. Thus Proposition \ref{propositionMRC}
applies, and the general fibre $F$ is given by the cases a)-f) of Proposition \ref{propositionindexk}.
If we are in case a), let $\ensuremath{\mathcal{H}}$ be a desingularisation of the unique component of the cycle space $\Chow{X}$
such that the general point
parametrises $\mu(F)$, and let $\holom{q}{\Gamma}{\ensuremath{\mathcal{H}}}$ be the normalisation of the pull-back of the universal family.
By construction the natural morphism
$p: \Gamma \rightarrow X$ is birational and $p^* H$ is $q$-ample and its restriction to the general fibre is the hyperplane divisor.
By \cite[Prop.4.10]{AD12}, \cite[Prop.3.5]{a18} the fibration $q$ is a projective bundle. If we are in the cases d)-f)
the MRC-fibration factors generically through an almost holomorphic fibration $X' \dashrightarrow W$ such that
the general fibre is a linear $\ensuremath{\mathbb{P}}^{k-1}$, so we use the same argument to construct a $\ensuremath{\mathbb{P}}^{k-1}$-bundle
$\Gamma \rightarrow \ensuremath{\mathcal{H}}$ that dominates $X$.
If we are in case b) let $\ensuremath{\mathcal{H}}$ be a desingularisation of the unique component of the cycle space $\Chow{X}$
such that the general point
parametrises $\mu(F)$, and let $\holom{q}{\Gamma}{\ensuremath{\mathcal{H}}}$ be the normalisation of the pull-back of the universal family.
Then $q$ is a quadric fibration by Lemma \ref{lemmaquadricbundle}.
If we are in case c) and $k=1$ the general fibre of the MRC-fibration is the Veronese surface. We repeat the
construction above to obtain $\ensuremath{\mathcal{H}}$ and $\Gamma \rightarrow \ensuremath{\mathcal{H}}$. If $k \geq 2$ the $(k+1)$-dimensional cone
over the Veronese surface is dominated by the projective bundle $\ensuremath{\mathbb{P}}(\sO_{\ensuremath{\mathbb{P}}^2}(2) \oplus \sO_{\ensuremath{\mathbb{P}}^2}^{\oplus k-1})$.
Thus we can repeat the construction of case a) to obtain a $\ensuremath{\mathbb{P}}^{k-1}$-bundle $\Gamma \rightarrow \ensuremath{\mathcal{H}}$ that dominates $X$.
\end{proof}
\section{The base of the MRC-fibration}
Proposition \ref{propositionfibrespace} gives a rather precise description of the Fano variety $X$, but the condition
on the MRC-fibration seems rather restrictive. In this section we will give strong evidence that this
condition is always satisfied when $\Nklt(X)$ is a quadric, in particular we prove
Theorem \ref{theoremkone}.
The following lemma generalises a part of \cite[Thm.2]{Ume81} to arbitrary dimension:
\begin{lemma} \label{lemmanotvanishing}
Let $Y$ be a projective scheme of pure dimension $m \geq 2$
such that the dualising sheaf is trivial. Suppose that there exists an irreducible component $Y_1 \subset Y$
having two points $\{p_1, p_2 \}$ which are not contained in any other component of
$Y$ such that $Y_1$ is normal near $\{p_1, p_2 \}$, and that $\{p_1, p_2 \}$ are isolated non-klt points.
Let $\holom{\mu}{Y'}{Y}$ be the birational morphism defined by the canonical modification of $Y_1$
in the points $p_1$ and $p_2$.
If $Y$ is log-canonical in $p_1$ and $p_2$, then
$h^{m-1}(Y', \sO_{Y'}) \geq 1$.
\end{lemma}
\begin{proof}
The image of the $\mu$-exceptional locus equals $\{p_1, p_2 \}$,
so the higher direct image sheaves $R^j \mu_* \sO_{Y'}$ have support in a finite set.
Our goal is to prove that we have
\begin{equation} \label{notvanishing}
h^0(Y, R^{m-1} \mu_* \sO_{Y'}) \geq 2.
\end{equation}
Assuming this for the time being, let us see how to conclude by a Leray spectral sequence computation:
since the sheaves $R^j \mu_* \sO_{Y'}$
have no higher cohomology for $j>0$ we see that
$$
H^0(Y, R^{m-1} \mu_* \sO_{Y'}) = E_2^{0,m-1}=E_{m}^{0, m-1}
$$
and
$$
\ensuremath{\mathbb{C}} \cong H^0(Y, \omega_Y) \cong H^m(Y, \sO_Y) = E_2^{m, 0} = E_m^{m, 0}.
$$
By \eqref{notvanishing} the first space has dimension at least two. Thus the kernel of the map
$$
d_m : E_{m}^{0, m-1} \rightarrow E_m^{m, 0}
$$
has dimension at least one, hence $\dim E_{m+1}^{0, m-1} = \dim E_{\infty}^{0, m-1}>0$.
Since the map $H^{m-1}(Y', \sO_{Y'}) \rightarrow E_{\infty}^{0, m-1}$ is surjective the statement follows.
For the proof of \eqref{notvanishing} note first that the claim is local in a neighbourhood of
the points $\{p_1, p_2 \}$. Thus we can suppose without loss of generality that $Y$ is a normal variety
with trivial canonical divisor such that $\Nklt(Y)=\{p_1, p_2 \}$ and $\mu\colon Y' \rightarrow Y$ is the canonical
modification. Since $Y'$ has canonical, hence rational singularities, we can replace it with a desingularisation,
which for simplicity's sake we denote by the same letter. Since $K_Y$ is Cartier we can write
$$
K_{Y'} \simeq \mu^* K_Y - E + F,
$$
where $E$ is a reduced divisor mapping surjectively onto $\Nklt(Y)$ and $F$ is an effective divisor
such that $E$ and $F$ have no common components. In particular $\omega_E \simeq \sO_E(F)$
is effective. By Kov\'acs' vanishing theorem \cite[Cor.6.6]{Kov11} we have
$R^j \mu_* \sO_{Y'}(-E)=0$ for all $j>0$, hence
$$
R^j \mu_* \sO_{Y'} \simeq R^j (\mu|_E)_* \sO_{E}
$$
for all $j>0$. By duality (in the sense of \cite[III, Sect.7, Defn.,p.241]{Har77}) we have
$$
H^{m-1}(E, \sO_E) \cong H^0(E, \omega_E).
$$
We have seen that $\omega_E$ is effective. Since $E$ has at least two connected components the
inequality \eqref{notvanishing} follows.
\end{proof}
\begin{definition} \label{definitionladder}
Let $X$ be a Fano variety of dimension $n$ and index $k$ with lc singularities, and let $H$ be a Cartier divisor such that
$-K_X \simeq kH$. We say that $X$ admits a {\rm ladder} if there exist $k$ general divisors $D_1, \ldots, D_k$ in $|H|$ such that
for all $i \in \{1, \ldots, k\}$ the intersection
$$
Z_i := D_1 \cap \ldots \cap D_i
$$
is a normal variety of dimension $n-k$ with lc singularities such that
$$
\Nklt(Z_i) = \Nklt(X) \cap D_1 \cap \ldots \cap D_i.
$$
\end{definition}
\begin{proposition} \label{propositionnotRC}
Let $X$ be a Fano variety of dimension $n$ and index $k$ with lc singularities,
and let $H$ be a Cartier divisor such that $-K_X \simeq kH$.
Suppose that $(\Nklt(X), \sO_{\Nklt(X)}(H))$ is a quadric of dimension $k$. If $k>1$ suppose also that $X$ admits a ladder.
Then we have
$$
h^{n-k-1}(X', \sO_{X'}) \neq 0,
$$
where $X' \rightarrow X$ is the canonical modification. Moreover the base of the MRC-fibration
$X' \dashrightarrow Z$ has dimension $n-k-1>0$.
\end{proposition}
\begin{proof}
Note first that by the Nadel vanishing theorem the restriction map
\begin{equation} \label{surjective}
H^0(X, \sO_X(H)) \rightarrow H^0(\Nklt(X), \sO_{\Nklt(X)}(H))
\end{equation}
is surjective. Since $\sO_{\Nklt(X)}(H)$ is globally generated, this implies that $|H|$ is globally generated near $\Nklt(X)$.
In particular if $Y \in |H|$ is a general divisor, then we can apply the adjunction
formula \cite[Lemma 1.7.6]{BS95} to see that $\omega_{Y} \simeq \sO_{Y}((k-1)H)$. Moreover the intersection
$$
Y \cap \Nklt(X)
$$
is a quadric of dimension $k-1$
and $Y \cap \Nklt(X)$ is a connected component of the non-klt locus of $Y$\footnote{The divisor $Y$ may have
several irreducible components, but by Bertini's theorem there exists a unique irreducible component that intersects
$\Nklt(X)$. Note that this component is normal near $\Nklt(X)$ so it makes sense to speak of the non-klt locus.}.
Let $\holom{\mu}{X'}{X}$ be the canonical modification, then
the strict transform $Y'$ of $Y$ coincides with the total transform, hence we have $Y' \simeq \mu^* H$.
Moreover the birational map $\holom{\mu|_{Y'}}{Y'}{Y}$ is the canonical modification of $Y$
along $Y \cap \Nklt(X)$.
Since $\mu^* H$ is nef and big, we have
$$
H^j(X', \sO_{X'}(-\mu^* H))=0
$$
for all $j \leq n-1$ by \cite[Thm.2.70]{KM98}. Since $n-k-1 \leq n-2$ we obtain
$$
H^{n-k-1}(X', \sO_{X'}) \twoheadrightarrow H^{n-k-1}(Y', \sO_{Y'}).
$$
We will now conclude by induction: if $k=1$, then $\omega_{Y}$ is trivial and
$\holom{\mu|_{Y'}}{Y'}{Y}$ satisfies the conditions of Lemma \ref{lemmanotvanishing}.
Thus we have $H^{n-2}(Y', \sO_{Y'}) \neq 0$.
If $k \geq 2$, then by hypothesis the Fano variety $X$ admits a ladder $D_1=Y, D_2, \ldots, D_k$, so $Y$ has lc singularities,
$\Nklt(Y)$ is a quadric and the divisors
$$
D_i \cap Y \in |H|_{Y}|
$$
define a ladder on $Y$. Thus the induction hypothesis applies to $Y$.
This also implies that the base of the MRC-fibration has dimension at least $n-k-1$.
In order to see that equality holds let us first deal with the case $k=1$. As above let $Y \in |H|$ be a general divisor,
and let $Y_1 \subset Y$ be the unique irreducible component that meets $\Nklt(X)$. Let $Y_1'$ (resp. $Y'$) be
the strict transform under the canonical modification $\mu$. Since $\Nklt(X) \cap Y= \Nklt(X) \cap Y_1$ is not empty
and $\omega_Y \simeq \sO_Y$ we see that $\omega_{Y'}$ is antieffective. Moreover we have a map
$\omega_{Y_1'} \rightarrow \omega_{Y'} \otimes \sO_{Y_1}$ that is an isomorphism in the generic point
of $Y_1'$, so $\omega_{Y_1'}$ is antieffective.
Thus we see that $Y_1'$ is uniruled. Since $Y_1'$ is general (note that by \eqref{surjective} we have $h^0(X, \sO_X(H)) \geq 3$),
it is not contracted by the MRC-fibration $X' \dashrightarrow Z$.
Since $Z$ is not uniruled \cite{GHS03}, we obtain $\dim Z<\dim Y_1'=n-1$.
If $k>1$ then by hypothesis we can consider the complete intersection
$Z_{n-k}$ defined in Definition \ref{definitionladder}. Then $K_{Z_{n-k}}$ is trivial
and by what precedes its strict transform $Z_{n-k}' \subset X'$ is uniruled.
As in the case $k=1$ we obtain $\dim Z<\dim Z_{n-k}=n-k$.
\end{proof}
Theorem \ref{theoremkone} is now an immediate consequence:
\begin{proof}[Proof of Theorem \ref{theoremkone}]
The dimension of the base of the MRC-fibration is a birational invariant for varieties with canonical singularities
\cite{HMK07}, so by Proposition \ref{propositionnotRC} we have $\dim Z=n-2$. Thus we can conclude
with Proposition \ref{propositionMRC}.
\end{proof}
For Fano varieties with high index we can verify the ladder condition in Proposition \ref{propositionnotRC}:
\begin{proposition} \label{propositionladder}
Let $X$ be a Fano variety of dimension $n$ and index $k \geq n-3$ with lc singularities,
and let $H$ be a Cartier divisor such that $-K_X \simeq kH$. Suppose that $\dim \Nklt(X)=k$.
Let $Y \in |H|$ be a general divisor. Then $Y$ is
a normal variety with lc singularities such that
$$
\Nklt(Y) = \Nklt(X) \cap Y.
$$
\end{proposition}
\begin{proof}
By the Nadel vanishing theorem the restriction map
$$
H^0(X, \sO_X(H)) \rightarrow H^0(\Nklt(X), \sO_{\Nklt(X)}(H))
$$
is surjective. By Theorem \ref{theoremnkltlocus} we know that $\sO_{\Nklt(X)}(H)$ is globally generated, so
we have
\begin{equation} \label{intersectionempty}
{\rm Bs} |H| \cap \Nklt(X) = \emptyset.
\end{equation}
We claim that the pair $(X \setminus \Nklt(X), Y \setminus \Nklt(X))$ is plt.
Assuming this for the time being, let us see how to conclude.
Since the pair $(X \setminus \Nklt(X), Y \setminus \Nklt(X))$ is plt we know by
inversion of adjunction \cite[Thm.7.5.1]{Kol95} that $Y \setminus \Nklt(X)$ has canonical singularities.
Since $H|_{X \setminus {\rm Bs} |H|}$ is a free linear system, a general $Y \in |H|$ is normal by \cite[Thm.1.7.1]{BS95}
and $(X \setminus {\rm Bs} |H|, Y \setminus {\rm Bs} |H|)$ is an lc pair.
Using the adjunction formula
\cite[Lemma 1.7.6]{BS95} we see that for a general $Y \in |H|$ we have
$-K_Y \simeq (k-1) H|_Y$.
By inversion of adjunction $Y$ has lc singularities \cite[Thm. p.130]{Kaw07} and
$$
\Nklt(Y) = \Nklt(X) \cap Y.
$$
{\em Proof of the claim.} We will deal with the case $k=n-3$, the other cases being simpler. We follow the argument of \cite[Thm.1.1]{Flo13}: note that $X \setminus \Nklt(X)$ has canonical singularities.
We argue by contradiction and suppose that the pair $(X \setminus \Nklt(X), Y \setminus \Nklt(X))$ is not plt.
Then there exists a $0 < c \leq 1$
and an irreducible variety $W \subset {\rm Bs} |H|$ such that the pair $(X \setminus \Nklt(X), c(Y \setminus \Nklt(X)))$
is properly lc and $W$ a minimal lc centre. By \cite[Thm.2.2]{Fuj11}
the restriction map
$$
H^0(X, \sO_X(H)) \rightarrow H^0(W, \sO_W(H))
$$
is surjective.
Since $W$ is contained in the base locus this implies that $H^0(W, \sO_W(H))=0$.
By Kawamata subadjunction \eqref{subadjunction}
there exists an effective divisor $\Delta_W$ such that $(W, \Delta_W)$ is klt and
$$
(K_W+\Delta_W) \sim_\ensuremath{\mathbb{Q}} (K_X+c Y)|_W \sim_\ensuremath{\mathbb{Q}} -(n-3-c) H|_W.
$$
If $\dim W \leq 2$ we apply \cite[Prop.4.1]{Kaw00} to see that $h^0(W, \sO_W(H)) \neq 0$, a contradiction.
If $\dim W \geq 3$ and $n-3-c>\dim W-3$,
then $(W,B_W)$ is log Fano of index at least $n-3-c$.
By \cite[Theorem 5.1]{Kaw00} this implies $h^0(W,\mathcal{O}_W (H))\neq 0$, a contradiction.
Thus we are left with the case when $\dim W \geq 3$ and
$\dim W\geq n-c$. Since $c \leq 1$ this implies $\dim W = n-1$.
Since the centre $W$ is minimal we know by \cite[Lemma 2.7]{Flo13}
that $c<1/2$. Thus we have $\dim W \geq n-1/2$, a contradiction.
\end{proof}
\section{Examples} \label{sectionexamples}
In \cite[$\S 2$]{BS87} the first-named author and Sommese observed that for a Fano threefold
of index one with $\dim \Nklt(X)=1$, the non-klt locus consists of rational curves. They also ask
how far $X$ can deviate from being a generalised cone with $\Nklt(X)$ as its vertex. In this section
we answer this question: all the classification results of Section \ref{sectiondescriptionX} are effective,
so in many cases $X$ is far from being a generalised cone.
\begin{example} \label{exampledimkminusone}
Let $Y$ be a projective manifold with trivial canonical divisor, and let $L$ be a very ample line bundle on $Y$. Set
$$
X' := \ensuremath{\mathbb{P}}( \sO_Y^{\oplus k} \oplus L ),
$$
then we have
$$
K_{X'} = -k \zeta - (\zeta - \varphi^* L),
$$
where $\zeta$ is the tautological divisor on $X'$. We have $\zeta - \varphi^* L=E$ where $E \cong Y \times \ensuremath{\mathbb{P}}^{k-1}$ is the
divisor defined by the quotient
$$
\sO_Y^{\oplus k} \oplus L \rightarrow \sO_Y^{\oplus k}.
$$
The divisor $\zeta$ is globally generated and defines a birational morphism $\holom{\mu}{X'}{X}$ that contracts $E$ onto
a $\ensuremath{\mathbb{P}}^{k-1}$. Using the canonical bundle formula above we see that $X$ is a Fano variety of index $k$ with lc singularities,
moreover the non-klt locus is a linear $\ensuremath{\mathbb{P}}^{k-1}$.
\end{example}
\begin{example} \label{exampledimk}
Let $Y$ be a projective manifold admitting a fibration $\holom{\psi}{Y}{\ensuremath{\mathbb{P}}^1}$
such that $\sO_Y(-K_Y) \simeq \psi^* \sO_{\ensuremath{\mathbb{P}}^1}(1)$. Then set
$X':= \ensuremath{\mathbb{P}}(A \oplus \psi^* \sO_{\ensuremath{\mathbb{P}}^1}(1) \oplus \sO_Y^{\oplus k-1})$ where $A$ is a very ample line bundle on $Y$.
Let $\zeta$ be the tautological divisor on $X'$, then $\zeta$ is globally generated and defines
a birational morphism \holom{\mu}{X'}{X} contracting the divisor $E$ corresponding to the quotient
$$
A \oplus \psi^* \sO_{\ensuremath{\mathbb{P}}^1}(1) \oplus \sO_Y^{\oplus k-1} \rightarrow \psi^* \sO_{\ensuremath{\mathbb{P}}^1}(1) \oplus \sO_Y^{\oplus k-1}
\simeq \psi^* (\sO_{\ensuremath{\mathbb{P}}^1}(1) \oplus \sO_{\ensuremath{\mathbb{P}}^1}^{\oplus k-1})
$$
onto a $\ensuremath{\mathbb{P}}^k$. Using the canonical bundle formula one easily sees that $X$ is Fano of index
$k$ with lc singularities and $(\Nklt(X), \sO_{\Nklt(X)}(H)) \cong (\ensuremath{\mathbb{P}}^k, \sO_{\ensuremath{\mathbb{P}}^k}(1))$, where $-K_X\simeq kH$.
\end{example}
\begin{example} \label{exampledimkquadric}
Let $X$ be a Fano variety of index $m$ constructed as in Example \ref{exampledimkminusone}, and let $-K_X\simeq mH$
with $H$ a Cartier divisor on $X$.
Set $k=m-1$.
By the Nadel vanishing
theorem the restriction map
$$
H^0(X, \sO_X(2H)) \rightarrow H^0(\Nklt(X), \sO_{\Nklt(X)}(2H))
$$
is surjective. Fix now a quadric $Q \subset \ensuremath{\mathbb{P}}^k \cong \Nklt(X)$ and fix a general divisor
$B$ in the linear system $|2 H|$ such that $B \cap \Nklt(X) = Q$.
Denote by
$$
\holom{\pi}{\widetilde X}{X}
$$
the cyclic covering of degree two branched along $B$\footnote{Note that by
the generality assumption the divisor $B$ is reduced even if $Q$ is not reduced. In particular
$\widetilde X$ is irreducible.}. By the ramification formula we see that
$-K_{\widetilde X} = \pi^* k H$,
so $\widetilde X$ is a Fano variety of index $k$.
Using again the ramification formula we know by \cite[Prop.5.20]{KM98} that $\widetilde X$ has lc singularities
if and only if the pair $(X, \frac{1}{2} B)$ is lc. Since $B$ is general this is clear in the complement
of $\Nklt(X)$, moreover by inversion of adjunction \cite[Thm.0.1]{Hac12} the pair $(X, \frac{1}{2} B)$
is lc near $\Nklt(X)$ if and only if $(\ensuremath{\mathbb{P}}^k, \frac{1}{2} Q)$ is lc. Since $Q$ is a quadric this is easily checked.
The restriction of $\pi$ to $\Nklt(\widetilde{X}) \cong \ensuremath{\mathbb{P}}^k$ induces a two-to-one cover
$$
\Nklt(\widetilde X) \rightarrow \Nklt(X)
$$
that ramifies exactly along $Q = B \cap \Nklt(X)$. Since $Q$ is a quadric in $\ensuremath{\mathbb{P}}^k$, we see that
$\Nklt(\widetilde X)$ is a quadric, the singularities depending on the singularities of $Q$.
Let $X' \rightarrow Y$ be the projective bundle dominating $X$ (cf. Example \ref{exampledimkminusone}).
Then $X' \times_X \widetilde X \rightarrow Y$ is a quadric bundle dominating $\widetilde X$.
\end{example}
\begin{example} \label{exampleveronese}
Let $Y$ be a projective manifold with trivial canonical divisor.
Let $L$ be a very ample line bundle on $Y$ and set
$$
B' := \ensuremath{\mathbb{P}}(L \oplus \sO_Y^{\oplus 2}).
$$
Denote by $\eta$ the tautological divisor on $B'$, then
$2 \eta$ is globally generated and defines a birational morphism $\holom{\nu}{B'}{B}$
onto a normal projective variety contracting the divisor $D$ corresponding to the quotient
$$
L \oplus \sO_Y^{\oplus 2} \rightarrow \sO_Y^{\oplus 2}
$$
onto a $\ensuremath{\mathbb{P}}^1$. Using the canonical bundle formula for $B'$ we see that
$$
K_{B'} \simeq -2 \eta -D \simeq \nu^* K_B - D,
$$
so $B$ has lc singularities and $(\Nklt(B), \sO_{\Nklt(B)}(-K_B)) \cong (\ensuremath{\mathbb{P}}^1, \sO_{\ensuremath{\mathbb{P}}^1}(2))$.
For some integer $k \geq 2$ we set
$$
X' := \ensuremath{\mathbb{P}}(\sO_{B'}(2 \eta) \oplus \sO_{B'}^{\oplus k-1}),
$$
and denote by $\zeta$ the tautological divisor on $\holom{\varphi}{X'}{B'}$. The divisor $\zeta$ is globally generated and defines a birational morphism $\holom{\mu}{X'}{X}$.
If we restrict $\mu$ to $\fibre{\varphi}{\ensuremath{\mathbb{P}}^2}$ where $\ensuremath{\mathbb{P}}^2$ is a fibre of $B' \rightarrow Y$,
the image is a generalised cone of dimension $k+1$ over the Veronese surface $(\ensuremath{\mathbb{P}}^2, \sO_{\ensuremath{\mathbb{P}}^2}(2))$.
If we restrict $\mu$ furthermore to $\fibre{\varphi}{\ensuremath{\mathbb{P}}^2 \cap D}$, the image is the generalised cone
of dimension $k$ over the line $\ensuremath{\mathbb{P}}^2 \cap D$, but polarised by $\sO_{\ensuremath{\mathbb{P}}^2}(2)$, so we
get a quadric $Q$ of dimension $k$ such that the singular locus has dimension $k-2$.
Since
$D \simeq \ensuremath{\mathbb{P}}(\sO_Y^{\oplus 2})$,
a straightforward computation shows that
$$
\zeta^{k+1} \cdot \varphi^* D = 0 \ \mbox{in} \ H^{2k+4}(X', \ensuremath{\mathbb{R}}),
$$
so the divisor
$E:=\varphi^* D$ is contracted by $\mu$ onto the $k$-dimensional quadric $Q$. Using the canonical bundle
formula we see that
$$
K_{X'} = -k \zeta - E = \mu^* K_X - E,
$$
so $X$ is a Fano variety of index $k$ having lc singularities and $\Nklt(X) \cong Q$.
Note also that $\mu$
factors through a birational morphism $\holom{p}{\Gamma}{X}$ where $\Gamma$ is a normal
projective variety admitting a locally trivial fibration $\holom{q}{\Gamma}{Z}$
such that the polarised fibre is the generalised cone of dimension $k+1$ over the Veronese surface $(\ensuremath{\mathbb{P}}^2, \sO_{\ensuremath{\mathbb{P}}^2}(2))$.
\end{example}
\begin{example} \label{examplereduciblequadric}
For some $k \geq 3$, let $Y \subset \ensuremath{\mathbb{P}}^{k-1}$ be a smooth hypersurface of degree $k$,
so $Y$ is a Calabi--Yau manifold. We set
$$
B' := \ensuremath{\mathbb{P}}(\sO_Y(1) \oplus \sO_Y),
$$
and denote by $\eta$ the tautological divisor on $B'$. Then $\eta$ is globally generated
and defines a birational morphism \holom{\nu}{B'}{B} where $B$ is the cone over $Y$.
We have $K_{B'} \simeq \nu^* K_{B} - D$, where $D$ is the divisor corresponding to the quotient
$$
\sO_Y(1) \oplus \sO_Y \rightarrow \sO_Y.
$$
Note that $B$ is a hypersurface of degree $k$ in $\ensuremath{\mathbb{P}}^{k}$, so $B$ is Cohen--Macaulay
and has exactly one non-klt point, the vertex of the cone. The anticanonical sheaf
$\sO_B(-K_{B}) \simeq \sO_{B}(1)$ is globally generated and $h^0(B, \sO_B(-K_{B}))=k+1$.
We define $W^*$ to be the vector bundle of rank $k$ that is the kernel of
the evaluation map
$\sO_{B}^{\oplus k+1} \twoheadrightarrow \sO_B(-K_{B})$. Dualizing we obtain an exact sequence
$$
0 \rightarrow \sO_B(K_{B}) \rightarrow \sO_{B}^{\oplus k+1} \rightarrow W \rightarrow 0,
$$
so $W$ is globally generated. Moreover by a singular version of Kodaira vanishing \cite[Cor.6.6]{KSS10}
we have $H^1(B, \sO_B(K_{B}))=0$, so we get $h^0(B, W)=k+1$.
Set now $W':=\nu^* W$ and let $A$ be the pull-back of a very ample Cartier divisor on $B$.
We set
$$
X' := \ensuremath{\mathbb{P}}(\sO_{B'}(A) \oplus W'),
$$
and denote by $\zeta$ the tautological divisor on $\holom{\varphi}{X'}{B'}$. The divisor $\zeta$ is globally generated and defines a birational morphism $\holom{\mu}{X'}{X}$.
Denote by $E \subset X'$ the divisor defined by the quotient
$$
\sO_{B'}(A) \oplus W' \rightarrow W'.
$$
Then by the canonical bundle formula
$$
K_{X'} \simeq \varphi^*(K_{B'}+A+\det W')-(k+1) \zeta = -k \zeta - (\zeta-\varphi^* A) + \varphi^* (K_{B'}+\det W').
$$
By construction we have $\zeta-\varphi^* A \simeq E$ and $K_{B'}+\det W' \simeq - D$, so we get
$$
K_{X'} \simeq -k \zeta - E - \varphi^* D.
$$
Since $D$ is contracted by $\nu$, the restriction of $\sO_{B'}(A) \oplus W'$ to $D$ is isomorphic
to $\sO_D^{\oplus k+1}$, so $\varphi^* D$ is contracted by $\mu$ onto a $\ensuremath{\mathbb{P}}^k$.
The divisor $E$ is isomorphic to $\ensuremath{\mathbb{P}}(W')$ and by construction $h^0(B', W')=k+1$,
so $E$ is also contracted onto a $\ensuremath{\mathbb{P}}^k$. Thus $X$ is a Fano variety of index $k$
with lc singularities such that $\Nklt(X)$ is a reducible quadric.
\end{example}
\begin{example} \label{exampleprojectivebundles}
Let $Y$ be a projective manifold with trivial canonical divisor and set $B := Y \times \ensuremath{\mathbb{P}}^1$.
Let $A$ be a very ample Cartier divisor on $B$ and set
$$
X' := \ensuremath{\mathbb{P}}(\sO_B(A) \oplus \sO_B(-K_B) \oplus \sO_B^{\oplus k-1}).
$$
Denote by
$\zeta$ the tautological divisor on $\holom{\varphi}{X'}{B}$. The divisor $\zeta$ is globally generated and defines a birational morphism $\holom{\mu}{X'}{X}$.
Moreover if $E \subset X'$ is the divisor defined by the quotient
$$
\sO_B(A) \oplus \sO_B(-K_B) \oplus \sO_B^{\oplus k-1} \rightarrow \sO_B(-K_B) \oplus \sO_B^{\oplus k-1},
$$
then $E$ is contracted by $\mu$ onto a quadric $Q$ of dimension $k$ that is singular along a subvariety
of dimension $k-2$. By the canonical bundle formula we see that
$$
K_{X'} = -k \zeta - E = \mu^* K_X - E,
$$
so $X$ is a Fano variety of index $k$ having lc singularities and $\Nklt(X) \cong Q$.
Analogously, if we set
$$
X' := \ensuremath{\mathbb{P}}\big(\sO_B(A) \oplus \sO_B(- \frac{1}{2}K_B)^{\oplus 2} \oplus \sO_B^{\oplus k-2}\big),
$$
the same properties hold; in this case the quadric is singular along a subvariety of dimension $k-3$.
\end{example}
\def$'${$'$}
| {
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} | 8,828 |
Q: Blank frame for jQuery Mobile Google Maps I am integrating Google Maps with jQuery Mobile and .NET. I am following the Google Code (example 4) documentation here: http://jquery-ui-map.googlecode.com/svn/trunk/demos/jquery-mobile-example.html#jquery-mobile-example-4.html
I've been careful in transferring the code, but I keep receiving a blank frame. The map doesn't show up in the frame.
Anyone else run into this problem? Any recommendations on additional documentation, tutorials, videos, and reading?
I greatly appreciate anyone's time and help, thank you.
A: I think your problem is outlined here : http://www.smashinglabs.pl/gmap/examples
If, for any reason, any dimension of div will be equal 0 during
loading process, maps will stop working correctly. It is quite common
issue while loading tabs, accordions, etc.
He goes on to outline specific problem resolutions. Some of them:
*
*Try calling the 'refresh' function manually google.maps.event.trigger($('#map').data('gmap').gmap, 'resize');
*If your #map container doesn't have a set size, it will default to 0x0 by normal HTML/CSS standards. Try setting a size manually, say 300x300
*etc...
A: It might be the google loader api key? (If you copy paste). Get any JS errors?
As Phill said, post some code and we'll be able to help you better.
A: If you are using jquery.ui.maps thats the wrong syntax. From what i can tell you are using another plugin.
A: Thank you for your time and help. After more research and additional help from others, I was able to find a Google Maps solution to get me moving more quickly. A great conversation that outlines resources I studied, used, and highlighted can be found in this google groups discussion.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 8,552 |
Insider Trading Alert - FAST, PBCT, ACAS, IBKR And TRLA Traded By Insiders
Stocks with insider trader activity include FAST, PBCT, ACAS, IBKR and TRLA
Yesterday, Jan. 28, 2014, 72 U.S. common stocks issued filings of shares being bought or sold by insiders. The transactions ranged in value from $440.99 to $7,539,344.56.
Fastenal Company (FAST) - FREE Research Report
Lundquist Nicholas J who is Executive Vice-President at Fastenal Company bought 4,000 shares at $44.79 on Jan. 28, 2014. Following this transaction, the Executive Vice-President owned 206,000 shares meaning that the stake was reduced by 1.98% with the 4,000-share transaction.
Ancius Michael J who is Director at Fastenal Company bought 485 shares at $44.50 on Jan. 28, 2014. Following this transaction, the Director owned 7,364 shares meaning that the stake was reduced by 7.05% with the 485-share transaction.
The shares most recently traded at $43.97, down $0.53, or 1.21% since the insider transaction. Historical insider transactions for Fastenal Company go as follows:
4-Week # shares bought: 4,300
4-Week # shares sold: 200,000
12-Week # shares bought: 8,800
24-Week # shares bought: 10,235
The average volume for Fastenal Company has been 2.3 million shares per day over the past 30 days. Fastenal Company has a market cap of $13.2 billion and is part of the industrial goods sector and materials & construction industry. Shares are down 6.52% year-to-date as of the close of trading on Tuesday.
Fastenal Company, together with its subsidiaries, operates as a wholesaler and retailer of industrial and construction supplies in the United States, Canada, and internationally. The company offers fasteners and other industrial and construction supplies under the Fastenal name. The stock currently has a dividend yield of 2.24%. The company has a P/E ratio of 29.5. Currently there are 3 analysts that rate Fastenal Company a buy, 1 analyst rates it a sell, and 6 rate it a hold.
Exclusive Offer: Get the latest Stock Analysis on FAST - FREE
rates Fastenal Company as a
. The company's strengths can be seen in multiple areas, such as its revenue growth, largely solid financial position with reasonable debt levels by most measures, expanding profit margins, increase in net income and notable return on equity. We feel these strengths outweigh the fact that the company has had lackluster performance in the stock itself. Get the full
Fastenal Company Ratings Report
People's United Financial (PBCT) - FREE Research Report
Daukas Galan G who is Sr. Executive Vice President at People's United Financial bought 11,400 shares at $14.66 on Jan. 28, 2014. Following this transaction, the Sr. Executive Vice President owned 11,400 shares meaning that the stake was reduced by 100% with the 11,400-share transaction.
The shares most recently traded at $14.37, down $0.29, or 2.01% since the insider transaction. Historical insider transactions for People's United Financial go as follows:
The average volume for People's United Financial has been 3.8 million shares per day over the past 30 days. People's United Financial has a market cap of $4.6 billion and is part of the financial sector and banking industry. Shares are down 3.44% year-to-date as of the close of trading on Tuesday.
People's United Financial, Inc. operates as the bank holding company for People's United Bank that provides commercial banking, retail and business banking, and wealth management services to individual, corporate, and municipal customers. The stock currently has a dividend yield of 4.49%. The company has a P/E ratio of 18.8. Currently there are 2 analysts that rate People's United Financial a buy, 4 analysts rate it a sell, and 8 rate it a hold.
Exclusive Offer: Get the latest Stock Analysis on PBCT - FREE
rates People's United Financial as a
. The company's strengths can be seen in multiple areas, such as its increase in stock price during the past year, growth in earnings per share, reasonable valuation levels, expanding profit margins and notable return on equity. We feel these strengths outweigh the fact that the company has had sub par growth in net income. Get the full
People's United Financial Ratings Report
American Capital (ACAS) - FREE Research Report
Flax Samuel Allan who is EVP, GC and Secretary at American Capital sold 261 shares at $15.71 on Jan. 28, 2014. Following this transaction, the EVP, GC and Secretary owned 415,137 shares meaning that the stake was reduced by 0.06% with the 261-share transaction.
The shares most recently traded at $15.76, up $0.05, or 0.32% since the insider transaction. Historical insider transactions for American Capital go as follows:
The average volume for American Capital has been 2.2 million shares per day over the past 30 days. American Capital has a market cap of $4.4 billion and is part of the financial sector and financial services industry. Shares are up 1.73% year-to-date as of the close of trading on Tuesday.
American Capital, Ltd. is a private equity and venture capital firm specializing in management and employee buyouts, leveraged finance, mezzanine, acquisition, recapitalization, middle market, and growth capital investments. The company has a P/E ratio of 24.5. Currently there are 2 analysts that rate American Capital a buy, 1 analyst rates it a sell, and 4 rate it a hold.
Exclusive Offer: Get the latest Stock Analysis on ACAS - FREE
rates American Capital as a
. The company's strengths can be seen in multiple areas, such as its attractive valuation levels, solid stock price performance and good cash flow from operations. However, as a counter to these strengths, we also find weaknesses including deteriorating net income, disappointing return on equity and feeble growth in the company's earnings per share. Get the full
American Capital Ratings Report
Interactive Brokers Group (IBKR) - FREE Research Report
Nemser Earl H who is Vice Chairman at Interactive Brokers Group sold 15,474 shares at $21.64 on Jan. 28, 2014. Following this transaction, the Vice Chairman owned 129,541 shares meaning that the stake was reduced by 10.67% with the 15,474-share transaction.
Brody Paul Jonathan who is Chief Financial Officer at Interactive Brokers Group sold 8,603 shares at $21.64 on Jan. 28, 2014. Following this transaction, the Chief Financial Officer owned 72,021 shares meaning that the stake was reduced by 10.67% with the 8,603-share transaction.
The shares most recently traded at $21.68, up $0.04, or 0.2% since the insider transaction. Historical insider transactions for Interactive Brokers Group go as follows:
The average volume for Interactive Brokers Group has been 603,600 shares per day over the past 30 days. Interactive Brokers Group has a market cap of $1.0 billion and is part of the financial sector and financial services industry. Shares are down 13.19% year-to-date as of the close of trading on Tuesday.
Interactive Brokers Group, Inc. operates as an automated electronic broker and market maker. The stock currently has a dividend yield of 1.92%. The company has a P/E ratio of 24.2. Currently there are 2 analysts that rate Interactive Brokers Group a buy, no analysts rate it a sell, and 2 rate it a hold.
Exclusive Offer: Get the latest Stock Analysis on IBKR - FREE
rates Interactive Brokers Group as a
. The company's strengths can be seen in multiple areas, such as its solid stock price performance, revenue growth and reasonable valuation levels. However, as a counter to these strengths, we also find weaknesses including deteriorating net income, generally higher debt management risk and disappointing return on equity. Get the full
Interactive Brokers Group Ratings Report
Trulia (TRLA) - FREE Research Report
Inkinen Sami who is Director at Trulia sold 5,800 shares at $34.40 on Jan. 28, 2014. Following this transaction, the Director owned 839,503 shares meaning that the stake was reduced by 0.69% with the 5,800-share transaction.
Flint Peter who is Chief Executive Officer at Trulia sold 9,200 shares at $34.40 on Jan. 28, 2014. Following this transaction, the Chief Executive Officer owned 1.5 million shares meaning that the stake was reduced by 0.61% with the 9,200-share transaction.
The shares most recently traded at $34.25, down $0.15, or 0.44% since the insider transaction. Historical insider transactions for Trulia go as follows:
The average volume for Trulia has been 1.5 million shares per day over the past 30 days. Trulia has a market cap of $1.3 billion and is part of the technology sector and internet industry. Shares are up 0.48% year-to-date as of the close of trading on Tuesday.
Trulia, Inc. provides tools to research homes and neighborhoods for consumers through Web and mobile applications. The company, through its tools, also enables real estate professionals to market their listings. The company has a P/E ratio of 226.6. Currently there are 4 analysts that rate Trulia a buy, 1 analyst rates it a sell, and none rate it a hold.
Exclusive Offer: Get the latest Stock Analysis on TRLA - FREE
rates Trulia as a
. The company's strengths can be seen in multiple areas, such as its robust revenue growth, largely solid financial position with reasonable debt levels by most measures and solid stock price performance. However, as a counter to these strengths, we find that net income has been generally deteriorating over time. Get the full
Trulia Ratings Report
Data for this article provided by
Zacks Investment Research | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 2,168 |
Prem1ere (označovaný také jako Premiere) byl britský placený filmový kanál vysílající v kabelových sítích ve Velké Británii mezi lety 1984 a 1989. Programové schéma tvořily zejména novější filmy a seriály. Dva roky po zahájení vysílání se kanál sloučil s dalším filmovým kanálem MirrorVision, jehož vysílání bylo v roce 1986 ukončeno. Filmový kanál Prem1ere, v důsledku velkých ztrát a významné konkurence ze strany televizního kanálu Sky Movies, skončil v červenci 1989 po necelých pěti letech své vysílání.
Historie
Přípravy na spuštění nového kanálu Prem1ere začaly již na jaře roku 1980. Placené televizní stanice HBO, Showtime a The Movie Channel spojily své síly s velkými filmovými studií Columbia Pictures, MCA, Paramount Pictures a Twentieth Century Fox s Getty Oil a společně se chystaly založit placený televizní kanál Prem1ere. Filmová studia garantovala devítiměsíční exkluzivní okno, kdy jejich filmy měly být vysílány nejdříve na Prem1ere a poté měly být uvolněny dalším zájemcům z řad televizních společností. To však americký Okresní soud (U.S. District Court) kvůli porušení Shermanova antimonopolního zákona nepovolil a spojenectví se krátce na to rozpadlo.
O dva roky později se o vznik nového kanálu pokusilo pět společností. American Express, MCA, Paramount Pictures, Viacom International a Warner Bros oznámily dohodu, podle níž začaly být Showtime a The Movie Channel provozovány jako společný podnik těchto společností. Aby předešly chybě z minulosti, prohlásily také, že novému kanálu nebudou poskytnuta žádná exkluzivní filmová práva. Showtime a The Movie Channel se v té době mohly pochlubit 6,5 miliony předplatitelů (4 miliony pro Showtime a 2,5 milionů pro The Movie Channel).
Filmový kanál Prem1ere zahájil vysílání 1. září 1984 za podpory předních amerických filmových studií Twentieth Century Fox, Columbia, Warner Bros, HBO, ShowTime/The Movie Channel, Thorn-EMI a britského filmového studia Goldcrest Films.
O rok později se provozovatel kanálu rozhodl svou satelitní distribuci zakódovat kódovacím systémem SAT-TEL, který již byl využíván například veřejnoprávními kanály BBC 1 a BBC 2. K tomu však nikdy nedošlo . I přesto, že Prem1ere vysílala na satelitu nekódovaně, pořízení satelitního vybavení, jakožto paraboly o potřebném průměru 1,5 metru (ve Velké Británii), bylo pro běžného uživatele velmi nákladné.
Miliardář československého původu, Robert Maxwell, prostřednictvím svého vydavatelství Daily Mirror, převzal dne 1. dubna 1986 41,2% podíl od Thorn-EMI a 9,8% podíl od společnosti Goldcrest Films a stal se tak většinovým majitelem filmového kanálu Prem1ere. V souvislosti s touto fúzi bylo rozhodnuto o sloučení obou, původně konkurenčních, filmových kanálů Prem1ere a MirrorVision ve prospěch prvně jmenovaného. Téhož roku společnost British Telecom oznámila spuštění nového filmového kanálu v britských kabelových sítích, který na rozdíl od Prem1ere měl být distribuovaný výhradně prostřednictvím VHS kazet. Nový kanál měl uzavřené smlouvy se společnostmi MGM/United Artists, Paramount a Universal.
Ke konci roku 1986 vysílal Prem1ere 12 hodin denně 6 až 7 filmů. Měsíčně se jednalo nejméně o 18 premiérových filmů. Ke sledování kanálů Prem1ere, The Children's Channel a ScreenSport spravovala licence ke sledování společnost Galaxy, která je nabízela za měsíční paušál 10 GBP.
V roce 1987 provozovatel kanálu Premiere rozšířil vysílací čas. Vysílání již začínalo v 16 hodin středoevropského času.
V srpnu 1987 odešel z Premiere generální ředitel Andrew Birchall, který našel své uplatnění v BSB (British Satellite Broadcasting) .
Provoz britského filmového kanálu Premiere, jež pocítil silnou konkurenci ze strany Sky Movies, byl v červenci 1989 ukončen z důvodu vysokých ztrát dosahující výše 10 milionů GBP
Dostupnost
Satelitní vysílání
Televizní pořady
1985 The PREM1ERE Review
1987 Premiere Movie Club
1988 Premiere July Review
1988 The Movie Club
Filmy
1985 Amityville 2: Posledlost (Amityville II) (1982)
1985 Amityville - Dům hrůzy (Amityville III) (1983)
1985 Bláznivá dovolená (National Lampoon's Vacation) (1983)
1985 Beze stopy (Without A Trace) (1983)
1986 Přes Brooklynský most (Over the Brooklyn Bridge) (1984)
1986 Okamžik záblesku (Flashpoint) (1984)
1986 Space Firebird (1980)
1986 The Princess and the Pea
1986 Autobiografie princezny (Autobiography of a Princes) (1975)
1986 Velké ticho (The Great Silence) (1968)
1987 Rychle vpřed (Fast Forward) (1985)
1987 A Single Light (1981)
1987 Starostliví medvídci (The Care Bears Movie) (1985)
1988 Zkázonosná kometa (Night of the Comet) (1984)
1988 Vedoucí místo (Head Office) (1985)
1988 Loyalties (Loyalties) (1987)
1988 Propustka do půlnoci (Cinderella Liberty) (1973)
1988 Chinese Boxes (1984)
1988 Vydařená dovolená (Summer Rental) (1985)
1988 Waltz Across Texas (1982)
1988 Rin-Tin-Tin: Hero of the West (1955)
1988 Slepá justice (Blind Justice) (1986)
1988 Návrat do budoucnosti (Back to the Future) (1985)
???? Posedlý krásou (The Man Who Loved Woman) (1983)
???? Blind Date
???? Going Undercover (1985)
???? Moucha (The Fly) (1986)
???? The Wild Life (1984)
1988-1990 Best Shot
1988-1990 Pinocchio a vládce noci (Pinocchio and the Emperor of the Night) (1987)
1988-1990 Dreamer (1979)
Seriály
1986 Nebezpečný záliv (Danger Bay) (1984)
1987 Defenders of the Earth (Defenders of the Earth) (1986)
1988 Dancin' to the Hits (1986)
1988 Mayberry R.F.D. (1968)
1988 Captain Harlock (1978)
???? Pásmo soumraku (The Twilight Zone) (1985)
1988-1990 Hříšný tanec (Dirty Dancing) (1988)
Generální ředitelé
1984-1987 Andrew Birchall
Odkazy
Reference
Zaniklé britské televizní stanice
Filmové televizní stanice
Vzniklo 1984
Zaniklo 1989 | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 2,664 |
package com.googlesource.gerrit.plugins.labelui.client;
import com.google.gerrit.client.GerritUiExtensionPoint;
import com.google.gerrit.client.info.AccountInfo;
import com.google.gerrit.client.info.AccountInfo.AvatarInfo;
import com.google.gerrit.client.info.ChangeInfo;
import com.google.gerrit.client.info.ChangeInfo.ApprovalInfo;
import com.google.gerrit.client.info.ChangeInfo.LabelInfo;
import com.google.gerrit.client.rpc.Natives;
import com.google.gerrit.plugin.client.Plugin;
import com.google.gerrit.plugin.client.extension.Panel;
import com.google.gerrit.plugin.client.rpc.RestApi;
import com.google.gwt.core.client.GWT;
import com.google.gwt.dom.client.Style;
import com.google.gwt.dom.client.Style.Cursor;
import com.google.gwt.dom.client.Style.Display;
import com.google.gwt.dom.client.Style.TextAlign;
import com.google.gwt.dom.client.Style.Unit;
import com.google.gwt.resources.client.ImageResource;
import com.google.gwt.user.client.rpc.AsyncCallback;
import com.google.gwt.user.client.ui.Grid;
import com.google.gwt.user.client.ui.HTMLTable.CellFormatter;
import com.google.gwt.user.client.ui.HorizontalPanel;
import com.google.gwt.user.client.ui.Image;
import com.google.gwt.user.client.ui.Label;
import com.google.gwt.user.client.ui.VerticalPanel;
import com.google.gwt.user.client.ui.Widget;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Map;
import java.util.Set;
import java.util.TreeMap;
import java.util.TreeSet;
public class LabelPanel extends VerticalPanel {
static class Factory implements Panel.EntryPoint {
@Override
public void onLoad(Panel panel) {
panel.setWidget(new LabelPanel(panel));
}
}
private static final String COLOR_GREEN = "#060";
private static final String COLOR_RED = "#F00";
LabelPanel(final Panel panel) {
new RestApi("accounts")
.id("self")
.view(Plugin.get().getPluginName(), "preferences")
.get(
new AsyncCallback<PreferencesInfo>() {
@Override
public void onSuccess(PreferencesInfo result) {
LabelUIPlugin.refreshDefaultLabelUi(result.ui());
ChangeInfo change = panel.getObject(GerritUiExtensionPoint.Key.CHANGE_INFO).cast();
switch (result.ui()) {
case LABEL_USER_TABLE:
displayLabelUserTable(change);
break;
case USER_LABEL_TABLE:
displayUserLabelTable(change);
break;
case DEFAULT:
default:
return;
}
}
@Override
public void onFailure(Throwable caught) {
// never invoked
}
});
}
private void displayLabelUserTable(ChangeInfo change) {
Set<String> labelNames = getLabelNames(change);
Map<String, AccountInfo> users = getUserMap(labelNames, change);
Map<Integer, VotableInfo> votable = votable(change);
Grid g = createGrid(labelNames.size() + 1, users.size() + 1);
int i = 1;
for (AccountInfo account : users.values()) {
g.setWidget(0, i, createUserWidget(account));
i++;
}
i = 1;
for (String labelName : labelNames) {
g.setWidget(i, 0, createLabelLabel(change.label(labelName)));
int j = 1;
for (AccountInfo account : users.values()) {
LabelInfo label = change.label(labelName);
ApprovalInfo ai = label.forUser(account._accountId());
g.setWidget(i, j, createLabelValueWidget(label, ai));
if (!votable.get(account._accountId()).isVotable(labelName)) {
formatNonVotable(g, i, j);
}
j++;
}
i++;
}
add(g);
}
private void displayUserLabelTable(ChangeInfo change) {
Set<String> labelNames = getLabelNames(change);
Map<String, AccountInfo> users = getUserMap(labelNames, change);
Map<Integer, VotableInfo> votable = votable(change);
Grid g = createGrid(users.size() + 1, labelNames.size() + 1);
int i = 1;
for (String labelName : labelNames) {
g.setWidget(0, i, createLabelLabel(change.label(labelName)));
i++;
}
i = 1;
for (AccountInfo account : users.values()) {
g.setWidget(i, 0, createUserWidget(account));
int j = 1;
for (String labelName : labelNames) {
LabelInfo label = change.label(labelName);
ApprovalInfo ai = label.forUser(account._accountId());
g.setWidget(i, j, createLabelValueWidget(label, ai));
if (!votable.get(account._accountId()).isVotable(labelName)) {
formatNonVotable(g, i, j);
}
j++;
}
i++;
}
add(g);
}
private static Grid createGrid(int rows, int columns) {
Grid g = new Grid(rows, columns);
g.addStyleName("infoBlock");
g.addStyleName("changeTable");
CellFormatter fmt = g.getCellFormatter();
fmt.addStyleName(0, 0, "leftMostCell");
fmt.addStyleName(0, 0, "topmost");
for (int c = 1; c < columns; c++) {
fmt.addStyleName(0, c, "header");
fmt.addStyleName(0, c, "topmost");
}
for (int r = 1; r < rows; r++) {
fmt.addStyleName(r, 0, "leftMostCell");
fmt.addStyleName(r, 0, "header");
for (int c = 1; c < columns; c++) {
fmt.addStyleName(r, c, "dataCell");
}
}
for (int c = 0; c < columns; c++) {
fmt.addStyleName(rows - 1, c, "bottomheader");
}
return g;
}
private static Set<String> getLabelNames(ChangeInfo change) {
return new TreeSet<>(change.labels());
}
private static Map<String, AccountInfo> getUserMap(Set<String> labelNames, ChangeInfo change) {
Map<String, AccountInfo> users = new TreeMap<>();
for (String labelName : labelNames) {
LabelInfo label = change.label(labelName);
for (ApprovalInfo ai : Natives.asList(label.all())) {
users.put(ai.name(), ai);
}
}
return users;
}
private static Widget createLabelValueWidget(LabelInfo label, ApprovalInfo ai) {
int accountId = ai._accountId();
String formattedValue = formatValue(ai.value());
String valueText = label.valueText(formattedValue);
if (label.approved() != null && label.approved()._accountId() == accountId) {
return createImage(LabelUIPlugin.RESOURCES.greenCheck(), valueText);
} else if (label.rejected() != null && label.rejected()._accountId() == accountId) {
return createImage(LabelUIPlugin.RESOURCES.redNot(), valueText);
} else {
return createValueLabel(formattedValue, valueText, ai.value());
}
}
private static Label createLabelLabel(LabelInfo label) {
Label l = new Label(label.name());
Style s = l.getElement().getStyle();
s.setCursor(Cursor.DEFAULT);
if (label.rejected() != null) {
s.setColor(COLOR_RED);
l.setTitle("Rejected by " + label.rejected().name());
} else if (label.approved() != null) {
s.setColor(COLOR_GREEN);
l.setTitle("Approved by " + label.approved().name());
}
return l;
}
private static Widget createUserWidget(AccountInfo account) {
HorizontalPanel p = new HorizontalPanel();
Label l = new Label(account.name());
if (account.hasAvatarInfo()) {
p.add(createAvatar(account));
l.getElement().getStyle().setMarginTop(3, Unit.PX);
}
l.getElement().getStyle().setCursor(Cursor.DEFAULT);
l.setTitle(formatToolTip(account));
p.add(l);
return p;
}
private static Image createAvatar(AccountInfo account) {
int size = 16;
AvatarInfo avatar = account.avatar(size);
if (avatar == null) {
avatar = account.avatar(AvatarInfo.DEFAULT_SIZE);
}
String url;
if (avatar == null) {
RestApi api =
new RestApi("/accounts/").id(account._accountId()).view("avatar").addParameter("s", size);
url = GWT.getHostPageBaseURL() + api.path().substring(1);
} else {
url = avatar.url();
}
Image avatarImage = new Image(url);
avatarImage.setSize("", size + "px");
return avatarImage;
}
private static String formatToolTip(AccountInfo ai) {
StringBuilder b = new StringBuilder();
b.append(ai.name());
if (ai.email() != null) {
b.append(" <");
b.append(ai.email());
b.append(">");
}
return b.toString();
}
private static Image createImage(ImageResource imageResource, String valueText) {
Image image = new Image(imageResource);
if (valueText != null) {
image.setTitle(valueText);
}
center(image);
return image;
}
private static void center(Image image) {
Style s = image.getElement().getStyle();
s.setProperty("margin-left", "auto");
s.setProperty("margin-right", "auto");
s.setDisplay(Display.BLOCK);
}
public static Label createValueLabel(String formattedValue, String valueText, short value) {
Label l = new Label(formattedValue);
if (valueText != null) {
l.setTitle(valueText);
}
Style s = l.getElement().getStyle();
s.setTextAlign(TextAlign.CENTER);
s.setCursor(Cursor.DEFAULT);
if (value > 0) {
s.setColor(COLOR_GREEN);
} else if (value < 0) {
s.setColor(COLOR_RED);
} else {
// make label invisible, we cannot omit it since we need the label to show
// a tooltip
s.setColor("transparent");
}
return l;
}
private static String formatValue(short value) {
if (value < 0) {
return Short.toString(value);
} else if (value == 0) {
return " 0";
} else {
return "+" + Short.toString(value);
}
}
private static void formatNonVotable(Grid g, int row, int column) {
Widget w = g.getWidget(row, column);
g.getCellFormatter().addStyleName(row, column, "header");
w.setTitle("cannot vote on this label");
}
private static Map<Integer, VotableInfo> votable(ChangeInfo change) {
Map<Integer, VotableInfo> d = new HashMap<>();
for (String name : change.labels()) {
LabelInfo label = change.label(name);
if (label.all() != null) {
for (ApprovalInfo ai : Natives.asList(label.all())) {
int id = ai._accountId();
VotableInfo ad = d.get(id);
if (ad == null) {
ad = new VotableInfo();
d.put(id, ad);
}
if (ai.hasValue()) {
ad.votable(name);
}
}
}
}
return d;
}
private static class VotableInfo {
private Set<String> votable;
void votable(String label) {
if (votable == null) {
votable = new HashSet<>();
}
votable.add(label);
}
Set<String> votableLabels() {
Set<String> s = new HashSet<>();
if (votable != null) {
s.addAll(votable);
}
return s;
}
boolean isVotable(String label) {
return votableLabels().contains(label);
}
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 9,927 |
Ginger…just the name gives me that spicy kick and it's almost as if I can sense its intriguing smell by saying it out loud! What would my Asian mother do without it in her fragrant kitchen and how to celebrate Christmas without ginger cookies? This spice has always been part of my life and a childhood memory is lying sick in bed and my mother making me ginger tea with lemon, honey and a whole lot of love, to battle that nasty cold. Years later she would serve the same brew to help ease my menstrual cramps.
In Ayurveda, ginger is the 'chest of medicine' thanks to its many health benefits and the name of this ancient herb (yes herb, but I totally agree. It does look like the toes of a creature from Lord of the Rings) comes from the Sanskrit word for "horn root." It is actually not a root, but the rhizome (underground part of the stem) of the perennial zingiber plant and is closely related to turmeric, cardamom and galangal. For the past 2,000 years, ginger has played an important role in Asian medicine. The Chinese consider it a yang, or hot food, that balances the cooling ying food. Ginger is considered among the healthiest spices and is loaded with nutrients and bioactive compounds that are beneficial for both body and brain.
Why is ginger good for me?
It has antihistamine properties and can be effective in treating allergies. A teaspoon of ginger juice and honey can relieve a cough and sore throat and one of the most applied ginger uses, is when treating various stomach issues such as food poisoning and also nausea. (Chinese sailors used ginger as an antidote to shellfish poisoning, thus explaining why it is found in so many seafood dishes) It provides relief from bloating and is a natural remedy for treating heartburn. It aids in digestion by improving your absorption of essential nutrients. The unique ginger fragrance and flavor come from its natural oils, of which gingerol is the most important. This oil is the main bioactive compound in ginger, responsible for much of its medicinal values. With its anti-inflammatory and antioxidant properties, gingerols act as painkillers. Studies are now showing that gingerol can also be effective in relieving migraines. Originally cultivated in China, but now found all over the world, ginger could very well be one of the "superfoods" actually worthy of that term.
Spice up your beauty routine!
In addition to its medicinal properties, ginger can give you that gorgeous glow on the outside as well! It is often used in a number of skincare products, as it contains around 40 antioxidant compounds that protect against ageing. You can apply ginger juice topically to treat several skin issues. It will for instance relieve pain from burnt skin and improve the appearance of your skin by stimulating circulation. It can also help clear blemishes as it is a powerful antiseptic and cleansing agent. Prepare a nourishing and softening mask by mixing 2 grated gingers with 2 tablespoons of honey and 1 teaspoon of lemon juice. Refrigerate it for at least 20 minutes. Apply on face and rinse with cool water after 30 minutes. You can also boil ginger paste in water and use as a facial toner. Just strain and store in fridge!
It is so easy to grow your own ginger (and it doesn't hurt to get some soil under your well-manicured nails every now and then!) Just hit one of Singapore's fabulous wet markets and pick a smooth, shiny looking root that has some buds beginning to form. Soak in some warm water overnight, plant the following day in a pot just beneath the soil and water well. After about three months you can harvest and enjoy your ginger! Little maintenance but high benefits! Store by wrapping it in a towel and place in a sealed plastic bag in the fridge or even freezer. Or why not pickle it in a bottle of yummy vinegar for about two to three weeks? This way it will keep up to a year in the fridge. And oh yes… if you want to zing up that Fancy Friday Martini- try letting it sit in vodka instead! Trust me. It's gorgeous!
I didn't know ginger contained antihistamine properties! I've had terrible allergies for the past couple of months and strangely last night I ate a lot of ginger and felt much better today. Now I know why! | {
"redpajama_set_name": "RedPajamaC4"
} | 965 |
Copyright © 2016 by Laurie Faria Stolarz
Cover design by Phil Caminiti
Cover photograph by Micael Nussbaumer/Shutterstock
All rights reserved. Published by Hyperion, an imprint of Disney Book Group. No part of this book may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or by any information storage and retrieval system, without written permission from the publisher. For information address Hyperion, 125 West End Avenue, New York, New York 10023.
Design by Phil Caminiti
ISBN 978-1-4847-2921-2
Visit www.hyperionteens.com
# Contents
Title Page
Copyright
Dedication
One
Two
Three
Four
Five
Six
Seven
Eight
Nine
Ten
Eleven
Twelve
Thirteen
Fourteen
Fifteen
Sixteen
Seventeen
Eighteen
Nineteen
Twenty
Twenty-one
Twenty-two
Twenty-three
Twenty-four
Twenty-five
Twenty-six
Twenty-seven
Twenty-eight
Twenty-nine
Thirty
Thirty-one
Thirty-two
Thirty-three
Thirty-four
Thirty-five
Thirty-six
Thirty-seven
Thirty-eight
Thirty-nine
Forty
Forty-one
Forty-two
Forty-three
Forty-four
Forty-five
Forty-six
Forty-seven
Forty-eight
Forty-nine
Acknowledgments
Also by Laurie Faria Stolarz
About the Author
_For Ed, Ryan, Shawn, and Mom,
with love and gratitude_
#
I notice him right away, from the moment he steps into the store: tan skin, broad shoulders, and standing at least six feet tall. But it's not just his looks that catch my attention; it's the way he walks, sort of hunched forward, with his eyes focused downward, like maybe he has some secret. He's hiding his face as well. It's partially shrouded by the hood of his sweatshirt. The sides of fabric fold inward, over his cheeks.
The guy—probably around my age, seventeen or eighteen at most—makes furtive glances around the store from behind dark waves of hair that have fallen in front of his eyes.
I look toward the store owner to see if he notices him. He does, and reaches for something beneath the counter. A phone? A baseball bat? Mace? Should I grab Jeannie and bolt?
Instead I take my cell phone out of my pocket, kick it into camera mode, and zoom in, over the shelves, as the guy looks at a display.
I take a snapshot of his profile, but the angle's bad. He won't look up.
"Can I help you?" the store owner asks him.
He doesn't speak, just shakes his head and moves to my aisle. Wearing dark gray pants that get caught beneath the bottom of his shoes, and a tattered zip-up sweatshirt, he's standing only a few feet away now, looking for something specific.
"Are you ready?" Jeannie asks me, moving toward the register with her predictable box of Bugles.
"Just another minute," I tell her.
I've come here on a mission, with a hard-core craving for taffy. The packages of Saltwater Twists are on the shelf above where he's looking. But he's obviously on a mission too, comparing tuna cans like they're diamonds. I mean, does it _really_ make that much difference if the tuna's packed in water versus oil? Or if it's albacore rather than chunk-light or yellowfin?
I wish I could freeze the moment—press PAUSE, take another snapshot—but I pocket my phone instead and take a few steps closer. "Excuse me," I say, just inches from him now.
He peeks at me—light brown eyes, a startled expression, a glance toward the mole by my mouth.
I step on the bottom shelf and then reach upward, standing on tiptoes. The box of peanut-butter-flavored taffy is inches from my fingertips. I stretch a little farther, finally able to grab it. But then I lose my footing. My heel drops, and I stumble back.
Off the shelf.
The box of taffy flies from my grip.
The guy stops me from falling by catching me in a backbend of sorts—like one of those ballroom dips they do on dance shows—with his hands around my waist.
I gaze up into his face, noticing a cut on his cheek—a horizontal slash that sits right below his eye. His breath smokes against my forehead. He smells like gasoline and something else. Salad dressing? Garlic oil?
I stand up straight, regaining my footing. "Nothing comes between me and my sugar fix," I say, in an effort to be funny. But it isn't funny and he doesn't laugh—not even a snicker.
The doorbells chime. "What's taking Day?" Tori asks, poking back inside, shouting to Jeannie.
The guy moves to retrieve my box of taffy.
"Thank you," I say, taking the box, telling myself to turn away. But something inside me can't.
_Won't._
Because I just have to know: Who is this guy? And what is he hiding from?
_"Day?"_ Jeannie calls out to me.
"Just another second," I holler back. At this point, he must know that I'm stalling because of him. I have my taffy. There's no other reason to linger. "Are you okay?" I ask him, half-stunned to hear the question in the air, out of my mouth.
He hesitates a moment before turning away and exiting the store.
It's time that I leave too. Armed with my box of peanut-butter-flavored math motivation, I pay at the counter and head outside.
Tori and Jeannie are already waiting for me. _"Finally,"_ Tori says.
I join them on the bench, placing my hand to my cheek, able to feel the lingering heat.
"Is everything okay?" Jeannie asks.
"Nothing is okay until we figure this out." Tori shoves her phone in my face before I can even get a grip. "What do you think it means?" she asks. "I mean, ' _maybe I'll see you around later..._ '"
It takes me a beat to figure out that she's referring to a text from Jarrod Koutsalakis, junior class animé artist and her crush-of-the-week.
"Call me crazy," Jeannie says, "but I think it means that maybe he'll see you around later. Of course, I'm only getting a B in English right now, so my interpretive skills might be lacking."
"Are you kidding?" Tori asks. "This message is reeking of subtext."
"More like it's reeking of dullness," Jeannie says. "I mean, come up with something original already."
"You're missing the point." Tori rolls her eyes. "I mean, like, _why_ would he see me around? Like, _where_? Because it's not as if I'll be out on the town someplace special. The highlight of my night includes a pint of Häagen-Dazs and a TV clicker."
"Maybe he's hoping that you _will_ be out on the town somewhere," I offer. "Like, at the library or something."
"Does Jarrod Koutsalakis even _know_ where the library is?" Jeannie asks. "My vote: he's giving you false hope. I mean, the boy _is_ rumored to be seeing Becky Burkus."
"Okay, but Becky Burkus is a total space cadet," Tori snaps, "straight from the Planet Bimbo."
"Right, and you're not," Jeannie says, poking a Bugle into her mouth. "So maybe Jarrod just needs to figure out what he really wants."
Tori drags a strand of her dark pink hair up to her mouth for a nervous nibble. "So where do you think Jarrod likes to hang out? Should I go to the mall tonight? Or maybe to Yoyo's for frozen yogurt...A lot of people like to hang out there...."
I take a deep breath, knowing I'll need at least a few—or twenty—pieces of taffy if I'm going to endure more Jarrod talk. I start to open the package, and that's when I spot him again.
The guy from inside the store.
He's at the opposite side of the parking lot, walking away, down the street.
_"Um, hello, is anybody there?"_ Tori sings, fanning her fingers in front of my eyes.
"I have to go," I tell them.
"Wait, what about Yoyo's?" Tori whines. "Should I go? And, if so, what should I wear? And is it hotter to get the brownie-batter yogurt or the pineapple?"
"Whatever you do, _don't_ get the rainbow sprinkles," Jeannie teases. "He'll think you're a ho, for sure."
I get up from the bench.
"No, seriously, what's the rush?" Jeannie asks.
"There's a photo I want to get."
"For real?" Tori sighs. "You're bailing on my crisis for _a photo_? As if the kagillion you have on your hard drive aren't enough..."
I blow Tori a kiss. "I'll call you later. We can discuss the Yoyo crisis then." I turn away and pull my camera out of my bag, my eyes locked on the guy.
#
I follow him for four blocks, keeping a good distance between us. He ends up at the train depot. I take out my phone, pretending to be monopolized by a text, and duck behind a metal post.
I watch him from there. My camera strapped around my neck, I adjust the lens to get a close-up view, able to see a flash of facial scruff on his chin. He moves to the end of the platform where there's a coffee vendor and some newspaper stands. He squats down to read the headlines.
I squat down too and take the shot, cringing at the click of the shutter. Meanwhile, he reaches into the pocket of his pants and feeds the machine a handful of coins.
I take a few more photos.
_Click._
_Click._
_Click._
The noise makes my heart pound, but still he doesn't seem to hear me. He takes a newspaper from the machine and flips it open to the middle to read.
I'm itching to see his hands up close; I wonder what kind of story they'd tell. There's a recycling bin just a few yards away, but if I ran to it, I'd be in complete open view.
The guy crumples the newspaper into a tight ball, kicks the side of the newspaper machine, and throws the ball into the trash, clearly enraged.
A moment later, my cell phone rings: "The Chicken Dance" song. The doors inside my heart slam shut.
I duck back, behind the post, grab my phone, and turn it off.
Holy.
Freaking.
Crap.
Hadn't I turned my ringer off? Did it click back on when I pocketed my phone before?
I venture to peek out again. He's standing now, by the trash can. It doesn't seem he heard my phone either. Or if he did, maybe he simply thinks there's someone waiting for a train, minding his or her own business.
I readjust my lens once more, looking to get an even sharper view. His eyes are fixed on a bag that's sitting at the top of the garbage heap.
He grabs the bag, opens it up, and pulls out what's inside. He turns the thing over in his hand—a half-eaten bagel—as if trying to assess its worth. And then he takes a bite. His eyes press shut. He chews slowly, relishing every bit.
I assume he must be on the run, hiding from someone maybe. His hands are in full view at his mouth; there appears to be something on one of his wrists. I edge out a little farther to take the shot.
My shutter clicks.
His head snaps up.
His eyes meet mine and he stops chewing.
I tuck myself behind the post again. My chest heaves in and out. Blood stirs inside my veins.
But I don't look back. I get up and scurry away, mixing in with other kids on the street, desperate to lose myself in the crowd.
_Tuesday, October 13_
_Evening_
_I slipped inside the convenience store, hell-bent on getting food, except there was someone in the aisle that I needed to go down: a girl, around my age. I told myself to be quick. I wouldn't make eye contact. The entire transaction would take twenty seconds, tops._
_But then the girl came closer. I could see her inching toward me, could feel her eyeing the side of my face. Was it possible that she knew me? Or did she recognize me from the news?_
_I gave her some space, assuming that's what she wanted. Meanwhile, intuition told me to leave. But curiosity caused me to look._
_I never should've looked._
_"Excuse me," she said, reaching for something on the top shelf. She even climbed up on the shelf._
_I started to turn away, but then she slipped and I caught her—like a reflex, without even thinking. My hands found the small of her back. My shoulder met her arm. For at least three seconds, her entire weight was supported in my grip._
_I haven't touched a girl like that in a long, long time._
_Her hair spilled out from the hood of her jacket. She smelled so good—the floral scent of her shampoo tangled with the cinnamon on her breath. She gazed up at me with the palest blue eyes I've ever seen._
_I went to pick up the box she'd grabbed. When I gave it back, she said something else—something about sugar. I wasn't really paying attention to her words—too focused on her smile and the giggle in her voice; both of which threw me, because she didn't look scared._
_She asked me if I was okay, but I bolted for the door, hating myself for crossing the line. My dad was right. I can be so incredibly stupid at times._
#
It's the following day, and I'm in my room, sorting through images, including some of the snapshots I took at the train depot. I've been thinking about that guy nonstop, wondering if he dropped out of school or ran away from home. _Where does he spend his nights?_
None of my pictures show much of his face, but I do have a nice shot of his hand. I've enlarged it on my computer screen and played with the colors, able to tell there's a tattoo there, on the underside of his wrist, but I have no idea what it's of.
On my way home from school today, I stopped inside that same convenience store and roamed the aisles, taking my time in choosing, half hoping he might show up. At one point, I could've sworn he was there—could feel someone's eyes watching me from across the parking lot. But when I stopped to look around, I saw that I was alone.
"Day?" my mother calls me.
I get up from my desk and head down the stairs. Mom is standing at the bottom, with her jaw locked in tense mode.
"Is something wrong?" I ask her.
She leads me into the living room, where two officers—a man and a woman—stand by the window, staring in my direction.
"I'm Officer Nolan," the woman says, "and this is Detective Mueller." She nods to the man; he reminds me a little of Mr. Burns from _The Simpsons,_ with his bulging eyes and shiny bald head.
Mom places her hand on my back. "The officers are looking for someone, and they were hoping that you could help."
_"Me?"_ I feel my face furrow.
"We're searching for a sixteen-year-old male," Officer Nolan says. "He's about six feet tall, with dark hair, olive skin, a medium build—"
Light dawns.
The answer clicks.
My skin starts to itch.
"The suspect escaped from a juvenile detention facility several towns away," Detective Mueller explains. "Someone said they might've seen him in this area."
"He was in the detention center for what?" Mom asks.
Officer Nolan pulls a photo from her pocket and hands it to me. "His name is Julian Roman," she says. "He's wanted for murder."
Wait, _what_? My head spins. My heart tightens.
It's him. The guy from the convenience store—the one from the train depot.
"Does he look at all familiar?" the detective asks.
"I think I remember this case," Mom says. "It happened in Decker, this past spring. Isn't that right?"
My body trembles. Heat rises up, encircling my neck. "I saw him." I nod. "At the food mart."
" _When_ did you see him?" Mom nabs the photo from my hand. "And why didn't you say anything?"
"I don't...I mean, I didn't..." I shake my head. The words aren't coming quickly enough. The air in the room doesn't seem ample enough.
"Wait, what's going on?" Mom moves to stand between the officers and me: my very own personal body shield. "How did you know to come here?" she asks them. "And why does this concern my daughter?"
The officers exchange a look. "We actually caught your daughter on the surveillance video from the food mart," Mueller says. "The owner of the store made a call to the authorities after the suspect left. It appeared that your daughter and the suspect might've had an exchange yesterday. Anything you want to tell us about?" He focuses on me hard.
"He seemed nice," I say, my voice cracking over the words. "He got my candy and caught me when I slipped. But I could tell something wasn't right. I thought that maybe he was hiding from someone, so I asked him if he was okay."
"And what did he say?" Mom asks.
"Nothing." I shake my head. "He left the store without an answer."
"And did you see which way he went?" Officer Nolan asks.
"I did," I say, proceeding to tell them how I had followed the boy to the train depot to take pictures for my project.
"You're kidding, right?" Mom shoots eye daggers at me. She's fully aware of my photography obsession, but said obsession probably doesn't excuse the fact that I shouldn't be stalking strangers (particularly ones that appear so suspect).
"We need to see those photos," Mueller says.
I look back at my mother, gauging her reaction. She gives me a slight nod, and I lead them upstairs to my room. The photo of the guy's hand is still enlarged on my screen.
"I like to take pictures," I try to explain. "To show different perspectives of the same subject...It's sort of hard to explain."
But it doesn't seem like they're interested anyway. They're going through my photos, discussing Julian's clothes, his weight loss, and the fact that he was taking a big risk by being out in broad daylight.
"He probably thought he could mix in with the high school foot traffic," the detective says.
"Do you think he's still in this area?" Mom asks.
Officer Nolan looks up from my laptop. Her hair is the color of cranberries. "My guess is no. Most escapees don't tend to stay in one place for very long. They may lay low for a few days, for fear of getting caught on the run, but after that they tend to flee."
"Okay, but _when_ did this boy escape?" Mom asks.
"Eight days ago," Officer Nolan says.
"That seems like a long time to _lay low,_ wouldn't you say?" Mom folds her arms, back to shooting eye daggers (thankfully not at me this time).
"Well, technically he isn't laying low. The detention center he escaped from is two hours away from here by car."
"Could he be staying with a friend?"
The officer fakes a smile. "Anything's possible."
"And you have _how many_ professionals working on this?"
Before the officer can answer, Mom's cell phone rings. She checks the screen and then silences the tone. "Okay, so are we done?" she asks.
"Just about," the officer says.
Mom's phone vibrates again. "Excuse me a moment." She ducks into her bedroom to take the call, desperate to free an American student from a Syrian prison. No joke; my mom is a real-life superhero as founder of Project W, an international nonprofit organization that fights for the rights of women. My dad's not too shabby either as president of the SHINE network, a place that gives second (or third or fourth) chances to those who need one.
I assist the officers by e-mailing my photos to their accounts. They leave shortly after, making me promise to contact them should I see the guy again.
Finally Mom emerges from her room. "What happened?"
I start to tell her about e-mailing the photos, but her phone vibrates yet again. She checks the screen. "I have to take this. Would you mind taking Gigi for a walk?"
Yes, I would. "No, I wouldn't." Still, I grab our neighbor's keys—as well as a bottle of pepper spray (courtesy of Dad)—and head out the back.
#
The leaves crunch beneath my steps as I head down the bike path. Gigi is our neighbor's bulldog. Her owner works as a nurse and often does double shifts, relying on us to make sure that Gigi gets exercise (and bathroom breaks).
It's chilly out, mid-October, and the ground is barely visible with all the fallen leaves. Normally Dad takes care of the yard, but since he and Mom have separated, I'm left to pick up the slack, quite literally.
It's nearing dusk. The smell of a nearby barbecue makes my stomach growl. I continue forward, thinking about the officers' visit, reminding myself that there's still plenty of daylight left, that the guy has probably fled the area, and that there's pepper spray in my pocket.
The wind rakes through the tree limbs, rustling the leaves. Birds twitter. Twigs snap. I tell myself that these sounds are normal and this sudden flutter of anxiety is purely psychosomatic—the result of the officers' probing.
But then I come to a sudden stop, able to hear branches breaking. It's two full breaths before I continue forward again. The roof of Rita's house peeks out over a cherry tree. I go to unlatch her gate, noticing something moving in the distance.
A tree shakes.
Its branches flutter.
There's another snapping sound.
Gigi's barking inside the house.
I pull the gate open. At the same moment I see someone—dark clothes, hunched posture, hooded sweatshirt—about ten yards away.
I tell myself it isn't him. I mean, it can't possibly be him.
My pulse racing, I scoot inside the gate, behind a tree, and pull the pepper spray from my pocket.
But it tumbles from my grip. And drops to the ground.
I look up again, my heart pounding, my head spinning, unsure if he's seen me. He's turned away now, his back toward me, headed for the center of town.
#
I race home—back down the path, across the yard, up the steps, and into the house—locking the door behind me: two bolts, plus the chain.
Mom's holed up in her office, still talking on the phone.
"Mom?" I knock, pushing the door open. It hits the wall with a thwack.
"Yes," she says into the phone, blocking her free ear with a finger.
"This is really important," I persist.
"Could you hold on a moment, Genevieve?" Mom places her palm over the speaking part of the receiver and finally looks up. "What is it?"
"I really need to talk to you."
"And I really need to free an innocent girl from prison. Can it wait a couple of minutes?"
"Not really."
She holds up her index finger, indicating another minute. "What's that, Genevieve?" She blows me a kiss. "I'll be off in just a bit."
I remain in the doorway for several seconds, listening to her ask questions about the accused girl's whereabouts at the time of her supposed crime.
Finally, I go up to my room, grab my laptop, and open it on my bed. A quick Google search with the words "Julian Roman," "Decker, MA," "Fairmont County," and "Roman murder" and several news stories pop up.
`JUVENILE SUSPECT MISSING FROM DETENTION CENTER`
`WEBER, MA—A male, 16, was reported missing from the Fairmount County Juvenile Detention Facility. The suspect, Julian Roman of Decker, had last been seen in the center's courtyard at approximately 4 p.m. on Tuesday, October 6th. An officer at the center reported Roman missing at 6:45 p.m. when he failed to show up for dinner. Roman, described by officers as quiet, keeping to himself and often writing in his journal, had been awaiting trial for the alleged murder of his father. Roman is reported to have dark hair, brown eyes, an athletic build, and to be six feet tall. He has a tattoo of a pickax on his wrist, and was last seen wearing an orange suit from the detention center. Anyone fitting his description should immediately be reported to the Weber Police Department.`
`BODIES FOUND—FOUL PLAY SUSPECTED`
`DECKER, MA—The body of a forty-five-year-old man, Michael Roman, was discovered at the family home in Decker Village Park at approximately 7 p.m. on Saturday, May 4th. Police were called to the scene. Investigators say the victim suffered head injuries.`
`The body of a forty-two-year-old woman, Jennifer Roman, was also discovered at the time of the investigation. Ms. Roman's body was found in the bathtub with the water still running. The cause of death is unconfirmed at this time.`
`The investigation is ongoing as officials wait for autopsy results.`
`INVESTIGATION CONTINUES IN DECKER VILLAGE HOMICIDE CASE`
`DECKER, MA—Autopsy results conclude that Michael Roman, 45, had been struck on the head with a blunt object on the afternoon of May 4th in his Decker Village Park home. The murder weapon has yet to be discovered. Mr. Roman was reportedly seen in front of the family home just prior to the estimated time of his death.`
`Autopsy results also conclude that Jennifer Roman, 42, died from asphyxia due to drowning. Roman's body was discovered in the family's bathtub. Results conclude that Roman had been under the influence of prescription medication, which may have contributed to her death. It's unclear at this time whether she died before or after her husband.`
`Chief Investigator Pat Chalmers states, "There are no clear-cut answers in this case. However, we're working hard to map out exactly what transpired during the last eight hours of this couple's life." If anyone has information pertaining to this investigation, please contact Investigator Pat Chalmers at the Decker Police Department.`
`TEEN ARRESTED FOR HOMICIDE`
`DECKER, MA—A 16-year-old juvenile male has been charged with the murder of his father, Michael Roman, 45, of Decker Village Park, three months after Roman's body was discovered in the family home on May 4th, having been struck with an unidentified blunt object. Michael Roman's son's arrest follows an intensive investigation.`
`A fellow student of the teen suspect states, "Julian always talked about hating his father and wanting him dead. It was actually pretty scary."`
`Another student adds: "Julian used to talk about _getting rid of his dad_. I wish I'd said something sooner. I just never thought he was serious."`
`Jennifer Roman's body was also discovered in the family home on May 4th. Mrs. Roman, 42, had reportedly died from drowning after taking an excess of prescription medication.`
`The teen suspect will stay at the Fairmount County Juvenile Detention Facility as he awaits trial.`
An online comment in response to the last news article states: _"This has got to be the most blatant corruption of justice I've seen to date. No murder weapon? Three months to make an arrest? And what seems obvious to be a murder-suicide situation? You say there are no clear-cut answers, but all you have for us taxpayers are incoherent quotes from a bunch of idiotic kids? Where are the facts of this case? Clearly this is yet another example of Weber and Decker police investigating at its finest. Why am I not surprised?"_
I close my laptop and go back downstairs. Mom is still on the phone. I peek my head into her office, but she's shouting now, into the receiver—something about due process and exculpatory evidence.
In the kitchen, I feed my confusion with leftover chow mein, straight out of the carton, while Officer Nolan's business card stares up at me from the table. Maybe I shouldn't wait for my mom to make the call.
But what if the guy I saw on the bike trail wasn't Julian Roman after all? Or what if the person who commented on the news article has a point about Julian's case being mismanaged?
Is that really my concern? Should I even care?
I reach the bottom of the Chinese food container, wishing there was an extra egg roll—or something—because I have way more questions in my head than Fung Wong's has takeout.
_Tuesday, October 13_
_Night_
_So I followed that girl from the train station, hoping I might be able to snatch her bag and take her camera. She obviously recognized me from the news—was probably planning to share her photos with the police. Part of me was also curious about her—about who she was, and why she bothered to take pictures rather than calling the police on the spot. I mean, she totally could've gotten my ass bagged._
_I used to follow my dad too. My brother Steven and I both did. We'd hide in the bushes when he was out mowing the lawn, and then sneak after him when he'd go down the street for beer and cigarettes, ducking behind parked cars every few yards so he wouldn't catch us spying._
_Dad was my hero then, back when Steven and I were five. I used to try to do everything the same as him: finger-whistle, throw a Frisbee, slick back my hair, snap my fingers. Crazy to think that it was just a few years after that when I started fantasizing about his death._
#
I wake up late the following morning.
My alarm. Never. Went off.
I fly out of bed and pull on some clothes. "Mom?" I call, figuring she must be in her office. But her office is empty, and so is the kitchen.
I find a note on the table.
_Good morning, Day!_
_I'm so sorry we didn't get a chance to talk last night. Sorry I'm missing you this morning as well. I had to run out for an early meeting at the state house, but I promise we'll talk tonight. Be sure to lock up, and have a great day! Good luck with your meeting._
_Love,_
_Mom_
_xoxo_
Beneath the notepad, there's a box of powdered doughnuts (so much for all her preaching about eating only wholesome, unprocessed foods).
I scurry up the stairs, two steps at a time, able to hear a clamoring sound outside. I rush to the window, but I don't see anything. Clearly I need to get a grip. But I didn't sleep well. Plus, I have a French quiz today, not to mention the first meeting of Peace, Brains & Justice (PB&J for short), of which I'm the founding president. I've been planning the meeting for weeks, preparing what I will say and making posters to entice people to come, trying to heed my parents' advice about putting my own personal stamp on the world.
With only ten minutes left before I'm supposed to leave for school, I pull my hair into a ponytail, hurry the cookies I made for the meeting into a container, and grab all my school stuff.
I head out the back door, catching a reflection of myself in the entryway mirror: no makeup, pasty-white face. There's a knot in my hair and a grease stain on the front of my sweatshirt, right over my left nipple.
So. Not. Presidential-worthy.
I close the door behind me, accidentally dropping the container of cookies. Luckily the cover remains intact, but I'm not brave enough to check the aftermath within.
It's still somewhat dark out. The moon sits in the center of a bright violet sky. I approach the bike path, able to feel anxiety stirring up inside me like a hot, bubbling cauldron.
A rustling noise startles me—like a shifting through the fallen leaves. I look all around—toward the back porch, at the windows of our barn, and around the perimeter of the yard—suddenly feeling like I'm being watched. But I don't see anyone lurking.
Still, I take the main road in front of the house, knowing this route will add at least seven minutes to my trek but that it's also the least likely to render me tied up in the back of a van en route to the nearest sinkhole. I haul ass the entire way, booting it for twelve blocks, hiking up the sledding hill, and cutting through the center of town.
Finally I make it to school, but I'm six minutes late and awarded with a big fat detention.
"Please," I beg the school secretary. "Can't detention wait until tomorrow? I have a meeting after school."
_"Should've thought about that beforehand,"_ she sings. There's an evil smile across her spray-tanned face.
"Okay, but I've never been late before—like _ever_...in my more than two years here."
"Sorry," she says, still smiling. "See you at two thirty in the Detention Dungeon."
Maybe a dungeon is where I belong, because I look like hell. And now I'll be late for my meeting. Plus, my cookies are all crumbled.
But I almost don't even care.
I'm just happy to not be alone.
#
I try my best to concentrate in classes, but between my lack of sleep, my train wreck of a morning, the PB&J launch meeting, and the fact that I'll now be late for said meeting because I've been blessed with detention, I'm lucky to spell my Frenchified name correctly ( _Jour,_ for the record; the French word for _day_ ), never mind convert _le plus-que-parfait_ to _le futur ant_ é _rieur_.
"How did you do on the French quiz?" Jeannie asks, peeking at me over the rims of her tortoiseshell eyeglasses. The frames go nicely with her new haircut—a chin-length, purposely lopsided dark chocolate bob that makes her blue eyes pop. "Because I totally bombed the bonus."
She, Tori, and I are sitting in our usual spot in the cafeteria—close enough to the exit doors that we can make a quick escape, but far enough from the kitchen that we don't have to endure all the funky fumes.
"There was a bonus?" My stomach twists.
" _Two_ bonuses, actually. Baudelaire questions...on the board. Didn't you notice? Madame E announced it."
I shake my head, with a sudden loss of appetite—and the cafeteria's gelatinous fish chowder doesn't help.
"Too busy thinking about your PB&J meeting today, am I right?" Her emerald-studded eyebrow shoots upward, accusingly. "This do-gooder organization is totally going to be the GPA-point-shrinker for you, isn't it?"
"It's supposed to be the college-application-booster, actually."
"Don't get me wrong," she says. "I'm sure it'll be huge. I mean, right?"
"A meeting about sandwich condiments?" Tori snickers. "Where's the sheet? Sign me up."
"Exactly." Jeannie smirks. "I mean, how could it fail? Plus, you _did_ promise store-bought cookies, right?"
"And cookies go _great_ with PB&J." Tori winks, her eyelids lined with thick black cat's-eye wings. Her style du jour is inspired by some rockabilly girl group from the '50s (or so she says): short-sleeved blouse, waist-cinching belt, pencil skirt, and red leather pumps that match her lipstick.
"For your information, the cookies are _homemade,_ " I tell them. "Plus, this meeting has nothing to do with food, and everything to do with social justice and human rights—with making the world a better place."
"One sandwich at a time." Tori wipes an invisible tear from her cheek.
"Ha-ha," I drone, flicking a carrot disk in her direction. It lands in her Wilma Flintstone hair (tunnel of bangs, length pulled back in a bun). "Sorry." I suck in a laugh.
Tori's laughing too. She takes a fork to her hairspray-shellacked bangs and tries to stab the carrot out.
"Public forking...real classy," Jeannie says.
"Ugh," I groan. "The meeting today is going to flop." I cover my face with my hands, accidentally plunking my elbow into the pool of ketchup—as if this day couldn't get any messier.
"Because of your wardrobe selection?" Tori frowns at my grease-stained sweatshirt.
"More like because I didn't get any sleep. Any chance the police came to either of your houses last night?"
"If only." Tori gives her yogurt spoon a serious lick. "I could've used me a little hunky-officer-jumping-out-of-a-cake and/or-singing-me-a-telegram excitement."
"I think you can take that as a no," Jeannie says to me.
"Well, they came to _my_ house," I tell them.
"And we're just hearing about it _now_?" Jeannie asks.
"Apparently, when we all went to the food mart after school the other day, the police caught us—or at least me—on the surveillance video at the same time that some guy who'd escaped from juvie was in there."
"And so the police came to your house, _because_...?" Tori asks.
"Because I talked to him—the escapee, that is. The police wanted to know if he said anything significant."
"And did he?" Jeannie asks.
I shake my head.
"Wait, was this the hot homeless guy?" Tori asks. "Because I totally remember: He was wearing a hooded sweatshirt."
"Okay, why can't I recall even a smidgen of this?" Jeannie asks.
"Apparently Hot Homeless Guy was arrested for killing his father," I explain. "He was being held in a juvenile detention center before he escaped."
"Okay, I think I vaguely remember this story," Jeannie says. "Didn't it happen last winter?"
"This past spring, actually."
"And now the guy's lurking around in convenience stores?" Jeannie asks.
"Not to mention on the bike trail behind my house."
"Seriously?" Jeannie gawks at me.
I look at the clock: only two minutes left before the bell rings. "Okay, the meeting," I say, completely switching gears. I slide the agenda in front of her.
"Whoa, wait, are you kidding me?" Jeannie balks. "An alleged murderer hanging out on your bike path, not long after conveniently bumping into you in a food mart, is way more important than some dumb meeting."
_"Dumb?"_
"Not dumb." She grimaces. "Just..."
"Curious," Tori says, stealing the conversation. "I am, that is...curious about your club's acronym. What does the _B_ in PB&J stand for? Boys? Babes?"
"Try _brains_." I give her a pointed look.
"And what, pray tell, do brains have to do with peace or justice?"
I roll my eyes, as if the answer's completely obvious. It isn't. I know that. But it's too late to turn back now. "Okay, fine. The idea was stupid, but I thought PB&J had a catchier ring than just P&J."
"Like a pajama party." She laughs. "At least we know of one peace-loving soul who's sure to show up to get his PB & Jam on."
She's talking about Max Terbador—no joke, that's his real name; his parents are obviously cruel. Max has been crushing on me since freshman year—since I linked my arm through his in the parking lot after a football game, pretending that we were a pair, thus saving him from Tommy Hurst and his posse of lemmings. They'd been bullying Max for months—for no other reason than the fact that they were assholes (of course, Max's name probably didn't help).
Max was eternally grateful, especially because Tommy had been crushing on me at the time. And so not only had I foiled Tommy's plan to de-pants Max in the parking lot that day, thus crowning him Max-terbater of the year, but I'd also publicly displayed my choice by resting my head on Max's shoulder.
"Max and I are just friends," I remind her.
"One appropriately timed exchange of tongue spit can change all that, don't you think?"
"I'm not even going to dignify that question with an answer."
"Being dignified is way overrated," she says, back to forking at her bangs. "What I wouldn't give for Jarrod Koutsalakis to get all PB & Jammy for me."
"Okay, um, _ew_." I make a face.
"Max is really sweet," Jeannie says, looking in his direction, four tables over.
He's sitting with the hipsters today. Somewhat of a social floater, he tends to gravitate from group to group, not really clicking with anyone in particular.
"Do I smell a crush?" Tori asks her.
"What you smell is your cheap hair spray." She reaches across the table to pluck the carrot from Tori's bangs, once and for all.
Meanwhile, Max looks up in our direction. He stops talking. His face brightens. A smile crosses his lips. His hipster friends turn to look at us too, pausing from their coconut water and bento boxes. Max waves in our direction.
"That boy is way too cute to be single," Tori purrs. "One of you _has_ to go say hello."
But before Jeannie or I can even consider the option, the bell rings and we're saved. I give Jeannie the folder for the meeting, also reminding her not to forget about my cookie crumbles. Or maybe that would be preferable.
#
By the time I get to the classroom for my PB&J meeting, I'm all out of breath, and almost out of hope. It seems the only one who bothered to show up—aside from Jeannie and Tori—is Max.
"Holy freaking flop," I say, thinking about all of the announcements I'd made and the posters I'd put up.
"It wasn't a _total_ flop." Tori nods to the empty container of cookies. "Your chocolate-chip crumbles were a hit. A bunch of the science league members grabbed a handful on their way out to hunt for crickets."
"As if that's supposed to make me feel better."
"There was a lot going on today," Jeannie says, trying to apply a verbal Band-Aid. "There were theater tryouts...."
"Plus a marshmallow-eating contest at Bubba Joe's Café," Tori adds. "The winner gets free hot cocoa for a month."
"Well, how can I compete with that?"
"But _we're_ here," Jeannie cheers.
"Despite the fact that we really love marshmallows," Tori continues. "Especially tall, dark, and handsome ones." She nods to Max.
While I've been busy squawking, he's been busy cleaning everything up, collecting the handouts and sweeping the cookie crumbles. Tori moves to stand behind him, turning her back to Jeannie and me to do that thing where you wrap your arms around your shoulders and tilt your head from side to side, making it look like you're hard-core kissing.
"Max, you really don't have to do all that," I tell him.
"I don't mind." He turns to face us.
_So cute,_ Tori mouths at me, followed by an exaggerated wink.
"So, are we ready to start the meeting?" Max slides a bunch of chairs into a circle and takes a seat in one of them. "Shall we wage the war on hunger? Create awareness of child labor? Or support prisoners of conscience, maybe?"
"And speaking of prisoners..." Jeannie folds her arms and glares at me. "Shall we discuss the _escaping_ variety?"
"Like the ones who off their fathers, break out of juvenile detention centers, and then stalk our good friends?" Tori asks.
"Precisely the variety I was thinking of." Jeannie gives her a high five.
"I'm not sure I know that kind," Max says.
Jeannie, Tori, and I join Max in the circle, and then I spend the next several minutes catching them all up on the convenience store encounter, the photo shoot afterward, and the visit from the officers last night.
"If he saw you taking his picture, he's probably lurking around to get his revenge," Jeannie says.
Max shakes his head. "I think this guy has way bigger problems than some girl who took his picture."
"Sounds like you're taking for granted that he's of sane and sound mind, rather than a deranged serial killer looking to flambé one of our best friends," Jeannie says.
"Deranged serial killers don't go to juvie," Max tells her.
"Do you speak from experience?"
He gives her a freakish look, complete with buggy eyes and a flash of teeth. "What do _you_ think?"
I pull my laptop out of my bag and read aloud a couple of the news articles I found.
Tori raises her hand, as if we're in class. "Why do you have creepy articles saved in your Favorites folder?"
"Because I was curious about him." I shrug. "About the case, that is. I mean, look at things from my perspective: I bump into some guy while shopping for candy. The next thing I know, he's an alleged murderer, on the run, lurking around not far from my house."
"And are you _still_ curious about him?" Jeannie gives me an accusatory look, with her eyebrow raised high.
"Maybe I'm not quite convinced he's guilty."
"Because hot guys don't kill?" Tori smirks.
"What if we made this case our mission?" I ask.
"You're kidding, right?" Jeannie glares at me over the rims of her glasses.
Meanwhile, Max has already done a search on Julian's name. He scrolls through the headings on his phone. "Okay, admittedly the case _does_ sound a little weak—at least just from these articles."
"But they must have hard evidence," Jennie says. "I mean, they don't just go arresting people without it."
"So how come the articles don't mention the hard evidence?" I ask.
Tori takes my laptop to read one of my "favorite" news reports. "How come Julian's not being blamed for his mom's death too?"
"Because it sounds like his mom committed suicide," Max says.
"But what if she didn't?" Tori taps her chin in thought. "What if her body was just made to look like she did? Or what if she _did_ commit suicide, but only after killing her husband?"
"Then Julian would be innocent," Max says.
"Think about it," I say. "We have a suicide. And we have murder. The two go together like..."
"PB&J?" Tori laughs.
"Don't you want to research this more?" I ask, completely stoked at the opportunity. "To find out if there's a chance he might really be innocent?"
"Okay, in theory, it might be fun," Jeannie says.
"But in reality, I have, like, a bajillion trig problems to do." Tori loops an invisible noose around her neck and pulls.
"Meeting adjourned." Jeannie stomps the heel of her shiny black Mary Jane—her makeshift gavel—against the laminate tile, totally bursting my proverbial bubble.
#
After the meeting, Tori nabs Jeannie, purposely—and obnoxiously—leaving me alone with Max.
"Thanks for coming to the meeting," I tell him.
"Are you kidding? I wouldn't have missed it." He smiles.
I smile back, but it isn't with the same emotion. Part of me wishes that it were—that I felt the same way about him. But to me he'll always be the boy who on the first day of kindergarten dressed up as Aquaman and peed on the slide, claiming it was anti-villain venom.
"Can I give you a ride home?" he asks.
My gut reaction is to tell him no. But since Tori and Jeannie have already left—and since I'm still feeling a bit creeped out about our resident detention-center escapee, I nod and say yes.
He takes my backpack, ever the gentleman, and we walk out to his car. On the drive to my house, I fill the awkward silence with small talk about things we pass along the way: the Pretzelria, the Taco Teepee, and my newly hated establishment, Bubba Joe's Café. Finally, after several painful minutes, we pull up in front of my house. The inside is dark. My mom isn't home yet.
"Thanks for the ride," I tell him. "Sorry the meeting was a bust."
"It wasn't a total bust. Three people showed up."
"Three of my closest friends."
"Do you really consider me a close friend?"
"Of course I do," I say, stretching the truth like rubber. In theory: I'd love to spend more time with Max. In fact: I don't want to give him the wrong idea.
I thank him again and grab the door handle to exit his car.
"Hold on," he says. "I'll walk you in. Rumor has it there are criminals lurking about." He takes my bag and follows me up the walkway, accidentally stepping into a hole in the ground. He stumbles forward, catching himself on one knee.
_"Are you okay?"_ I blurt.
He gets up. The knee of his jeans is covered in mud. "Groundhog problem?"
"Gardening problem." I grimace. "Believe it or not, that was my dad's attempt at trying to plant a tree."
"Is he aware that one needs to refill the hole once the seed is planted?"
A banging noise startles me. It came from the side of the house, behind the fence. I peer in that direction, wondering if a squirrel might be picking at the trash or scampering in the gutter.
_"Day?"_ Max asks.
"Want to come in for a minute?"
"Sure." He perks up.
I lead him up the front steps, and we go inside.
"You know, for as long as we've known each other, I've never been in your house," he says.
"Well, you haven't exactly missed much." I lock the door behind us and flick on some lights so he can get a better view. Only half of the stairwell is painted. The floors are bare and splintery, and our furniture—what we found at yard sales, mostly—is sparse and retro (and not in a funky, eclectic sort of way). It's not that my parents are lacking funds; what they're lacking is time and interest. "Can I get you a washcloth for your pants? And maybe something to drink?"
"A drink would be great."
We go into the kitchen. Max takes a seat at the island, and I open the fridge. There's a half-gallon of milk (expiration date: four days ago), a bottle of tomato juice, and one of my mom's green drinks (which has now turned brown). "Water?"
"Perfect."
I set our drinks down on the counter and take a seat beside him, still wondering about the noise at the side of the house.
"So, what do you think about starting your club with just the four of us?" Max asks. "I'm sure more people will eventually join."
"Honestly?" I sigh. "I don't know what to think."
Max takes a sip from his glass (a recycled relish jar) and makes a face, startled by the ridges on the rim.
"Sorry." I swallow down a giggle. "My parents are wannabe recyclers."
"Wannabe?"
"Meaning that most of our recycle bins have turned into storage containers." I nod to the bins full of cat food in the corner.
Max swivels to look, and I take a mental picture of him. Gone are the iron-creased pants and shiny leather loafers, replaced with dark-washed jeans and suede ankle boots. His hair has changed too—no longer cut into a bowl, but waved to the side with a sharp razor edge. He looks so different than just two years ago. So, where have I been? Why hadn't I noticed?
He swivels to face me again, totally catching me spying. "Well, I could help if you want." He bites back a grin. "With the marketing, that is. We could put flyers on everybody's windshields and come up with a clever catchphrase to nab people's attention."
I can hear the excitement in his voice. I wish I could bottle it up and drink it down. This meeting—the PB&J organization—was supposed to make me feel that way...give me a sense of purpose. But right now, the only thing that sounds exciting to me is delving into Julian Roman's case.
"It didn't seem as if anyone liked my idea for a first mission," I venture.
"The father-killer from juvie. Were you actually serious about that?"
"Why not? Someone's freedom may be in jeopardy."
"Okay, but you don't even know this guy."
"I know that I have questions. I mean, what if he's really innocent?"
"If he's really innocent, then he should go to trial and be exonerated. Why be on the run at all?"
"Good question."
"You're not planning to go all _CSI_ on me, are you?"
" _CSI_? No. But Chelsea Connor, maybe."
"Chelsea Connor?" His face scrunches up with confusion.
"My mother. She's a legal superhero, remember?"
"Oh, right." He nods, still every bit as confused.
"More water?" I stand up from the island, purposely looking out the window. One of the larger tree branches—behind the barn, at the beginning of the bike path—has fallen onto the ground.
"Everything okay?" Max asks.
"Broken tree limb."
He stands beside me to look. "How far down the bike path did you see that guy?"
"About a five-minute walk."
"I'm sure it's a coincidence, but just in case"—he reaches into his pocket and hands me his cell phone—"you should probably give the police a call."
I nod and start to dial.
_Thursday, October 15_
_Evening_
_I was standing at the side of the house when I heard a loud bang. It was followed by another bang. I peered out through the gate. There was a dark green Wrangler in the driveway._
_Day was there. Some guy with her. They were just getting out of his car, and he was totally scoping her out—so much so that he tripped. He stepped into a hole, nearly falling flat on his face. Day reached out to steady him, and his whole body stiffened. If they're seeing each other, it's the start of a new relationship, because she definitely makes him nervous._
_My mother used to get nervous too—all the time, when I was younger. "Can I get you anything?" she'd ask my dad. "More steak? Another drink? Are the potatoes warm enough?" She'd pace back and forth in the kitchen, itching her palm, watching him eat, nibbling her nails down to the quick—until the nubs of her fingers were raw and bleeding._
_It wasn't until Dad was done with his food that I was allowed to eat. Mom never ate. Instead, she'd go into the room I'd shared with Steven. I'd watch her from the kitchen table. She'd sit by his bed and read aloud from one of his books, as if Steven was tucked in beside her._
_She'd never done that with me._
_"Want to come in for a minute?" Day asked that guy._
_The cool autumn air swept over my shoulders, giving me a chill. I looked down into the trash can. I'd wanted to pack up more food, but I suddenly felt sick._
_While Day and her boyfriend headed for the front of the house, I yacked up the contents of my stomach, able to hear my mother's voice inside my head reading Steven a bedtime story._
#
The police arrive about thirty minutes after I call them. Max stays until they get here, promising to call me later, after his shift at the boat shop (for which he's already late).
While I stay inside the house, the police search the bike path. It isn't until forty minutes later that Detective Mueller finally emerges from the woods. Officer Nolan follows.
I unlock the door to let them back in. "Did you find anything?" I ask them.
"Looks like someone might've been trying to make a path through the woods," the detective says. "There was an area about thirty yards down where the bushes got trampled and some of the tree limbs were broken, but it only stretched about ten feet."
"Our guess is that whoever did it either found another way or simply changed his mind," Nolan says. "Otherwise, it all looked pretty clear, but we'll have some officers patrolling the area, just in case."
"In case he comes back?"
"If it even was him," she says. "You didn't see his face, correct?"
"No." I shake my head.
"And, as you probably well know, these woods are pretty popular at night. We found beer cans, cigarette butts, and lots of empty bottles. Seems we may need to have some of our officers on party patrol."
It's true. My parents are always complaining about the kids who abuse these woods. They've called the police on more than one occasion, and have gone out themselves to break things up.
"We recently received two calls from the town of Millis," Detective Mueller adds. "It seems that someone fitting the suspect's description was seen early this morning digging inside a Dumpster and then breaking into a parked car."
"Millis?" I ask, trying to picture where it's located.
"The train by the high school goes to Millis," the detective says. "It's about three hours north."
Three hours away.
The tension in my heart lifts.
Officer Nolan hands me another business card. "But please, call us for anything—even if you think it's nothing."
"Thank you," I say, watching them leave—out the back door and around to the side yard—trampling through the six inches of leaves that I still have to rake.
_Thursday, October 15_
_Night_
_"Serves you right"—Dad's voice was inside my head. "What were you even thinking? Steven would never have been so stupid."_
_I woke up. My clothes were soaked. My hair felt wet. I was burning-hot, and shivering from my sweat. I tried to get up, but the motion made me sick. The sound of my retching filled the dark silence, but I couldn't help it. My stomach convulsed. My nostrils filled with acid as I heaved over and over._
_My mother continued to read from Steven's storybook. Her voice played over my father's words: "But Detective Panda had another idea in mind: he was going to help save the town of Panderville by finding that pesky sock thief."_
_My head ached. The room wouldn't stop spinning. I covered my ears, trying to muffle their voices._
_"You have to dig a whole lot deeper than that," Mom said. "Keep going until the soil changes color. That's when you know you've gone deep enough."_
_"It's because of you that your brother's gone," Dad told me._
_Their words were haunting me. My body was punishing me._
_The door flew open then. Footsteps moved in my direction. The toolboxes opened and closed behind me with a clank. I closed my eyes, huddled against the wall with a tarp pulled over me like a blanket._
_Was that the mower being moved? The blower being jostled? My water bottle being kicked?_
_There was more shifting against the floor. Someone was getting closer, just to my right and then over to my left. Where had I left my backpack?_
_I sucked in my breath. Droplets of sweat dripped down my face. My throat burned._
_Things went silent for a moment—all except for my heart. It pounded in my chest; the sound echoed inside my brain. I clenched my teeth, half-tempted to come clean. Were they watching me shivering my ass off? Was the tarp jangling along with my nerves?_
_I lay there, frozen, trying not to breathe, feeling like I was going to yack again. There were voices outside. They mixed with the words in my head._
_Finally, the person moved away. The door closed with a thwack. I got up to bolt._
#
I open the door to the barn. The air inside smells damp, like rotten wood. There's a row of tools hanging on the wall. I go to reach for the rake, wondering where the leaf bags are. I search around, suddenly noticing that the space looks off. The snow blower and lawn mower have both been moved. Dad's toolboxes are all lined up in a row. The sandbags are no longer collected in the corner.
There's a tarp stretched out on the floor—the same one Dad uses for camping trips. I go to pick it up.
And that's when I see him.
His face is only partially obscured by the tarp.
My heart tightens. The room starts to whir.
"Day?" Mom calls.
I peer over my shoulder. The door to the barn has fallen partially closed.
"Are you out here?" Mom shouts.
I exit the barn, feeling like I've just been shot out of a cannon: dazed, confused, shocked, out of sorts. Did that really just happen? Did I really just see him?
Mom's standing on the porch. There's a smile on her face—the first one I've seen on her in weeks. It fades when she sees me. "Is everything okay?"
I cross the yard. My head feels woozy.
Mom places her hands on my shoulders and looks straight into my eyes. "What's wrong?" she asks.
If I tell her the truth, the police will come. Is that what I want?
My body trembles from the cold. I need time to process everything. "I'm feeling a little dizzy," I tell her. It's the truth, after all.
"Come inside," she says, taking my hand.
I turn to look over my shoulder at the barn, wondering if he knows I saw him.
Mom leads me up to my room and tucks me beneath the covers. "I'll fix you some tea and toast. Then we can talk, sound good?"
It does. I nod and then turn over in bed. I pretend to fall asleep so I don't have to talk. But the truth is that I don't sleep all night. I just stare toward the window, hoping he'll be gone by morning.
_Friday, October 16_
_Afternoon_
_I tried to leave, but barely two steps away, I came to a sudden halt. Stars shot out from behind my eyes, and the room started to tilt. I grabbed the wall for stability and sank down to the floor, waiting for the police to come._
_But no one came. Even hours later. Had she not seen me?_
_Early this morning, feeling better, I put everything back the way I found it, like I was never even here—like the way Mom and me used to clean up before my father got home from work._
_"Get every crumb," she'd say. "Chairs need to be tucked beneath the table, ten inches apart. No streak lines when you wash the cabinets: smooth, smooth, smooth. Daddy doesn't like a mess. Everything needs to be spick-and-span."_
_Luckily, every time I puked, it landed on the tarp. I rolled it up, glanced out the window, and that's when I saw her._
_Day._
_She was headed this way, holding a bag in her hand. I backed away from the window, keeping my eye on the knob, waiting for it to turn, flashing forward to what I would say._
_But she didn't come in._
_I saw her walking away again, her fists tucked into the pockets of her jacket._
_While she went back inside the house, I opened the door. Inside the bag was more food than I'd had in days—granola bars, applesauce, bananas, a loaf of bread—as well as a couple of bottles of water._
_But there was something else too. An envelope. A note for me?_
_I opened it up._
I would like to talk to you about your case. I'll be back later today.
_At the bottom of the bag was a pad of paper and a pen. Does she expect me to write her back? Nothing makes sense. Who _is_ this girl? Why isn't she calling the police? What could possibly be in it for her?_
#
It's after school, and the bag of food is still hanging on the door handle of the barn, which means he either a) left last night or b) has yet to come out of the barn.
I'm assuming the first option is the correct one. I mean, at this point he's got to suspect that I'm onto him, so why risk sticking around?
I approach the barn door, pretending to be talking on the phone. "No, that's fine," I mutter into the voice piece, feeling stupid for doing so, but if he _is_ still here, I don't want him to know that I'm totally alone.
Rain droplets pelt against my face. I mutter a few more words. Meanwhile, a swarm of questions storm inside my head: What will I ask first? Why didn't I think to make a list? What if he doesn't want me butting in?
I take another step, trying to get a grip, but my pulse races and my insides shake. I peer over my shoulder to make sure that no one's lurking behind me, and then I grab the bag, hating the noise it makes: the crinkle of plastic, the jostling of containers.
I look inside it. My heart instantly clenches. The container I used for the sandwich appears to be empty. The granola bars are gone, and so are the bananas, my envelope, and the notebook and pen.
There's a folded-up note. He wrote me back. Should I read what it says? Or knock on the door?
I close my eyes, reminding myself that my mom has always been notorious for this kind of thing—getting to the bottom of questionable cases, that is. But does that help ease my anxiety?
A big. Fat. Walloping. No.
"Hey, Sunshine," a voice shouts from behind, making me jump.
I swivel around to look, hearing a gasp escape from my throat.
It's Dad. He crosses the yard, trampling through the fallen leaves. "Sorry if I startled you." He wraps his arms around me.
I hold him close, pressing my nose into the nylon of his jacket; he smells different somehow—like cinnamon breath mints. "It's really good to see you," I tell him. It's been almost a week.
He takes a step back, breaking the embrace moments too soon. His hair looks shorter than normal, like he just got it cut; it's been purposely messed up with gel, rather than parted to the side in his usual dad do. His clothes are different too—his jeans are darker; his shirt's snugger against his chest.
"Your mother's working late tonight," he says.
"How do you know? Did you come to see her?" I can hear the hope in my voice, can feel the desperation in my heart.
"I came to see _you_." He smiles birthday-cake wide, as if that's the answer I want to hear. "Your mom and I were texting earlier and she mentioned a late meeting, so I brought dinner. Sound good?"
Before I can answer, he motions to the bag I'm holding.
"What's that?" he asks. "And what were you doing? Did I interrupt you from something?" He looks toward the barn door.
"Nothing." I shrug, tucking the bag behind my back, as if he can no longer see it. "I was just cleaning up some stuff."
"Cleaning... _right_." He kicks a pile of leaves. "I imagine you've worked up quite an appetite."
"Definitely." I nod and follow him inside, into the dining room, where he's already cleared the table. The familiar white tote from Tuchi's Thai House is sitting on the buffet. While Dad unloads it, I place the bag beneath my chair, out of eyeshot, and begin setting the table.
He's ordered all of my and Mom's favorites: fried lemongrass tofu, drunken garlic noodles, sweet-and-sour spring rolls, and caramelized eggplant dumplings. He also got us extra white rice and Tuchi's famous sticky peanut sauce.
"This looks incredible," I say, taking a seat and piling up my plate.
Dad sits across from me and lights a candle.
"What's the occasion?" I ask.
"Do we need an occasion for candle-lighting?"
"Normally? Yes. A birthday, a power outage..."
"How about we change that policy?" He winks. "How about we light a lot more candles." He opens the wrapper on his package of chopsticks, and instantly I get a gnawing sensation in my gut.
Because he never uses chopsticks.
Because Mom and I would always offer to teach him, explaining that part of the culinary experience is eating with the utensils of the country of the food's origin. But still he'd always insist on a fork.
So, what's the difference now? And when did he start winking?
"It's been a while since we had Thai food, hasn't it?" He smiles.
I nod, unable to take my eyes off the way he holds the sticks, incorporating his thumb and ring finger. He's no longer wearing his wedding band. There's a mark on his skin in its place—a blank white circle.
He smiles wider, even though he's not supposed to be happy. "I've missed our Thai nights."
We used to order Thai food most Friday nights; it was our way of starting the weekend right. But that was all BS (Before the Separation, that is), four weeks and five days ago now.
"So," he begins, "how have things been around here? Anything exciting going on?"
I'm tempted to tell him about Julian, especially considering that Dad's entire career revolves around mentoring people from all walks of life. Dad himself came up with the organization's acronym: SHINE (Second chances, Honoring each individual, Instilling dignity, Nurturing talent, Equality for all).
I open my mouth to broach the topic, but before I can utter a sound, music starts to play—an old '80s song, something about a rose having a thorn....
Dad fishes inside his pocket for his phone. A new ringtone. A shiny metallic case.
"What happened to your boring beep?"
"If you haven't noticed, I'm trying to put the brakes on boring." Dad checks the screen and mutes the song.
"Anything important?"
"Nothing that can't wait while I'm having dinner with my number-one girl." Another stupid grin.
I hide the revulsion on my face with a giant bite of broccoli.
"So, tell me, I almost forgot," he says, "how did your first Peace & Justice meeting go? Did you already have it?"
"It was yesterday, actually."
His phone vibrates against the table. Someone left a message. He checks the screen again. Meanwhile, I try to tell him about the lack of interest at my meeting, but barely three sentences in, he cuts me off, reminding me how Mom had stormed the state house at the ripe old age of twelve, demanding stricter laws on animal testing.
"And they actually sat back and listened to her." He laughs. "Your mom...she was a firecracker right out the gate. You should've seen her in grad school: everyone wanted in on her action—on whatever cause she stood behind. That kind of fire...it's magnetic."
And apparently I don't have it.
"Sounds like you miss her," I say.
He looks at me. His smile falls flat. "I miss the way things used to be—here, with all of us."
"Does that mean you'll be coming home soon?" I can already tell that it doesn't.
Dad reaches for something else in his pocket—a handful of cash, of all things. He slides it across the table at me—five ten-dollar bills. "Since I haven't been around to give you an allowance," he says.
"Since when have I gotten an allowance?"
"Use it toward your Peace & Justice mission."
"Thanks," I say, staring at the long string of numbers and letters across one of the bills, wishing it were a code that I could crack—something to make sense of all that's going on. "But this doesn't answer my question about you coming home."
He stares at me for five long seconds without uttering a single sound. It's in that silence that the truth becomes clear: He isn't coming home. He doesn't ever want to come home. "I love you and I love your mother."
"But..." I say, feeling my heart strings tighten.
"But I think it's better if your mom and I part ways for a while."
I swallow down the truth, almost wishing that I could take the question back, that I could un-hear his horrible answer.
"Of course that doesn't mean I'm parting from you," he continues.
"There's something I need to tell you," I blurt, still thinking about Julian. Maybe that will bring Dad home.
"There's something I need to tell you too." His eyes go funeral-serious. His mouth is a straight, tense line.
My stomach drops, already anticipating the worst. I cross my fingers beneath my chair—the way I did when I was five—as if it will bring me luck.
"I found an apartment," he says.
"And?" I ask, already knowing the answer, but I need a moment. This is happening way too fast.
"And I put down a deposit."
"So you're no longer staying at the motel?"
"Better than the motel." His face brightens. "I'll be right downtown, near one of your favorite places...the independent movie theater. Maybe you'll use some of that money to see a show and then come visit me."
I scoot back in my chair, trying to digest what all of this means.
"I know." His voice softens. "This probably wasn't what you wanted to hear. But you have to understand; it has nothing to do with you."
I hate the tone of his voice. I hate his Dr. Phil–speak even more. I just want to hit stop, press rewind, and go back ten years—to my six-year-old princess-themed birthday party, when everything was just horse-drawn carriages and Cinderella castles. "Does Mom know?"
"About the apartment?"
"About the fact that you're no longer wearing your wedding ring, and that you're not ever coming home."
He lets out a sigh, but he doesn't deny any of it. "I wanted to talk to you first." He picks up his chopsticks and begins plucking at noodles, trying to make things normal, except the noodles never make it to his mouth.
"Normal for you is a fork," I snap.
Dad makes a face; he doesn't understand. We're not speaking the same language.
My phone chirps. I check the screen. It's a text from Mom. Her ears must be burning. "Mom will be home in less than an hour," I tell him, though I thought she was working late. Is she cutting things short to see him? "Will you be sticking around to see her?"
He peeks at his watch (a braided leather band, a bronze face; it must be new as well). "I can't tonight."
"Why am I not surprised?"
"Look, Day..." There's yet another grin on his face, as if there's anything even remotely grin-worthy going on. "You're a smart girl, but this isn't some Disney movie where the parents get back together in the end and everyone lives happily ever after."
"Then what's with this whole scene: the candlelit dinner, the surprise visit, the nice words about Mom..." I set my phone to burst mode to take shots of him—in his new clothes and with his new hair—holding a pair of chopsticks the wrong way.
"What are you doing?"
"Capturing this moment."
"I won't have you disrespecting me."
"And I won't sit here while you patronize _me_. I deserve more than spring rolls and a wad of cash. Thank you for the food, but I've lost my appetite." I go up to my room and shut the door.
He doesn't follow.
#
I sit down on the edge of the bed and wait for a knock on my door. When it doesn't come, I take my cell phone out of my pocket and flip through the pictures of Dad, trying to make sense of what just happened.
I focus in on one of them. The grin on his face looks forced. He's leaning back, as if somewhat at ease, even though nothing about our conversation was easy.
I go to my computer and upload the photo, setting it on the screen beside a handful of older photos—one from Christmas, several years back: Mom and Dad sitting on the sofa. Dad's wearing a lumpy sweater. His hair is perfectly parted to the side. He looks so happy, leaning in toward Mom, his eyes focused on her smile.
There's also a picture from the camping trip we took the summer I turned thirteen: Mom and Dad snuggled by the fire, unaware that I was looking on from the tent. Dad's got his lips pressed against Mom's cheek. His eyes are closed. There's a smile curled across Mom's lips.
I open yet another folder and move my cursor over a photo taken a couple of summers ago: Mom and Dad sitting at opposite ends of a porch swing, angled away from each other, faking awkward smiles for the camera. Beside it there's a picture from this past July: Mom's sitting by herself at the picnic table, staring off into space, while Dad stands idle only a couple of feet away.
When did he stop trying to make things better?
When did they both start forcing smiles?
I move to stand in front of my mirror to take a picture of myself: this person who doesn't see, this girl who's been so naive.
There's a door slam downstairs. I go across the hall to look out the bathroom window—to watch Dad get into his car, start the engine, and pull away, driving right over my heart.
I head downstairs. The food's been cleaned up, but the bag from the shed remains tucked beneath my chair. Dad obviously didn't see it; he must've been in a hurry. The reality of that helps dry my tears.
Back up in my room, I pluck the note out of the bag and open up the folds.
_Thanks for the food (and the place to stay). As you probably guessed by now, I followed you home from the train depot. I can't really make up a worthy excuse as to why—at least not one that won't make me sound like a creep._
_I didn't intend to stay, and I would've left by now, but I got sick while I was here. I was going to leave this morning, but your note stopped me._
_I'm curious why you want to talk about the case. If you change your mind, that's fine. If not, you know where to find me—for the next few hours anyway._
I read the letter one more time, feeling my skin chill.
My phone chirps. It's a text from Mom: `Just another 20 min and I'm leaving—promise! Is Dad still there??? Xoxo!`
I flop back onto my bed and gaze up at the ceiling, unsure what to call this feeling. Insecurity? Anger? Frustration? Fear? All of those emotions roll up into a ball and wedge beneath my ribs, making it hard to breathe.
My cell phone rings ("The Chicken Dance"). I check the screen. It's Tori. "Hey," I answer.
"So?"
"So _what_?"
"Are you kidding? I didn't want to bring it up at lunch—in case Jeannie really _does_ like him; she can be such a mysterious mouse at times—and then you took off so fast after school today, I didn't even get to ask..."
_"What?"_
"Max...after the meeting yesterday...dish."
"There's not too much to dish about. He drove me home. I invited him inside for a glass of water, and then he left."
"Was there tongue?"
"Seriously?"
"Friends can play tongue tag, you know. No judgment."
"I refuse to have this conversation."
"You don't find him even the slightest bit good-looking?"
"Sure, he's good-looking. But why do I need to have a boyfriend?"
"Who said anything about boy _friend_. How about a boy _toy_?"
"There are way more important things in life than toys."
"Like what? Saving the world?" She yawns. "You can't cuddle up with that at night, you know. Humans need love and companionship, in addition to a sense of personal fulfillment."
"Have you been reading your mother's self-help books again?"
"Do I sound wiser for it?"
"No, you just sound more annoying." I sit up and gaze out the window, startled to see Julian outside. There's a water bottle in his hand. He's going for the hose. "Can I call you later?"
"Have I inspired you to give Max a booty call?"
"What do you think?"
"Call me later."
I hang up, pocket my phone, and grab my camera. I head into the living room, where the view into the backyard is best.
Shielded by the curtain, I can see him clearly. Julian is crouched behind a stack of firewood, drinking from the hose, with his back toward me. His hair is chin-length and wavy, the color of chocolate kisses. His pants look even bigger now than just days ago. They hang low on his hips, exposing the small of his back. He angles toward me, slightly, and I zoom in with my camera lens, able to make out the sharpness of his cheekbones and the dimple in his chin. He uses the water to wash his face, to wet his hands, to run his fingers through his hair. The front of his T-shirt gets soaked. Water drips down the center of his chest, making a beeline toward his abdomen.
He must be absolutely chilled. Meanwhile, my face flashes hot. I shouldn't be doing this. This is an invasion of his privacy. Still, I take several snapshots, inspired to set them beside the photos from the train depot—to see if his shoulders look just as broad; to check if his skin resembles the color of apple butter, the way it does now.
I go to zoom in a little closer.
But then his eyes snap open.
And he looks in my direction.
I duck behind the window, feeling my heart pound.
My phone chirps again. I pluck it out of my pocket. It's another message from Mom: _Im so sorry! Is Dad still there? We r so close to getting Pandora home!!! Just one more hour._
Just one more hour.
Just twenty more minutes.
Just two more days and _"I'll be done with this case, this plight, this violation of justice."_
But minutes turn into hours. And days turn into weeks. Meanwhile, we're becoming more and more like tenants who inhabit the same space rather than mother and daughter.
I peek back at Julian as he rolls up the hose, thinking how I've never been one to keep things from my parents. But nothing is the same now. This "separation" feels more like a wide, gaping hole.
My stomach growls. I need to eat. There's no sense wasting good Thai food. I'm sure Julian's hungry too. I head into the kitchen to fix us both a plate.
#
Plate of food in hand, I head out to the barn, my nerves absolutely shot. Standing at the door, I knock a couple of times, but it makes no sound.
I try again, slightly louder.
The door opens. Julian's standing there. He towers over me by at least six inches. His golden-brown eyes focus hard on mine, stealing my thoughts, blanking my mind. And suddenly I have no words.
I hand him the plate of food. There's a confused expression knotted up on his face.
"I thought you might be hungry." I shove my hands into my pockets, one hand wrapping around the pepper spray, the other clutching my cell phone.
He opens the door wider to let me in.
I step inside, feeling the rush of my adrenaline. "So, I've been researching your case."
_"Why?"_ He closes the door behind me.
"Because you were here, loitering around my house and staying inside my barn."
"So how come you didn't call the police?"
"I _did_ call them. And I'll call them again if I have to."
He takes a step closer, as if to challenge me. "How come you're not calling them right now?"
"Because maybe I want to learn more about your case," I say, trying my best to sound brave. "Maybe the details of your arrest don't add up for me."
"How do I know you won't turn me in—that whatever I say won't be used against me?"
"You don't." I swallow hard. "But if you _aren't_ guilty, or if the case _is_ being mishandled, then I want to try to help."
His expression turns cold: a vacant, unblinking stare. "Need I remind you that I've been accused of an unspeakable crime?"
"No reminders necessary. I'm aware of the allegations."
"You're committing a crime too, you know—by helping me."
I can feel my face turn pink, and can feel the dark red hives around my neck. "Are you planning on turning me in?"
"Your parents can't possibly know I'm here. They'd ground you for good."
"You might be surprised about that one."
"Oh, yeah? Why's that?"
Droplets of sweat form at my brow. "Do you want my help or not?"
"What's in it for you?"
"I'm not looking for anything."
"Everybody's always looking for something." He takes another step closer.
But I don't budge an inch. "What are you still doing here? Why aren't you at least a hundred miles away by now?"
The question takes him off guard. I can tell by his body language. He looks downward. His posture angles away. "I already told you: I got sick."
"But still...That can't be the only reason. Why aren't you in Canada or something?"
He turns to set the plate down. "I guess I was kind of hoping that in the time I'm laying low, new information would surface in my case, exonerating me."
I bite my lip, focusing hard on _him_ now, trying to decide if he's being honest. "Well, maybe, with your help, I'll be able to find that new information."
"You don't even know if I'm innocent."
"I'm going to assume you are—until I prove otherwise, that is."
He comes closer again, standing just inches from me now. "And then what?"
"And then I'll call the police back." I pull my cell phone out of my pocket for no apparent reason. My hand shakes. My face burns. "We can start tomorrow. Are you in?"
He looks away again. Meanwhile, my mouth turns dry and my heart won't stop hammering.
"Well?" I ask, trying to feign indifference.
His breath has quickened; I can tell from the motion in his chest.
"I'm in," he says, finally.
#
It isn't until after eleven that my mother finally comes home.
"Day?" she calls out.
I hear the clank of her keys as she drops them on the table in the entryway. The floorboards creak as she makes her way up the stairs. I quickly minimize the screen on my computer—the list of questions I'm drafting for Julian—and go into my virtual gallery, making it look like I'm arranging photos.
"Sweetie?" she says. There's a light rap on my open door. "What's this...working on a Friday night?"
"Like mother, like daughter."
"Well, how about a peace offering?"
I turn to look. She's holding a box from Brewer's Bakery.
"I got us some red velvet cupcakes," she says. "Your favorite."
I swivel back around to my screen. "Isn't it you who always says it isn't good to eat after seven?" Something about the body not having sufficient time for proper digestion.
"Couldn't we make an exception, just this once?"
I move my cursor over a photo of a girl I saw at the park. I snuck the shot on a walk home with Jeannie a few weeks ago. I asked Jeannie to pose in front of the swirly slide. Little did she know that I was missing her entirely, zooming in on the girl just over her shoulder.
In the photo, the girl is sitting on a bench with her boyfriend. He's caught in a laugh with his mouth arched wide. She's smiling too, but it's clearly forced. Her eyes look teary and her posture's pointed away from him. I drag the photo under a heading that says "Alone with Other People."
"I know you're upset," Mom begins. "I haven't been available much."
But...
"But you have to know," she continues, "I'm doing some very important work."
"More important than being home with your family?"
"Not _more_ important, just different-important. Was Dad upset?"
" _I_ was upset. Doesn't that count for anything?"
"I'm sorry." She sighs, coming farther into the room. She sits down on my bed. "I know this has been an adjustment for you too."
"It has," I say, thinking how ever since her and Dad's separation—leaving a wide, gaping hole in our musketeer trio—Mom and I have been on two entirely separate pages: she, distracted by work; me, in a trio of one (which makes absolutely no sense, which is why it doesn't work).
"I never got to ask: How did your Peace & Justice meeting go? It was yesterday, wasn't it?"
"It didn't go as well as I'd hoped."
"Did you have a nice turnout?"
"Define _nice_."
"Ten? Fifteen people?"
"Try three, including Jeannie and Tori." I pivot in my seat to face her.
"Sounds like you'll just have to work harder."
"I already _do_ work hard."
Mom snickers. "I once had to work eighteen-hour days for five weeks straight, and that still wasn't 'hard work' enough."
"When will this household be your hard work?"
"Excuse me?" Mom's jaw stiffens. Her eyes narrow.
"Sometimes I feel like I need to get locked up in jail if I want to see you ever."
"Don't take your failed meeting out on me." She gets up and leaves the room.
But I'm not done fighting yet. I grab my folders full of Peace & Justice plans: my meeting's agenda, the articles I found concerning various human rights movements (for fair trade, free love, environmental justice), the extra posters I made up, and the research I did on similar clubs at other schools. I barrel down the stairs and storm into the kitchen. Mom's at the stove. I drop everything onto the table with a satisfying thud. "Do you still think I haven't been working hard enough?"
But Mom continues to stir her pot, refusing to turn around.
_"Tell me,"_ I shout, desperate for a reaction. "This is a month's worth of research right here...."
Mom shakes her head. _Stir, stir, stir._
"Nothing I do is ever good enough, is it?" I continue. "Is that why you barely come home? Why you hole yourself up in your office for hours on end? Why we never talk anymore?"
_Stir, stir._
"Do I remind you too much of Dad?" I blurt, grasping at straws. "He was here today. Where were you? How come you're not even trying to make this family work?"
Still she doesn't answer, which makes tears well up in my eyes. Why am I not even worthy of a fight?
I reach into my pocket for my phone. I take a picture of her back as she stands at the stove, sampling whatever's in the pot with her wooden spoon. I can see her reflection against the microwave door. Her face is neither sad nor angry. Her eyebrows furrow as she smacks her lips together and then adds more salt.
Like I'm not even here.
Like hot bubbling tears aren't streaking down my face.
I turn the camera lens on me and take a snapshot of myself, with my puffy eyes and my blotchy cheeks. I imagine the two photos in an album, side by side, under a heading that says "Dysfunction."
When Mom still doesn't say anything, I gather up all of my Peace & Justice paraphernalia and go for the door, making a beeline for the trash cans, assuming she'll try to stop me or change my mind.
She doesn't.
_Saturday, October 17_
_Afternoon_
_I waited until early morning before going out to see what Day had thrown into the trash._
_Poster boards stuck out from beneath a trash can lid. I grabbed one and held it up in the moonlight: the letters PB &J were huge across the front. The date was listed too. I'd been on the run for almost two weeks._
_I pulled a couple of folders out as well, picking through old banana peels and a bunch of other half-eaten crap too gross to salvage. A stream of papers blew out from one of the folders. I scooted down to pick them up, just as a light shined in my direction._
_I dropped everything. And looked up._
_It was Day. She aimed her flashlight straight into my eyes._
_I stood, holding my hands up like I was suddenly under arrest. "I heard you," I attempted to explain. "That is, I saw you throwing this stuff away."_
_She was dressed in a robe and slippers, and some sort of long silky pants._
_"I'll leave if you want," I told her._
_She looked away instead of answering. Her hair blew back in the wind, away from her face, revealing skin that seemed to glisten. "I shouldn't have dumped this stuff," she said. "It was a bad decision in the heat of the moment."_
_I've made enough of those._
_She put away her pistol of a flashlight and scooted down to take her things. I scooted down too, trying to help, able to smell her—a mix of vanilla and cinnamon, like something out of a bakery._
_She paused to look at my wrist—at the tattoo of the pickax on the underside. I watched her stare at it, unable to tell what she was thinking. Finally she met my eyes again, but instead of showing fear, her expression seemed softer somehow. The tension in her mouth had melted. The muscles around her eyes were relaxed. Maybe I'd been locked up for too long, but she was the most beautiful thing I'd ever seen._
_I looked away again, stood up, and handed her a stack of folders. "I should go," I said, peering back at the barn._
_"I was actually hoping you might want to get started now, since we're both up."_
_"Get started?"_
_"With your case."_
_Right. My case. I think I nodded. I'm pretty sure she said "great."_
_She came to the barn not long after, carrying a couple of tote bags. She pulled a jacket from one of them, held it up to my chest, and then forced it into my hands. "I have others if it doesn't fit. My dad is a regular at yard sales."_
_She took out a blanket next, explaining that she'd knitted it in the eighth grade as part of a fund-raising event for the children's hospital. "It was just sitting in my room," she explained. "I'm happy it'll actually get some use."_
_I lifted the blanket up to my face, without even thinking. It smelled like her—that vanilla-bean scent._
_"Thank you again for salvaging my stuff from the trash," she said. "I'm kind of embarrassed, actually...that you heard my mother and me fighting." Her face turned bright pink. "I was kind of being a brat—not exactly one of my prouder moments."_
_The comment took me off guard, because if she was embarrassed for fighting with her mother, then I should've been mortified for ending up in juvie._
_She opened another bag and took out a bunch of stuff—soap, hand towels, napkins, food supplies—setting it all on a toolbox. She held up a can of tuna. "I heard this was a personal favorite of yours. The only problem is that I didn't know if you preferred freshwater or oil-packed. Do tell. Inquiring minds want to know."_
_"Oil, for the fat. Believe it or not, small cans pack big protein—at least in the case of tuna."_
_"Good to know." She nodded like she actually gave a shit._
_"And now my inquiring mind wants to know: Why are you doing this? Giving me clothes, food, and water, and letting me use this place as shelter? You don't even know me."_
_"I actually don't know any of the people who receive my charity."_
_"Is that what I am to you? A charitable cause?"_
_She shrugged like the term was no big deal—like there was no shame in getting help. "Would you prefer it if I called you something else?"_
_"How about a felon? That seems the most obvious choice."_
_She let out a sigh. "I technically can't call you that if you haven't been proven guilty."_
_"Who are you?"_
_Her face messed up in confusion. "What do you mean?"_
_"I mean, who are you?"_
_We were standing just inches apart, and I had no idea how we'd gotten that way. Had she moved closer? Had I? Would it have been too obvious if I stepped back? She could sense the awkwardness too—I could tell because she suddenly didn't know where to look. Her gaze flicked back and forth between the stuff she brought and the door to the barn before finally resting on my chest. There was a smear of something red in the corner of her mouth. Strawberry jam? Residual toothpaste? I wanted more than anything to wipe it with my thumb._
_I backed up, looked away, and threw the blanket down on a toolbox. I didn't want to smell it. I didn't want to feel this. She needed to go. I needed some space. "I have to get some sleep."_
_"I thought we were going to get started." She pulled a tape recorder from her pocket—one of those handheld ones—and explained that she wanted to tape our conversations. "That way, I can go over the details of the case as many times as I need to."_
_I hated the idea—the possibility that she could use my words against me. My father was always using my mother's words against her:_
_"You promised you were going to stop taking pills."_
_"You said you were going to clean this house."_
_"You told me you were going to make sure the kids wore their seat belts."_
_I don't trust words—not my parents', nor my own._
#
I place the tape recorder on the bale of hay between us and pull a list of questions from my pocket. Instantly he withdraws, backing away, avoiding eye contact.
"I'm not going to share this with anyone," I tell him.
"Even if I say something that could pin me? Or reveal a clue that could possibly exonerate me? Then, seriously, what's the point?"
He's right. There would be no point. "You're just going to have to trust me," I say, looking toward the side of his face.
His jaw is locked. His lips look tense. "I don't really trust anyone."
"Did you trust your parents?"
He shakes his head. "I especially didn't trust them."
I take a deep breath, thinking how no matter what information I'm able to dig up, this case isn't just about his guilt or innocence. He lost both his parents in a really traumatic way. "I'd like to try to help you," I tell him. "But if you've changed your mind, that's okay too. You can leave by tonight. I never saw you here."
"I want your help," he says, quickly, quietly.
"Okay, then I'm going to have to record our conversations."
It's silent between us for several seconds, which I totally understand. I mean, he doesn't even know me. What reason does he have to give me his trust? Except for the fact that I haven't turned him in yet.
"Let's go," he says, nodding to the tape recorder.
I push RECORD before he can change his mind.
`ME: Where were you on Saturday, May 4th, the day of your parents' deaths?`
`JULIAN: I mowed my neighbor's yard first thing in the morning, around ten. After that, I drove to Dover Beach; that was at noon.`
`ME: Did you come home between mowing the lawn and going to the beach?`
`JULIAN: Yes, but I didn't change.`
`ME: You went to the beach in your mowing clothes?`
`JULIAN: Yeah. I was wearing a pair of shorts and a T-shirt. I don't go to the beach to suntan. Plus, it was May—too cold to swim. I just like to sit on the rocks and write. Sometimes I also read. I've kept a journal for most of my life.`
`ME: How long did you stay at Dover Beach?`
`JULIAN: Until four thirty or five.`
`ME: Did you see anyone while you were there?`
`JULIAN: I did. A girl named Ariana. We bumped into each other.`
`ME: So, you have an alibi.`
`JULIAN: I thought I did. Ariana said she saw me there too, but then the police got her all confused. By the time she was done talking to them, she didn't know if it was Saturday or Sunday that she saw me.`
`ME: How about the security cameras? I know that Dover Beach has them.`
`JULIAN: They do, but they only caught me there on Sunday.`
`ME: Were you there Sunday too?`
`JULIAN: Yep.`
`ME: And how about Ariana?`
`JULIAN: She was there both days.`
`ME: Did the camera catch her there both days?`
`JULIAN: Yep again. I should add: I later learned that one of the security cameras was broken.`
`ME: Which one?`
`JULIAN: The one in the far left corner of the parking lot.`
`ME: Is that where you bumped into Ariana?`
`JULIAN: No. I saw her by the showers.`
`ME: But you weren't taking a shower.`
`JULIAN: I was just walking by that area when I bumped into her.`
`ME: Did the police talk to others who were at the beach on that date—anyone else who might've confirmed that you were there? Or did you order any food at the snack bar? Might you have a receipt?`
`JULIAN: Negative. To all of the above.`
`ME: And nothing out of the ordinary happened while you were there?`
`JULIAN: Nope.`
`ME: Okay, so you left the beach around four thirty or five. What did things look like when you got home?`
`JULIAN: Just like normal, I guess.`
`ME: Did it appear as though someone had broken in?`
`JULIAN: No.`
`ME: Is this too hard for you?`
`JULIAN: It's just a lot—picturing everything, remembering my mom like that.`
`ME: And your dad?`
`JULIAN:...`
`ME: Do you want to take a break?`
`JULIAN: No, it's fine. Keep going.`
`ME: Who do you think killed your father?`
`JULIAN:...`
`ME: Julian?`
`JULIAN: I think my mother did it.`
`ME: But investigators say no?`
`JULIAN: They think she was too weak to be able to strike my father over the head with the kind of force that caused his brain hemorrhage.`
`ME: And what do _you_ think?`
`JULIAN: I think people are capable of a lot when they're really pissed off.`
`ME: Are you cold?`
`JULIAN:...`
`ME: You're shaking.`
`JULIAN: I'm fine. Really.`
`ME: Why do you think your mother killed your father?`
`JULIAN: Why does anyone kill? Because they want that person dead.`
`ME: Did your mother want your father dead?`
`JULIAN: Yes.`
`ME: How do you know?`
`JULIAN: She told me—many times, actually.`
`ME: According to police reports, your mother was found in the bathtub with the water still running. Did you find her?`
`JULIAN: Uh-huh.`
`ME: And there was something in the reports about prescription medication`....
`JULIAN: Yep. She'd recently taken enough to gag a horse.`
`ME: Do you think she took them on purpose? Or by accident?`
`JULIAN: Hard to accidentally swallow an extra twenty-seven pills.`
`ME: Could someone have forced her to take that many?`
`JULIAN: Yeah, it's called her inner demon—the same demon that made her slit her wrists twice.`
`ME: Didn't she ever get help?`
`JULIAN: She was seeing a therapist at one point. You can see how well that worked out for her.`
`ME: And after that?`
`JULIAN: She said that therapists were a waste of her time.`
`ME: So, how did she keep getting pills?`
`JULIAN: Who says she was getting them legally?`
`ME: Did your father know about any of this...her slashed wrists, the illegal medication, or her attempts to get help?`
`JULIAN:...`
`ME: You're shaking again. Do you need to grab a blanket?`
`JULIAN:...`
`ME: Do you want to take that break?`
`JULIAN: That's probably a good idea.`
#
I spend the following day trying to catch up on schoolwork, but failing miserably because I can't stop thinking about Julian's case. At night, I toss and turn in bed, unable to sleep. There are way too many questions bouncing around inside my head:
Why didn't Julian trust his parents?
Why did the surveillance cameras only catch him at the beach on Sunday rather than Saturday, when they caught Ariana there on both days?
Is it true that Mrs. Roman really wanted her husband dead? And, if so, why?
I try to distract myself with thoughts of happy-funny times—like Halloween, two Octobers ago, when Tori showed up at Lesley Thibodeau's party dressed as a tampon, even though it wasn't a costume party.
I didn't really know Tori back then. To me she was just the pink-haired girl in my study hall that always doodled geisha girls on the covers of her notebooks and wore mismatched socks. But I still tried to help her out that day (not that her tampon-wearing self really needed it) by giving her my sweater to break up all that white. Unfortunately the sweater was red, and so she ended up looking like a used tampon, which was sort of gross and funny at the same time—at least, it was funny to us.
Needless to say, we didn't last long at the party, but that turned out to be perfectly okay, because we laughed the entire way to Dino's, where we fit right in beside a busload of senior citizens after their Halloween-costume-wearing bingo night party. Tori and I ordered root beer floats and a basketful of onion rings, and really got to know each other.
We've been close ever since. As nutty as she can be, she often has the enviable ability of seeing the world through a crystal-clear lens, which is why I should've called her last night instead of losing it on my mom and throwing away all my meeting stuff.
I roll over in bed and stare out the window. The light from the moon casts over me like a blanket. A soft breeze filters in through the open crack. In textbook terms, this is an optimum night for sleep. And yet I couldn't feel more restless.
"Day?" Mom knocks lightly on the door.
I sit up, just as she comes in.
"Is it safe in here?" she asks.
"Safe?"
"Yes. Is this a war-free zone?"
"I don't want to fight," I tell her. "But I also don't want to be ignored."
Mom sits on the edge of the bed. Her hair's pulled back in a messy heap. Aside from a trip to the grocery store, she's been working in her office all day. "I didn't feel like I had much choice. You weren't acting rationally last night—at least not for a serious discussion."
"Do all of your serious discussions involve cupcake-shaped Band-Aids?"
She smirks. "I guess I deserved that. I'm sorry I haven't been so available lately. That's what this is about, isn't it...rather than your less-than-successful club meeting?"
"It's about everything." I sigh. "Dad and I were waiting for you to have dinner with us last night."
Her jaw stiffens and she looks away. "I doubt that he was waiting."
"Since when are you Miss Insecurity?"
"It's just that your dad seems happier on his own."
"Are _you_ happier?"
She repositions on the bed. Her eyes fill up with tears; the sight of them takes me aback, because Mom has always been the confident one—so courageous and unbreakable.
"Work helps keep me distracted from worrying too much about happiness," she says. "It also gives me a sense of value—like what I'm doing is really meaningful. But the deeper I dig into my work, the more needed I become. There are people really counting on me, Day. And I know that you're counting on me too. It's just...It's hard to find a balance, you know?"
I reach out to touch her forearm, thinking how tiny and fragile she looks all of a sudden, like a little girl, rather than the pillar of strength I've grown so accustomed to standing behind.
"I'm sorry," she says again, taking my hand, wrapping her fingers around my palm. "For not being around, for getting emotional like this."
"It's human to get emotional," I tell her. "You should try it more often."
She moves to give me a hug. I stroke her back, grateful for this moment. This is the most human I've ever seen her, and so I take a mental picture, reminding myself, once again, that no story is complete without listening to all sides.
#
"Day?" my mother calls.
"Just a second," I holler back.
It's Sunday morning, I'm in my room, working on my list of questions to ask Julian.
"Breakfast is ready!" she calls again.
I get up and head downstairs. Mom's loaded up a serving dish with stacks of French toast; they're dripping with maple syrup. There's also a separate plate of sausage links.
"What's the special occasion?" I ask her, suddenly feeling on high alert.
"How about hunger?" She motions for me to take a seat at the kitchen island, beside her. She looks way too put-together for just a lazy Sunday at home. She's showered and changed. Her hair's been freshly flat-ironed and there's a subtle layer of pink shimmer on her lids and cheeks. Her phone sits on the island, between us—the third wheel in our party of two.
I fork off a piece of my French toast and take a bite. The thick wad of syrupy goodness all but melts in my mouth. "Did you somehow channel Paula Dean to make this?"
"Not good?"
"More like _delectable_."
"Really?" She straightens up on her stool. "Go, me!"
I spoon a couple of the sausages onto my plate, noticing the suspicious pale brown color. "Real?"
"What do you think?"
Tofu; I'm sure of it. I can tell by the super-shiny casing. Mom likes to think of herself as a health nut, but in reality the majority of our meals come out of a cardboard box.
"Are you working today?" I ask, already anticipating the answer.
"Not if I can help it. Maybe one video conference call. Two at the most." She checks her phone for the time.
I take a sip of coffee, wondering if I only imagined our conversation last night. "How are you so sure that Syrian-prison Pandora is innocent? I mean, you've never even met her."
Mom's syrupy mouth drops open, her eyebrows shoot up, and she lowers her fork to her plate with a clank. Shit, meet Fan. I've evidently hit a nerve.
"I may have never met her," Mom says, enunciating every syllable, "but that doesn't mean I haven't looked into her story, pulled it apart, consulted with the officials in charge of keeping her imprisoned. I've also talked to her family, friends, schoolteachers..."
"I get it," I say. Mom practices what she preaches, examining the facts from different angles—at least when it comes to her work. "It's just weird," I continue. "I mean, in theory, guilty people are supposed to get punished, but there are plenty that don't, thanks to plea deals, mishandled evidence, and different tiers of attorneys—from freebie public defenders to million-dollar lawyers who know how to work the system. In the end, where lies the truth? Thousands of dollars and hours later...do any of the players even care?"
"You're starting to sound like me." She taps her coffee mug against mine. "It's an imperfect system, which is why I'm working so hard to do my part. Believe me, if I didn't truly believe that Pandora was innocent, I wouldn't be working on her case." She checks her phone for the time once again. An entire minute has passed.
I eat my frustration with a bite of tofu sausage. It has the consistency of gummy bears, but not in a good way.
"So, what's on _your_ agenda for today?" She's glaring at me now.
I peer out the window. The door to the barn is closed. She wouldn't have had reason to go out there this morning. Plus, she's not one for subtlety; she'd be far more direct if she knew or suspected something. "Why do you ask?"
"No reason. Just curious." Her eyebrows knit together and she gives me a puzzled grin.
I take a sip of coffee, trying to formulate my answer. But her phone rings before I can.
"It's Genevieve," she says, already off her stool. She holds up her finger, indicating that she'll only be a minute.
But I've heard that drill before.
While she heads to her office, I peek back out the window, wondering about Julian's truth. What is his version of what happened on the day his father was killed? The day he lost both his parents.
_Sunday, October 18_
_Afternoon_
_I woke up on the morning of October 6th knowing it was a good day to escape. I could feel it deep inside me—like an electrical current that charged through my veins, making me feel on fire._
_I could barely sleep the night before, couldn't concentrate in classes on the day of, couldn't stomach a single morsel. Like the Christmas Eves you see on TV—kids tossing and turning in bed, unable to sleep a wink._
_"Are you going to eat that pancake?" Jones asked. "If not, can I have it?"_
_Jones was fourteen years old, in juvie for stealing cars. I gave him my whole tray, too excited for food—giddy even, like I'd ever felt giddy about anything; never had any use for the word. Sort of ironic. It took me going to juvie to feel the excitement of Christmas._
_It was drizzling, but we were still allowed to go outside for some fresh air. Stickney, the new guard, had been assigned to watch us—that was mistake number two. Mistake number one was that he'd been hired at all._
_Stickney had his head so far up his ass that he couldn't see straight. I knew it. He knew it. He knew I knew it._
_During the weeks that led up to the escape, I watched Stickney closely. Saw him flip out, royally, over Jordan's messy cell, ultimately pinning him to the ground (infraction: overreacting, resulting in a warning). I then saw him give a mere slap on the wrist when Williams jumped Douglas in the cafeteria, nearly knocking Douglas unconscious (infraction: underreacting, resulting in a meeting)._
_When Stickney started getting a little too social with the other inmates—detainees, we're called—by oversharing about his supposed hot ex-girlfriend and all his sexy conquests (most likely the product of his warped imagination), I knew his fate was sealed._
_I had my way of letting him know that Big Brother was watching. Whenever he so much as sneezed in the wrong direction, I'd be there, eyes wide, silently judging. It got so that whenever he laughed too hard or did something shady—slipping a candy bar to Williams when he thought no one was looking, letting Jones skip morning classes for no reason other than he didn't feel like going, telling anybody who'd listen about some girl he'd been working at the bar he frequents—he'd look for me, checking to see if I'd noticed._
_I always noticed._
_Dad always noticed too—whenever Mom looked a little too happy or treated Steven's half of the room as anything other than a sacred shrine (collecting a pile of clothes on his bed or using his dresser to store extra bedsheets), Dad noticed and called her on it: Howdareyoudisrespectmyson.Wipethatstupidsmileoffyoursmuglittleface.Whatistheretobehappyabout?Iwon'thaveyoudisrespectingthisfamily.Iworksohardwhileyousitaround._
_The night before my escape from the detention center, I zeroed in on Byron Hensley, one of the newbies. I'd handpicked Hensley for being thirteen years old, scared shitless, and way too pretty to stay safe around here. Other detainees had noticed him, and I knew that freaked him out. Sexually abused since he was five, Hensley sought revenge by murdering his mom and stepdad—or _allegedly_ murdering them, like me._
_Committing a crime like that at thirteen, I knew he was capable of acting out of desperation. I also suspected that he was just a wee bit crazy. I mean, who wouldn't be after growing up like that? Or committing a crime like that?_
_"You don't belong in here, man," I told him. "You should totally plead insanity. They'll transfer you to a hospital. You won't even have to stand trial."_
_"The lawyer said something about that too," Hensley said, "but I got sent here instead. I think my hearing will decide if I'm sane enough for trial."_
_"So, show you're not sane."_
_"How do I do that?"_
_The wheels in my head started to turn. This would be easier than I thought. After a little coaching from me, the plan was set. Hensley's tears had dried up. He now had something to look forward to. Merry Christmas once again—I'd probably just given him his best gift. A temporary stint in a mental institution—until he received the proper meds and therapy that would magically turn him "sane" again—beat prison any day. At least that's what I told myself._
_And so, there we were, a pack of nineteen of us, outside in the yard, getting some fresh air. Like most days, some of us were doing laps. Others were shooting baskets on the court or talking on the sidelines. A few more were playing a game of capture the flag, using an old sock as the flag._
_Stickney was in the center of it all. One man, expected to have eyes in the back of his head: mistake number three._
_I stood off to the side, by the fence that surrounded the yard. There was an area that curled around behind the building, out of eyeshot: mistake number four._
_Was it a coincidence that a section of that fencing had been turned upward, just enough, where there'd been some construction going on? Or was that mistake number five?_
_Hensley gave me a nod and then kicked off his shoes, dropped his pants and boxers. He whipped off his T-shirt and started running around stark raving naked, singing "Santa Claus Is Coming to Town."_
_Stickney lost his shit. He blew his whistle, shouted at the top of his lungs, and started chasing Hensley around. But Hensley was too quick, skipping in circles, shaking his bare ass._
_Other detainees started cheering, laughing, whistling, storming. Meanwhile, the bell rang, alerting us to line up and go in._
_I bolted instead, slipping around to the side of the building. I'd planned on trying to scale the fence until I saw the damaged panel. I scooted beneath it. A jagged piece of the metal scratched my face, ripped my pants, and dug into my back. Blood ran down my cheek. But still I kept on running, never stopping to look back._
#
Roger Mason has this weird habit where he tears tiny scraps of paper from the pages of his notebook, chews them up into tight, round wads, and then collects them into a heap. When I first saw him doing it, I assumed he was making spitballs, but I soon stood corrected. Roger uses the saliva balls to erect various sculptures. I know this because he sits beside me in the library for every single B-Block. I even have a picture of his Eiffel Tower of balls.
It's B-Block now, and I'm trying to ignore the sound of him swishing paper around in his mouth, but it's so completely distracting, especially because he keeps sniffing up phlegm, like he has a bad cold, and so I can't help picturing snotty saliva balls. Normally it wouldn't bother me as much, but my nerves are shot. I'm so overtired.
Still, I'm using this study block to do research on Julian's case. According to another article I find, it seems that Julian was fairly well liked by his peers, even helping out the drama club by building sets. One classmate was quoted as saying that Julian "was a quiet guy, always writing in a journal. He never made any problems."
Another student said, "If I ever have a problem and need to talk stuff out, he's my first go-to."
Similarly, there are teachers and neighbors who claim to have been shocked by his arrest. "Something isn't right," said Madeline Romano, a recently retired English teacher at Julian's high school. "Julian is a gifted writer with a gentle soul. He was respectful in my class, and always worked well with his peers. I really think there's a major piece of this story that's missing."
"Hey, is that the Bates Motel?" a voice asks, from behind, instantly making me jump.
I swivel in my seat to find Tori.
"Whoa, looks like someone's a little on edge. Too much Red Bull in your Apple Jacks this morning?" She tsk-tsks before looking back at Roger's sculpture. " _Psycho_ 's one of my all-time faves. Vince Vaughn as Norman Bates...totally hot, right? Though Anthony Perkins wasn't too shabby either. Bonus points if you can re-create the infamous vacancy sign that stands in front of the motel."
Tori's got her hair in pigtails today, the tips of which match the bright gold stars on her knitted scarf. "Hey, there." She smiles at me. "Got a minute? I'm in major cri-cri mode."
"What's the crisis?" I ask. "Did Mr. Garblecki pass the history tests back?"
"Jarrod Koutsalakis is totally taking someone else to Hannah Hennelworth's 'It's-Saturday-let's-party' party."
"Oh, right. _That._ "
"Seriously?" She lets out an audible sigh. "Word's even spread to _you_?"
"Rest assured I actually have no idea what you're talking about. And, P.S., who is Hannah Hennelworth?"
Tori makes a confused face, her lips bunched up and her eyebrows knitted together. "How the hell am I supposed to know?"
"Well, you're going to her party, aren't you?"
" _Jarrod's_ going." She rolls her eyes, frustrated that I can't keep up. "Apparently Hannah's some freshman girl who lives on the curve." (Note: the houses on the curve overlook the water and generally have their own servant quarters, which means that Hannah Hennelworth is rich—or at least that's the perception.) "Anyway, Hannah is having this party to put herself on the map."
"In other words, to buy people's friendship?"
Another eye roll. "You're totally missing the point here, Day."
"I'm not. Really. You want to go to the party, but Jarrod is taking someone else."
"Not just _some_ one, _the_ one. Becky Freaking Burkus. I mean, seriously, have you not noticed her skanky attire lately? Low-cut blouses, ho-length skirts, fishnet stockings, and visible string."
"As in shoelaces?"
"As in _G_ ," she barks, snagging the attention of Mr. Czarnecki, the librarian. "Becky's like a walking peep show," she whispers.
"And Jarrod's rumored to be dating that peep show. I must say, I'm kind of surprised to hear a boy has got you sinking to such shallow depths. I mean, honestly, using some girl for her curvy house party?"
Tori holds up her fist. "This is point." She waves her opposite hand in the air. "This is you." She passes her waving hand over the fisted point. "And this is you missing the point. Do I make myself clear?"
"Crystal."
Tori drags a chair in between Roger and me to sit. "Bottom line: we need to go to that party. Word is that Max is going to ask you."
"Okay, but I refuse to go to a party thrown by someone I don't even know, whose intention it is to buy a bunch of shallow leeches—present company excluded, of course."
"Oh, come on, Ms. Scruples. Won't you even go for me? _Please?_ I'll picket at your next save-the-kids/protect-the-rain-forests/help-the-flying-squirrels rally." She bats her puppy dog eyes. "Remember that flying squirrels campaign last spring?" She giggles. "You had us planting trees everywhere."
"I'll think about it," I tell her.
"Well, think hard. I want to show up looking smokin' hot." She runs her palms over her red-and-white striped sweater.
I wonder if she knows how much her outfit looks like something out of Where's Waldo's closet.
"I'm so excited now." She claps silently and then glances at my computer screen. "Is that for the psych paper?"
"PB&J stuff, actually," I lie, feeling an instant ping of guilt.
"I already told you, PB&J belongs between two slices of bread rather than as a club. Get it?"
"You don't think social justice is important?"
"Well, um, _duh_." She makes the missing-the-point gesture with her hand and fist again. "But I think your own happiness is even _more_ important."
"And you don't think I'm happy?"
"I think you have most of the right ingredients in your pantry for happiness, but it's like you're using the wrong recipe."
"Okay, I'm thoroughly confused."
"I just think you're much more of a curried-lentil-soup kind of girl rather than a ho-hum sandwich. You know...bold, strong, hearty, motivating. The kind of soup that flies under the radar but is spicier than all the rest; the soup that all others are measured against."
"Huh?" I make a face.
"What's so 'huh?' about it? You're the main course, but you're so busy trying to be a side dish, you can't see the entrées through the appetizers."
I'm not so sure my "sandwich" is ho-hum, nor am I even sure what Tori's talking about. Sometimes it seems like she's speaking a language of her own. Other times, like now, though I may not totally understand her, I think the things she says sound profoundly genius.
She gets up from the chair, giving a thumbs-up to Roger's Bates Motel sign. "See you in J-Block," she tells me.
I nod, watching her clomp away in her humongous astronaut boots—like one of Waldo's clan walking across the moon.
#
It's after school, and Max is waiting by my locker as I come out of physics. He waves when he spots me.
"Hey," I say, dodging the mob of students en route to the exit doors.
"So, I've been thinking about the next meeting."
_"Next meeting?"_ My head fuzzes.
"PB&J."
"Oh, right," I say, fumbling with my padlock.
"Yeah, I was thinking that we could join forces with one of the other similar-interest clubs on campus to boost our visibility—like the Eco Warriors for an environmental project or Amnesty International for a human rights effort."
"That actually sounds pretty genius, but I've sort of gotten involved in another project and it's taking all of my time."
"So, wait, you're abandoning ship?"
"Not abandoning ship, just chartering a boat elsewhere."
"Can't you just stay onboard with me?" He smiles. "For the next thirty minutes or so? Because I'd really love to strategize, and ultimately change your mind. I have some great ideas."
"That's really sweet of you," I say, finally getting my locker open. "But I can't today."
"So, how about Saturday, around eight?"
"You want to strategize on a Saturday night?" I swap my books for my camera and jacket.
"No." He shakes his head. "I mean, Saturday night, around eight. There's a party."
"Hannah Hennelworth's," I say, connecting the dots.
"You know her?"
"I know _of_ her."
"Well, I was thinking that maybe we could go to her party together." He points back and forth between himself and me, like we're playing a game of charades. "It'd be good exposure for us—for PB&J, that is."
_"Max Terbador!"_ someone shouts—a boy on the hockey team—complete with a jerking fist.
"At what age can one legally apply for a name change?" Max asks.
"I believe that would be eighteen." I grin.
"It can't come soon enough."
"Hey, guys," Jeannie says, sneaking up behind us. She's all smiles, as if someone wedged a boomerang in her mouth. "What's going on?"
"Max was just telling me about a party this Saturday."
" _Really?_ Details, please," she chirps.
Her enthusiasm is mind-boggling, because super-serious/disses-parties-in-lieu-of-extra-credit-projects/in-bed-by-ten-unless-there's-a- _Nova_ -marathon _Jeannie_ is not exactly the chirping type.
"Are you interested?" I ask, unable to help gawking at the pinking of her cheeks.
"Why not?" She pushes her glasses up farther on her face—a nervous tic she developed in middle school, whilst dealing with the _B_ s (a group of girls whose names all began with _B_ who took pleasure in making her life miserable, i.e., taping coupons for acne cream to her locker, barking in her direction, and leaving dog biscuits on her desk). The joke's on the _B_ s now, however, because Jeannie is absolutely stunning—only she doesn't even know it.
"We could all go to the party," Max offers, ever the gentleman.
"Superific," she bursts.
"Great," Max says, focused on me. "I'll give you a call." He starts to walk away, accidentally colliding with Ms. Matherson, the gym teacher, as she transports an armful of Hula-Hoops to the gym.
Hoops go flying. Max scrambles to help her pick them up. Meanwhile, Jeannie and I turn away, pretending not to notice. Only once he walks away again do we burst into a fit of giggles.
"Okay, what's the deal?" I ask her. "You're totally crushing on Max, aren't you?"
"No way."
"Yes way. I mean, _seriously_? _Superific?_ "
_"What?"_ She shrugs. "I'm just trying to expand my social circle a bit."
"By going to some freshman wannabe's party?"
"Exactly. It's a _party_ , Day, so don't overanalyze it. Just have some fun. Is that really so hard?"
I can feel the smirk on my face. I can also smell BS from a mile away. "Let's table this discussion for now, shall we?"
"Happily," she agrees, already headed down the hallway.
We move out the exit doors and around to the back of the school. The assignment for my photography class is to capture a mood, and Jeannie has insisted on coming along.
I lead her to the trail behind the field house—the one that leads to Juniper Hill. It's narrow and rocky, making me wish I'd opted for boots over ballet flats.
"Does the mood you're trying to capture have something to do with misery?" Jeannie asks, picking a cobweb out of her hair.
"Is hiking really that bad?"
"In a word: yes."
From the very peak of the hill, the ocean is like the background of a canvas. "I'm thinking of getting a shot of a lone tree, with the ocean peeking through the branches, under a late-afternoon sky."
"And what mood would that capture?"
"Good question."
"You should've taken a picture of me getting my calc test back today. It would've conveyed pure loathing. I'll bet you anything that Mr. Bedrosian has devil horns hiding in that mass of 1960s curls on his head."
"And the devil tail?"
"Down his pant leg, naturally."
"You've obviously given this a lot of thought."
The smell of burning charcoal hangs in the air, making me miss summer. We continue up the hill, finally reaching the peak. The clouds look like cotton candy that's been pulled apart and dipped into salmon-pink paint. I take a bunch of shots—some of the sky and the ocean alone, a lot more of the sky and the ocean as a backdrop to an evergreen tree.
Jeannie sits down on a rock. She takes off her glasses and closes her eyes. Her hair blows back in the breeze, away from her face. I take the shot. My shutter clicks. "Anything mood-worthy yet?"
I squat down to take her picture, able to capture the pursing of her lips and the furrowing of her brow. I scoot down even lower, stretching out on the ground, eager to get an upward angle, noticing a tear running down her cheek. She looks sad and beautiful at the same time.
I take the shot. My shutter clicks again.
Jeannie opens her eyes and glares at me. "What do you think you're doing?"
"Capturing a mood, remember?"
"And which mood do you think I am?"
"Only you can say for sure."
"Dark, frustrated, gloomy, depressed. Take your pick."
"I'll take 'Gloomy for a thousand, Alex,'" I say, trying to cheer her up by playing _Jeopardy!_
"Today's the anniversary."
I move to sit beside her, racking my brain, wondering what she's referring to. "Josh's death," I say. The answer hits me like a truck.
Josh was Jeannie's older brother. He died three years ago while walking along the side of the road, hit by a car that had lost control during a rainstorm. It was thirty-five minutes before the Jaws of Life were able to pry him out from beneath the car. By that time he was dead.
"It's supposed to get easier, right?" she asks.
I wrap my arms around her, remembering summer four years ago, when Josh tried to teach us how to surf, and the winter after that when we all went snowboarding.
"I miss him," she says, breaking the embrace, voicing my very thoughts. "And what makes things worse...Josh was the wonder boy—good at everything, loved by everyone, turning whatever he touched into gold. And I know it sounds totally whiny—and I actually hate myself for saying it—but it's kind of hard to live in the shadow of your perfect dead brother." She looks at me again. Tears slide down her face.
My mind immediately flashes to my superhero parents. "You know, you're pretty _wonder-girl_ yourself."
"Whatever." She rolls her eyes.
"I mean it. You're one of the smartest people I know, with an Aretha Franklin voice, not to mention you're stylish, beautiful, fun—"
"Even if part of me wanted to believe those things were true, my heart tells another story." She wipes her eyes with her sleeve.
"Well, then I'll keep telling your heart...until the words finally stick."
"But they'll just be words. How can I ever make myself believe them when Josh is gone, when I keep trying to live up to his memory?"
"Okay, seriously? You could become the first female president and find the cure for cancer. You could end world hunger and stop global warming...but that still won't change the fact that Josh is gone and that you have to go on living."
"I know." She nods. "Logically, anyway."
I wrap my arms around her again, wishing I could take my own advice about living in other people's shadows. But I haven't figured that out yet either. For now— _for her_ —I'll just pretend that I have.
#
When I get home from school, the house is overwhelmingly desolate. I switch on some lights and click on the TV, trying to trick myself into believing that I'm not really alone. I also send out a couple of texts—one to Jeannie, including a picture of the two of us with Josh, standing at the top of Mount Snow during our ski trip. My other text is to Tori, looking for more details about the party this weekend (not that I even want to go).
I just want to feel less alone.
In the kitchen, I heat up some dinner for Julian, feeling anxiety bubble up in my gut, unable to help thinking about that one classmate who said that Julian used to talk about getting rid of his dad.
Of course there was also the teacher who stated that Julian had a gentle soul, and the friend who said that Julian had been his first go-to. But does either of those last two testimonials help ease the wad of tension burning beneath my ribs?
Unfortunately, no.
Still, I head out to the barn with my tape recorder, my list of questions, and my cell phone and pepper spray. Julian comes to the door. The waist of his pants has been gathered on one side, the slack wrapped with a rubber band.
"Hungry?" I ask, handing him a container filled with mac 'n' cheese, along with a plastic fork.
He tears off the lid, stabs the noodles, and shovels them into his mouth as if he hasn't eaten in days.
"I probably should've brought more."
"You don't have to bring me anything at all. I'm not some caged bird that you need to feed."
The comment feels like a slap across my face, heating up my cheeks. "You're free to leave whenever you want. Caged birds can't."
"You're right. Past tense: I _was_ a caged bird." He turns to clean off a couple of bales of hay and then sits down on one of them.
I sit down beside him, catching another glimpse of the pickax tattoo on his wrist. "And did that help you unlock the cage?"
He yanks down his sleeve. "It's not what you think."
"How do _you_ know what I think? Are you having a bad day?"
"Every day for me is bad."
"If you want I could come back another time."
"No. It's fine." He takes a deep breath. "Let's do this."
I press the RECORD button and place the tape player between us.
`ME: When you went to the beach on the weekend of May 4th and 5th, you mentioned that one of the surveillance cameras had been broken.`
`JULIAN: Right, one of the cameras in the parking lot.`
`ME: You said that the surveillance cameras picked you up on Sunday. Where did they spot you and when?`
`JULIAN: Coming back from my spot on the rocks.`
`ME: What time was that?`
`JULIAN: Around 4:40 maybe.`
`ME: Did you walk by the shower area?`
`JULIAN: No, I think I must've gone the other way—along the deck side, where people eat—because that's where the camera caught me.`
`ME: Do you always take two different routes to and from the rocks?`
`JULIAN: Which route I take depends on where my car is parked.`
`ME: Where did you park on Saturday versus Sunday?`
`JULIAN: On Saturday, I got a spot on the right side, by the entrance. On Sunday, I was way over on the opposite end of the lot, by the boardwalk.`
`ME: What time did you get to the beach on Sunday?`
`JULIAN: Maybe around ten or eleven in the morning.`
`ME: The morning after the bodies were found, correct?`
`JULIAN: Yes.`
`ME: Had the police come by then?`
`JULIAN: Yeah. I called them the night I found the bodies.`
`ME: And where did you stay that night?`
`JULIAN: Protective Services came for me, but since I don't have any relatives in this area, my friend Barry's mother convinced them to let me spend the night at her house. The following morning, Barry's mom made breakfast and was trying to get me to talk about stuff, but I just wanted to get away, so I went to the beach.`
`ME: Stuff, meaning your parents? And the details of what happened?`
`JULIAN: Yes.`
`ME: And did you talk to her about either?`
`JULIAN: No. I didn't want to. I was still too shocked about everything.`
`ME: What was your relationship like with your father?`
`JULIAN: Let's just say he wasn't the nicest guy to be around.`
`ME: Not nice because _he..._`
`JULIAN: Drank, had a temper, made my mom feel like crap most of the time.`
`ME: Why did he make her feel that way?`
`JULIAN: Because he resented her.`
`ME: _Because..._`
`JULIAN: It's a long story.`
`ME: We have plenty of time.`
`JULIAN:...`
`ME: Julian?`
`JULIAN: I used to have a brother—a twin. His name was Steven, and he died at five years old.`
`ME: Julian...I'm so sorry. I had no idea.`
`JULIAN: Yeah.`
`ME: How did he die?`
`JULIAN: Car accident.`
`ME: Did he get hit by a car?`
`JULIAN: No. He was in the car. I was too. Our mom was driving.`
`ME: And what happened?`
`JULIAN: She was angry. My dad hadn't come home when he said he would, so she had to bring us on her errands. The car lost control and slammed into a tree, on Steven's side.`
`ME: Did she hit a patch of ice?`
`JULIAN: No. Mostly she was just driving too fast. She'd swerved to avoid slamming into another car, but instead she slammed into a tree.`
`ME: Did help come right away?`
`JULIAN: It did. An ambulance, the police, people on the street...But it was all too late. Steven's death was instant.`
`ME: I'm so sorry.`
`JULIAN: I am too. It should've been me.`
`ME: How can you say that?`
`JULIAN: Steven and I'd been fighting about car seats. I liked the blue one, but he wanted it too. In the end, I won out, and Steven...`
`ME: Do you want to take a break?`
`JULIAN: No, it's okay.`
`ME: Did you and your mom get hurt?`
`JULIAN: Not physically.`
`ME: But emotionally.`
`JULIAN: Emotionally, everything just fell apart. I blamed myself. My parents blamed themselves. They both blamed each other for not making different choices.`
`ME: Do you remember what life was like _after_ Steven's death—how you all dealt with the loss?`
`JULIAN: My mom sunk into depression and my dad started drinking.`
`ME: And you?`
`JULIAN: I cried every night. I hated myself after that. I think my dad hated me too.`
`ME: I can't even imagine how hard that must've been.`
`JULIAN: Yeah, not exactly an ideal upbringing. Aside from my friend Barry, I never had any close friends—never wanted anyone to see what was going on inside my house.`
`ME: I'd almost think your parents would've been _extra_ protective of you after something like that happened—that they'd have been afraid of losing you too.`
`JULIAN: My mom shut down. Maybe she didn't want to get too close in case she somehow lost me too. My dad resented me for insisting on the blue car seat and then walking away without a scratch.`
`ME: How did you deal with his resentment?`
`JULIAN: I'm here, aren't I?`
`ME: Yes, but for what reason?`
`JULIAN: Because people think I killed my father—that I got so mad after finding my mother's body in the tub...`
`ME: Julian?`
`JULIAN:...`
`ME: The people that think you killed your father...what's their theory? How do they say the details of the crime went down?`
`JULIAN: Most of them think that I became so enraged, blaming my father for my mother's death—for driving her to suicide—that I killed him.`
`ME: What is that theory based on? Where is the proof?`
`JULIAN: I used to talk a lot of shit, telling friends that I _wanted_ to kill him. I didn't mean any of it for real. But imagine seeing your mom so depressed all of the time. Imagine hearing your father whittle her down—until she no longer spoke above a whisper or got out of bed, until she barely weighed ninety pounds and had razor marks on her wrists. I wish I could say that I didn't hate my father. But I did. I _do_. And I'll tell anyone who asks me the same.`
`ME: Still, talking about killing people isn't exactly proof.`
`JULIAN: Having a crappy alibi doesn't help the situation.`
`ME: I'm almost surprised your parents didn't get a divorce.`
`JULIAN: Why divorce when there's so much torture to be had?`
`ME: You said before that you think your mother is responsible for your father's death.`
`JULIAN: That's right. I think she'd probably been planning it for a while.`
`ME: What makes you say that?`
`JULIAN: She hated him more than anything. She hated the way he treated us, but she was always too broken to do anything about it. So, I think that finally, yeah...this was her way of making up for lost time.`
`ME: And then after she supposedly killed him?`
`JULIAN: I think she took a shitload of pills and drowned herself in the bath. I think she...`
`ME: Julian? Maybe we should take a break.`
I press STOP, trying to imagine what this must be like for him—having lost his parents, being accused of an unspeakable crime, unable to see his friends...."Is there anything I can do?" I ask him.
He peeks up at me. His face is red. His eyes look swollen. "You can tell me something about you now."
"About me?" I shift uneasily against the bale. A blade of hay pokes through my jeans, into my thigh, sending a hot, prickly sensation straight down my leg. "Like what?"
"Anything."
"Okay, well, my real name is _Sandra_ Day, rather than just Day. Our family name is Connor, which my parents took as an opportunity."
"To name you after a Supreme Court justice?"
"Not just _any_ justice—the _first female_."
"Except your last names aren't _exactly_ the same, right?"
"No." I sigh. "I'm missing the _O_."
"Pretty rough." He grimaces. "Missing vowels right out of the gate."
"Seriously." I smirk. "Being named after someone like that...it pretty much puts a curse on your whole life—like, there are all these expectations right out of the womb."
"Is that why you go by Day?"
I nod. "It adds a layer of distance."
"And how about all of that stuff you threw into the trash? Did it have anything to do with living up to those expectations?"
I grin, impressed that he gets it. "It was some meeting materials for a club at school—a social justice club, basically. My meager attempt to make a difference."
"Well, you've made a _big_ difference to me." His gaze makes a zigzag line from my eyes to my cheeks, landing on my mouth, causing my heart to stir.
"I should probably go," I say, feeling my face flash hot.
"Yeah," he says, getting up, averting his eyes, taking a couple of steps back. He replaces the lid on the mac 'n' cheese. "Thanks for the food and for listening to what I have to say."
I muster a polite smile, and then go for the door, part of me wanting to listen more, another part scared out of my mind that I've already heard too much, that I've gotten involved at all.
#
It's three in the morning and I've yet to fall asleep. My heart is racing. My skin won't stop sweating. The ceiling is like a giant movie screen, replaying the images inside my head: Julian and his brother in the backseat of a car; Julian crying; his mother screaming; her body floating in a tub.
It's all too much.
I'm sleeping too little.
Finally, around four, I grab a notebook and write stuff down.
`FACTS SO FAR`
`1. It's unclear whether Mrs. Roman's death occurred before or after Mr. Roman's.`
`2. Her body was found in the bathtub, with the water still running, assumed to have been a suicide because she'd taken a lot of pills. (Though it's also possible her overdose could've been accidental; i.e., perhaps Mrs. Roman didn't realize how many pills she was taking.)`
`3. According to Julian, Mrs. Roman had suicide scars on her wrists.`
`4. Mr. Roman was last seen in front of his house not long before his death.`
`5. It didn't appear as though anyone had broken into the family home on the day of Mr. Roman's murder.`
`6. According to Julian, he's the one who called the police when he found the bodies.`
`QUESTIONS`
`1. Had Mr. Roman just arrived home? Or was he home already? If the first is true, why didn't he call for help when he discovered his wife's body in the tub? If the second is true, why didn't he notice the running water? Surely there must've been water spilling onto the floor, seeping beneath the door crack (unless Mr. Roman was already dead by the time the water was an issue).`
`2. Was Julian really at the beach the whole time this was happening?`
`3. How many surveillance cameras are at Dover Beach? And where are they located?`
`4. Is it a coincidence that Julian happened to walk by a working surveillance camera on Sunday and by an area that didn't have any camera at all on Saturday?`
`5. Is Julian innocent?`
`6. Did Mrs. Roman murder her husband and then kill herself?`
`7. Did this crime have any other suspects? And, if so, who were they?`
I gaze toward the window, unable to stop obsessing over the timing of it all—Mr. Roman's murder occurring on the same day as his wife's alleged suicide...Why weren't investigators able to figure out the order of their deaths?
I do a quick Google search with the words "autopsy" and "time of death estimation." There are numerous sites devoted to crime-scene forensics. I click on one of them. It seems there are several factors involved in determining the time of death, including body temperature, rigor mortis, and the cessation of organs.
But what about when a body is immersed in water? According to Forensic Fred, self-proclaimed _CSI_ fanatic, if the tub water is warm it might quicken the cessation of organ function while also speeding up rigor mortis. On the flip side, if the temperature's cold, those same reactions might be slowed down. I'm assuming the water in the tub was warm—at least initially, until the water in the heater emptied.
But what if it wasn't?
I get up and pace back and forth, the questions bopping around inside my brain like an annoying pinball game. I really need to sleep. I have a history test tomorrow.
The blare of fire trucks nearby fills the loud silence. I wonder if Julian hears it too. I look toward the window of the barn, willing to wager a bet, desperate to ask him the one obvious question that's been raging inside my brain. How else will I ever be able to get any sleep?
_Tuesday, October 20_
_Morning_
_I woke up, all out of breath, to the screeching of sirens. It was dark out. Late night? Early morning?_
_I got up and stumbled across the barn, accidentally bumping into the mower, wishing I had a flashlight. I went to peek out the window and spotted Day._
_She was standing in front of her bedroom window, staring in my direction. The lights were on in her room. I backed away and placed my hand over my chest, able to feel the pulsating beat._
_What the hell am I doing? Why the hell am I staying? I mean, yes, I still have unfinished business, but why aren't I doing it?_
_Day got up and swung open the door to her room. The light downstairs flicked on. She was in the kitchen, grabbing something from behind the door. The porch light went on. The back door opened._
_Standing on the porch, she clicked on her flashlight. I moved to the door, wrapped my fingers around the handle, and held my breath, fearing she was coming to see me, half-hoping she was coming to see me._
_There was a light rap on the door. I edged it open._
_Day was there. And I immediately got that feeling: a fluttering in my stomach, a tightening in my chest like I suddenly couldn't breathe. I took a mental step back, trying to get a grip, wondering how the hell this happened. It had to change. I needed to go._
_"I couldn't sleep," she said. "Your case has been spinning around inside my head—"_
_"And?"_
_"And are you really, truly innocent?"_
_I closed my eyes, flashing back to being five years old, sitting on the floor of the living room—in my fuzzy red pajamas, on the dark blue rug—playing with my Matchbox cars while my father yelled at my mother in the kitchen._
_"Did you do it on purpose?" he snapped at her. "Was the accident part of some scheme to get me back for coming home late? Did you even bother to check the kids' seat belts?"_
_Mom sunk down against the cabinets and cried like I'd never heard before—a deep-throated wail, like nothing that sounded human._
_"Julian?" There was a concerned look on Day's face: parted lips, scrunched brow._
_What was the question?_
_"Did you do it?" she asked; the very same words my father used._
_I want to tell her I did. I want to make her hate me. "That's the hard part," I said, instead, "because who would ever answer yes to a crime like that? And yet, at the same time, you don't even know me. You have no real reason to believe me if I answer no."_
_"What if I told you that I don't care if the answer's no."_
_" Then who'd be lying?"_
_"Are you guilty?" she asked, for the third time._
_I clenched my teeth, still able to picture my mom, the last time I saw her, lying in the bathtub with a dead stare in her eyes. "No." I shook my head._
_She twitched from the cold, wrapping the coat tightly around her. "I'm trusting that's the truth."_
_"And I'm trusting you won't turn me in."_
_If only that made us even._
#
After school the following day, Tori picks up Jeannie and me, having scored her mom's car for the week.
"Is your mom feeling extra charitable or something?" Jeannie asks, peeling an ice-cream wrapper off the seat.
"No, she's just feeling extra guilty."
"Guilty _for_..." I open the window a crack. The interior smells like fuzzy cheese.
"Sucking up my life, basically." Tori puts the car in drive and pulls out of the parking lot, but instead of turning left toward home, she merges right, slamming on the accelerator.
Jeannie flips the sun visor down to gawk at me in the mirror. Her expression—bulging eyes, raised brows—matches my thoughts exactly.
"You need to slow down," I insist.
Tori blows out a raspberry, denoting her disagreement, but thankfully she eases up on the accelerator, so that Jeannie and I can breathe. "Wouldn't it be great if we could Wite-Out entire chunks of our life?" she asks. "Like, if the liquid inside that tiny white wonder bottle could erase all of our screwups and annoyances?"
"Would that include facial protrusions?" Jeannie lifts her glasses to run her finger over the nonexistent bump on her nose.
I edge forward in my seat, placing my hand on Tori's headrest. "What would you Wite-Out?"
"Only the fact that my mother is preggers."
Jeannie's mouth gapes open. "You're joking."
"No joke. Sixteen weeks. And here I thought Mom's recent rolls were the product of too many Mr. Goodbars."
"But instead they're the product of your dad's good bar?" Jeannie asks.
An image of Tori's dad immediately pops into my mind: beer belly, suspenders, tiny round glasses. He's basically a darker-haired version of Santa Claus; even Tori calls him that.
"Okay, um, _ew_ ," Jeannie says, once again reading my mind. "Are you sure she's pregnant and not just bloated?"
"Definitely sure. I found the pee stick in the garbage. Two lines, unmistakable."
"And this sucks up your life, _because_...?" Jeannie asks.
"Because Santa isn't the father."
"Pull over," Jeannie demands.
Tori does as told, coming to a full stop at the side of the road—ironically, outside Millie's Maternity. She puts the car in park and rests her head against the steering wheel. "Do you guys remember a few weeks ago, when I went home during C-Block to get my history paper? I saw them. That is, I walked in on them... _together_."
_"Ew,"_ Jeannie repeats.
"Wait, you saw _who_?" I ask.
"My mother and Hugo the electrician. Evidently he'd been coming over to screw more than just her bulbs." Tori lifts her head from the wheel. "It's like a cheesy Lifetime movie, except for the fact that I have no idea how this ends. She's keeping the baby, by the way, even though she and the baby-daddy have broken up."
"Does your dad know?" I ask.
She nods. "He knows everything—about the pregnancy and the fact that the baby isn't his."
_"And?"_ I persist.
"And how does he feel about the fact that my mom was playing hide the Mr. Goodbar with the man who lights up her life— _literally_?" Tori asks.
"Okay," I say.
"Miraculously, he's already forgiven her. And P.S., he's excited about the baby. But you know Santa. He's overly generous, always merry to trim her tree and jingle her bell."
"Okay, I'm seriously going to yack." Jeannie rolls down her window.
"Can we go get double-fudge lattes now?" Tori asks.
"We can get anything you want," Jeannie says.
"But only if you let me pay," I insist, remembering Dad's money in my wallet.
Tori gives us the thumbs-up and begins on the road again. We pass through the cities of Marshton and Wallington, finally crossing into Decker, Julian's hometown.
I already know where we're headed. Tori's favorite coffee shop is a place called the Pissy Ragdoll. Its logo is a Raggedy Ann–looking doll giving the middle finger.
We pull up in front and go inside. The place is frequented by an eclectic mix of hipsters, drama rats, emos, and artsy types. There's a huge bulletin board that takes up the wall by the pickup counter. It's littered with postcards, posters, job ads, and moody quotes. We order our drinks and gravitate to the board, per usual. Someone's posted a bunch of illustrations—ink drawings of famous couples (John Lennon and Yoko Ono, Luke Skywalker and Princess Leia, Prince William and Princess Kate).
"Ken and Barbie," Tori cheers, looking somewhat like a Barbie doll herself (or at least the superhero version of one), complete with a hot-pink bodysuit that matches her hair, white ankle boots, and shimmery gold cuff bracelets. "I wish I had my own Ken right about now."
Jeannie rolls her eyes. "You need a Ken like I need a monkey on my head."
"Actually, a monkey _could_ come in handy to carry all of our drinks." Tori turns on her heel to get her Whiny Ragdoll but instead of coming back to join us, she heads in the direction of the gaggle of boys in the corner.
"So much for girl bonding," Jeannie says.
" _We_ can bond," I offer.
"Over French vocab, I hope. Quiz tomorrow, remember?"
"Right." I cringe, reminded of the history test I took today. Though, on barely three hours of sleep, it actually wasn't as terrible as I thought it'd be.
While Jeannie grabs her Funkin' Ragdoll (a mint-mocha latte), I move to the far end of the bulletin board, noticing a group of kids swarming a poster.
A tall girl nods to it. "I'm surprised they're using this photo. I mean, isn't that his yearbook picture? Shouldn't they be using a mug shot rather than a head shot?"
"Maybe that's the whole point," another girl says; she's dressed in soccer gear. "To nab our attention. Like, who's that hottie convict?" She laughs.
I peek between them. A picture of Julian's face sits beneath the word WANTED, sending a shockwave through my body.
"I can't believe he's still missing," Tall Girl says.
" _I_ can," a boy pipes up; his hair is as red as the Pissy Ragdoll's. "The cops in this town are a joke. And the guards at the juvie? Useless as decaf. Isn't this, like, the third breakout this year?"
Julian looks so different in the poster. His face is fuller. His hair's much shorter. His eyes appear less tired. But still I'm able to recognize his smile: the curious grin that curls up the side of his face.
"I actually think it's the fourth breakout," Tall Girl says. "At least that's what my dad told me."
"I'm glad Julian got out," Soccer Girl says. "I mean, he never really talked much—at least not in my bio class—but he always did his work and stuff."
"He was always writing in his notebook," the red-haired boy says. "Probably plotting out his crime."
"I'll bet he was really sweet," Soccer Girl says.
"Sweet for an ax murderer maybe." A girl with jet-black curlicues uses a plastic knife as a makeshift ax to chop through the air. "I heard he used his bare hands."
"His father suffered a blunt-force trauma to the head," a guy with a spiked faux-hawk says.
"Are you suddenly the authority on Julian's case?" Curlicue goes to take a sip of her large iced coffee, but the straw misses her mouth and shoots up her nostril.
"Wait, didn't Mrs. Roman have _some secret ex-lover_?" Soccer Girl makes her voice go sexy-sultry.
"Holy shit," Faux-hawk says, checking his watch. "I have to go."
"So do I." Soccer Girl looks up at the clock. "My shift starts in ten minutes, and I still have to change." She pulls a hat from her bag. The café's pissy ragdoll sits on the visor, giving me the finger.
The group quickly disperses, as if I suddenly smell like the inside of Tori's car.
"I guess _you_ know how to clear out a room," Jeannie says, standing by my side now. She hands me my drink. "Who's the guy?"
At first I assume she's talking about Faux-hawk, but then she moves closer to the poster of Julian.
"He looks so familiar," she says. "Do we know him?"
"That's the guy," I tell her. "Julian Roman."
She angles closer to get a better look. "The bike-path-stalking-convenience-store-daddy-murderer? I totally recognize him from the news."
" _Alleged_ daddy-murderer," I say, correcting her.
"Where's Tori, by the way?"
"There." I nod to the cushy chairs in the corner of the café. Tori's sitting with a couple of Jimi Hendrix look-alikes. "I guess somebody's feeling better."
"I guess somebody wants a distraction."
"Nothing wrong with that," I say, suddenly eager for a distraction too. "So, how about that French vocab?"
"Right this way, _mon amie_." Jeannie taps her Funkin' Ragdoll against my Dolly Latte and then leads me to her table.
#
Before we head back to town, I ask Tori if we can make a pit stop at Dover Beach.
"Because you're looking to freeze your ass off?" She nods to the temperature gauge on the dashboard. "It's forty-seven degrees."
"More like because I want to check out the surveillance cameras."
"Planning something shady?" She tsk-tsks. "If so, I'd pick something a little less conspicuous than a beach."
"Like a library reference room or something?" Jeannie laughs.
"It's sort of a long story," I tell them.
"And does the premise have anything to do with a certain juvenile-detention-center escapee?" Jeannie peeks at me in the visor mirror.
"Am I that transparent?"
"Like window glass." She yawns.
"It was those kids," I tell her. "In the coffee shop. They were talking about Julian's case. His alibi was a girl who originally said she saw him at Dover Beach on Saturday, but the surveillance cameras only peg him there on Sunday."
"I seriously don't even understand why you care," Jeannie says.
"Because I'm interested in his case," I remind her. Why is the idea of that such a mystery to people? "I want to make sure that his arrest was justified."
"And how do you propose to do that? Interview key players? Ask to see the surveillance tape? Take a crash course in forensics?" Jeannie snickers. "Who has that kind of time, not to mention the resources?"
"We're here," Tori declares, pulling the plug on our conversation.
The car rocks from side to side as we drive onto the gravel lot. Things look vacant without the summer traffic. Sully's Snack Bar is closed. All of the picnic tables have been put away.
"I'll just be a second." I grab my camera from my bag and get out. The snack bar's ordering and pickup windows are boarded up for the season. A surveillance camera points down at them from the corner of the building. I take a snapshot of it, remembering how Julian mentioned bumping into Ariana by the showers.
I move around the corner. The showers are in open view, on a platform, under a wide overhang. There's no surveillance camera anywhere, but then why would there be? Who'd shower if they knew they were being videotaped?
I take photos of the shower area anyway, trying to picture what the scene looked like: Julian had just arrived after mowing his neighbor's lawn. It was around noon. He said he parked his car on the right, by the entrance, and then walked on this side of the building, which makes perfect sense. He wouldn't have walked around to the other side. This route would've been more direct.
There's another surveillance camera in the corner of the building, but it's pointed at the deck area, where people eat. I take a photo of it, figuring it must've been the camera that caught Julian on Sunday, when he parked on the opposite side of the lot.
I take photos of the beach, as well as the rocks to the far right, where Julian said he liked to sit. The rocks form a mountain of sorts—about as tall as a one-story house. There are also a few flat slabs, and a couple of alcoves where one could find shade. But there are no cameras out that way.
A flagpole sits a few yards from the deck. There's a surveillance camera attached to it. More cameras point down from poles along the boardwalk, to the left. I take photos of all of them, especially the one in the far corner of the parking lot. According to Julian, that's the camera that was broken. But why would that even have mattered for him if he'd parked by the entrance like he said on Saturday? And if the camera by the deck caught him on Sunday...
I head back to the car, my mind whirling with questions.
"You're seriously researching this case, aren't you?" Jeannie turns in her seat to gawk at me.
"Um, were you not conscious for the last twenty minutes?" Tori asks her. "I'd say the answer's a big fat yes."
"It _is_ a big fat yes," I admit.
"Because you really think the police screwed up?"
"What I think is that the published details don't add up, and so I'd like to find more facts. If it ends up being a waste of my time, so be it—at least I'll know."
_"It's never a waste of time if you learned something in the process,"_ Tori preaches.
"Reading your mom's self-help books again?" I ask her.
"I know. I should stop. Those books are obviously full of crap. My mother wouldn't be boinking other guys if her life were so evolved."
Jeannie shudders once again.
#
It isn't until after five that Tori pulls up in front of my house, after having dropped Jeannie off at home.
I give her a hug. "Call me for anything, okay?"
"Does anything include adoption?"
"You want this new baby to be adopted?"
"No, I want _myself_ to be adopted."
"By _my_ parents?"
She puckers her lips in thought. "Okay, maybe not. They'll sense my mediocrity before the papers are even signed."
"Are you kidding, my parents love you": the truth. Another truth: my mom has said on more than one occasion that Tori is very sweet, but that she's also as flighty as an airport. "Call me, okay?" I blow her a kiss and step out of the car.
As usual, the house is empty. At least when my parents were together, they made it home for dinner, but now there's really no point. I'm sixteen, old enough to eat by myself and keep busy with my studies.
In other words, I'm pointless.
In the kitchen, I load up a bag of food, wondering how long it's going to take my mom to notice that our groceries are evaporating faster than beer at a fraternity house. I also fill a box with more donation clothes and bathroom essentials. Arms full, I take everything out to the barn and rap lightly on the door.
Julian opens it up.
"Hey." I smile.
He smiles back, but I can tell he doesn't want to; I can see the resistance in the tightening of his lips.
He takes the box and peeks inside, plucking out the pair of scissors I packed. "This is very trusting of you."
"If you really wanted to hurt me, you'd have done it by now." I glance at my dad's toolboxes. They're filled with enough sharp objects to stock a hardware store.
"How do you know for sure?"
I _don't_ know for sure. "Do you want this stuff or not?" I ask, pretending to be tougher than I am.
He turns away, sets the box down, and picks up the hand mirror I packed him. "Wow," he says, looking at his reflection.
"Wow... _different_?"
"Wolflike."
"I actually saw a picture of you recently, _pre–_ Teen Wolf."
He looks up from the mirror. "Online?"
"On a poster, at a coffee shop in Decker—"
"The Pissy Ragdoll?"
"That's the one." I grin.
"Was the picture sitting underneath the word WANTED?"
"Being wanted isn't such a bad thing," I say, trying to be funny, but quickly realizing how wrong it sounds.
Julian nods, glancing at my mouth before turning away again.
"Some of your classmates were there," I segue. "A boy with red hair, a girl who plays soccer...There was also a really tall girl and some guy with a faux-hawk."
"And what were they saying?"
"It seems you have at least a couple of people in your corner: The girl who plays soccer and the boy with the faux-hawk...I'm pretty sure they think you're innocent."
"And the others?" Julian moves to sit on a bale of hay.
I sit down beside him and pull the tape recorder from my pocket. "There's actually something else I wanted to talk to you about."
He looks down at the tape recorder, but he doesn't make a comment, and so I push RECORD.
`ME: Someone at the coffee shop mentioned your mother might've been seeing someone else.`
`JULIAN: Misty said that, right?`
`ME: I don't know anyone's name.`
`JULIAN: The girl with straight dark hair, dressed in soccer gear. She also works at the coffee shop.`
`ME: Yes, that's the one. Why would she say that? How would she know?`
`JULIAN: Because Misty's friend used to ride at that guy's ranch.`
`ME: That guy?`
`JULIAN: The one my mom used to cheat with. He owns a horse ranch in Brimsfield. Their relationship happened a long time ago. I'm surprised Misty's still talking about it.`
`ME: How did _you_ know about your mom's relationship?`
`JULIAN: I remember coming home and seeing a truck parked in front of our house. At first I thought it was part of a surprise for me. The sign on the door said Hayden's Horse Ranch, and I'd always wanted to try riding. I was around eight or nine at the time.`
`ME: But it wasn't part of a surprise...`
`JULIAN: My mom and that guy were kissing inside the truck. They didn't see me coming.`
`ME: How long did their relationship last?`
`JULIAN: Not long—maybe a couple of months.`
`ME: How do you know it didn't last longer than that?`
`JULIAN: That's what my mother told me.`
`ME: Did your dad know about the relationship?`
`JULIAN: No.`
`ME: So it's possible that your mom and this guy could've still been seeing each other.`
`JULIAN: I doubt it.`
`ME: But it's possible.`
`JULIAN:...`
`ME: Was he questioned at all—this ranch guy, I mean?`
`JULIAN: I don't know.`
`ME: Did the police ever talk to you about him?`
`JULIAN: No.`
I press STOP. "You need a good lawyer—someone who's going to ask these questions and interview the right people."
"No lawyer would be able to help me unless I turned myself in."
"Maybe that's not such a bad idea."
"I thought _you_ wanted to help me."
"I do. It's just...this is way too important to screw up."
"So don't screw up."
"No pressure or anything." I take a deep breath and let it filter out slowly. "Can you talk about your grand plan?"
"My _grand plan_?" His face is a giant question mark.
"You escaped from juvie, laid low, found my barn, and got sick. But then what?"
"Then I met you."
"But what if you hadn't? What were you planning to do? Where were you planning to go?"
He bites his lip, mulling the question over. Is it possible that he had no plan—that he was just taking things day by day? Was the juvenile detention center really that awful?
"If I'm going to help you, you have to be honest with me—about your planning and your parents, about what happened at home, and everything that's going on in your brain."
He's not even looking at me now. He's angled away, facing the wall. I reach out to touch his forearm, and suddenly everything else stops: my babbling, his lip-chewing, the sound of hammering outside...
Julian's eyes lock on my hand. "This is all kind of new to me." His voice is fragile—like it could shatter with just the right words.
"What is?"
He pulls his arm away, putting an invisible wall between us. "You really need to go." He gets up and goes for the door.
"Tell me first."
_"Go!"_ he shouts.
His tone cuts through my core. A chill runs down my spine.
I get up and wrap my hand around the pepper spray in my pocket. "You don't scare me," I lie.
His hand balls into a fist, like he wants to strike out. "You _should_ be scared. You should go home and forget you ever met me."
I move closer, just a few feet from him now. "I already am home. This is _my_ barn. And I don't have to go anywhere."
He opens the door a crack, as if about to leave, then shuts it instead and turns to face me. His jaw is stiff. His eyes look red.
I position my finger over the nozzle of the pepper spray, just in case. "You won't hurt me," I say, nodding to his fists; both of them are clenched now.
"How do you know?"
"Because you're not a monster."
_"How do you know?"_
I take a step closer, feeling my insides shake. He's shaking too. Maybe it's because he's holding himself back. Or could it rather be that he's just as scared as I am?
"Don't you have anything better to do?" he asks, after several moments.
"Like what?"
"Like being with your boyfriend."
I maintain a poker face, wondering why he's asking. Could it possibly be that he saw me with Max? My gut reaction is to correct him, but I keep silent instead, because he doesn't need to know.
"What did you mean before," I ask, "when you said that this is all kind of new to you?"
"I meant this. You. _Us_. Talking to each other, that is." He peers over his shoulder, as if there's anything there to look at besides a stone-cold wall. "Aside from my one friend, I never really told anybody anything. I just wrote stuff down."
"Journals are great"—I take another step—"but they can't replace real people, real relationships...those we can trust."
"They can when there's so much to hide." His gaze roams all around the room—at the toolboxes, the mowers, the ceiling, and Dad's golf stuff—except at me.
"I really want to help you," I say, eager for him to hear the words again, to know he has someone in his corner—for now at least, until I have reason not to be.
_Tuesday, October 20_
_Evening_
_Day put her hand on my forearm, and I don't know what it was, but I totally lost my shit. My head went spinny and my heart started to race like I'd just run a marathon. I bolted for the door, but I couldn't bring myself to go, and she wouldn't leave._
_Finally, I searched the room for something to distract myself, digging back into the box she brought. I took out a comb. I hadn't seen one in weeks._
_"I thought you might want to spruce up a bit," Day said. "I mean, no big deal—just if you want..."_
_I attempted to run the comb through my hair—to show her I was so far beyond sprucing. As expected, it got stuck._
_"I actually have a trick for that." Day grabbed a jar from the box. The next thing I knew, she was sitting me down, standing behind me, spreading peanut butter on my hair._
_"You really don't have to do this."_
_She maneuvered the comb free, then unscrewed the cap to one of my water bottles. Water spilled over my head like a baptism. She washed my hair next. The shampoo smelled like strawberries and felt like an egg yolk. She massaged it through, scrubbing every inch of my scalp._
_"I can probably handle things from here," I said, feeling ridiculously self-conscious._
_She rinsed my hair again, and then started to comb it once more. This time it worked. No knots. Smooth sailing. She grabbed the pair of scissors. "Would you like a cut too?"_
_I knew that she should go, and part of me really wanted her to. But another part would've sat for an entire head shave if it meant spending more time with her. I watched as chunks of my hair fell to the floor._
_"This is going to be great," she said, angling the scissors around my ears and clipping strands from in front of my eyes._
_Several minutes later, she scooted down in front of me. Sitting between my knees, she pulled at the ends of my hair, checking to make sure that the length was even. In doing so, she accidentally bumped her hip against my leg, sending a wave of heat straight down my thigh._
_"Can you imagine?" She laughed. "A lopsided frizzball...It was pretty hilarious."_
_I pretended to be listening—to know what she was talking about—but she lost me at the thigh bump. "Pretty funny," I said, trying to play along, unable to help staring at her lips. They were so completely distracting: the color of dark roses. The corners of her mouth turned upward as she pushed back my layers._
_"So, do you?" she asked._
_I opened my mouth to answer, but no words came out, because I didn't know which ones to use—words to describe a bad haircut I once got, or to explain why I had no idea what she was asking me._
_She continued to pick at my hair, moving strands forward and back, like I had anyplace to go._
_"I'm sure it's fine," I told her._
_Her fingers slid down the sides of my face. It was almost too much to handle—her attention, her touch._
_I wanted to stand up. I should've moved away. What the hell was I still doing here?_
_"Never trust a woman," my father used to tell me. "They'll mess with your head and take everything that's yours, including your every thought."_
_Her fingers stopped at the cut below my eye. "Where did you get this?" she asked._
_"When I left the detention center."_
_"When you escaped," she said to clarify, not letting me forget: I didn't just leave. I wasn't simply released._
_"When I escaped." I nodded. There was so much I wanted to tell her—so much she didn't know. "My face met a jagged piece of metal fencing."_
_"Lucky that it didn't meet your eye." She sat back on her heels. There was a weird expression on her face, like she was suddenly confused about something._
_"For the record, I don't really care if you screwed up my hair."_
_"It's just that you look really different."_
_"Different good?"_
_"Different_ different." _There was something else on her mind. "Here," she said, forcing the mirror into my hands._
_I peeked at my reflection, less than interested in my hair. I would've given almost anything to read her thoughts or to kiss those dark rose lips. "It's great," I said, noticing that it looked a lot like it had before my arrest—shaggy, just an inch or so past my ears, longish layers, and waved to the side. "Do you do this for a living?"_
_"If I did, I'd have to charge you." She got up from the floor. She smelled like the shampoo—like something I wanted to bottle up and wash all over me. "So, do you think you could give me some names?"_
_"Names?" I asked._
_"Yeah. The names of the people I should talk to about your case, or a list of the things you'd like me to check out. Think of me as your very own private investigator."_
_"Except once you start asking questions and probing into the case, people will find out who you are. And then figure out where I am."_
_"Not if we're smart about it." She looked at me, waiting for a response, so excited about the prospect of helping me and saving the day._
_I wanted to believe she could. But instead my dad's words continued to play in my mind's ear: "Don't trust 'em for a second. They'll promise you the moon, stab you in the back, and leave you more alone than ever."_
#
In my room, I curl up on my bed with a slice of blueberry pie, eager to feed this ache: this stirring sensation inside my heart, the weight of Julian's loneliness on top of my own. In one way, I wish I'd never even started this investigation—this view into a world that's so much darker than my own—but in another way, I wish I were back inside the barn, holding Julian's hand, and giving him back a bit of light.
I grab my phone, seeking some sort of connection, noticing a missed call from Max. I dial Tori instead.
"Forgot to ask," she says, in lieu of hello, "did you manage to score any numbers this afternoon? I was so focused on my own score sheet that I lost track of you and Jeannie."
"As if the Pissy Ragdoll is a score-sheet kind of place."
"Did I not spot you in a swarm of hunky hotness sipping something tall, dark, and delicious?"
"Um, _huh_?"
"I scored two numbers, for the record, thanks for asking."
I take another bite. "I was only eavesdropping on the swarm. I kind of wish now that I'd actually talked to it... _them_."
"Which has got to be one of the most overrated of pastimes, if you ask me—talking, that is."
"Maybe if our parents did more talking, there'd be less family drama going on."
"And maybe if our parents did _less_ talking, there'd be more lusting going on."
"Okay, that's gross."
"You're right, but I'm feeling a little bit better about things, FYI. Of course, the guys at the coffee shop helped. Bojo told me that he has six half siblings he's yet to meet—and those are just the ones he knows about."
"Bojo?"
"Remember this: Bojo equals boho."
"As in, from Bohemia?"
"As in free-thinking, unconventional, totally nonconforming."
I look at the receiver, suddenly wishing I'd called Jeannie instead. "Have you tried talking to your mom?" I ask, in an attempt to switch gears.
"Talking, overrated, remember? Though there was one thing that Bojo said that really hit home: the choices our parents make—that we all make, for that matter—have a distinct purpose that may not seem apparent on the surface."
"For the record, my head is officially spinning."
"This is Life School," she says. "And there are specific lessons we need to learn in this lifetime. And so we choose different paths, based on how we respond to those lessons, thus creating our own unique consequences."
"Are you sure Bojo didn't slip you a special brownie with that double-fudge latte?"
"My mother's decision to cheat on my dad is part of her journey," she says, ignoring me. "Hers, Santa's, the electrical baby-daddy's...and mine as well."
"How is it part of _your_ journey?"
"That's the best part, because I don't know yet. It'll be one of my many life's missions to figure it all out."
I lean back in bed, almost jealous of her newfound perspective—even though I don't quite get it. "You sound so evolved."
"Bojo is ah-maze," she says. "I just spent the last two hours on the phone with him."
"Even though talking is overrated?"
"I'm just _so_ glad I met him," she says, ignoring the comment. "And _see_ : our choice to go to the coffee shop after school...it was meant to be, because I met him."
And I got to eavesdrop on some of Julian's classmates.
"Bojo's father is the minister at this new-age ministry in Glenville," she says. "He invited me to an ice cream social Saturday night. I know what you're thinking. It sounds totally blue-haired-ladies-in-a-church-basement-playing-bingo-and-eating-sour-cream-and-onion-dip, right? But Bojo promises it'll be epic."
"And what about Hannah Hennelworth's 'It's-Saturday-let's-party' party, aka Operation Make Jarrod Koutsalakis Jealous?"
Tori lets out a sigh. "And how do you suppose I make him jealous if he's already taking someone else?"
As if the operation was my idea.
"Am I supposed to dress like a ho and flirt with every guy in his path?" she continues.
"Wasn't that the plan?"
"You really think I'm that shallow?"
I look at my phone, wondering if I'm on some hidden camera show, or if she's taping this conversation as a joke.
"Whatever, it doesn't matter." She lets out another sigh. "I no longer have time for cat-and-mouse games. What I need is a man who'll help me grow into a better person."
"Like Bojo."
"You totally get me, don't you?" I can hear the smile in her voice. "Not many people get me, you know."
"Go figure." I stuff my mouth with more pie.
_Tuesday, October 20_
_Night_
_I ran from juvie without ever looking back, cutting through the woods behind the facility, swiping branches and brush from in front of my eyes._
_A road was coming up. I could hear the swish of cars._
_I tripped over a low branch, falling on my face. Blood ran from my nose. A stick stabbed into my neck._
Swish. Swish. _Two cars whisked by. I got up, my back aching, and I continued to move forward, stopping just a few yards from the road. All was quiet. I crept a little closer. Three more cars went by before there was an empty road._
_I raced across, spotting a strip mall in the distance. Half of it looked abandoned. The other half consisted of a drugstore, a liquor store, and a twenty-four-hour market. There were two cars in the parking lot. It didn't appear that anyone was in them._
_The facility's siren screeched. I could feel it in my bones. Standing in open view, I didn't know what to do. Cross the street again? Go back into the woods? I looked at the strip of stores and then at the parked cars. Did I still remember how to hot-wire? But both cars looked too new for hot-wiring._
_Beyond the strip was another road. No houses. Not much traffic._
_The door of the liquor store swung open. I hurried behind the strip before the person saw me, spotting a Dumpster._
_I climbed inside without looking down, landing on a pile of bags—wet, plastic, shit-smelling, stomach-turning. Something stung my face. I touched the spot. Blood came away on my hand._
_Broken glass. An old wine bottle._
_Police sirens blared. I moved into the corner, burying myself with crap—boxes and bags and old, half-eaten food—flashing back to the day we buried Steven. In the cemetery, Mom was sitting in a chair. There weren't many people. My parents liked to keep things private—just a couple of cousins I'd never met and an aunt who lived 2,000 miles away._
_Dad didn't cry. He stood off to the side, watching as the casket was lowered into the ground. He hadn't spoken in days except to say that since Steven could no longer speak, we shouldn't either._
_I wanted to cry. But I wanted to be like Dad even more, and so I sucked in my tears and bit my shaking lip, watching as the priest sprinkled holy water._
_"He's buried now," Mom said later. "All gone."_
_I remember thinking that I liked to bury things too: string beans in my mashed potatoes, candy wrappers between the sofa cushions. Though those things never really went away._
_And neither did Steven._
#
There are more than fifty photos loaded up on my computer screen, old photos that I worked so hard to get, that capture vivid colors and/or play with things like natural and artificial light or macro-filters for magnification. They're all so perfectly staged: the product of countless hours spent planning how I'd wanted things to look.
But what do they really say? They don't show anything real. They only give the illusion of reality, which somehow feels dishonest.
I start to dump them into a folder labeled "Make Believe," just as the phone rings. It's Max.
"Hey," I answer.
"What are you up to?"
"Trying to get inspired, but failing miserably."
"Sounds like someone could use a little caffeinated motivation. Can I bring you a coffee from Java, the Hut?"
I look at the clock. It's just after seven. Should I let him?
"It's not that hard of a question," he says.
I wish that it weren't.
"Or is it?" he asks.
"How about a rain check?"
"Sure. Consider me your caffeine source."
"I'll remember that." I smile, really wishing this weren't so hard. I hate that I'm disappointing him. But I hate, even more, that we can't be friends rather than awkward acquaintances.
I hang up and take a snapshot of myself: I'm the picture of confusion. But still, as confused as I am, I'm suddenly feeling inspired. I pocket my tape recorder, run downstairs to grab the keys to Dad's old clunker (or, as he likes to call it, his priceless antique Scout), and pull out of the driveway.
The roads are quiet tonight, but Dad's antique is not. It rumbles every time I step on the accelerator and stalls when I hit the break.
I reach the Pissy Ragdoll in twenty-five minutes flat. Misty, aka Soccer Girl, is still here, cleaning one of the coffee machines.
My pulse quickens as I approach the front counter. Her back is to me as she continues to clean: _wipe, wipe, spray, repeat._ I push RECORD on the tape player and clear my throat.
"Can I help you?" She tosses her rag into the sink.
I look up at the menu, wondering if I should order something.
She turns to face me. "Hey, do I know you?"
"I was in here earlier," I say, glancing back at the poster of Julian on the wall. "And I heard you talking about Julian Roman."
Her expression shifts from neutral to annoyed in under a blink. _"And?"_
"And I'm a student at the university. We have a class called Crime and Caseload, where we delve into local and semi-local cases to pick them apart. My group is researching Julian's case."
An older guy—the manager maybe—passes behind her to fiddle with the espresso machine. Misty grabs another rag and pretends to wipe the counter. Meanwhile, the guy pours himself a fresh cup of coffee and moves out of eyeshot.
"To be honest, I don't really know Julian that well," she tells me.
"Okay, but do you think I could ask you a couple of questions anyway? I really need to do well on this project. I bombed the first assignment, and he gives us credit for effort."
She studies my face before peering over at some guy stocking the shelves. "Tag, can you cover for me?"
Tag nods, and Misty leads us to a table by the window. We take a seat, opposite each other.
"His case doesn't exactly look too good, does it?" she says.
"What makes you say that?"
"Well, the fact that he got arrested is a big tip-off. Word also has it that he hated his dad. Plus, his alibi didn't check out. And it seems there was so much he lied about."
"Like what?"
"Well, the lawn-mowing gig, for starters. He said he mowed the neighbors' lawn in the morning, but the owner of the house swears it was more like three in the afternoon, when Julian was supposed to be at the beach. And speaking of the beach...he claims he was there all day, but the cameras didn't catch him, even though it seems they caught everybody else. Then he said he came straight home to find the crime scene, but he wasn't wearing beach clothes. He was still dressed from mowing the lawn."
"I think I read somewhere that he didn't go to the beach to sit out or swim. It was May anyway—probably too cool for either. I heard he liked to sit, write, and read," I say.
"Still, wouldn't you change after mowing a lawn? Especially if you planned on spending the entire day at the beach?"
Honestly, I don't know.
"And then I heard that Julian went out somewhere after coming home from the beach...but I'm not sure if that was before or after his parents were found dead. I don't know." She shrugs. "It's all so confusing."
She's right. It is.
"What was your name, by the way?" she asks.
"Day," I say, but just as soon as I say it, I wish I could take it back.
" _Day_? Weird." She laughs. "Not that 'Misty' is totally normal. Anyway, the other sticky piece in all this is that the cameras _did_ place Julian at the beach on Sunday, the day after his parents both died, and if that's true, it's seriously messed up. I mean, who goes to the beach after that?"
"You don't think his mom could've done it?"
"Sure I do. I mean, that's the logical choice. Even though I didn't know him well, I've been going to school with Julian since kindergarten, and it seems that things in that family have gone from bad to worse. Mrs. Roman went from showing up at pickup and walking Julian home from school to hiding in her parked car and then to not showing up at all."
"Did you know Julian's brother?"
Her eyes widen with surprise. "Julian Roman had a brother?"
"Forget it." I wipe the words away by swatting through the air. "Why do you think Mrs. Roman got progressively worse over the years?"
Misty shrugs again. "People say that she was hard-core depressed—like in-need-of-a-warning-label depressed: Keep all sharp objects away."
"Is it true that she was seeing someone else?"
"I heard that too. And I think she probably was—the guy who owns the horse ranch in Brimsfield—but it had to have ended years ago. I mean, seriously?" She rolls her eyes toward the ceiling. "You don't even understand: The woman was a walking zombie. I bumped into her once at the supermarket; it was like the _Night of the Living Dead_ buys a loaf of bread and a pound of cheese. I can't even imagine what she was like at home."
"Did anyone ever question the guy from the horse ranch?"
" _What,_ am I FBI?"
"Misty?" Tag says, nodding toward the clock.
"I have to go. I still have a shitload to do before closing time." She stands from the table.
"One last question: Do you know how I can reach Ariana, the girl from the beach? Or that guy with the faux-hawk?"
"Barry," she says, correcting me. "You should definitely talk to him. He was, like, Julian's one and only. I think he'd love the idea of a college doing research on Julian's case."
"Misty?" the manager calls.
Misty takes out her phone. "What's your number? I'll share Ariana's contact info with you—she won't care. But Barry? I can see him getting all moody about it unless it's on his terms, you know. I could have him text you."
"Great." I rattle off my number.
"Good luck with your assignment."
"Thank you. So much." I stand from the table.
"And, hey, if you learn anything scandalous, you know where to find me." She turns away just as my cell phone vibrates with her text.
#
I round the corner of my street. My house is still dark. No one's home. I pull into the driveway, pressing the trigger that opens the garage, noticing a car parked in front of my house. Not either of my parents'.
A Jeep. Olive green. The light clicks on inside it, just as the door swings open.
Max steps out. And I don't know what it is. The deserted house? The empty sensation I feel after dipping deeper into Julian's world? Or just seeing Max's familiar face (a reminder of my own world)? But I couldn't be happier to find him here.
I lock the Scout away in the garage and begin walking toward him.
"Cool wheels."
"My dad's. He'd die if he knew I took it out."
"Don't tell me you went on an emergency coffee run without me."
My heart instantly clenches. "Were you following me?"
"Following you? No. That would make me a creep." He hands me an iced coffee; it's the perfect shade of mocha-brown. "I thought I'd surprise you. That's a medium brew, by the way, with two splashes of almond milk and a packet and a half of sugar."
"You remembered," I say, flashing back to last spring, when he took my order on a coffee run during finals week. "Thank you."
"No problem." He smiles.
I take a sip, trying to hold it all together—the details of Julian's case, the homework I've yet to finish, this paranoia I'm experiencing.
"Is everything okay?"
I can feel the emotion on my face, spreading like a fever across my cheeks. "Do you want to sit for a minute?"
"Definitely."
We take a seat on the front steps. The chilly autumn air blows against my skin, making me shiver—and the icy coffee isn't helping. "Have you ever felt as though you're in way over your head?" I ask him.
"Pretty much on a daily basis," he jokes. "Are we talking about the PB&J club?"
"A PB&J-club type of situation—well, kind of. In the same stratosphere, maybe."
"That sounds pretty clear." He smirks.
I know. It doesn't. "Let's just say that I'm trying to solve the situation single-handedly, and I'm feeling completely overwhelmed."
"Why? I'm happy to help." He bumps his shoulder against mine, causing the ice in my cup to rustle.
"I know."
"Then what?"
I stare downward, at my shoes. My fingertips are turning numb. "I really want to help this person, and part of me thought I could, but now I'm not so sure."
"Wait, you're not talking about that case again, are you? The guy from juvie?"
I press my eyes shut, feeling my insides cringe.
"Holy crap, you are."
"I just thought that I could help him."
"Help him _what_? You haven't talked to the guy, have you? Do you know where he is?"
"No," I lie. "It's just...we're talking about someone's entire future here. I wanted to make sure that his arrest was warranted, because from everything I've read, it seems he's being used as a scapegoat."
"Wow."
" _Wow_ , I'm totally crazy?"
" _Wow_ , you're pretty incredible."
I shake my head, holding back tears. "I'm not. Really. I actually feel like I'm failing him."
"Even though you don't even know the guy?"
I hold in a breath, wondering how well I _do_ know Julian.
"Well, honestly?" he continues. "If I were in that sort of dire situation, with my future depending on it, you'd be the person I'd want in my corner."
"For real?" I look up from my shoes.
"No doubt."
"You're really sweet, you know that?" I say, noticing once again how blue his eyes are—the color of sea glass.
"I'm not trying to be sweet. Ever since I've known you—"
"Since kindergarten," I remind him.
"Right, since kindergarten...you've always stood behind whatever you felt passionate about. Remember, in second grade, when Ms. Meany wanted us to collect caterpillars so that we could research their life cycles? You wrote a letter of complaint to PETA. None of us even knew what PETA was. Then, in sixth grade, you stood before the school committee asking if you could help raise money for healthier food initiatives, including educating the nutritional staff on the harmful effects of food additives, pesticides, and TMOs."
" _G_ MOs," I correct him.
"No one knew what you were talking about."
"And so they did nothing, including Ms. Meany, who ended up with five sacrificial caterpillars because, let's face it, re-creating the natural conditions of a monarch takes a whole lot more than branches, grass, and an overhead light."
"See that?"
_"What?"_ I sigh, feeling more defeated by the moment.
"You fight for what you think is right."
Correction: I've fought for what I thought would make my parents proud. "And you can see how far my fighting has gotten me."
"Probably a lot further than you think. Who knows what kind of ripple effect you've caused—all the people who've watched, and listened, and admired you over the years. Like me."
"Well, thanks," I say, thinking how everything he's saying...it's sort of how I've always felt about my parents, but never about myself.
"If there's anything I can do—with this situation or anything else—to help you, remember, I'm always here." He flashes me a shy smile.
I smile back, wishing I could be the person he thinks I am: the superheroic woman I've always aspired to be.
What would that feel like?
Even for just a moment?
He looks back up, and I venture to touch his hand.
"Day?" His face furrows in confusion.
I lean in closer and kiss his questions away. His fingers tangle up with mine as he pulls me toward him. I can sense how into the moment he is—much more of a kiss than I anticipated.
And still I don't feel superheroic at all.
I pull away, and our lips make an unpleasant sucking sound. "I'm really sorry," I tell him.
"Don't apologize," he says, running his hand along my forearm. His touch fills me with guilt, because I know he doesn't get it. And because I know that's my fault.
"I should probably go inside," I say, hating the sound of my voice. "I still have a bunch of homework."
His eyes remain locked on mine, probably trying to figure me out. Sandra Day Connor: the Queen of Mixed Messages. Finally, when he sees I really mean it, he backs away slightly, letting go of my forearm. "Sure." He tries to smile, but I can see the disappointment on his face, wriggled across his lips.
"But I'll see you tomorrow, okay?" I say, as if that's supposed to make everything better.
We stand from the steps. Max waits until I get the door unlocked and open—until I've inserted, turned, and extracted the key; twisted the knob; and pushed the door wide.
"Good night," I say.
There are so many questions on his parted lips, but he doesn't speak one of them, which somehow makes things worse.
I watch him walk away, toward his car. The night sky swallows him up. It also creeps inside my heart and tears a gaping hole.
_Tuesday, October 20_
_Night_
_I remember it was scorching out that day, because I was barefoot in the driveway, and the hot-top burned the bottoms of my feet. I could hear the cartoon show inside the house._ Little Ferngrow's Garden _—the part where the snail sings the song about moss._
_I was five years old._
_"Go stand in the grass where it's cool," Mom said._
_We'd been locked out of the house. I wasn't sure why, but I suspected it had something to do with Steven._
_"Come on, Juju," Mom said, taking my hand and bringing me into the backyard. "I want to show you something." She grabbed a couple of shovels from my sandbox, along with a few pieces of colored chalk._
_She led me to the picnic table and crawled beneath it. She started to dig a hole._
_"Help me out here, will you?" she asked._
_I joined her under the table and dug in with a shovel, happy to be playing this game with her. I loved my mother more than anything._
_She fished one of Dad's handkerchiefs from her pocket, and with the chalk, wrote a word across the fabric. "See that," she said, pointing to it. "It's the word PAIN. The_ p _makes the_ puh _sound_ , a-i _makes_ ay, _and the_ n _sounds like_ nnn. _Pain."_
_"Pain," I repeated. "Are you in pain?" I asked her._
_Her eyes looked sad. "If we bury our pain, we can make it go away." She dropped the handkerchief into the hole._
_"Just like we buried Steven."_
_"That's right," she said. "We can bury anything we like. Pretty neat, huh?" She smiled. "Now, it's your turn. What would you like to bury?"_
_I wanted to bury Steven's bed and storybooks. I thought that if they went away, maybe we could go back to the way things were before. But things never went back, no matter how much I buried._
_I started to distrust my mother then. She didn't protect me. She hadn't protected Steven. And she never protected herself. What kind of a mother is that?_
#
In my room, I grab my phone and look for Misty's text, eager to distract myself from the fact that Max and I kissed.
Our lips mashed.
Our tongues touched.
I close my eyes, able to picture the confusion on his face, almost unable to believe that it happened.
But it did.
And I did it.
I push RECORD on the tape player, set my phone to speaker mode, and press Ariana's number. The phone rings, and suddenly I realize that I have no idea what I'll say to her.
`ARIANA: Who's this?`
`ME: Is this Ariana?`
`ARIANA: It is, and _who's this?_`
`ME: I'm a student at Crest Hill State University.`
`ARIANA: Oh, right. Misty texted that you might call me.`
`ME: Is it okay if I ask you some questions about Julian Roman's case?`
`ARIANA: For the record, I'm _not_ friends with Julian, so I have no reason to try and cover for him or anything.`
`ME: Cover for him?`
`ARIANA: Like when I told the police that I saw him at the beach on Saturday rather than Sunday. To be honest, it was weird to even be talking to Julian Roman. He'd never said a word to me prior to that day.`
`ME: Do people think that you were lying about the day?`
`ARIANA: Apparently some people do.`
`ME: So, was it Saturday or Sunday?`
`ARIANA: That's obviously the problem. I mean, I originally thought it was Saturday. But when I really stopped to think about it, I was at the beach on both days. I remember because I was participating in this volleyball tournament thing that weekend. Anyway, when the police told me they caught Julian on surveillance video on Sunday, rather than Saturday, and then when they asked me if I was a hundred percent sure about the date, I couldn't help but second-guess myself. I mean, could it have been Sunday?`
`ME: I guess that's a good question.`
`ARIANA: I know, right?`
`ME: Why did you originally think it was Saturday?`
`ARIANA: Because I had a soccer game that day. I vaguely remember him asking me about it. I think we might've even laughed over the fact that I'd headed my soccer cleat—by accident, mind you—during the second half of the game.`
`ME: Did you tell that to the police?`
`ARIANA: I did, but then they kind of messed me all up, pointing out that we could've been talking about the soccer match from the day before. I couldn't really argue. I mean, my mind was scrambled. My heart was racing hard-core. I seriously hate talking to cops. But wait, I thought the whole alibi-at-the-beach thing wasn't even relevant anymore.`
`ME: Why wouldn't it be relevant?`
`ARIANA: Because when Julian came home from the beach, his father was still alive.`
`ME: Wait, _what_?`
`ARIANA: You don't know?`
`ME: Know what?`
`ARIANA: Okay, so I don't have all the details, but apparently a UPS guy delivered a package to the Romans' house sometime after Julian had gotten home from the beach that day. The guy overheard Julian and Mr. Roman fighting, and so he peeked into the window.`
`ME: And what did he see?`
`ARIANA: Julian and his dad, in the living room. I guess the fight was pretty loud. The UPS guy confirmed it happened on Saturday, by the way.`
`ME: So then Julian lied about coming home from the beach and finding his parents dead?`
`ARIANA: Who knows. I mean, maybe he lied. Or maybe, like me, he got mixed up, too. Let's face it: police aren't exactly the easiest people to talk to.`
`ME: How come I'm just hearing about this UPS guy now? Why wasn't he in any of the news reports?`
`ARIANA: Well, for one, I guess the guy came forward really late, which is why I initially got raked over the coals about when and where I saw Julian at the beach. And, for another, I don't think news reports disclose everything. I mean, right?`
`ME: Do _you_ think Julian did it?`
`ARIANA: I don't know. He never struck me as the killing type. But then again, like I said, I barely knew the guy.`
`ME: I really appreciate your talking to me.`
`ARIANA: So cool that your group is researching the case. You have my number if you think of anything else.`
I press STOP, suddenly realizing that, like Misty, Ariana has my number now too.
#
"We need to talk." It's after nine when I push past Julian into the barn.
"Did something happen?" he asks.
I turn to face him, noticing right away: smooth tan skin and chiseled jawline.
He shaved his face.
And changed his clothes.
Wearing a pair of jeans that hug his thighs, and a blue waffle shirt that clings to his chest, he looks undeniably beautiful.
I look away, trying to stay focused. "I read something," I utter. "A news report. It said that a UPS guy spotted you and your father fighting after you got home from the beach that day."
"That's right," he says, without the slightest flinch.
"So then you _didn't_ come home to find the bodies."
"I did. It's just..." He moves to sit down on a bale of hay. "I was so screwed up after coming home and finding them, I didn't think to mention going out for a drive in between. And then, when I did think to mention it, it was way too late."
"Hold on," I say, pulling the tape recorder from my pocket. I sit down beside him and push RECORD.
`ME: What do you mean "it was too late"?`
`JULIAN: I mean, I was too scared to correct myself, and so I just stuck to my original story.`
`ME: We need to back up. What time did you get home from the beach?`
`JULIAN: Probably around five.`
`ME: And what happened once you got there?`
`JULIAN: My dad and I got into a heated argument that ended up getting physical.`
`ME: What were you fighting about?"`
`JULIAN: I don't know.`
`ME: You don't remember?`
`JULIAN: What difference does it make?`
`ME: It could make a big difference in the scheme of things—what you and your dad were fighting about shortly before his death`....
`JULIAN:...`
`ME: Okay, so you got into an argument that became physical. What happened after that?`
`JULIAN: I took off before things got _really_ ugly. About an hour later, I came back. That's when I found his body—in the middle of the living room floor.`
`ME: Where did you go when you took off?`
`JULIAN: I went by Barry's house. No one was home, and so I just ended up driving around.`
`ME: Where was your mother during the fighting?`
`JULIAN: Honestly, I don't know. She didn't come out.`
`ME: Did you hear the bathtub water running?`
`JULIAN: Not that I can remember. I'm thinking she must've been asleep in her room.`
`ME: And she wouldn't have heard the fighting?`
`JULIAN: Not if she'd taken some of her sleeping pills.`
`ME: Is there a chance she wasn't home?`
`JULIAN: That would've been highly unlikely for her. She was almost always home.`
`ME: In which room were you and your father fighting?`
`JULIAN: It started in the kitchen and ended in the living room.`
`ME: Is the bathroom visible from both of those rooms?`
`JULIAN: Yes. It's a small house, but we keep the bathroom door closed for the most part.`
`ME: So, you came home from the beach, got into a fight with your dad, took off, returned an hour later, and found your father dead.`
`JULIAN: I found them both dead.`
`ME: And what did you do then?`
`JULIAN: I called the police. They came. I told them what happened, but I left out the part about the fighting.`
`ME: Intentionally?`
`JULIAN: No. To be honest, I was lucky to form sentences, never mind explain precisely the way things had played out. Days later, the story was out there, that I'd come home from the beach and found my parents dead. I didn't want to correct the story at that point. I didn't think I needed to either. I mean, what was the point? I wasn't guilty. But then that UPS guy came forward, and suddenly it looked like I'd lied.`
`ME: How come you never mentioned any of this when we were talking about your beach alibi?`
`JULIAN:...`
`ME: Lying by omission is still lying. Didn't you think I'd eventually find out?`
`JULIAN:...`
I press STOP and get up from the bale. "You lied to me."
"That's right. I did." He stares straight into my eyes. There isn't a hint of remorse on his face. "You should tell me to go."
"Is that what you really want?"
He stands, towering over me. "I lied to you. I've been accused of a heinous crime. How many more red flags do you need?"
"That doesn't answer my question." I turn away and go for the door.
At the same moment the words "please don't go" float in the air.
I stop, my hand wrapped around the door handle. "What did you say?" I swivel to face him.
"I said 'please just go.'"
My jaw tenses. "You're lying again."
"So, what are you going to do about it?"
I open the door a crack, able to feel him coming closer: a hot, tingly sensation that spreads like fire across my skin. The smell of burning leaves fills the dank space. "I really need some air."
"Nobody's stopping you."
I swallow hard, spotting his lip quiver. "Do you want to come too?"
"Is that what _you_ want?"
I nod and exit the barn. Julian follows me.
#
I lead Julian through the yard, toward the wooded conservation land that borders our property. With the town's permission, my dad made a path that cuts through the land and extends to a clearing. "Just stay on the wooden planks," I tell him, wishing I had a flashlight. Still, I know these woods by heart—every tree, rock, bough, and shrub.
With each step, it gets colder, darker, the moon blocked out by the tops of trees. I swipe a tangle of brush from in front of my eyes, able to hear Julian behind me—the snapping of twigs beneath his step, the sound of his breath blowing through the air.
My mind starts to wander, thinking how far we're getting from the house, remembering how the cell reception can be patchy in these woods.
Could I call someone if I needed to?
If I screamed, would anyone hear me?
I reach into my pocket for my phone. It slips from my grip and tumbles to the ground. I scurry to find it. Julian crouches down beside me. Together, we sift through fallen leaves and broken tree limbs, until Julian finally plucks the phone from a heap.
"Thank you," I say, taking it from his hand. His skin is rough and calloused. I imagine how it'd feel against my palm. "Maybe this wasn't such a good idea."
His forehead furrows. He looks surprised and disappointed at once.
My mouth trembles open, but I don't know what to say or how to explain this uneasiness I feel.
"You're right." He turns away so I can't see his face. "This wasn't the smartest."
I check my phone screen. There are still two bars. "No," I say, on second thought. "Let's keep going. There's something I want to show you." I begin on the path again, using my flashlight app to pave the way.
After a couple more minutes of walking, we reach a clearing with boulders set up in a circle. There's a fire pit in the center, dug into the earth, with rocks all around it.
I take a seat on one of the boulders. "Come on," I tell him, switching off the flashlight app and pointing up at the sky. "The moon followed us here." It shines directly over us like a spotlight of sorts.
Julian sits beside me.
"My dad created this space," I say. "We used to come up here as a family—like our own personal campground. We'd toast marshmallows and tell ghost stories or sing songs."
"Used to? Not anymore?"
"It's probably been a couple of years, sort of a reflection of how distant we've all become."
"Not toasting marshmallows at the fire pit hardly constitutes a family in distress."
"You're right," I say, feeling stupid for bringing it up. "It's just they're separated now. I kind of wish I'd seen it coming."
"I watched my parents' dysfunction for years and it didn't make me any better off."
"Were things always tough at home? Were there ever happy times?"
"Not after Steven's death."
I venture to touch his forearm, wishing I had something inspiring to say. But the truth is that I don't. I have nothing to compare. And I don't want to pretend I do.
"Sometimes I think that maybe Steven was the lucky one."
"Don't say that."
"It's true though. Maybe my father wouldn't have been so angry. Maybe my mom wouldn't have sunk into depression."
"And maybe it wouldn't have made a difference at all, at least not as far as your parents were concerned."
"But, for _me._ I wouldn't have felt the loss of Steven or the guilt of living. Or had to have put up with years of my parents' bullshit."
"Yes, but you also wouldn't be here right now," I say, thinking out loud, trying my hardest to understand.
"You're right. And being here is actually the only good that's come from all of this."
I look up at his face, checking to see if I heard him right, but he's staring off into space. "How come you didn't tell me that when you came home from the beach that day your father was still alive?"
"Because I really wanted your help, and I was afraid that if you knew I screwed up my original story, you wouldn't believe me about anything."
"What else are you keeping from me?"
"Just one thing: I meant what I said before. You should forget you ever met me."
"If you really feel that way, then why don't you leave?"
He swallows hard; I watch the motion in his neck. Finally, he meets my eyes again. "Because I can't bring myself to go."
I slide my hand down his arm and cradle my fingers around his palm, able to feel his warm, rough skin. Julian rubs his thumb along my wrist, and I can't help but wonder, how many nerve endings are in the hand? Five hundred? A thousand?
It's as if I can feel every last one.
We remain like this—holding hands—for several seconds without uttering a single sound. I gaze up at the sky. It's the perfect shade of midnight blue. There's a perfect number of stars in the sky. Everything about this moment feels perfectly amazing.
Except this is only the illusion of perfection.
Julian is on the run.
We have so much work to do.
I steal my hand away, putting an end to the moment. Julian responds by grabbing a long stick and poking at the fire pit, moving the brush around inside, as if there's an actual fire burning.
I look at his hand, wanting to touch it once again, imagining sitting on the boulder just in front of him, with my back pressed against his chest, and his breath heating the nape of my neck, while a fire crackles before us.
"Everything okay?" He's staring right at me.
My face is absolutely blazing. I look away, trying to refocus, and press the record button on the tape player in my pocket.
`ME: I read that there was some confusion about when you mowed your neighbor's lawn.`
`JULIAN: The neighbors say I did it in the afternoon on Saturday, but they weren't even home that day. They'd left the keys to the shed in the mailbox, as usual. I mowed the lawn in the morning.`
`ME: And you were still wearing your mowing clothes at the time the police arrived to the crime scene.`
`JULIAN: Yes, and they were drenched at that point, from lifting my mother's body out of the tub.`
`ME: You mentioned before that the fight with your dad started out verbal but ended up physical. Was that the norm for you two?`
`JULIAN: No.`
`ME: So, what _was_ the norm for you and your dad?`
`JULIAN:...`
`ME: _Julian?_`
`JULIAN: My father and I went our separate ways, for the most part.`
`ME: Can you look at me and say that?`
I press PAUSE. Still Julian doesn't move; he just keeps jabbing the stick at nothing.
_"Look at me,"_ I insist.
Finally he does. His eyes look broken, as if they could drown me in just one blink.
"I'm on your side as long as you're being honest with me."
"You just don't get it, do you?"
"No, I don't. Because you won't tell me."
He looks away again. "What do you want to know?"
"How is it for you...no longer having your parents around, I mean?"
"It's surreal," he whispers. "Like a nightmare that I can never wake up from. I wish I'd done more to protect my mom. Maybe then she'd still be alive."
"You can't blame yourself for your mother's death."
"Why can't I?" He shrugs. "I do it all the time."
"Do you feel she protected you?" I ask, fully aware the question's loaded.
But this time Julian doesn't deny the fact that he needed protection—that he and his father didn't simply go their separate ways.
"We used to bury stuff," he mutters. "My mom and I."
"What stuff? Bury it where?"
"My mom used to say that if we buried the stuff we didn't like—the stuff we wanted to go away—it would just disappear, the way Steven had. And so we'd crawl underneath the picnic table and bury all of our demons—symbols of the things that we wanted to go away. We'd bury them like a corpse."
"What were the things you buried?"
"Steven. I buried him more times than I'd like to admit. There must be at least a hundred slips of paper in the ground with his name, not to mention things of his that I was able to sneak away without my dad noticing: storybooks, race cars, mittens, a shoe. But still his memory never faded."
"And how did that affect you?"
"I could never live up to the person Steven would've been—could never do as well in school or at sports. I wasn't nearly as good-looking. I didn't run as fast, didn't speak as well."
"And all of this was according to your dad?"
He shrugs again. A stray tear rolls down his cheek. "After a while, I started to believe it too."
"Even though it's crazy. I mean, who knows what kind of person Steven would've become. And as for burying your problems...it doesn't work. They'll just show up someplace else."
"I know, but when I was younger I didn't. That's probably when my hope died."
I reach out to touch his arm, running my fingers over the pickax tattoo, noticing the goose bumps on his skin. "Is this to dig a hole—to bury what bothers you?"
He looks into my face; his eyes are raw and red. "You're the only one who knows," he says, in a voice that's just as broken.
"I really wish I'd known you back then."
"We should probably head back." Julian pulls away and continues to pick, prod, and poke at the invisible fire.
I scoot in closer and take his hand again, forcing him to drop the stick, able to feel him trembling against my touch.
"You don't know what you're doing," he says.
"I do." I weave my fingers through his, able to feel that charging sensation again, pulsing through my veins, sending tingles all over my skin. "You don't have to bury your pain anymore. You can tell it to me or whisper it to the stars."
Julian looks up at the sky, perhaps making a wish on a star. I hope that's what he's doing for real. I hope I've given him a reason to be optimistic, because, aside from love, I can't think of anything better.
_Tuesday, October 20_
_Late Night_
_Mom and I were at the park, sitting side by side on the swings. I tried to keep the same pace as her, but she kept making her swing go twisty._
_"Come on, Juju!" She leaned back, let her feet shoot up in the air. "Look at me!" she squealed. Her head tilted back. Her hair reached the ground._
_I flipped my legs up, but not like her. They didn't touch the chain. Mom rolled backward, fell to the ground. A stick punctured her forehead._
_"Are you okay?" I hopped off my swing._
_"Whoa," she said, looking out into space. Blood ran from her cut, but she didn't seem in pain. She touched her forehead. Her thumbs pressed against her temples; her hands reminded me of bird wings: frail, white, fluttering._
_"Can we go home?" I asked her._
_She looked at me, taking a moment to focus. The pills she'd started taking made it hard. They stole her away, brought her into a fog. I imagined that I looked cloudy._
_"We're not going home yet," she said. Her eyes were full of bloody vessels—"from lack of sleep," she told me._
_"Jackson's grandma died," I said. "He went to her funeral. Are we going to have a funeral for Steven?"_
_"We already buried Steven. He went bye-bye into the ground, remember?"_
_"But everyone just went home after that. There wasn't a party to say good-bye."_
_"Daddy and Mommy didn't want a party for our son's death. Daddy will be leaving for work in a half hour. We can go home then. But for now, let's just play." She got up. Her skirt was covered in leaves. The ends of her hair were dirty. She ran straight for the monkey bars._
_I followed after her, more confused than ever. Jackson had said that funerals were for saying good-bye. I wanted to say good-bye to Steven, more than I wanted presents on my birthday or Christmas to ever come again, because I thought that maybe that was the missing key, the reason Steven still had such a heavy presence in our house. Even though we'd buried him in the ground the year before, we'd never officially said good-bye. It was as if his corpse had somehow come home with us, filling our days with nothing but sadness, guilt, anger, and blame._
#
When I get back to the house, Mom is pacing the kitchen floor with her phone clenched in her hand.
"Hey," I say, shutting the door behind me, already able to sense the tension in the air.
"Where were you?" Her tone is sharp. "I've been texting you for the last hour."
I reach into my pocket for my phone, noticing the missed messages.
"A friend needed my help."
Her eyebrow shoots up, accusingly. "What friend? Tori? Jeannie?"
"A new friend."
Mom turns her back to go into the cupboard. I wonder if she notices how suddenly bare it is. "Hungry?" she asks, grabbing a couple boxes of cereal.
"Starving, actually."
She plucks the milk from the fridge and then sets us up at the kitchen table with bowls and spoons. I take a seat and pour myself some Alphabet Crunch.
Mom sits down across from me. "Is this new friend a boy?"
I add some milk to my bowl. "It's no one that you know. Just someone who needs my help."
"That's not exactly clear."
I know. It isn't. But, "I can't really talk about it."
Mom looks toward the door, the light just dawning on both of us. "Why did you come in through the back? You didn't walk home, did you? At this time of night?"
I stir my bowl of cereal, trying to spell the word _screwed_ with the cinnamon letters.
"Day?" Her eyes are wide, like fishbowls.
"I wouldn't have walked in the dark, especially not by myself. You've raised a smart girl. You have to trust me on that."
"You didn't use the bike path at this time of night, did you?"
I shake my head, almost able to see the wheels turning inside her head as she tries to figure things out—why I'm out so late, who this friend might be, why I came in through the back if I supposedly didn't walk. "Someone's in trouble," I say. "And they're trusting me with their problems—really personal stuff—so I really can't say anything about it."
She looks toward the window. I pray that Julian doesn't come out of the barn.
"Trouble, as in physical trouble?" she asks. "Is this person in an abusive situation?"
"Not anymore."
"I see." She chews her bottom lip, the wheels still turning.
"I could have lied," I remind her. "But I figured that you, of all people, would understand. I mean, you help people all the time and don't say much about it."
"Because sometimes I _can't_ say much about it. Sometimes there are confidentialities that I need to uphold."
"Exactly, so you understand."
"Are _you_ in trouble?"
"No." I take a bite.
"Are you sure? Would you even tell me?"
"I told you this, didn't I?"
She stirs her cereal, continuing to study my face. "The police were only recently here," she reminds me. "There's a boy on the loose."
"I know that."
"Do you? He's been accused of murdering his father."
"But maybe he isn't guilty. Maybe that's why he escaped from juvie."
"Could be, or he could've escaped juvie because he _is_ guilty, and because he knew he'd be convicted at a trial."
"Okay, why are we talking about this boy?" I grin.
" _You_ tell _me_." She stares at me—hard—without a single blink.
I shrug in lieu of answering, feeling my face burn, unsure what she's thinking. But I can tell she's unsure too.
"Well, I don't want you walking around by yourself at night," she continues. "I need to know where you are. And you shouldn't be out past nine without my permission."
I hold back from reminding her that she's not exactly available to ever give me that permission.
"You should've texted me," she says, as though reading my mind.
"You're right. I should've. I'm sorry I made you worry."
The tension in her face finally lifts. "Is there anything that I can do to help your friend, or to help _you_ help your friend?"
"Not at this point."
"But you'll let me know..."
"I will," I promise.
She continues to stare at me, as if there's writing all over my face.
I shift uneasily in my seat, trying to maintain a neutral expression. "Is something wrong?"
Her bowl of cereal is full; she's yet to take a bite. "I'm just really proud of you," she says.
The words hover in the air before finally landing on my head and seeping into my brain. "Really?" I ask, completely befuddled.
"Really." She smiles.
"Well, thanks." I say, thinking about the irony. After all my years of trying, it took something like this—something I truly care about—to finally get her attention. And, for once, I wasn't even trying at all.
#
At school the following day, I make a beeline for Max's homeroom, hoping to catch him before class. He's sitting at his desk, positioned away from the door. I go inside and sneak up behind him, noticing he's working on something for French.
"What's this?" I ask, going for humor over melodrama. "Did someone not get to finish all of his homework last night? Too busy delivering iced coffee to under-caffeinated damsels?"
"I'm pretty busy," he says, refusing to look up from his notes.
"I'm really sorry about last night," I tell him.
"It was no big deal."
"Well, to me it was." I sit down in the seat in front of him. "It's just...you were being so nice to me, telling me what a difference I make. I kind of just wanted to feel like that person."
"And you thought that kissing me could help?"
"I know. It was stupid."
Max looks up at me finally. "I'm busy," he says again. His face is stern, like he really wants me to go.
The response slices through my heart. I leave the room, feeling even worse than just moments ago—and so much worse than last night.
Later, at lunch, I tell Tori and Jeannie about the kiss: "I totally regret it," I say, focusing on Jeannie, suspecting how she feels about him.
"Wait," Tori says, dropping her fork mid-bite; a splattering of tomato sauce lands on the table with a splat. "You and Max Terbador exchanged actual tongue spit."
"Can we please refrain from using his full name while I'm trying to eat?" Jeannie asks.
"We did," I say, to answer Tori's question.
_"And?"_ Tori asks, her eyes gaping wide.
"And I feel terrible now," I say, still angled at Jeannie. "I mean, Max has got to be one of the sweetest guys I know."
"And you just stomped on his heart." Tori tsk-tsks.
"Thanks. I feel so much better now." I feed my funk with a bite of brownie.
"How was the kiss, at least?" Tori asks. "On a scale of one to thigh-quivering, that is."
"Honestly, maybe a three." I grimace. "But it wasn't his fault. There just wasn't any spark."
"Well, then why did you kiss him in the first place?" Jeannie bites.
"Part temporary insanity?" I tell her. "Another part curiosity?"
"A third part general horniness?" Tori laughs.
I roll my eyes. "The kiss had nothing to do with being horny."
"Maybe that's your problem." Tori points at me with her fork.
"Okay, so I still don't get why you kissed him," Jeannie says.
"Is it terrible to say that maybe part of me _wanted_ to feel something?"
"Which part?" Tori winks, revealing an orange-and-yellow striped eyelid that matches her scarf.
I'm tempted to ask who her look du jour is inspired by, especially since she's also wearing a navy-blue jumpsuit and a super-high faux-ponytail (that matches her pink hair). She looks a little like Belda Bubble from the Cartoon Channel, a superhero girl who fights crime with her bubblegum.
"That's not what I mean." I sigh.
"What were the two of you even doing together in the first place?" Jeannie asks. "And what activities and/or dialogue transpired _pre_ -kiss?"
"It's a really long story," I tell them.
"Well, I'm all ears," Jeannie insists, leaning in to listen better.
"Okay, but I need a little longer than just the six minutes left before the bell rings." I nod to the clock on the wall. "For now, let's just say that I've been on a bit of an emotional rollercoaster—"
"And so you decided to take a ride on the Max Terbador?" Tori proceeds to do the Cabbage Patch (the seated version of it, anyway), complete with circling hips and an arm motion that always reminds me of caldron-stirring.
"Again"—Jeannie snaps—"with his full name. And, wait, does this recent lapse in judgment mean that Max _won't_ be taking us to the party on Saturday?"
"Honestly, I don't know." I take another bite of brownie.
"I really wanted to go," Jeannie says.
"Because partying it up on a Saturday night is so up your academic alley." Tori feeds a forkful of ziti into her mouth. "Will you be squishing it in before or after your six-hour study session at the university library? Or perhaps between the library and your volunteer shift teaching refugees how to read?"
"For your information, I no longer volunteer at Power to Read," Jeannie says. "I'm at the soup kitchen now."
"Right." Tori rolls her eyes. "Your lecture on diversifying the college portfolio must've somehow slipped my mind."
"Going to parties is also diverse," Jeannie argues. "Who wants a girl that's all work and no play?"
"You could play with me on Saturday night," Tori offers. "I'm going to Bojo's church social. The theme is forgiveness, and it's BYOCF&S (Bring Your Own Comfort Food and Slippers). Want to come?"
"Is that a rhetorical question?" Jeannie asks.
"I'm not so sure that Max wants anything to do with me right now," I tell her, "but I'm sure he'd still be happy to take you to the party."
"Which is what you'd secretly prefer anyway, am I right?" Tori snatches a Bugle from Jeannie's bag and gives her a knowing look.
Jeannie's face turns as red as my raspberry Jell-O. "How many times do I need to say it? I do _not_ have a crush on Max Terbador."
"Would you mind refraining from using Max's full name at the lunch table?" Tori mocks her. "I'm trying to properly digest my food."
I give Tori a high five, after which the bell rings and both Jeannie and I are saved.
#
After school, I sit outside by the Eco Warriors' memorial garden and check my phone for messages, hoping to find one from Julian's friend Barry.
Instead there's a voice mail from my dad. "Hey, there," he says. "Any chance you could stop by my new place on Friday? It's on your way home from school, 33 Macomber Avenue, right across from the post office. I have the day off, so I'll definitely be home. Hope to see you. Bye."
I click off the phone and swallow down his words. They taste like battery acid and burn a hole in my gut. I hate that home for him is anyplace other than with Mom and me.
"Hey," Jeannie says, suddenly appearing out of nowhere. She takes a seat beside me on the bench. "Sorry if I was being kind of weird at lunch, about that Max stuff, I mean."
"Are you kidding? _I'm_ the one who should apologize."
She shrugs, but she doesn't deny it. "So, what's up?"
"My dad. He wants to show me his new place. I guess it's really happening."
"And the 'it' in that statement would be..."
"Permanent separation, imminent divorce."
"Well, there's a sobering thought. Of course, there's no point in hitting fast-forward. Let the movie of your life play out on its own."
"Okay, you're starting to sound like Tori."
"Guilty." She raises her hand. "I stole that line from her. Scary?"
"A little."
"Okay, but stolen lines aside, maybe your dad and you will have an even better relationship now that he has his own place. That happens, you know. In the book I'm reading, Charlotte and her mother couldn't even stand to be in the same room together without throwing sharp objects at each other, but after Charlotte moved out, the two were like best friends."
"Except my parents and I already _were_ like best friends. Ugh," I grunt. "I can't even stand listening to myself anymore. Seriously, how do you do it?"
"Earplugs," she jokes.
"I really wouldn't blame you." It feels bratty complaining about my parents' problems after hearing about Julian's upbringing.
Jeannie gazes out at the stretch of lawn in front of the school—all the fallen leaves. "I feel like everything's changing."
"That's because it is."
"Including Josh's death."
I look over at the maple tree, planted in Josh's memory. It's about three feet tall now. "Color me confused," I try to joke. "But last I checked, death was a permanent condition. Curable only by reincarnation."
"Okay, so maybe the memory of his death, then. It feels different now that I'm the same age that he was when he died. I can't stop thinking about that—about how he never got to go to prom, or graduate, or even get his driver's license, and how I'm getting to do all of the above. In some way, I feel like I'll be doing those things for both of us now."
"Which may seem sad on the surface, but in another way it's kind of amazing. I mean, if you're crossing these milestones for the two of you, it's almost as if he's still right by your side."
"I'd like to do something in his memory," she says. "Like maybe set up a scholarship or something. Remember how much he loved track? Maybe I could organize a marathon. People could pay to run a certain number of miles, and all proceeds would go to a scholarship fund."
"I think that's a great idea."
"I just want to do something more meaningful...not that working at the soup kitchen or any of my other volunteer pursuits aren't. It's sort of hard to explain."
"I get it. It's like that for me too—with the whole PB&J thing. It's not that the mission wasn't needed or worthwhile, it's just—I don't know—not what I'm feeling driven by at the moment. I guess when I really think about it, none of my past projects have been about passion. They've always been the product of brainstorms I've had: causes I thought might impress my parents or help me make my mark. That probably sounds pretty selfish, right?"
"It actually sounds pretty deep."
"And my name isn't even Bojo," I joke.
"You and I are so much alike." She smiles. "While you play superhero to try to impress your parents, I play it to try to get into the Ivy League."
"Okay, well, I'm done trying to impress my parents."
"And how's that mentality working for you so far?"
"Actually"—I smirk—"I've never felt more confused in all my life."
"Well, I'm glad I'm not the only one."
"It's just one of the many things we have in common, along with our mutual interest in Max." I give her a pointed look. "And before you try denying it _yet again,_ I've seen the way you light up at the mere mentioning of his name—his first name, anyway." I laugh. "You're like my great-grandma's birthday cake with all ninety-seven candles."
"Okay, but you're the one that Max is crushing on."
"Crush- _smush_. If Max is half the guy I think he is, he'd be an idiot not to see what an amazing person you are."
"So does this mean you wouldn't be terribly upset if I still wanted to go to the party with him on Saturday?"
"I'd only be upset if you didn't go because of me."
"Well, thanks," she says, giving me a hug.
It feels really good to hold her like this and to have this chat—so much so that the thought of visiting my dad at his new bachelor pad almost seems like a fun idea.
_Almost._
#
I knock lightly before edging the barn door open. Julian's sitting in the corner, writing in his journal.
"Mind a little company?" I ask.
He flips his notebook shut, and I sit down on the floor beside him. He smells like strawberry soap.
"Writing anything good?" I glance at his notebook cover, wishing I could read the pages inside.
"Depends what you consider _good_."
"Something funny or insightful?" The key to breaking this case, perhaps.
"I mostly like to write about stuff that's already happened. It helps me understand it more."
"I do the same thing—not with writing but with pictures." I pull my laptop out of my bag and go into my virtual gallery. I show him a bunch of stills I've done—of seashells, beach rocks, willow trees, and birds—before revealing my latest album. "I haven't given the project a title yet, but I have eight pairs of photos so far." I arrange them on the screen starting with a snapshot of a woman I spotted at the bus stop months ago. She's wearing a short sequined skirt paired with a white tank and stiletto heels. From the back it looks like she might be a model in the midst of a fashion shoot. But in the next photo, from the front, she's at least eight months pregnant. "I thought it was interesting." I shrug. "That moment of surprise...just not what you're expecting. And this one's my favorite." I point to a picture of a father and son holding hands on a walk. It's a sweet shot on the surface, but a close-up of the boy in the very next photo shows the tears running down his face.
"These are pretty amazing," Julian says, pointing to my photos of the beach. One of them depicts a pretty ocean scene. The other shows that same scene but with a wider angle, capturing a trail of strewn trash. "What's your inspiration?"
"For as long as I can remember, my parents have taught me to look at life from different angles before forming opinions or making big decisions. And so that's what I've always done. Taken pictures, that is—snapshots of the things that I don't understand completely in an effort to gain perspective."
Julian looks up from the screen. "That actually explains a lot."
"Does it?" I ask, staring at the dimple in his chin.
"You look at me through your camera lens—you're even using it now—but you don't pass judgment. You just keep searching for the best angle, going in for close-ups, retreating back to get a broader view, making sure you don't miss anything."
"Am I missing anything now?"
"Do _you_ think you are?"
"I'd really like to get to know you better—more about your family, what you write about in that notebook, what you want out of life."
"I think that last part is pretty shot, don't you?"
"You have to have faith."
"Faith that one day I won't have to run?"
"Faith that one day your life will be everything you dreamed."
"See, that..." He smirks. "That's the difference with you. You think I have possibilities."
"You do," I tell him. "You still have choices and a long life to live."
He smiles, seemingly amused by my optimism. "Maybe I've just never been brave enough to dream."
"News flash: it doesn't take bravery to dream."
"It does if you know you'll wind up disappointed in the end."
I reach out to touch his hand. "Then I guess I'm asking you to be brave."
His fingers weave through mine, sending heat all over my skin. He moves our clasped hands against his chest, over his heart. I can feel the rapid beat.
"I suppose you have more questions to ask." He lets go of my hand, erecting his invisible wall.
I take a deck of cards from my pocket. I was going to give it to him for solitaire, but instead I slide the cards out of the box and begin shuffling them. "Do you know how to play gin?"
"Hell, yeah." He smiles.
We spend the next hour or so playing round after round of cards and laughing at stupid jokes. If I didn't know better, I'd swear he were a boy from school, hanging out at my house after a full day of classes.
But instead I do know better.
And that's the hardest part.
_Wednesday, October 21_
_Late Afternoon_
_In one way, I feel so grateful for bumping into Day at that convenience store, following her home, and getting sick inside her barn. But in another way, I feel so much lonelier knowing that people like her exist and that I found out way too late._
#
It's barely four thirty when my phone vibrates with a text. It's Mom, telling me she won't be home for another few hours. I grab my laptop and do a search for Hayden's Horse Ranch, checking the hours. It doesn't close until eight.
Tape recorder in my pocket, I scurry downstairs and grab the keys to Dad's Scout, hoping he doesn't take note of the mileage. About an hour later, I pull onto the ranch's street, passing by a pumpkin patch and a giant corn maze. I turn into the drive and roll down the window. The air smells sweet—like apple pie and maple sugar. Over the years, I've had friends who've taken riding lessons or gone to summer camp here, but I've never visited myself. The grounds of Hayden's Horse Ranch couldn't be more beautiful. There's a giant arena with wide-open doors, and an outdoor corral where horses roam.
I park the car and get out. A sign points me to the office. I go inside. There's a woman sitting at the front desk. She's older, sixties maybe, with a long silver braid that hangs over her shoulder.
She pauses from a Sudoku puzzle to look up at me. "Can I help you?"
I push the record button. "I'm interested in taking some riding lessons."
"Well, you've certainly come to the right place." A necklace of strung horse-shaped beads hangs around her neck. "Have you ever taken lessons before?"
"No." I shake my head. "And I'd really like to take them with the owner. I heard he's really good."
"The owner here doesn't actually _give_ riding lessons."
"Really?" I cock my head, feigning confusion. "I'm pretty sure the person I spoke with said she took lessons from him."
"What was the person's name?"
"Jennifer Roman."
The woman's eyebrows shoot upward in response.
"Do you know her?" I ask.
"I do, but Jennifer Roman didn't come here for any lessons."
_"Really?"_
"She and the owner knew each other pretty well, if you catch my drift." She winks. "But that was years ago."
"How many years?"
"Oh, I don't know." She glances back down at her puzzle. "Four? Five? Must be around there, because we now have a four-year-old horse we call J.R." She nods toward a side window. There are stables just beyond it.
"Wait, J.R. for Jennifer Roman?"
"Are you interested in taking lessons with anyone else?" she asks, forgoing an answer.
"I guess I'm just really confused. Do you think I could meet the owner anyway?"
"I'm pretty sure he's left for the day." She pulls at her horse necklace and makes a clicking sound with her tongue. "But let me check. Can you hold on for a few minutes?"
"Sure." I nod.
The woman exits the office, and meanwhile I head for the doorway behind the front counter. I move down the hallway, checking all the rooms: a bathroom, a sitting area, a kitchen, and an office.
I step inside the office. There's a desk littered with all sorts of files and equestrian magazines. A calendar hangs behind the desk. It's covered with marked dates for appointments, horse shows, meetings, programs. I flip back to May 4. The words DAY OFF are scribbled across it. I pull my cell phone out of my pocket and take a snapshot of the date, just as a thwacking sound startles me.
I freeze in place. My chest instantly tightens.
But the noise is outside—the sound of wood against wood, like the opening and closing of a gate.
I let out a breath and open the top drawer of the desk. It's full of junk, including random toys: a Slinky, a yo-yo, Silly Putty eggs, and a few mismatched dice cubes. I close the drawer and open another one; it's a file cabinet, loaded with folders. I do a quick scan, spotting a tab labeled "receipts." I pluck the folder out and go to peek inside it, just as I notice something else.
On the desk.
A picture of a pony.
I pick up the frame and turn it over in my hands.
"Peter?" a male voice shouts.
I dart out from around the desk, tucking myself behind the door.
The picture frame is still in my hands. The folder's tucked under my arm. The calendar's still set for May.
"Pete?" the person asks. He's standing in the doorway now. I can see him through the crack below the hinge.
I hold my breath, trying to keep from making a sound, but then my stomach growls and I'm sure he can hear it.
"Hello?" he asks, taking a step inside the doorway.
Part of me is tempted to come out, but not two seconds later, he turns away; I hear his footsteps move down the hall.
With trembling fingers, I open the back of the picture frame, thinking how I sometimes like to tuck notes or letters behind key photos. I don't get the latches undone on the first try. The cardboard's too thick. I have to pry upward on the latch with my thumb.
That works.
The latch slides open.
I do the same with the other latches. They open as well. I remove the cardboard backing. There's something hidden behind the horse photo. I take it out—a four-by-six photo of a woman, mid-laugh.
She's pretty, with dark hair, green eyes, and a heart-shaped face. I go to take a photo of the picture just as the file folder slips from under my arm. Receipts scatter onto the floor. They're everywhere—by the door, under the desk, in the far corner.
I scurry to pick them up, on my hands and knees.
The main door opens. I can see it from where I'm standing. The woman from the desk is back.
"Hello?" she shouts.
My heart pounds. My skin starts to sweat. I still need a picture of the photo. With trembling fingers, I take the shot.
Something falls; there's a loud clank sound; it came from another room.
I return the photo behind the pony picture, place the cardboard back, then fasten all the latches.
I go to set the photo where I found it on the desk, but it topples over, against the wood, making a knocking sound that echoes inside my bones. Footsteps move across the floor—heavy boots, wooden heels.
I turn to look.
No one's there.
My pulse racing, I put the frame back before gathering up the remainder of the receipts. I stuff them into my bag, along with the folder. There's no time to return things inside the desk.
I move out into the hallway. The woman's positioned away from me.
"Thank you," I say. I'm all out of breath. "I found the restroom."
The woman looks me up and down, as if trying to figure me out. "Peter's already gone for the day."
"Okay, well, maybe I'll come back on Saturday to see him. Does he work on Saturdays? Or maybe he's only here on some Saturdays," I say, suddenly remembering that I never fixed the calendar in his office.
"He works. On Saturdays." She goes back to her Sudoku cells, clearly done with me.
"Well, thanks," I say, still puzzled as to why he took off Saturday, May 4.
Coincidence? Or something more?
#
At home, I park Dad's car back in the garage and head straight for the barn.
"Hey." Julian smiles as soon as I come through the door.
"I have something I want to show you," I blurt, plucking my cell phone out of my pocket. I find the snapshot I took of the woman's photograph. "Does this person look familiar to you?" I ask, angling the screen so he can see it.
Julian takes my phone and turns away. "Where did you get this?"
"It was a photo that I found. I took a picture of it."
" _Where_ did you find it?"
I move to stand in front of him. "Tell me who it is first."
"It's my mother. Now, where did you find it?"
I nod to the bales of hay, and we sit down beside each other. I tell him about my visit to Hayden's Ranch, including about the calendar and the pony named after his mom. "I really think this might be a major break for us. I mean, if they were seeing each other even _four_ years ago...that's a lot more recent than the seven or eight you mentioned before."
But Julian appears less than convinced. He takes a deep breath and lets it filter out slowly. "It was a long time ago."
"But not as long as you thought. Right?"
He gives me back my phone. His mouth is a straight tense line. I thought he'd be more excited.
I look at the picture of his mom—her smiling face, the brightness in her eyes. "Is it hard seeing your mother this happy?"
"Only because she was capable of such happiness, and because I didn't get to see it much. Life would've been a lot different if I had."
I stare toward the side of his face, trying to imagine what this must be like for him, learning that his mom might've had this whole other secret life. "It must be weird to think about her being with someone else."
"I think 'sad' is a better word."
"Sad because she was cheating on your father?"
"No, sad because she kept that happiness from me—because she didn't take me to the place where happiness existed."
"Maybe she was too scared to take you there."
"Too scared, too selfish, too weak. Take your pick. Which would be the most acceptable?"
"I'm really sorry."
He nods. His chin quivers. "In some way, even though I was little, I kind of knew how she felt about that guy. I saw how happy she was when she got out of the truck that day. But I guess I didn't realize it was—"
"Pony-naming serious?"
"Yeah." He bites his lip—to stop the trembling maybe—and gazes at my mouth.
I venture to reach into my pocket for the tape player, thinking about all the info I've already missed. "Is this okay?"
Julian turns away in response. His whole body stiffens. Recording these sessions puts a definite wedge between us. But I push RECORD anyway.
`ME: Do you have any idea why your mother and Peter Hayden might've broken up?`
`JULIAN: Her depression might've been a motivating factor; either that or the fact that she was married, or her fondness for prescription meds. Once again, take your pick.`
`ME: Do you think it was your mom who broke off the relationship, or Hayden?`
`JULIAN: I'm assuming it was my mom. She'd never leave my dad, even if she did love someone else.`
`ME: What makes you say that?`
`JULIAN: Well, for one thing, she never _did_ leave my father. I also don't think she wanted to leave me...even though, in reality, she was never really there for me after Steven's death.`
`ME: She could've taken you with her.`
`JULIAN: I really wish she had.`
`ME: Why do you think she didn't?`
`JULIAN: Because my father made her feel worthless, and deep down—even though it probably sounds nuts—I think that's how she wanted to feel.`
`ME: You think your mother wanted to feel worthless?`
`JULIAN: I think that's all she felt she deserved after what happened to Steven.`
`ME: She looks so happy in the photo. Do you remember her like this?`
`JULIAN: I remember her being like that _before_ Steven's death.`
`ME: Not after?`
`JULIAN: Only a handful of times, maybe. But then she'd walk into my room and see Steven's bed, and that would be the end of that. I remember in a couple of instances Dad giving her crap about smiling too big or laughing too hard. As soon as you crossed the threshold of our house, it was like walking into a morgue.`
`ME: I'm almost surprised she ever came home at all.`
`JULIAN: You really think this is smart: going to Hayden's Ranch, asking suspicious questions, and rifling through someone's office?`
I push STOP. "No one suspected anything."
"How do you know?"
"You're going to have to trust me."
Julian gets up and runs his fingers through his hair in frustration. "Maybe this was a big mistake."
"Which part?"
"This, me, staying here."
"You can leave anytime you want," I remind him.
"Is that what _you_ want?" He turns to face me again. His golden-brown eyes fix on mine.
"No." My face heats up. "I'd really like to help you. But if I'm going to help you, I need to ask questions and do some investigating. How else am I going to find a loophole? And, to be honest, I think we may have found one. Where was Peter Hayden on the day of your parents' deaths?"
"So, what are you proposing? That he came over, found my mother like that in the tub, then killed my father?"
"Could be."
"But there was no forced entry."
"So, maybe your dad let him in for some totally unrelated reason. Maybe Hayden then revealed who he was and killed your father in the heat of the moment? What if your mother didn't know how to deal with your father's death, took some pills, and then got into the tub? What if she even committed suicide to take the rap?"
Julian sits down beside me again and stares out into space. "So what now? Ask more questions? Go back to the ranch? I really don't think that's smart."
"You can't live in this barn forever, Julian. What happens when my dad comes back for his power tools? Or my mom goes looking for her gardening gloves?"
"I really want to trust you."
I reach out to touch his wrist, running my fingers over the pickax tattoo. "So, trust me to dig up the truth."
He looks at me. There's a startled expression in his eyes. "Just promise me."
"What?"
His mouth trembles open, but he doesn't utter another sound. He looks so fragile—like he could collapse from a single nudge.
I rest my head against his shoulder, able to see the motion in his chest. "I promise," I say, not finishing my thought either. But maybe the silent vow is enough for the moment.
We don't speak again until it's time for me to go—until I hear the slam of Mom's car door in the driveway.
"Good night," I say, hating to pull away.
"Good night." He musters a smile. His voice is soft, like velvet.
If only I could curl up inside his voice.
If only there could be another way.
#
Later, in my room, I empty my bag. It's full of Peter Hayden's receipts. I collect them in a heap on my bed, cringing at the thought of having left some behind—on the floor, under his desk, behind the door.
How long would it take for him to find a couple? To notice the folder's missing? And then to ask the woman at the desk if anyone went into his office? How long after that would a lightbulb click above the woman's head, remembering my visit?
Remembering me.
I sift through the pile, trying to put the receipts in order, from January until the present. The whole reason I took the folder was to see if there might've been any romantic purchases made—flowers, candy, dinners, trips—hoping to prove somehow that Hayden was still seeing Julian's mother.
Most of the receipts are for obvious work-related expenses: hay, feed, grooming supplies, cleaning stuff. I form a series of stacks. There have got to be at least three hundred pieces of paper here, small ones, full sheets, in every color of the rainbow.
Finally, after about forty minutes of searching, I find it: the needle in the haystack. Not a romantic purchase, but one made on Saturday, May 4.
The heading on the receipt says Wallington Hardware. The purchase was made in the morning, at nine a.m., and paid for in cash. There are two five-digit strings of numbers, for each of the items bought. The prices are $17.99 and $29.99.
I grab my laptop and search for Wallington Hardware's contact information. It closed two hours ago. I type one of the item numbers into the product search box. An error message pops up right away, informing me that the item cannot be located. I try the other number. The same message appears.
I attempt to do a Google search, but nothing relevant comes up—just real estate stuff (address numbers and area codes).
It'll have to wait until tomorrow.
_Wednesday, October 21_
_Night_
_I stood outside the bathroom and knocked on the door. There was a puddle at my feet. Water had seeped beneath the door, sopping into the rug._
_"Mom?" I shouted, jiggling the knob. When she didn't answer, I shoved my weight against the door panel until it finally gave way._
_Mom was lying in a tub of water. Her body had sunk beneath the surface._
_I saw her eyes first: piercing green, angled up toward the ceiling. I told myself it wasn't her. I mean, it couldn't possibly be her. This couldn't possibly be real._
_She was still in her nightgown from that morning. Her slippers were still on her feet. Water spilled over the porcelain rim. _Splash. Splash._ At least three inches on the floor. A couple of empty pill bottles floated too. Painkillers, antidepressants._
_I can't describe what I felt in that moment. It was like every horrible experience I'd ever had hitting me at the same time—only it was worse than that._
_I sank to the floor, able to hear my father's voice playing in my ear: "Steven would've been a far better son than you."_
_I'm not sure how long I stayed like that—if it was for an hour or a minute—before I shut the water off. The silence made things worse somehow._
_I tried to pull her out. Her limbs were already stiff. Water gushed over the rim, over me. I held her body in my arms. She was so tiny. Her ribs poked through the fabric of her nightgown. The bones in her neck were almost visible through the skin. Why hadn't I done more to help her?_
_Why hadn't she done more to help me?_
#
It's early morning, before school, and Mom's in the kitchen making breakfast.
"Waffles on a weekday? What's the special occasion?" I ask her.
"I couldn't sleep. I have a meeting with a new client, and then I have to work late again tonight." She's dressed in her navy blue pantsuit (the one she reserves for all-important meetings), and her hair's hiked up in a bun. "Syrup? Nutella? Whipped cream?" She's standing over the plate of waffles, armed with all three.
Before I can answer, the doorbell rings. My insides jump.
Mom's eyebrow darts up in suspicion. "I'll take that as a 'none of the above' on the waffle toppings. You're jittery enough without the added sugar. Better to just eat them straight up. Now, would you mind getting the door?"
I head for the front entrance, wondering who it could possibly be at this hour. Standing on tiptoes, I look through the peephole.
Max is there.
Still dressed in my sweats from bed, I open the door. "Hey," I say, stepping aside to invite him in. "You're up early."
"I have an early-morning soccer practice." He hands me a cup of coffee. "Let's try this again, shall we? Me bringing you coffee, that is, without any weirdness."
"I take full blame for the weirdness. I think I must've been temporarily body-snatched by the aliens of Planet Bizarro."
"There's a response to a kiss that I haven't heard before. Most girls just don't answer my calls."
"Max—" I cringe. "That's not what I meant."
"I know." He smiles. "Anyway, I'm sorry that I was such an ass when you came to talk to me before class."
"It's fine. I deserved the asshole treatment. Oh, wait"—my face goes fireball red—"that totally didn't sound right."
Max laughs. "But I didn't come here just to apologize and bring you coffee."
"You didn't?" I bristle slightly, afraid he might still be getting the wrong message.
"I was hoping you wouldn't mind if I still went to that party with Jeannie. I mean, if it's weird, please say so. It's just—"
"It's not weird at all," I say, cutting him off.
"Okay, cool." He smiles. "And, of course, you're welcome to come too. It's just that she asked me. Last night. On the phone. And, I don't know, but I was pretty excited she wanted to go."
" _So_ cool," I agree, psyched to hear that Jeannie called him. "You guys will have a great time together."
Max smiles wider, seemingly relieved. I'm relieved as well, and not just because he's no longer upset, but because maybe—finally—we've arrived at a mutual place.
After he leaves, and once Mom's gone off to work, I head out to the barn, en route to school, with a plate full of waffles. I rap lightly. Julian opens the door. The sight of him, despite my unending questions, makes my entire body quake.
"Good morning," he says.
I force myself to look away. "Breakfast?"
He takes the plate. But still I linger in the doorway, half wanting to go in, but knowing I should go.
"Did you want to come in for something?" he asks.
I open my mouth to tell him no, but instead I step inside. His journal is open on the floor. I rack my brain for something to ask him—some detail about the case, some reason beyond waffles for me to even be here right now. "Will I ever get to read your writing?"
He sets the waffles down and comes a little closer.
"Do you ever write about us?" I ask, before he can answer. "About our time together, I mean?"
Julian takes my hand and traces the lines of my palm. "What do _you_ think?"
I swallow hard, looking down at our hands, knowing I'm in way over my head.
"So, I was just kind of wondering..."
"What?" I ask.
"Who's that guy?"
"That guy?"
He peeks up from my palm. "The one who drives the Jeep."
"Oh." My heart hammers. "He's just a friend."
The tiniest of grins forms across his lips. "So I guess I'll see you later. After school."
But I don't want to go. I squeeze his hand, and he draws me slightly toward him. His mouth is so close—just a hairbreadth from mine—that if either of us were to speak another word, our lips would bump together.
I close my eyes, feeling the warmth of his breath smoke against my mouth.
"You should go," he says, taking a step back, and making my heart squelch.
Still, I know.
It's true.
He's absolutely right.
I turn away and slip out the door, grateful to him for halting the moment, disappointed in myself for not.
#
All during school, I try my best to concentrate on the case. In my study block, I go over my audio transcripts, come up with a list of more questions, reread news reports, and create a timeline for Saturday, May 4.
But then my mind wanders back to this morning—what coud've happened, that almost-kiss.
And all other thinking stops.
After school, in my room, I grab Hayden's file folder and open it up. The receipt from Wallington Hardware is sitting on top. I dial the store's number. A male voice answers right away.
"Hi. I'm wondering if you could help me," I begin. "I have a receipt for a couple of purchases I made at your store back in May. I'm trying to figure out what they were. It's sort of a long story." I fake a laugh. "But I have the item numbers and I was hoping that you could look them up."
"Wait, are you looking to make a return? Just bring in the unopened items, along with the receipt."
"No. I'm not making a return. I want to figure out what I bought. I have the item numbers," I tell him again.
"Um, okay. But I'm not really sure how to do that."
"I think you can just type the numbers in. I've seen people do that."
"Wait, can you hold on for a second?"
"Sure." I sigh, hoping that someone's there to help him.
He comes back on the line a few moments later. "The manager will be in tomorrow. Do you think you could call back then? Sorry, I'm new here."
"Okay," I say, thoroughly disappointed.
I hang up and head down to the kitchen to fix dinner for Julian, reminding myself that I need to stay focused on the case. I can't be getting emotionally involved. I cross the yard to the barn, wondering if I should broach the "need-to-stay-focused" topic, but the door opens before I can decide.
Julian looks just as amazing as he did this morning, with his wide brown eyes and perfectly rumpled hair. There's a thin layer of stubble over his chin and cheeks.
"Could we talk some more?" I ask, handing him a bag of food and closing the door behind me.
We sit down across from each other, and I do my best to avoid looking into his face, or staring at his mouth. Instead, I take out the tape player, putting a palpable wedge between us, and push RECORD.
`ME: I need you to remember back. Is there anything at all—ticket stubs, restaurant receipts, lies your mother told—that might've suggested that she and Peter Hayden were still dating these past couple of years?`
`JULIAN: My mom hadn't been well these past couple of years. She barely even left the house.`
`ME: But you were in school most of the day. Is there a chance someone might've visited her while your dad was at work?`
`JULIAN: I suppose there's a chance, but I really don't think she was still seeing that guy.`
`ME: Because...`
`JULIAN: She was frail. She barely spoke. She slept most of the time.`
`ME: All because of your father?`
`JULIAN: He certainly didn't help.`
`ME: Can we talk about the way your father treated you? You said before that he would often compare you to Steven—the person he imagined that Steven would become.`
`JULIAN: That's right.`
`ME: Why do you think he did that?`
`JULIAN: Hell if I know. Maybe to put distance between us. Maybe if he didn't love me, it wouldn't have been hard to lose me if something happened.`
`ME: What were you and your father fighting about on the day of his death?`
`JULIAN: It was just something that he said.`
`ME: What did he say?`
`JULIAN:...`
`ME: Julian?`
`JULIAN: He said he wished that it was Steven who lived and...`
`ME: What?`
`JULIAN: And me who died.`
`ME: He probably wasn't thinking when he said it.`
`JULIAN: He knew what he was saying. He said it all the time, blaming me for taking Steven's car seat and distracting Mom from driving that day. He said it was because of me that she hit the tree.`
`ME: You know those things aren't true though, right?`
`JULIAN:...`
`ME: Julian?`
`JULIAN: Steven should've been the one to live.`
I press PAUSE. Julian's turned away now.
"I know this must be hard," I say, referring to his openness. I'm not his journal; he's probably never told these things to anyone. "But you have to understand: your father comparing you to Steven...it wasn't rational. He was making comparisons about things that hadn't even happened yet, not giving you a chance to grow into the person you were meant to be."
Julian shrugs. "My dad comparing me to Steven, it just became normal."
"Do you see now that it's not?" I reach out to touch his hand, stopping him from picking at the skin on his palm.
He turns to look at me. His eyes are red. He's holding back tears. "What is it like to be normal—the way normal is for you?"
"Who's to say that _my_ normal is the _right_ normal?"
"It's got to be a whole lot 'righter' than mine."
"So, let's be normal," I say, without a second thought.
His face furrows. He doesn't get what I mean. I'm not sure I get it either. Still, I go for the bag of clothes, pulling out the pair of jeans from yesterday and the blue waffle top. "Put these on," I tell him. "I have some other things in my room."
"What for?"
"Just do it." I head back to the house before he can argue.
#
"Are we done yet?" Julian asks, sitting on a toolbox in lieu of a makeup chair.
I apply a thick layer of concealer to mask the scar beneath his eye. I follow up with foundation across his cheeks, to hide the spray of freckles.
"Now?" he asks.
"Almost," I say, pulling a knitted hat over his head to completely cover his hair. I also give him a pair of clunky black nonprescription eyeglasses, fished from our Halloween costume bin, and a puffy winter jacket to add layers to his midsection.
"Can I look?"
I hold the hand mirror up to show him.
"Wow," he says, pushing the glasses up farther on his face. "But I still don't know if this is a good idea."
"It'll only be for a couple of hours. Come on," I say, taking his hand and leading him outside.
We leave the barn just as it's turning dark, and walk along the bike path toward town. Julian barely says two words the entire way there. He just keeps looking up at the sky, waiting for the sun to go down altogether.
"Don't worry," I try to assure him. "No one's going to recognize you."
I pick a pizza place on the fringe of town, behind the local college campus. It's always full of college students, so I never know anyone here. We slip inside, and I make a beeline for a two-seater table in the far back corner. I take the seat that faces outward, while Julian sits with his back to the other tables.
The waitress comes right away, not even giving Julian a second glance. She hands us the menus and then scurries on her way.
"Good?" I ask him.
"Weird." He smiles.
"Normal," I say, correcting him.
We order a caramelized-onion pizza with a side of curly fries and two limeades. And we start off by talking about _normal_ stuff—like favorite foods and best ice cream. Him: enchiladas and fudge ripple. Me: veggie pad thai and butter pecan.
"So, what's the one thing you're most excited to do or see once all of this legal stuff gets cleared?" I ask him.
" _If_ it gets cleared, you mean."
"Finish school? Go on a vacation? Walk down the street without having to wear three inches of makeup and clunky glasses?"
"I don't know." He toys with the prongs of his fork. "I guess I don't really have any expectations."
"In other words, there's nothing you'd do if you could?"
"I'd love to go to the beach again. Pretty basic, I know, but it's sort of my special place, where I've always felt most safe. When I was little, I used to want to be a lifeguard."
"So that you could save other people?"
"Maybe." He shrugs. "I guess. I never stopped to think about it."
"And what do you want to do now?"
"I don't really dwell on what I want to do for work. I mostly just think about the kind of person I want to be."
"And what kind of person is that?"
"More like you, actually." He sets his fork down.
"Seriously?" I ask, waiting for the punch line.
"Absolutely serious." He stares at me from behind the black rims; they make the gold in his eyes look brighter. "It's pretty amazing the way you help people, without looking for something in return. I hope that doesn't weird you out."
"It's actually pretty flattering. I mean, I've never really thought of myself as anything other than ordinary."
"Well, you should," he says, gazing at my mouth. "Because you're the most incredible person I've ever met."
My insides warm up like toast, and I don't know how to respond. While he's been wanting to feel normal, I've been striving to be _super_ -normal—as if normal isn't good enough. As if _I_ have never been good enough.
Our food and drinks arrive. The waitress pushes aside the floral arrangement on our table to make room for the plates.
"Forget-me-nots," I say, catching Julian admiring the tiny blue petals.
"I guess someone knows her flowers."
"Only because I used to photograph them."
"A perfect choice for our table, don't you think?" He smiles.
I smile too. Things are just as I'd hoped. The food is good. Julian is relaxed. There's not a single soul I recognize or who recognizes us.
But then the door jingles open.
And Tori walks in.
She's with that Bojo guy from the Ragdoll. They search around for a table. Meanwhile, my body instantly shrinks. I look downward, sipping my drink, paranoid she might recognize him from the convenience store and put two and two together.
"What's wrong?" Julian asks.
I peek back up. Tori's looking in my direction. She waves. I wave back. And then she crosses the restaurant toward me.
I straighten back up, unable to help noticing that she's dressed like Frida Kahlo, with a big red scarf, a blue floral dress, and flowers in her hair.
"Fancy finding you here," she says, standing at our table. But she's not even looking at me; she's completely focused on Julian. "Aren't we one for secrets."
"Hey," Julian says to her. "I'm James."
"Tori," she says, extending her hand for a shake. "Have we met? Because you look so familiar. Debate team? Middle school?"
"I don't think so." Julian bows his head slightly.
Finally, she looks back at me. "I think we definitely have some catching up to do."
"Well, you've been pretty preoccupied."
"Right," she says, taking Bojo by the hand. He's wearing striped harem pants and a matching hat that looks like a tissue box. "We're just grabbing a quick bite before our movie."
"Well, we were just finishing up." Julian nods to the half-eaten pizza.
"You _do_ look really familiar," Bojo tells him. "Do you go to Crest Hill?"
Julian shakes his head.
"Well, I never forget a face, especially not this one," he says, turning to Tori. He smells the flowers in her hair and then kisses her cheek—not once but _three_ times. "Table?"
"Definitely," she purrs.
While they head off to a booth, Julian and I pack up and leave. It's completely dark out now, making the air seem suddenly cooler.
We walk along the sidewalk, toward the south end of the street, and once again Julian has fallen silent.
"Did Tori and her friend bother you?" I ask him. "The stuff they said about never forgetting a face?"
"How could it not? I mean, I'm really out on a limb here."
"By being outside, you mean?"
"By all of it: being outside, befriending you, talking about stuff that no one else really knows."
I stop him from walking by grabbing his forearm. The clock on the bell tower chimes, reminding me that we don't have time to waste. "But all of that stuff—opening up, being vulnerable, trusting others, forming relationships—that's normal too."
Julian stares at me— _hard_ —studying my every blink and breath. "I have to go back, you know. You have your own life. And I can't pretend to be anyone other than—"
"I've never asked you to pretend. And you don't have to go back right now."
"You're right." He takes my hand and brings me across the street.
We continue for four more blocks, before he leads us between two houses, where there's a pathway made of beach shells. We move down a grassy hill, and the ocean makes its appearance. The moon shines over it, painting stripes on the incoming waves. I take a few pictures, including one of Julian, able to smell the sea-tangled air.
"Zigmont Beach," he says. "Ever come here?"
I shake my head.
"So then what are we waiting for?"
I hop onto the sandy beach and kick off my shoes. There isn't a single other soul here. I gaze back at the row of houses behind us. A couple of them have their porch lights on. Someone's barbecuing food. There's music playing in the distance—a flute, a piano, a violin. People are enjoying life.
People, including us.
Julian takes off the hat and glasses and begins toward the water. The cool beach sand feels like powder beneath my feet. We roll up our jeans and sit by the ocean's edge.
"Thanks for letting me bring you here," he says. "The ocean always makes me feel invincible somehow—like anything is possible."
"Anything _is_ possible."
"You make me feel that way too."
My heart pounds in response. "I know something that'll make you feel even more invincible. Ever hear of the polar bear plunge?"
He shakes his head.
"Okay, well, technically, it's a _pre_ –polar bear plunge, since it's not winter yet, and normally there's a fund-raising component, but we can just skip that part."
"Okay," he says, but still there's a question on his face.
"So, let's take the plunge." I get up and nod toward the water.
"You can't be serious."
"You're not chicken, are you?"
"Hell, no," he says, getting up too. He peels off the waffle shirt, revealing a thin white tee.
I follow suit, pulling off my sweater, leaving the tank top underneath.
Julian kicks off his boots and wriggles out of his jeans. I take my jeans off too, trying not to peek at his boxers, unable to help staring at his legs—the muscles in his calves, the hair sprouting from his skin—all the while tugging at the length of my tank.
"Last one in is a polar bear," I shout, running for the water.
Julian follows. We splash through the incoming waves. Together, we swim out, toward the moon. The water is absolutely freezing, but there's warmth here too.
"So, now what?" Julian asks.
"That's it. We took the plunge."
"So now we leave?"
"Yeah." I shrug, twitching from the cold.
He moves a little closer—until we're standing just a few inches apart. "Except I don't want to leave just yet." He reaches out, finding my hands beneath the water.
I weave my fingers through his, wishing he could be someone else—even for a moment—rather than this person on the run, this person I'm trying to help.
The moon lights up the sharp angles of his face. "We're from two entirely different worlds," he says.
But that doesn't change how I feel.
Julian clenches his teeth and looks away. Perhaps he's just as conflicted. Still, all I can think about is wrapping my arms around him. And never letting go.
I feel myself floating toward him, forcing him to look at me.
"Day," he whispers into my ear. His breath is against my neck. "We should stop."
"I know."
He takes a step back. His eyes meet mine. But I draw him closer again and press my lips against his cheek, able to feel his heart throbbing against my chest.
His hands encircle my waist. My leg tangles with his as I swallow him up in my arms, melting into his embrace.
"Just this once," I whisper.
He nods slightly. His lips graze mine—once, twice, three full times—before he kisses me, finally. And it tastes like warm, salted caramel inside my mouth, over my tongue, awakening an aching deep inside me.
His hands cradle my face. His fingers glide down my spine, beneath my tank, all over my skin. If I didn't know better, I'd think the heat between the two of us could set this ocean on fire.
He lifts me upward and I wrap my legs around his waist, wishing I could take the picture, desperate to capture the moment. As if moments could ever be captured. As if time could somehow stand still.
_Thursday, October 22_
_Afternoon_
_I was nine years old the first time I saw my mother's scars. On her wrists. Thick red slash marks, crusted over with dried blood._
_She was crouched beneath the picnic table, still dressed in her nightgown from the morning, even though it was approaching nighttime._
_"What happened?" I asked, joining her under the table, nodding to the cuts._
_"Just a scrape." Her eyes were vacant—so far gone from all her pills._
_There was a hole in the soil between us. Inside was a beaded bracelet that Dad had given her for a wedding present, as well as a couple of her pills, and one of Steven's baby socks. Tiny scraps of paper lined the walls of the hole. Scribbled across them were the words GUILT, MARRIAGE, FEAR, and MY LIFE._
_"Can I have a slip of paper?" I asked her._
_"Sure." She brightened. There were dried up tear tracks down her cheeks. "What would you like to bury?"_
_"Dad," I told her._
_She didn't so much as flinch, just handed me the pen. I wrote his name down. She kissed my cheek. Then, together, we refilled the hole._
#
After school the following day, I check my phone, noticing a missed call. I don't recognize the number, but still I press it to dial, wondering if it might be Barry's.
"Hello?" A male voice.
"Hi, I think you called me?"
The phone goes radio silent.
"Hello?" I ask.
"Yeah," he says. "I heard you're doing an assignment on Julian Roman's case."
"That's right. Is this Barry?"
"Which college?"
"Crest Hill State University. Would it be okay if I asked you some questions?"
"Not over the phone. Let's meet someplace. I've got some free time now."
"Um, sure," I say, completely _un_ sure. My tape recorder's back at home. But still I don't want to miss this opportunity. "Where?"
"Orange Park? I'll be on one of the benches by the dog park."
I agree and hang up, both anxious and excited to question him. I cross the street in front of the school and take the number-four bus into the town of Decker. On the way, I do a search of the local headlines with Julian's name, looking for any updates.
An article pops up right away. It was posted just this morning:
`SEARCH CONTINUES FOR TEEN ACCUSED OF HOMICIDE`
`WEBER, MA—The search continues for Julian Roman, 16, of Decker Village Park. Roman was reported missing from the Fairmount County Juvenile Detention Facility on October 6, while awaiting trial for the alleged murder of his father. Officials know Roman escaped from the courtyard through a section of wire fencing compromised during construction. Roman is reported to have dark hair and eyes, an athletic build, and to be six feet tall. He was last seen on surveillance video taken from a convenience store in Bethel, wearing gray pants and a hooded sweatshirt. Officials have reason to believe he's still in the Bethel area, and urge anyone who might have information about his whereabouts to contact their local police department.`
I click off my phone, feeling my stomach twist. Officials have reason to believe he's still in the Bethel area? What is their reason? Didn't the police say that someone fitting Julian's description was spotted in the town of Millis?
About forty minutes later, the bus pulls over in front of the park's entrance gates. I get out. The doors close behind me with a hard, heavy thwack. The park looks smaller than I remember it last—fewer benches, not as many trees. There's a skating rink in the center that my parents used to take me to when I was first learning to Rollerblade. It looks smaller too.
I peer all around, spotting the dog park in the corner. I move in that direction, scanning all of the benches. I'm just about to walk around the perimeter of the gate.
But then: "Day?"
I whirl around. The boy from the coffee shop is sitting on the ground, beneath a tree. I recognize him right away: the faux-hawk hair, his olive skin. Dressed in baggy jeans and a zip-up sweatshirt, he comes and extends his hand toward me.
"Barry?" I shake his hand.
"Yeah. You're a lot different than I pictured."
"What did you picture?"
"I don't know. Some mousy college girl, I guess." He laughs. "By the way, I think it's way cool that you're researching Julian's case for an assignment. For once, schoolwork that actually has a point."
I take a notebook and pen from my bag.
"Julian is a really good friend of mine," Barry continues. "We grew up together, in the same neighborhood."
"So you know his parents?"
"I know everything," he says, giving me a pointed look.
"Well, then can you please explain why he was arrested in the first place? Because I'm having a hard time trying to piece together enough of a reason. So much seems circumstantial."
"Do you mind if we walk and talk?" He gazes over his shoulder at the street. "I think better when I'm in motion."
"Sure," I say, following him toward the exit gate.
There are cars whizzing by on the main road, and a strip of shops in the distance. The smell of car exhaust is thick in the air. Barry stuffs his hands into the pockets of his jacket, and we walk along the sidewalk, toward a major intersection.
"First, I just want to say that I don't think Julian's guilty. I mean, yes, he hated his dad pretty hard-core, but who didn't? The guy was a total asshole. But did Julian kill the dude? That just doesn't seem like something that Julian would do."
"And so who do _you_ think killed Mr. Roman?"
"Julian's a good guy," he says, in lieu of a response. "But he got a really raw deal—not just with this case. His life has always been pretty shitty. A real shame, too—the guy is, like, a genius. Not many people know that."
"He'd have to be smart to escape a detention facility and remain on the run."
We come to the end of the sidewalk, and Barry crosses the main road.
"Where are we going?" I ask him.
"Just a little bit farther," he says, turning down Cherry Street. It's a relatively quiet road, with cars lining both sides and a gas station on the far corner.
_"Where?"_ I insist.
He doesn't answer, just keeps on moving, his pace quickening with every step. I'm almost tempted to turn around, but I stay beside him for a few more blocks, my cell phone clenched in my hand.
I look upward. The clouds have collected over us, and it suddenly appears darker. _"Barry?"_ I demand.
He stops, finally, and turns to me. "This is it," he says, nodding to the house.
We're standing directly in front of it.
I recognize the house from news articles: the yellow police tape, the screened-in front porch, the faded white shingles. "Julian's house," I mutter.
"I thought that coming here might give you a better picture of things."
"It does," I say, trying to imagine Julian coming home from the beach that day, parking his car out front, and climbing up the broken steps.
"I live just around the corner."
"And the neighbor whose lawn Julian mowed?"
Barry points to a red Victorian across the street and a few houses down. "The guy's pretty nice, but he's hardly ever home."
"If he's hardly ever home, how can he say for sure what time Julian mowed his lawn?" Not that it even matters much.
"Apparently the wife came home for lunch around noon and the grass wasn't cut."
"But that's still hearsay if nobody else can corroborate the detail."
"You sound like a cop."
"I actually sound a lot like my mother."
"Is _she_ a cop?"
"No. She's just good at picking stories apart, catching people in lies."
"That must suck for you." He laughs.
I gaze back at the house. The windows look vacant—no curtains, nothing propped on the sill. The mailbox hangs crooked by the door, its flag pointed downward. "I wish I could see inside."
Barry glances over both shoulders before pulling a knife from his back pocket. "Come on," he says, moving to the side of the house.
I remain firmly in place, watching as he walks along a row of bushes that separates the Romans' land from the neighbor's.
"We'll just have ourselves a little peek," he says, stopping in front of the window toward the back. He cuts a couple of the police tape ribbons.
I grab the keys in my pocket and run my finger over the sharpest one, ready to use it if I need to. I begin toward him, my curiosity piqued.
Barry points inside. "This is Julian's bedroom."
I peer through the glass, keeping Barry in my peripheral vision, especially since he's still holding the knife. Four stark white walls surround two single beds, a broken dresser with lopsided drawers, and a trash barrel that only partially covers a gaping hole in the carpet.
"See...nothing out of the ordinary," Barry says.
"I guess." If ordinary is a room that resembles a prison cell.
"The bed on the right was Steven's." He points to it. There's a stack of storybooks where there should be a pillow. "Do you know about Julian's brother that died?"
I nod. "Someone in the group found out about him somewhere."
"Yeah, sucks. When Steven died, it pretty much killed the family."
"Did you know Julian back then?"
"Yeah. We weren't in school yet, but we played together—with Steven too. I remember that Steven had the funniest laugh, more like a cackle, and always carried fake bugs in his pockets."
"Do you remember a change in the parents after Steven's death?"
"I remember that Mrs. Roman went pretty quiet and stopped inviting me over for lunch, and that Mr. Roman would flip out over the littlest thing—like this one time when I sat down on Steven's bed. The guy went totally ballistic."
"Do you think Mrs. Roman could've killed her husband?"
"You obviously never met Mrs. Roman." He laughs. "People called her the walking zombie, because she was ninety pounds and completely checked out on painkillers. If you so much as sneezed in her direction, she would've fallen down."
"So maybe she threw something heavy at his head."
"Not with enough force that it would've killed him. Apparently forensics investigators were able to estimate the force that hit Mr. Roman—something to do with weight and speed. Anyway, they said that Mrs. Roman wasn't physically capable."
"How do you know all this?"
"Julian told me, before the arrest. He used to tell me everything." He taps the blade of his knife against his chin in thought. "My theory: she either offed herself once she saw her dead husband, or she did it earlier, before he was killed, which would explain Mr. Roman's really bad mood that day."
"Bad mood?"
"You didn't hear about the UPS guy witness?"
"Oh, right. Julian and his father's argument-turned-fight."
"I figure the fighting must've been pretty explosive. Why else would the UPS guy go spying in the windows?"
"Did the UPS guy call the police?"
"Nope. And I'll bet he's lost a few good nights' sleep over that, because imagine if he _had_ called. The police would've appeared on the scene. No chance for a homicide with cops hanging around to mess it all up." He laughs again. "Did anyone in your group find out about the fingerprints?"
I shake my head.
"Yeah, I guess nobody really knows about that. The police didn't leak it."
"Leak _what_?"
Still holding the knife, Barry places his hands around his neck in a choke hold, rolls his eyes upward, and sticks his tongue out to be funny. "There were fingerprints found around Mr. Roman's throat."
"Wait, _what_?"
"They were on some necklace he was wearing, as well as on his skin. I know, right? Who knew you could get prints off skin, but apparently it's possible. Something about sweat residue, lipids, and amino acid shit—way too science-class for my taste." He laughs some more. "Anyway, they were Julian's fingerprints—and not from a pulse-check, if you get what I'm saying."
The detail goes straight through my chest, like a sharp-pointed spike.
"I know, freakin' sucks, right?" he says.
"It had to have been some mistake. Maybe Julian had touched his father's neck earlier in the day."
"I take it your group is Team Julian, then?" He grins.
"I'm just trying to play devil's advocate."
"The prints were made from the front, with the thumbs right between the clavicle. But, even so, all the prints prove is that Julian was trying to defend himself from his father's bullshit."
"I thought his father was killed from a blunt trauma to the head?"
"He was."
I shake my head. "Then I guess I'm even more confused."
"The police think that Julian tried to strangle his father," he explains, using his knife-holding hand. "But then when that didn't work, he grabbed something in the heat of the moment and hit him over the head."
"And you know all of this because...?"
"Like I said, Julian told me everything. He said his father had him pinned that day, and so he had no choice but to try and protect himself. When I asked him—for the millionth time—if he killed his father, even by accident, he said he didn't. He swears he left the house after the fight. He says he went for a ride, looking for me, but I was at work at the restaurant. It wasn't until Julian got back home that he found the bodies."
"Wow," I say, taking his words in, feeling my pulse race.
"I know. But, hey, three cheers for no murder weapon yet, right? At least we've got that going for us."
"Do we even know what the murder weapon is?"
"No." He sighs. "And believe me, the police have looked." He moves to another window—the one that's closer to the street.
I follow along and look inside. The living room's been ransacked, the sofa cushions thrown askew. An end table drawer's been dumped out onto the floor.
Barry smooshes his face up against the glass, making a weird humming sound as he does.
"All these theories..." I turn toward him again, noticing how he's frequently looking upward, avoiding eye contact. "What's your theory on who did it?"
"Hell if I know." He uses the back end of the knife to scratch his forehead. "But his dad wasn't exactly short on enemies, myself included."
"Okay, but being an enemy doesn't mean that you want to kill that person."
"You might've asked me that question about six months ago, when he shoved me up against a fence and said that I was a worthless piece of shit. Thankfully I have an alibi for his death; I was at work. Otherwise, who knows; maybe they'd have locked my ass up too."
"Someone in our group said that Mrs. Roman might've had a boyfriend."
"Yeah, but that was years ago, at least according to Julian. But who knows? Maybe that's just what she told him. But, then again, who would date a zombie?"
"Is it possible that a former lover might've sought retaliation for Mrs. Roman's zombie state?"
_"Bam,"_ he says, using his knife as a baseball bat through the air. "I think you might be on to something. Is that what your group thinks?"
"We're exploring all possibilities, including the one that involves Mrs. Roman seeking help in the death of her husband."
"Help as in a hit man? I'd give that lady major props if that were true."
"Do you know if the police questioned the neighbors to see if anyone was spotted coming into or out of the house?"
"Yes, and negative. But then again, half the neighbors here are drunk by two in the afternoon. The other half don't want any dealings with the cops."
A police siren sounds in the distance. Barry scurries to bury his knife inside his boot. "We should go."
I start to mutter a good-bye, but Barry has already turned away and headed for the street.
#
Instead of taking the bus to the stop by my house, I get out in the center of town and walk three blocks to my dad's new apartment. It's sandwiched between the movie theater and a French bakery, which, admittedly, gives it a definite edge.
I search the door buzzers for my dad's name. It's there, in bold black typeface. I press it and wait for him to appear.
"Hey!" His face brightens when he sees me. He pulls me in, gives me a hug. He smells like the cologne version of grapefruit. "I'm so glad you came. I wasn't sure." He checks his watch.
"I made a detour first."
"Well, I'm really glad to see you." He leads me up a stairwell. "No elevators here. No need for a gym, either."
We climb four flights. The door to his new place is already open. I follow him inside. If I thought our house was sparsely decorated, Dad's apartment gives new meaning to the word "scant." There are two metal folding chairs positioned in front of a fuzzy green ottoman.
"Wow," I say, for lack of descriptive words.
"I know. I obviously have some work to do. But I was hoping that you could help me. We could go furniture shopping together."
"To make things more permanent?"
"I really want you to be comfortable here," he says, avoiding the question. "Come on, I'll give you a tour." He crosses the room and points to the kitchen.
From this angle, I can see a puke-green fridge and a tiled counter to match. The floor is the same as in the living room—wide-planked, dark-stained wood.
Dad points to two more rooms. "The one on the right is mine. Yours is on the left."
I move to have a look. The walls are painted lemon-yellow. There's also an armoire and a bed.
"It obviously needs decorating too," Dad says. "So start looking at catalogs to get ideas of what you might like."
"Why do _I_ have a room here?" I ask, trying to process what all this means, as if it isn't already obvious. Dad's told me. I've clarified it. How many other ways do either of us have to say it?
My parents have grown apart. They're not getting back together—at least not anytime soon.
"You'll always have a place wherever I am," Dad says.
My eyes instantly fill, and I'm not even sure why. It's not just because of my parents' separation, or the fact that Dad has a new apartment, or that I have a room here.
It's everything. Just like Jeannie said. Life is changing, and I guess I'm having a hard time keeping up.
Dad comes and wraps his arms around me just as rain pelts down against the window screen behind him. "It's going to be okay. You'll see."
I wipe my eyes and take a step back. "I know. I just have a lot on my plate right now."
"With school? Your peace and justice club?"
I shake my head. "It's way more complicated than that."
"What is?"
Tears slide down my face. I take a seat on one of the metal folding chairs. "How do you do it?" I ask him. "How do you help people who've done bad things?"
He scoots down in front of me and takes my hand. "Where is all of this coming from?"
"I just don't get it." I shake my head. "You give those people a chance despite the fact that some of them have robbed banks or stolen cars. Or hurt others."
"I give them a chance because, in a lot of cases, they haven't been given one before."
"And what happens when they blow that chance—when you find out they're not the person that you thought?"
Dad gives my palm a squeeze. "Well, then that's a choice they've made today, and maybe tomorrow they'll choose more wisely. But at least I've given them some tools, as well as my trust and the benefit of the doubt. Believe it or not, those things are luxuries to some people— _gifts,_ even. Has someone disappointed you?"
"Honestly, I don't know." All I know is that Julian's lied to me. Twice now. But does that make him guilty? Or does it just make things more complicated?
"Does whomever you're talking about need the kind of support I'm referring to?"
I bite the inside of my cheek, so tempted to spill my guts. "Do you think that good people can do bad things?"
"I know they can. Just look at your mother." He grins.
"Seriously now."
"I _am_ being serious. Or maybe half-serious." Dad lets go of my hand and moves to sit on the fuzzy green ottoman, only it doesn't have enough stuffing, and he nearly topples off. "During some of her demonstrations, let's just say that things could get a little bit ugly. But _you've_ heard the stories of throwing paint on strangers, linking arms across a highway, and destroying public property. Of course, for every one of those cases, she felt that her actions were justified. That's another tricky piece to all this. Everyone has their story—their own version of the truth, a rationale for how they act."
"Because everyone has a unique perspective," I say, thinking about my photo project.
"Exactly. In most cases, your mother's political escapades aside, I'd say that people act out when they've lost their way, or when they aren't getting the support they need. They've fallen through the cracks and gotten desperate. I'm not saying that what they do is justified, but you have to wonder: if those same people were given different opportunities—"
"They wouldn't rob banks?"
"Maybe or maybe not. The answers aren't so black and white, especially when there are other variables too, like mental illness, addiction, or trauma."
"Your clients are really lucky to have you."
"I'm lucky to have them too." He reaches out to take my hand again. "But I'm even luckier to have such an amazingly intelligent daughter, who asks all the right questions in her quest to do what's right." He holds my gaze for several seconds, perhaps waiting to see if I'll tell him what's _really_ on my mind.
I clasp my hand around his, wondering if he'll persist with questions. But he doesn't—because maybe he trusts me to do the right thing, and that trust, as he said, feels like a gift unto itself.
_Friday, October 23_
_Night_
_There was a knock at the door, scaring me shitless, startling me awake. I sat up, all out of breath, and looked toward the window. It was dark out. The moon shone in through the glass, painting a narrow strip across the floor._
_In the strip of light was a bag of supplies. A towel hung out. There were food cans on the floor and a pile of clothes. I was getting way too comfortable. I should've been ready to bolt at all times._
_I got up and crept over to the window, tripping over a sandbag, barely catching myself from falling forward. It was raining out. I angled my face against the glass, trying to see the door. But it was too dark._
_Another knock._
_"Julian?" Day's voice._
_I went to the door and opened it an inch—just enough to assess the situation. It appeared that she was alone. She was standing there with a flashlight—not an umbrella—clenched in her hand. I widened the door to let her in, but she didn't move. Her face was wet from the rain. It looked like she'd been crying._
_"Is there something you have to tell me?" she asked, before I could say hello._
_Panic struck my heart like a match, burning through my veins, making my skin feel hot._
_"Why didn't you tell me about the fingerprints around your father's throat, on his necklace?"_
_I clenched my teeth, wishing the floor would swallow me whole. More rain pelted down against her head, soaking her hair, draining down her neck._
_"Just tell me. Is it true?"_
_My eyes slammed shut. Every inch of me shattered._
_"They were your fingerprints?" she continued. "How could you leave a detail like that out? I trusted you to be honest with me." Her voice cracked over the words._
_My heart cracked because I'd hurt her._
_"So, now what?" she asked._
_"It may sound selfish, but I didn't want you to know that about me."_
_Day shook her head and went back to the house, leaving me in darkness, taking all the light with her._
#
I spend the following morning catching up on the non-Julian-related aspects of my life. I work on my photography project, finish my French and Chaucer essays, study for a physics exam, and call Jeannie to wish her luck on her date with Max tonight (at the "It's-Saturday-Let's-Party" party).
After lunch, in my room, I gaze out the window, feeling a gnawing sensation inside my gut. I haven't spoken to Julian since last night. But still I've been thinking about him.
A lot.
Am I surprised that he didn't tell me about the fingerprints? Someone who barely confided in anyone? Who writes his feelings down in a notebook because that's safer than revealing them to other people?
No.
Not at all.
He hasn't been honest with me, but I'm not willing to give up on his case. I'm way too invested now. Plus, it's no longer just about him. This case is about me too—about having a sense of purpose, and feeling as though what I'm doing matters.
I grab my camera and bag, then ask Mom to borrow her car for a trip into town, which isn't entirely a lie. I will drive into town, straight down Main Street, on my way to Wallington.
Mom says yes. I grab her keys. Wallington Hardware is a tiny shop in the center of the city, about thirty minutes away. I park right in front and fish Hayden's receipt from inside my pocket. The doorbells chime as I enter the store. There's a bearded guy at the counter.
"Can I help you?" he asks.
"I'm looking for the manager," I tell him.
An older woman emerges from the back room. She can't be more than four feet nine, with hair hiked up in a cone-shaped bun (perhaps to add a few more inches). "Look no further," she says.
"I bought a couple of items here back in May," I explain, showing her the receipt. "I was hoping that you could tell me what they were."
She gives me a befuddled look, with a creased forehead and pouty lips. Still, she goes behind the counter and types one of the item numbers into the register.
The register beeps. Words flash across the screen: PIPE, STEEL, 24-IN.
A shiver runs down my spine.
The woman raises an eyebrow at me. "Looks like you may have had some sort of plumbing issue back in May."
"Right." I nod. "Could you also check the other number? I don't remember what I bought with the pipe."
She types that number in too. "Gloves," she says, reading the screen.
_"Gloves?"_
"That's right." Her face furrows as she studies my expression. "Working gloves. Lots of people use them, including you if this is indeed your receipt."
Working gloves.
A steel pipe.
My head spins.
I feel my face flash hot.
"Anything else?" she asks.
"Could you tell me how heavy a twenty-four-inch steel pipe might be?"
She moves from around the counter and disappears down one of the aisles, returning a few seconds later, holding a steel pipe. It's about three-fourths the length of a baseball bat. "Feel for yourself," she says, handing it to me.
I wrap my hand around it. It's easy to hold, about an inch and a half thick, and short enough to hide, but still it has ample weight, at least five pounds. Is it possible that Peter Hayden concealed a pipe like this behind his back, tucked inside his pants, with his shirt draped over the end? Was he wearing gloves at the time?
I pull my camera out of my bag and take several pictures of the pipe. "Would you mind showing me the gloves too?" I ask her.
The woman exchanges a look with the guy at the counter. "I must say, I've never had a customer take photos of items they purchased in the past. What is this _really_ about?"
"A school project. Photography class."
Her eyes squint. I can tell she doesn't believe me. Still, she retrieves the gloves from one of the aisles: black leather, size large. I take a series of shots, suddenly noticing the surveillance camera over the cash register. Would the police watch the recording? Would the manager call them after I left?
"Thank you for your time." I snatch up the receipt and bolt for the door.
#
Back in the car, I grab a notebook and add to my lists of facts and questions, trying my best to get a grip.
`FACT: Peter Hayden bought a steel pipe and some construction gloves on the morning that his girlfriend's husband was killed.`
`FACT: Mr. Roman was hit over the head with a blunt object that's yet to be identified.`
`QUESTIONS: Could the purchases have been a coincidence? Does either of the above factors really mean that Peter Hayden is guilty?`
I spend a few more moments coming up with a list of interview questions, then I grab my phone, as well as the tape recorder from my bag, and dial the number for Hayden's Ranch.
A woman answers.
"Could I please speak with Peter Hayden?" I ask her.
"Can I tell him who's calling?"
"Paula," I lie, pulling my tape recorder close.
The woman doesn't question it, just tells me to hang on. I push RECORD, set the phone to speaker mode, and take a deep and cleansing breath.
`PETER HAYDEN (P.H.): Hello?`
`ME: Hi. Is this Peter Hayden?`
`P.H.: It is.`
`ME: A friend of mine took riding lessons with you a little while back and recommended that I do the same.`
`P.H.: What did you say your name was?`
`ME: Paula.`
`P.H.: And who was your friend?`
`ME: Her name was Jennifer Roman.`
`P.H.:...`
`ME: _Hello?_`
`P.H.: I don't give lessons, Paula.`
`ME: Did you use to—within this past year maybe? Because she said she took them from you.`
`P.H.: I haven't given lessons in a couple of years.`
`ME: _Really?_ Because I didn't get the impression that it was _that_ long ago.`
`P.H.: It's been a couple of years.`
`ME: Since you've seen Jennifer?`
`P.H.:...`
`ME: Do you think you could make an exception for the friend of a friend? I'd love to try a lesson, and she said I shouldn't go to anyone else.`
`P.H.: When did she say that?`
`ME: When I saw her last—maybe three or four months ago. It's taken me since then to muster up the nerve to go forward with this idea.`
`P.H.: Are you aware that Jennifer Roman passed away?`
`ME: Wait, _what_?`
`P.H.: She died, back in May.`
`ME: There must be some mistake.`
`P.H.: No mistake. I'm sure you can look it up online.`
`ME: I feel like I just saw her.`
`P.H.: Well, you haven't seen her since before May.`
`ME: How did she die?`
`P.H.: She took her own life.`
`ME: Oh my god.`
`P.H.: I'm sorry to have to be the one to tell you.`
`ME: I should've called her. I should've visited. I mean, I knew she was unhappy, but I never thought she'd...`
`P.H.:...`
`ME: When was the last time that _you_ saw her?`
`P.H.: It'd been a while.`
`ME: More than five months, like me?`
`P.H.:...`
`ME: What was the date she died?`
`P.H.: Saturday, May fourth.`
`ME: Had you seen or talked to her that day?`
`P.H.: No.`
`ME: Because you were working? You work on Saturdays, right? That's what the woman at the front desk said.`
`P.H.: I wasn't working on _that_ Saturday.`
`ME: Just by sheer coincidence?`
`P.H.:...`
`ME: _Hello?_`
`P.H.: Who is this?`
`ME: I told you already. My name is Paula.`
`P.H.: Who is this _really_?`
`ME: What were you doing on Saturday, May fourth?`
`P.H.: I've already spoken to the police.`
`ME: About an alibi? They questioned you?`
`P.H.: That's right. I was at home changing a gas pipe—not that it's any of your business.`
`ME: So you _don't_ have an alibi for Saturday, May fourth. You were at home, all day?`
`P.H.: The police don't have anything on me, and neither do you, _Paula_. Now, I suggest that you hang up and forget we ever spoke.`
`ME: And if I don't?`
`P.H.:...`
`ME: _Hello?_`
`P.H.: Don't call back here again.`
The phone clicks. I press STOP. My whole body chills.
I start the ignition and pull away from the curb, more suspicious than ever that he's getting away with murder.
#
I come in through the front door, able to hear voices in the kitchen. Mom's talking to someone. There's a male voice—not my dad's. I head down the hallway to see who it is.
They're standing by the sink. Staring straight at me. The same two officers that were here before.
"What's going on?" I ask.
"We got a call," Officer Nolan says. She comes closer and flashes me a photo of Julian—the same one she showed me before.
"The boy from the convenience store." I nod. "His posters have been all over town."
"Do you know where he is?" the detective asks.
I shake my head, telling myself that I honestly can't be sure. He could be in the barn. He could also be in the woods. Or, maybe he ventured out on the bike path.
"We've already checked the barn." Detective Mueller gives me a knowing look, his eyebrows darted upward.
"Okay." I try my best to keep a poker face, but I can feel the emotion speckled across my neck, the bright red hives.
What did the officers see? Were they able to tell that Julian was here? Did Julian sweep up all the hair from when I cut it?
I peek over at Mom for help.
"You heard my daughter," she says. "She doesn't know where this boy is."
"Well, we still have more questions for her."
"Not now," Mom says, using the same assertive tone she reserves for her clients. "My daughter just got home, and I'd like to speak to her first."
"This will only take a few minutes," Mueller says.
"Well, then it can take a few minutes another time," Mom insists. "Need I remind you that she's a minor?"
Officer Nolan reaches for her card. "Please call us as soon as you can. The suspect is considered highly dangerous."
"As opposed to mildly dangerous?" Mom asks.
"This isn't a game," Nolan says. "If you _do_ see him, call nine-one-one right away. Don't try to apprehend him on your own. I'll be following up before the end of the day."
Mom takes the card, and I move to the kitchen window to watch the officers leave. They cut across the yard, pausing in front of the barn before heading down the bike path.
Mom locks the door and turns to face me with her arms folded. "You have some explaining to do."
There's no point denying it: "I've been helping him."
"The boy they're looking for?"
I nod. "Julian Roman."
She clenches her teeth. "I don't even know what to say to you right now."
"Say that you love me and trust me, and that you know I'd never do anything I didn't believe was right."
She opens up a carton of eggs and breaks three of them into a pan, with the stove turned off, not even bothering to throw out the shells.
"At first I was just curious about his case," I venture. "He was a boy who seemed to need help. But then I got to know him..."
"And it became personal," she says, smashing another egg into the pan.
"I don't think he's gotten a fair deal."
"He hasn't been convicted yet, either. Why is he hiding instead of pleading his case, putting up a fight?"
"You know how it works without the right people in your corner. It's a losing battle."
"And where do _you_ fit in?" she asks, picking the shells out of the pan.
"I've been gathering clues, offering support. He's been staying in the barn."
Mom turns to face me again. "So, now we're aiding and abetting?"
"You can just plead ignorance. It's more likely that I'd have kept Julian a secret."
"Which you did."
"Until now."
"I see." She sighs, folding her arms again. "Well, I don't think he'll be staying here much longer. The police will be back—with search warrants next time. And who knows about this phone call tip they got—who it's from and what they know."
"What did they find in the barn?"
"They didn't actually go inside. I caught them peeking through the windows. A sneaky pair too: they didn't even park out front; they must've hidden their car somewhere."
"So, where do we go from here?"
"You should've told me about him."
"I was respecting his privacy and giving him my trust—the way you do with your clients and the way Dad does with his."
Mom turns back to the pan of eggs, unable to deny it. "Well, I suspect your friend isn't stupid, since he's made it this long. He'll probably be on the run again—that is if he isn't already. But if you really believe he's innocent, maybe there's something I can do to help." Her cell phone rings, cutting through our conversation. "Shit," she says, checking the screen. "I have to take this. It's about Pandora's case. But we're not finished yet, you hear me? I want to meet with this boy."
While she talks on the phone, I hurry out to the barn. I open the door and step inside.
Everything's been cleaned up, put back—like he was never even here. The clothes and blankets are collected in a corner. The food and water bottles are gone.
I grab the knitted blanket I lent him as tears roll down my face. There's a hollow sensation inside my heart. How could he leave? Just like that. Without even a hint of a good-bye.
#
It's one day later. Julian hasn't come back—at least not to stay. But this morning, when I passed by the barn on my way to take Gigi for a walk, there was a forget-me-not in the window box, making my heart instantly clench.
I peered over my shoulder before going to have a look. The whole window box had been filled with potting soil, the flower freshly planted. I moved closer to have a sniff. It smelled like honey. And reminded me of our date. I had to assume that Julian had done this—and that he was sending me a message.
He isn't far away.
The police have yet to follow up like they said they would. Mom thinks it's because they don't have sufficient evidence to make a connection. "Of course, that also gives them all the more reason to find that evidence," she says.
It'll only be a matter of time.
Until then, while Mom's been busy with _her_ case, I've been trying to find out more about mine. I picture myself going back to the horse ranch, talking to the woman at the desk again, and sneaking into Hayden's office. But what if my showing up there for a second time raises a red flag?
I resort to a Google search (to start with, anyway). In my room, I type a bunch of words into the search field:
_Peter Hayden, Jennifer Roman_
_Peter Hayden, Michael Roman_
_Peter Hayden, homicide case_
_Peter Hayden, alibi_
_Peter Hayden, police questioning, alibi, May 4, Jennifer Roman_
The latter combination of words does the trick. An article pops up about the case. It was published a few weeks after the crime. I'm pretty sure I've read this article before, from the _Decker Daily Journal_. But the part that I didn't read? A recent remark in the comments section. All of my words are highlighted:
_I just heard that Peter Hayden was questioned about the Roman murder. Don't the police know what a lying son of a bitch he is? What's his alibi? Not that you could believe it. That crook has more friends in low places than I have credit card debt. I saw him and Jennifer Roman together a couple of summers ago. She didn't look well, but frankly I'd be sick too if I spent longer than two minutes in Hayden's company. No wonder she killed herself._
I close my laptop, not quite sure what to think. How is Peter Hayden supposedly a crook? And how did this person find out that Hayden was questioned by the police? My mind spinning with questions, I go into my virtual gallery, looking for a little diversion, not to mention a much needed brain break.
I have twelve pairs of photos for my project. I arrange them on the computer screen, starting with the snapshot of Jeannie—the one I took on our hike. She looks so peaceful, with the sun setting behind her, illuminating her skin. But in the next photo, as soon as she's turned her head, you can see the angst welled up in her eyes.
I've titled the project "My Excavation: An Exploration of Perspectives," because while some people dig to unearth the truth, others strive to bury it. I'm hoping to submit the project for consideration into the Shutter Exhibition at the Contemporary Art Institute. But before I do, there are just a couple more photos I need to get.
#
Instead of going home after school, I take the bus into the town of Decker and get out at the Orange Park stop—the same place that I met Barry.
I retrace my steps to Julian's house, feeling the rush of adrenaline the closer I get to his street. There's a police car parked in front of a drugstore on the main road. I readjust the scarf around my neck, trying to partially conceal my face, fearing it might be one of the officers that came to my house.
I duck down a narrow road that runs parallel to Julian's street, and then cut over, crossing two intersections, finally arriving by his house. The yellow police tape flaps in the wind, gets caught up in the bushes.
I grab my camera, feeling totally self-conscious. Standing at the corner of the property, I aim my lens at the front entrance, careful not to get the police tape, angling instead on the bright red door and the matching shutter beside it. An ivy plant snakes up the clapboard shingles. I retreat back a little, able to get that too, as well as a patch of wildflowers growing among the weeds.
I take a handful of more shots before pausing to check them out. The photos are just what I intended. They give the illusion of home.
My next series of photos uses a wider angle; it's the same view of the house, but also with the police tape; the overgrown lawn; and the wide, gaping hole in the porch lattice, like someone kicked it in.
I move around to the side of the house and aim my camera lens into the living room window, focusing on the navy blue sofa with the plaque hanging over it. The plaque looks to be about two feet wide: blue and yellow embroidered letters that spell out the word FAMILY.
_Click, click, click._
I step back for a wider view, capturing a shot that includes the overturned end tables with the dumped-out drawers and a broken ceramic lion.
_Snap, snap._
I continue to the window of Julian's room, zooming in on the storybooks sitting on Steven's bed, capturing the bright red and yellow book covers; the top one shows a dancing pig. There are bookmarks sticking out from the pages of the other books—like a well-loved stash of library loot.
I zoom out for the next shot, getting the rest of the room—the broken dresser, the hole in the carpet, a crack in the wall, and a corner of Julian's bed—imagining sleeping here. Steven's obviously been gone for years, but I wonder if his ghost still lingers.
I move around to the rear of the house, suddenly feeling like I'm being watched. There are houses surrounding the yard on all sides. The curtains shift in the first floor window of the apartment building directly beyond Julian's fence. Meanwhile, a police siren blares, and my whole body trembles. I take a deep breath, telling myself that I haven't done anything wrong (aside from trespassing, maybe). Still, I need to be quick.
Like the front, the backyard is overgrown with weeds. A metal shed sits in the center of the lot with its doors splayed open, facing me. There's also a large sandy area with an uneven rock border. I wonder what the space was used for. A grill? An old patio or sandbox?
I edge closer for a better look, but then come to a sudden halt.
Julian's here.
The breath in my lungs stops.
He's crouched beneath a picnic table with his back toward me.
My gut reaction is excitement to see him. But then my brain kicks in and confusion takes over. What is he doing? Why is he here?
The table is tucked in the corner of the lot, behind the shed. The benches have been pulled away. There's a shovel in Julian's hand and a wide gaping hole in the ground.
I take a photo of the mound of dirt beside him.
The shutter clicks.
He looks back at me.
I stare at him through the lens of my camera, desperate to see things clearly, angling close on his face. It's covered in stubble. His lower lip trembles.
But still I'm just as confused.
Julian crawls out from the table. He stands, dressed in the clothes I first saw him in—the hooded sweatshirt, the dark gray pants. He looks like he did that day, at the convenience store, with his cowered posture, when I asked him if he was okay.
"What are you doing here?" I look beyond him at the table. It's big, at least eight feet long and four feet wide. There's a collection of items by the mound of dirt.
And that's when the answer clicks.
I move closer for a better look and scoot down beside the hole. He's been digging up what was buried: a bracelet, a child's shoe, a wedding band, and some old pill bottles.
They're all caked with dirt.
I zoom in close on the ring, imagining it on Mrs. Roman's finger, wondering when she buried it. Five months ago? A couple of years after Steven's death? Did her husband notice when it went missing?
Did he notice the missing shoe? It's a brown lace-up bootie, about the size of my hand, and with a bright red rubber sole.
"Is that Steven's?" I ask.
Julian nods, following my gaze. He comes and sits beside me on the ground. "I was probably seven or eight when I buried it."
"And the bracelet?"
"It was a wedding present to my mom from my father. She obviously didn't want to be married anymore."
"Looks like she didn't want to be taking pills, either." I point my camera lens at the collection of items. Julian doesn't comment, and so I take a couple of snapshots, trying to capture the sparkle of the amber beads through the layers of dirt. They must've been beautiful once.
I peek down into the hole, curious to know what else might be buried, able to see something down there, sitting at the bottom. "What's that?" I ask him.
Julian doesn't answer. He's turned away. His knees are tucked against his chest.
I reach into my pocket for my phone, click on the flashlight app, and aim it into the hole. "It looks like an underground steel pipe." My mind zooms to Peter Hayden. Is it possible that there's a connection? Does Julian know something key?
"What is it?" I insist, pointing the flashlight in deeper. The rod has an iron base with carvings of some sort. Rosettes, swirling vines? The object has a long slender neck and a dishlike platform at the top.
I flash back to years ago, as a kid, digging up old silverware in our yard. Dad said that before there were banks, people used to bury their treasures on their property.
_"Julian?"_
"What do _you_ think it is?"
"I don't know." I peer back into the hole, and then reach in to grab it.
But Julian stops me before I can, grabbing my arm, yanking me back. My phone slips from my grip and falls into the hole, about three feet down.
_"What is it?"_ I insist.
"Do you really want to know?"
I nod. My heart pounds.
Julian pulls on some gardening gloves, repositions on his knees, and lifts the object out. It's an iron candleholder, about fourteen inches long. There's a round crevice at the top for the candle's base.
"Did your mom bury that?"
"No." He shakes his head. His eyes lock on mine. "I did."
My mind reels, imagining what kind of symbolism it held. Did his father used to burn candles in Steven's memory? Was Julian forced to sit still until the candle burned out?
There's a smear of something on the platform top.
Dark red.
Like dried blood.
I look back at Julian's stark white face. "Is this...? I mean, it can't be."
The murder weapon.
"It was an accident," he says; his voice breaks over the words.
The light behind my eyes goes dim. The ground tilts. The world around me whirs. How can this possibly be? And what about Peter Hayden? It was supposed to be him. This was supposed to get fixed.
"My father and I were fighting," Julian continues.
But I almost don't want to hear the words.
"I'd just come home from mowing the neighbor's lawn," he says. "My father was already drunk. And my mother was dead. She was lying in the bathtub, having taken all her pills. Dad said that it was my fault. He came at me, blaming me, calling me a no-good son of a bitch."
I clasp over my mouth. Every inch of me feels like it's racing—like a motor's been clicked on inside my heart, revving up my nerves, rattling every bone.
"He swung at my head with his beer can–holding hand. I swiped it away; the can went flying. It didn't end there. He came at me again, pinning me against the wall by driving his fingers into my throat. I fought back, wrapping my hands around his neck."
"Julian," I whisper. Tears slide over my lips. I can taste the salt inside my mouth.
"His fingers eased from my neck," he continues. "His mouth arched open, and he let out a sputter. But I couldn't do it—couldn't stand to see him in pain. I let go and turned away. But then he came at me again. I grabbed the only thing within reach. Before I knew it, everything went quiet. He wasn't breathing. I went into a panic. I left the house and drove around. When I got back, I buried the evidence, called the police..."
"And gave them the whole beach story."
He nods. "It just seemed easier to say I was at the beach all day. I even went to the beach the following day, so desperate to make the story true. The police seemed to believe me. Everything was going fine on the outside, but I couldn't sleep. I wasn't eating. I just kept looking over my shoulder, convinced I was being watched. They did an autopsy and found the prints around my dad's neck."
"Did they know they were yours?"
"No, and still everybody seemed to assume that my parents were the victims of their own murder-suicide. But then the UPS guy came forward. He told the police about the fight with my dad. Everything turned upside down after that. My only hope was that they hadn't found the murder weapon. But then they got my prints."
"So that's why you came here, isn't it?" I ask, thinking aloud. "Not to dig up the past, but to get the murder weapon, to hide it someplace more secure. It's why you've stuck around so long."
"It's not the only reason." His body twitches. "Your friendship's meant everything to me. I mean, meeting you, it's almost made things worse. As if things could've gotten any worse. Not only have I lost my parents, but I'll also be losing you."
I reach out to take his hand—to pull off his glove and weave my fingers through his—able to feel his body shake. "You don't have to lose me."
"I don't want to lie to you anymore."
I wipe my eyes. "No more lies."
"So, what do we do?" His eyes are red. His face looks pale.
I picture him and his brother in the backseat of his mother's car just minutes before it crashed. "We deal with things once and for all." Still holding his hand, I reach back into the hole for my phone. I click it on.
"Day. _No_."
"Yes," I say, giving his hand a squeeze. "You're no longer on your own, remember? Trust me."
I can tell he wants to—can see it in his hesitation. His lip quivers. His chin shakes. But still he doesn't utter another word.
And so I press my mother's number. "There's someone I want you to meet."
_Monday, October 26_
_This is my last journal entry in this notebook—not because the pages are all filled, but because I'm giving it to Day. It's all dug up here. There's nothing left to bury._
#
`ONE MONTH LATER`
When I get home from school, Mom is already here. She's in the kitchen. I can hear the clanking of dishes. I drop my bag and head in to join her.
"Hey," she says, looking up from a saucepan. There's a wide smile across her glowing face.
I glance over at the table. The crystal glasses are out. The napkins are folded into origami-like swans. "What's the special occasion?"
"I won Pandora's case," she bursts out. "She was released from prison two hours ago."
"You're kidding."
"Not kidding." Mom does a little cheer thing with her balled-up fists, punching the air and shimmying her hips.
"Congratulations!" I smile at her excitement; she hasn't seemed this happy in months.
"So, we're celebrating. I've made fried ravioli. Dad's coming to dinner, too."
He's been coming for dinner at least once a week, including last Friday night, when we ordered all of our favorite Thai dishes, just like old times (and when Dad ate his meal with a fork).
Will the two of them get back together? The vote is still out on that one. But it almost doesn't even matter. They're getting along. _We're_ getting along. And I'm spending time with both of them.
After dinner, in my room, I pull Julian's journal from my backpack. It's filled with entries about his childhood, as well as about his time spent on the run. I run my fingers over the cover, thinking how differently his life could've ended up had the car accident never happened, had his father come home on time that day, or had his parents reacted differently to Steven's death.
I've added photos of Julian to my project: a snapshot from the train depot; pictures of him in the backyard, washing with the hose; and then a photo I snuck at the beach on our date, when he couldn't have looked more beautiful.
"Are you ready?" Mom calls me.
I'm not really sure. I haven't seen Julian since the night he turned himself in, the same night he dug the hole, and I have no idea what to expect.
"Visiting hours are at seven," she continues, "but we have to get there early to register."
Mom's read Julian's journal too. As soon as she heard his confession to the crime, she insisted on taking the case.
I grab the photo album I put together. It's filled with images I thought Julian would like: shots of the ocean at sunrise and sunset, pictures of the moon shining down over Zigmont Beach, and photos of forget-me-not flowers.
I go downstairs and hug Dad good-bye, promising to stop by his apartment tomorrow to fill him in.
"Nervous?" Mom asks, as we climb into her car.
"Nervous, anxious, excited, scared. I don't know what I'll say to him." All I know is that Julian needs friendship and trust the most right now, and so that's what I intend to give him.
"No matter what happens with his case, I know he feels grateful to you."
I feel the same. "I learned so much by helping him."
"Well, then maybe you should tell him that."
Julian's not being kept at the Fairmount County Juvenile Detention Facility like before. He's been moved to the detention center in Chesterville, known for its high security, a little over an hour away.
We enter the facility through a set of iron gates. A tall brick wall topped with barbed wiring surrounds the entire place. I gaze out at the grounds. There's a grassy field and a basketball court, as well as a track for running and an outdoor patio space.
Mom parks the car. It looks crowded here tonight. There's a long line for security, but Mom gets us through it pretty quickly by flashing her bar card.
"Are you ready?" she asks, leading me into one of the visiting booths.
I sit down beside her and look toward the long glass window, itching my palms, taking deep breaths, and waiting for Julian to finally arrive.
He appears a few moments later, dressed in an olive-green suit. His skin is smooth. His hair's been cut. The scar beneath his eye has finally healed.
He smiles when he sees me.
I smile too. "I'm ready."
`THE END`
#
I would first like to thank my brilliant and amazingly talented editor, Tracey Keevan, for her invaluable feedback, critical suggestions, and attention to detail. This book is so much stronger because of her. A big thank-you also goes out to Ricardo Mejías for his careful read, and for knowing all the right questions to ask.
Thanks to my agent, Kathryn Green, for her literary guidance and advice. Twelve books together later, I'm enormously grateful for all she does.
Thanks to friends and family members, who are a constant source of support and encouragement. Thank you for reading my work, coming to my events, bringing me coffee (tall, black, no sugar, with a sprinkle of cinnamon), and keeping me inspired. I am truly blessed to have you all in my life.
And lastly, a very special thank-you goes to my readers, who continue to support me and cheer me on. Thank you for reading my books, attending my workshops, coming to my events, entering my contests, sending me your letters and artwork, making book-inspired videos and playlists, choosing my work for your school projects and reports, etc., etc., etc. I'm so truly grateful. You guys are the absolute best.
_Also by_
**LAURIE FARIA STOLARZ**
_Welcome to the Dark House_
_Return to the Dark House_
LAURIE FARIA STOLARZ is the author of _Welcome to the Dark House_ , _Return to the Dark House_ , and the Touch series, as well as _Project 17_ ; _Bleed_ ; and the highly popular _Blue Is for Nightmares_ ; _White Is for Magic_ ; _Silver Is for Secrets_ ; _Red Is for Remembrance_ ; and _Black Is for Beginnings_. Born and raised in Salem, Massachusetts, Stolarz attended Merrimack College and received an MFA in creative writing from Emerson College in Boston. For more information, visit www.LaurieStolarz.com.
# Contents
1. Title Page
2. Copyright
3. Dedication
4. One
5. Two
6. Three
7. Four
8. Five
9. Six
10. Seven
11. Eight
12. Nine
13. Ten
14. Eleven
15. Twelve
16. Thirteen
17. Fourteen
18. Fifteen
19. Sixteen
20. Seventeen
21. Eighteen
22. Nineteen
23. Twenty
24. Twenty-one
25. Twenty-two
26. Twenty-three
27. Twenty-four
28. Twenty-five
29. Twenty-six
30. Twenty-seven
31. Twenty-eight
32. Twenty-nine
33. Thirty
34. Thirty-one
35. Thirty-two
36. Thirty-three
37. Thirty-four
38. Thirty-five
39. Thirty-six
40. Thirty-seven
41. Thirty-eight
42. Thirty-nine
43. Forty
44. Forty-one
45. Forty-two
46. Forty-three
47. Forty-four
48. Forty-five
49. Forty-six
50. Forty-seven
51. Forty-eight
52. Forty-nine
53. Acknowledgments
54. Also by Laurie Faria Stolarz
55. About the Author
# Guide
1. Cover
2. Title Page
3. Copyright
4. Contents
5. One
| {
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using System;
using System.Threading;
using System.Threading.Tasks;
namespace Discord.Audio.Streams
{
///<summary> Decrypts an RTP frame using libsodium </summary>
public class SodiumDecryptStream : AudioOutStream
{
private readonly AudioClient _client;
private readonly AudioStream _next;
private readonly byte[] _nonce;
public override bool CanRead => true;
public override bool CanSeek => false;
public override bool CanWrite => true;
public SodiumDecryptStream(AudioStream next, IAudioClient client)
{
_next = next;
_client = (AudioClient)client;
_nonce = new byte[24];
}
public override async Task WriteAsync(byte[] buffer, int offset, int count, CancellationToken cancelToken)
{
cancelToken.ThrowIfCancellationRequested();
if (_client.SecretKey == null)
return;
Buffer.BlockCopy(buffer, 0, _nonce, 0, 12); //Copy RTP header to nonce
count = SecretBox.Decrypt(buffer, offset + 12, count - 12, buffer, offset + 12, _nonce, _client.SecretKey);
await _next.WriteAsync(buffer, 0, count + 12, cancelToken).ConfigureAwait(false);
}
public override async Task FlushAsync(CancellationToken cancelToken)
{
await _next.FlushAsync(cancelToken).ConfigureAwait(false);
}
public override async Task ClearAsync(CancellationToken cancelToken)
{
await _next.ClearAsync(cancelToken).ConfigureAwait(false);
}
}
}
| {
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Herrensee station is a railway station in the village of Herrensee in the municipality of Rehfelde in the Märkisch-Oderland district of Brandenburg, Germany. It is served by the line .
References
Railway stations in Brandenburg
Buildings and structures in Märkisch-Oderland | {
"redpajama_set_name": "RedPajamaWikipedia"
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Home Local News Club salutes 'humanitarians'
Club salutes 'humanitarians'
By LISA CAPOBIANCO
Every year, the Bristol Boys and Girls Club honors individuals for their dedication, accomplishments and sacrifice in humanitarian service to the community through the Humanitarian Service Award. Whether helping children by working to improve the quality of education or helping people of all ages by building jobs and promoting safety, the recipients of this award have made the Bristol community a better place in a variety of ways.
This year, the Boys & Girls Club recognized Nancy Brault, Nancy O'Donnell, and David Preleski with the Humanitarian Service Award during a dinner held at the DoubleTree last Thursday.
Growing up in a family of eight children, Brault said the need to give back stemmed from seeing the way her own father made a difference. Brault said her father taught her how to give back at a young age, whether watching him serve as a catechism teacher at church or in other civic groups.
Brault spent more than 12 years volunteering in leadership positions at Bristol Hospital. She has served three years on the board for the Bristol Hospital Development Foundation and previously served as chairman of Bristol Hospital Board of Directors from 2008 to 2011. A founding member of the Forestville Village Association and president/ majority owner of The Ultimate Companies, Brault also served as chairman of the advisory board for the Parent and Child Center at Bristol Hospital for three years.
Also a volunteer for Bristol Hospital, Preleski has dedicated his time to different local organizations for more than 35 years, first starting his service at the United Way of West Central Connecticut where he served on the board of directors as well as on the finance, investment and executive committees. One of the founders of the Main Street Community Foundation, Preleski also has been a volunteer at St. Stanislaus Church and previously served on the Family Center of Bristol's board of directors for eight years. He started discussions with the Bristol Boys Club, which eventually led to the merger of those two organizations.
"When you give your time and talent to these community groups, you often get much more back then you think you give," said Preleski, who was president of Bristol Savings Bank. "
O'Donnell's involvement with the Bristol community began when she worked as a teller at the Bristol Federal Savings and Loan Association. An active member of the United Way of West Central Connecticut, O'Donnell's service has extended beyond Bristol. She served two terms as president of the Plymouth Chamber of Commerce and now serves as a director. A founding director of the Plymouth Community Food Pantry, O'Donnell also serves as treasurer of the Rotary Club of Terryville.
During her speech, O'Donnell said when she researched the definition of humanitarian, "it means having concern for or helping to improve the welfare and happiness of people."
"I think that definition can be applied to almost everyone here," said O'Donnell, who works as vice president-compliance and risk officer at Thomaston Savings Bank.
Besides the Humanitarian Service Award, the event also recognized several other community members through the PLUS Award, Oliver Gaudreau Award, and the Special Service Award.
The PLUS Award honors a woman, family, or civic organization that "unselfishly gives their time, energy and heartfelt devotion to people within the Bristol area," according to the Boys & Girls Club event program. Chairperson of the Board of Finance in Bristol, Cheryl Thibeault serves in several local organizations, including the Forestville Village Association. A youth leader and Sunday School teacher at Grace Baptist Church, Thibeault helped start the annual Pequabuck Duck Race and Duck Parade, and has been a Girl Scout leader and PTA president.
As a recipient of the PLUS Award, Thibeault challenged the community to "find an intentional act of service."
"We hear the phrase 'random acts of kindness' everywhere we go," said Thibeault, who works at non-profit agency Community Solutions, Inc. "How about intentional acts of service? When you have a purpose…when you have a target group or charity that you wan to help out…there's nothing random about it—it's something you're passionate about."
Giving back to non-profits in her hometown of Bristol, Deidre Tavera served as vice president of the St. Anthony School Board when her children attended St. Anthony's. During that time she offered volunteer consulting services to create a strategic plan for the school and advance fundraising efforts. A volunteer for the Women & Girls Fund of the Main Street Community Foundation, Tavera also facilitated a series of focus groups at St. Paul Catholic High School to create and action plan for a marketing communications program to raise awareness of the school. Outside Bristol, Tavera has served on various boards in the Greater Hartford region, including the Connecticut Alliance for Arts Education.
Tavera said her volunteer work gave her "immense opportunities," as she not only enhanced her skills, but also better understood the needs of the community and met new friends.
During her speech, Tavera also congratulated other award recipients.
"Their work is a testament to the talent and dedication that is so evident in our community of Bristol," said Tavera, adding how her parents set the foundation for her own volunteer service. "We serve and we volunteer…because it's just what we do."
Recipients of the Oliver Gaudreau Award embody the characteristics of Ollie (Oliver Gaudreau), a dedicated Boys and Girls Club member who also was a 70-year member of the Older Members Association. Ollie was known for spending the majority of his adult life working to benefit the Club.
This year, Richard Neill received the award. From the time Neill joined the club at the age of seven, Neill got involved in a variety of club activities, including the Hornets, the swim team. He also served as a volunteer at Camp Wangum, where he worked as a camp counselor and in the kitchen. A long-time member of the Older Members Association, Neill served as chairman of the 50th annual OM Show, and has been a cast member in nearly every show since he joined the organization.
"For 39 great years, [the OMs] are the best guys in the world to do something for the Bristol Boys and Girls Club," said Neill. "They work hard, they perform, and things come out right"
Ninety Nine Restaurants in Bristol and Torrington are known for their "passion to serve" the Bristol Boys & Girls Club as well as the OM's by providing water and other supplies as well as staff. Last year, Ninety Nine Restaurants donated $540,000 to the Boys & Girls clubs of America.
"There's no better cause than taking care of the future of kids," said Matt Keal, general manager of 99 Restaurant in Bristol.
Bristol Boys and Girls Club
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Bristol Blues are ready to fill the sports void this summer
Local fishing stores gear up for opening day
Stay safe, stay fishing: State moves up opening day | {
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A Blommersia dejongi a kétéltűek (Amphibia) osztályába, a békák (Anura) rendjébe és az aranybékafélék (Mantellidae) családjába tartozó faj.
Nevének eredete
Nevét Wilfried W. de Jong biokémikus tiszteletére kapta.
Előfordulása
Madagaszkár endemikus faja. A sziget keleti részén, a Sainte-Marie-szigeten és Toamasina környékén honos.
Megjelenése
Kis méretű békafaj, a megfigyelt hét hím hossza 18,6–21,1 mm, a három nőstényé 21–23,6 mm volt.
Természetvédelmi helyzete
A vörös lista a nem veszélyeztetett fajok között tartja nyilván.
Források
Vences, Köhler, Pabijan & Glaw, 2010 : Two syntopic and microendemic new frogs of the genus Blommersia from the east copast of Madagascar. African Journal of Herpetology, vol. 59, p. 133-156.
A Blommersia dejongi az Amphibiaweb oldalon
Amphibian Species of the World 6.0
Jegyzetek
Blommersia
Kétéltűfajok
Madagaszkár endemikus kétéltűi | {
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Pleasant Stocks Of American Girl Bitty Baby Doll Clothes Patterns Free – Through the thousand Photograph on the web about american girl bitty baby doll clothes patterns free, we all offer the top list having best possible resolution absolutely for you all, and now this images ,in actual fact, one of graphics libraries in our very best pictures gallery in relation to Pleasant Stocks Of American Girl Bitty Baby Doll Clothes Patterns Free. I feel you can want it.
published simply by admin at 2003-01-30 07:58:54. To come up with all models inside Pleasant Stocks Of American Girl Bitty Baby Doll Clothes Patterns Free pictures gallery be sure to follow this specific website hyperlink. | {
"redpajama_set_name": "RedPajamaC4"
} | 4,248 |
Freshman Night
by | Jun 1, 2018 | Front Page News, News & Events, News and Announcements, News Archives
We are so happy to see all the future Nazareth freshman who joined together for the first time as a group as the Class of 2022. Congratulations for becoming a part of the Nazareth family, and we can't wait to see you either for the Summer Bridge Program or the...
Four Nazareth Students Receive Sacrament of Confirmation
by | May 21, 2018 | Front Page News, News & Events, News and Announcements, News Archives
On Sunday, May 20 four Nazareth students received the Sacrament of Confirmation at St. James Cathedral in Brooklyn. Bishop Guy Sansaricq celebrated the Sacrament of Confirmation for Nadia DeFreitas , Kaiya Hamilton, Arianna Rentas, and Juleanna...
Kayla Rodriguez and Brianne Santos Sign Scholarship Letters
by | May 18, 2018 | Athletics News, Front Page News, News & Events, News and Announcements, News Archives
An exciting day for two outstanding senior athletes at Nazareth, Kayla Rodriguez and Brianne Santos both signed their letters of intent to play college basketball last night at the Sports Awards. Kayla signed to play at the College of New Rochelle, while Brianne will...
Coach Dolan Inducted into CHSAA Hall of Fame
by | Apr 20, 2018 | Athletics News, Front Page News, News & Events, News and Announcements, News Archives
Congratulations to Rick Dolan on being inducted into the Girls Catholic High School Athletic Association Hall of Fame! Rick began teaching at Nazareth Regional High School in 1983, coaching Girls' Varsity Basketball, Girls' Softball and Girls'...
Gary Gooden '85 Relives Memories of 1989 NFL Draft
Nazareth alumnus and track coach Gary Gooden was the feature of an article written by The Tablet sports reporter Jim Mancari, chronicling his story of coming into the school and and trying out for football as a freshman all the way through his impressive two-sport...
Erin Holloway and Tiana Marshall make ESPNW Top-25 Recruits
Congratulations to Erin Holloway '21 and Tiana Marshall '21 for being ranked as top-25 recruits for the class of 2021, according to Dan Olson and the Collegiate Girls Basketball Report on ESPNW. Olson's watchlist can be viewed by clicking here, and you can visit...
XBSS Retreat Planning for Leader
Dr. Martin Luther King Jr.'s Birthday – School Closed
Regents Exams
Junior Retreat (AM) | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 5,332 |
Als Młoda Ekstraklasa (Abkürzung ME) wurde die höchste polnische Junioren-Fußballliga bezeichnet.
Geschichte
Die Młoda Ekstraklasa wurde 2007 vom Polnischen Fußballverband (PZPN) ins Leben gerufen, um die Nachwuchsmannschaften der 16 Vereine der Ekstraklasa gegeneinander antreten zu lassen und junge Spieler an die Profimannschaft heranzuführen. Die Spieler dürfen nicht jünger als 16 Jahre und jahrgangsmäßig nicht älter als 21 Jahre sein. Jeder Mannschaft ist es aber auch gestattet drei Spieler im Kader zu haben, die älter sind. Deshalb werden oft Spieler der 2. Mannschaft oder Profispieler, die sich im Aufbautraining nach einer Verletzung befinden, in der Młoda Ekstraklasa eingesetzt. In der ersten Saison 2007/08 nahmen jedoch nur 15 Teams teil, da Widzew Łódź auf die Teilnahme verzichtete.
Im März 2013 wurde bekannt gegeben, dass die Liga am Ende der Saison 2012/13 eingestellt wird und durch die Centralna Liga Juniorów ersetzt wird.
Spielmodus
16 Mannschaften traten in Hin- und Rückrunde gegeneinander an, um den polnischen Jugend-Meister zu ermitteln. Für einen Sieg gab es drei Punkte, für ein Unentschieden einen Punkt und für eine Niederlage gab es keine Punkte. Die Mannschaft, die am Ende der Saison die meisten Punkte hatte, war polnischer Jugend-Meister. Sollten zwei Mannschaften am Ende der Saison gleich viele Punkte gehabt haben, so entschied der direkte Vergleich der zwei Saisonspiele zwischen diesen zwei Mannschaften, wer besser platziert war.
Statistik
Meister
Torschützenkönige
Ewige Tabelle
Die Ewige Tabelle der Młoda Ekstraklasa ist eine Darstellung aller in der Młoda Ekstraklasa absolvierten Spiele und berücksichtigt sämtliche Mannschaften, die seit der ersten Saison 2007/08 und bis zur Einstellung des Ligabetriebs nach der Saison 2012/13 an dem Wettbewerb teilgenommen haben. Fettgedruckte Werte zeigen jeweils den Spitzenwert in einer Sparte an. Der Berechnung wird die 3-Punkte-Regel zugrunde gelegt (drei Punkte pro Sieg, ein Punkt pro Unentschieden).
Weblinks
Offizielle Internetpräsenz der Ekstraklasa (polnisch, englisch)
Unabhängiges Informationsportal zur Ekstraklasa (polnisch)
Młoda Ekstraklasa auf 90minut.pl (polnisch)
Einzelnachweise
Fußballwettbewerb in Polen
Młoda Ekstraklasa | {
"redpajama_set_name": "RedPajamaWikipedia"
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layout: post
date: 2018-02-21
title: "Jonathan James Couture Gabriella"
category: Jonathan James Couture
tags: [Jonathan James Couture]
---
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| {
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} | 5,284 |
La diocesi di Arassa (in latino: Dioecesis Araxensis) è una sede soppressa del patriarcato di Costantinopoli e una sede titolare della Chiesa cattolica.
Storia
Arassa, identificabile con Ören nel distretto di Fethiye in Turchia, è un'antica sede episcopale della provincia romana di Licia nella diocesi civile di Asia. Faceva parte del patriarcato di Costantinopoli ed era suffraganea dell'arcidiocesi di Mira.
La diocesi è documentata nelle Notitiae Episcopatuum del patriarcato di Costantinopoli fino al XII secolo.
Sono quattro i vescovi noti di questa antica sede. Il primo è Toanziano, che Le Quien chiama Teotimo, che partecipò al concilio di Costantinopoli del 381. Leonzio fu presente al concilio di Calcedonia nel 451 e sottoscrisse nel 458 la lettera dei vescovi della Licia all'imperatore Leone I dopo l'uccisione del patriarca alessandrino Proterio. Teodoro fu tra i padri del concilio in Trullo del 692 e infine Stefano prese parte al secondo concilio niceno nel 787.
Dal 1933 Arassa è annoverata tra le sedi vescovili titolari della Chiesa cattolica; la sede è vacante dal 13 aprile 1989. Il suo ultimo titolare è stato Philip Joseph Furlong, vescovo ausiliare del vicariato castrense degli Stati Uniti d'America.
Cronotassi
Vescovi greci
Toanziano (Teotimo ?) † (menzionato nel 381)
Leonzio † (prima del 451 - dopo il 458)
Teodoro † (menzionato nel 692)
Stefano † (menzionato nel 787)
Vescovi titolari
Louis Morel, C.I.C.M. † (21 marzo 1938 - 11 aprile 1946 nominato arcivescovo di Hohot)
Jean-Baptiste Victor Fauret, C.S.Sp. † (13 febbraio 1947 - 14 settembre 1955 nominato vescovo di Pointe-Noire)
Philip Joseph Furlong † (3 dicembre 1955 - 13 aprile 1989 deceduto)
Note
Bibliografia
Michel Le Quien, Oriens christianus in quatuor Patriarchatus digestus, Parigi, 1740, Tomo I, coll. 973-974
Pius Bonifacius Gams, Series episcoporum Ecclesiae Catholicae, Graz, 1957, p. 449
Sylvain Destephen, Prosopographie chrétienne du Bas-Empire 3. Prosopographie du diocèse d'Asie (325-641), Paris, 2008
Collegamenti esterni
La sede titolare su catholic-hierarchy.org
La sede titolare su gcatholic.org
Arassa
Arassa
Arassa | {
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{"url":"https:\/\/www.physicsforums.com\/threads\/greens-theorem-w-holes.661305\/","text":"# Green's Theorem w\/Holes\n\n1. Dec 28, 2012\n\n### Vorde\n\nHey all,\n\nI was working through some problems in my spare time when I realized that I wasn't so satisfied with my understanding of how to use Greens theorem with holes. Can someone refresh my memory?\n\nMore specifically:\n\nLets say I want to take the line integral in some vector field of a curve C which is the union of the circle of radius 1 and the circle of radius 2 (meaning that the region of integration would be between r=1 and r=2).\n\nHow do I go about doing this again? The book says that sometimes I can just take the line integral around the outer curve and ignore the inner curve but doesn't say when\/why this can be done.\n\nThanks.\n\n2. Dec 28, 2012\n\n### lurflurf\n\nlet\nC1 be a circle of radius r1\nC2 be a circle of radius r3\nR the region bounded by C1 and C2\n\n$$\\int\\int_R \\left(\\dfrac{\\partial v}{\\partial x}-\\dfrac{\\partial u}{\\partial y}\\right) \\text{ dx dy}=\\oint_{C_2} (u \\text{ dx}+v \\text{ dy})-\\oint_{C_1} (u \\text{ dx}+v \\text{ dy})$$\n\nIn particular we can find area by choosing for example\nu=-y\/2\nv=x\/2\n\n$$A=\\int\\int_R \\text{ dx dy}=\\frac{1}{2}\\left(\\oint_{C_2} (-y \\text{ dx}+x \\text{ dy})-\\oint_{C_1} (-y \\text{ dx}+x \\text{ dy})\\right)=\\pi(r_2^2-r_1^2)$$\n\n3. Dec 28, 2012\n\n### Vorde\n\nAh! Okay, if only my damn book wrote that!\n\nThat makes things lovely.\n\nIs there anything to the fact that sometimes you can ignore the hole though?\n\n4. Dec 28, 2012\n\n### I like Serena\n\nGenerally you cannot simply ignore the hole.\nOne of the conditions in applying Green's theorem, is that the partial derivatives exist and are continuous in the entire region.\n\nIn this particular case there is a work around for the hole though.\nYou can connect the 2 circles with 2 line segments that (almost) coincide.\nThat way the relevant region is really the region between the 2 circles, so there can be a hole in the middle.\nSince the partial derivatives have to be continuous, it does not matter that an infinitesimal area is missing (the part \"between\" the 2 line segments).\n\nSuppose G is the curve containing the 2 circles and the 2 line segments, but not the center.\n\nThen properly we have:\n$$\\int\\int_R \\left(\\dfrac{\\partial v}{\\partial x}-\\dfrac{\\partial u}{\\partial y}\\right) \\text{ dx dy} =\\int\\int_{R \\text{ without the area between the line segments}} \\left(\\dfrac{\\partial v}{\\partial x}-\\dfrac{\\partial u}{\\partial y}\\right) \\text{ dx dy}$$\n$$=\\oint_{G} (u \\text{ dx}+v \\text{ dy}) =\\int_{C_1 \\text{ reversed}} (u \\text{ dx}+v \\text{ dy}) + \\int_{L_1} (u \\text{ dx}+v \\text{ dy}) + \\int_{C_2} (u \\text{ dx}+v \\text{ dy}) + \\int_{L_2} (u \\text{ dx}+v \\text{ dy})$$\n\nSince the line segments L1 and L2 (almost) coincide and are opposite in direction, their respective integrals cancel.\nAnd since the area where the circles are integrated is continuous, the open circle integrals are the same as the closed circle integrals.\nSo we get:\n$$=\\oint_{C_2} (u \\text{ dx}+v \\text{ dy})-\\oint_{C_1} (u \\text{ dx}+v \\text{ dy})$$\n\nSo yes, in this case you can ignore the hole.\nActually, the trick is to circumvent the hole, so there is no hole.","date":"2018-01-18 10:46:51","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.8564612865447998, \"perplexity\": 451.3926917802842}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2018-05\/segments\/1516084887224.19\/warc\/CC-MAIN-20180118091548-20180118111548-00441.warc.gz\"}"} | null | null |
A biotech firm made a smallpox-like virus on purpose. Nobody seems to care
By Gregory D. Koblentz | February 21, 2020
Seth Lederman, the CEO of Tonix Pharmaceuticals, heads a company that recently synthesized the vaccinia virus, a germ closely related to the one that causes smallpox. Credit: Bulletin/Barryfc101 CC BY-SA 4.0.
In 2017, the virologist David Evans made headlines when he used synthetic biology to recreate the extinct horsepox virus, which is closely related to the virus that causes smallpox, a disease eradicated in 1980. Evans and his team, ordering the genetic material they needed through the mail, reportedly spent $100,000 on the research, an amount that seems small given the momentous implications of their work. "No question. If it's possible with horsepox, it's possible with smallpox," German virologist Gerd Sutter told Science magazine in a press account of Evans's work. A number of biosecurity experts and even The Washington Post editorial board joined him in voicing their concerns. Given the reaction Evans met, one might expect the news that yet another microbe related to the smallpox virus had been synthesized to set off similar alarm bells.
Yet when the American biotech company that funded Evans's horsepox work, Tonix Pharmaceuticals, announced this January that it had successfully synthesized just such a microbe, vaccinia, no one seemed to take note.
Since the World Health Organization eradicated the smallpox-causing variola virus from nature, the only known samples of it have been held in two high-security facilities in the United States and Russia. But developments in synthetic biology, a field which includes the art and science of constructing viral genomes, have made it possible to create the smallpox virus in a lab. While there's no evidence that anyone has done that yet, as Tonix's work indicates, researchers are inching incredibly close to that line. Before it was eradicated, smallpox was responsible for 300 million deaths in the 20th century. The re-introduction of the disease—through negligence or malice—would be a global health disaster. As I wrote in International Security 10 years ago, global biosecurity can be endangered not just by biological warfare and bioterrorism, but also by laboratory accidents with dangerous pathogens.
Tonix announced the new synthetic vaccinia virus quietly, burying the news in a press release for a poster that the firm presented at the American Society for Microbiology's annual biodefense science and policy conference. The poster focused on the progress the company was making in testing Evans's synthetic horsepox virus for use as a vaccine against smallpox, which Tonix calls TNX-801. Current smallpox vaccines are based on live vaccinia virus that is grown using cell culture technology. Tonix's poster also references another smallpox vaccine candidate the company is testing, one based on a synthetic version of the vaccinia virus that Tonix is calling TNX-1200. While the vaccinia and horsepox viruses are not themselves serious threats to human health, there are several reasons why this new development in synthetic biology is problematic.
Tonix has apparently ignored the concerns that many biosecurity experts, including myself, have raised. Given the close genetic similarity among orthopoxviruses like the horsepox, variola, and vaccinia viruses, the laboratory techniques that can be used to create one can also be used to produce others–most worryingly, the smallpox-causing variola virus. Indeed, Evans has said as much himself, once pointing out that his research "was a stark demonstration that this could also be done with variola virus." Evans's lab used the same technique to produce the synthetic vaccinia virus for Tonix as it did to synthesize the horsepox virus.
Unlike in other cases of controversial dual-use research, the risks posed by the synthesis of orthopoxviruses are not offset by any significant benefits. In 2018, I wrote that the benefits of using Evans and Tonix's horsepox virus as a smallpox vaccine rested on a weak scientific foundation, and an even weaker business case. The case for synthesizing vaccinia is more dubious. Tonix cannot claim that synthesizing the vaccinia virus was the only way to obtain it. Unlike horsepox virus, which went extinct in the 1980s and for which the only known sample is held by the Centers for Disease Control and Prevention, vaccinia is widely available from multiple sources.
The business case for a new smallpox vaccine based on novel platforms such as synthetic horsepox or synthetic vaccinia is even weaker than it was a few years ago. One of Tonix's key talking points about the vaccine based on the synthetic horsepox virus is that it would be safer than older vaccine varieties. Since the company's synthetic vaccinia strain in the TNX-1200 vaccine is "very similar" to the vaccinia strain used in one of the older, so-called second generation, smallpox vaccines, it's hard to see how this new synthetic vaccine could have an improved safety profile. Further complicating Tonix's case is that there is now a newer and safer third-generation smallpox vaccine available. Last year, the US Food and Drug Administration licensed Bavarian Nordic's JYNNEOS vaccine, which is based on a non-replicating strain of vaccinia. This vaccine doesn't damage the heart, unlike second-generation smallpox vaccines, and can even be given to people with compromised immune systems. Tonix will likely find it difficult to attract the venture capital or government funding needed to win approval and licensing for either of its synthetic smallpox vaccine candidates.
Given the current level of interest among scientists in using orthopoxviruses, as well as related pox viruses, to develop new vaccines and cancer therapies, there is already a well-established foundation of laboratories that could use synthetic biology to further their research. Indeed, Evans had previously expressed his hope to synthesize genetically engineered vaccinia strains to develop new anti-cancer treatments. As evidenced by the relatively muted reaction to Tonix's synthetic vaccinia announcement, there's a strong risk that orthopoxvirus synthesis could gradually be viewed as normal, legitimate research. It's not difficult to imagine the emergence of a global cadre of labs and scientists capable of developing synthetic versions of the infectious smallpox virus.
While orthopoxviruses are among the most complicated and expensive viruses to synthesize, a World Health Organization scientific advisory panel found that "a skilled laboratory technician or undergraduate students working with viruses in a relatively simple laboratory" could be up to the task. The genome sequence of variola virus has already been determined and is available online. The key ingredient needed to synthesize a viral genome is DNA. In the case of variola virus, what's required is about 186,000 base-pairs of genetic material. And there is now a global industry of DNA synthesis companies that produce and sell DNA for use in biomedical research and biomanufacturing.
As described by the World Health Organization panel, once a lab has acquired the necessary DNA molecules, it would need to assemble the material into a complete genome and use a helper virus to generate an infectious variola virus. By my count there are at least 100 laboratories around the world with the expertise to do so.
Worryingly, there are few meaningful national or international safeguards to prevent access to the DNA needed to synthesize the variola virus. According to a 2019 global survey of biosecurity practices by the Nuclear Threat Initiative, a nonprofit that tracks biosecurity risks and other threats, no country requires the companies that sell synthetic DNA to prevent "questionable parties" from acquiring materials. The think tank also found that less than 5 percent of countries regulate dual-use research, such as the use of techniques that might also be used to synthesize dangerous viruses.
The only positive development in this area in the last few years is that the International Gene Synthesis Consortium, a group of DNA synthesis companies that screens customers and their orders, has prohibited its members from synthesizing gene sequences unique to the smallpox virus genome. Unfortunately, the consortium represents only 80 percent of the global DNA synthesis market, leaving an uncomfortably large number of companies operating without any sort of regulation on what they can make and who they can sell it to.
The loosely regulated market for synthetic DNA, the normalization of synthetic orthopoxvirus research, and a large number of capable facilities and researchers creates an environment in which a rogue state, unscrupulous company, reckless scientist, or terrorist group could potentially reintroduce one of the worst microbial scourges in human history.
Unless world bodies, national governments, and scientific organizations put in place stronger safeguards on synthetic virus research, the next press release touting a new breakthrough in synthetic biology might announce that an unknown scientist in an obscure lab has successfully resurrected the smallpox virus.
Keywords: David Evans, Tonix Pharmaceuticals, smallpox, synthetic biology, vaccinia virus
Topics: Disruptive Technologies, Synthetic biology
Brian Whit
Can we pass laws to send these folks to jail?
Crimes against humanity?
Regulation is lacking, laws need to be created.
This article's conclusion is — disappointing in its bland response.
They should be treated as terrorists.
We humans continue to insist on creating problems for ourselves, for Mother Earth, and for or future
RBHoughton
What we have learned about nuclear tech is that every country that has mastered it will use it when it knows its losing the war. These biotech products are the same. We are all under the control of political masters with only national authority. That's not good enough.
Gregory D. Koblentz
Gregory D. Koblentz is an associate professor and director of the Biodefense Graduate Program at the Schar School of Policy and Government at George... Read More
Disruptive technologies in 2022
By Sara Goudarzi | {
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Matilde Noemí Lalín is an Argentine-Canadian mathematician specializing in number theory and known for her work on L-functions, Mahler measure, and their connections. She is a professor of mathematics at the Université de Montréal.
Education and career
Lalín is originally from Buenos Aires, and is a double citizen of Argentina and Canada. As a high school student, she represented Argentina twice in the International Mathematical Olympiad, in 1993 and 1995, earning a silver medal in 1995.
She earned a licenciatura in 1999 from the University of Buenos Aires. After starting graduate study at Princeton University and spending a term as a visiting student at Harvard University, she completed her doctorate in 2005 at the University of Texas at Austin. Her dissertation, Some Relations of Mahler Measure with Hyperbolic Volumes and Special Values of L-Functions, was supervised there by Fernando Rodriguez-Villegas.
She became a postdoctoral researcher at the Institute for Advanced Study, Mathematical Sciences Research Institute, Institut des Hautes Études Scientifiques, Max Planck Institute for Mathematics, and Pacific Institute for the Mathematical Sciences, before obtaining a tenure-track faculty position in 2007 as an assistant professor of mathematics at the University of Alberta. She moved to the Université de Montréal in 2010, earned tenure as an associate professor there in 2012, and was promoted to full professor in 2018.
Recognition
Lalín is the 2022 winner of the Krieger–Nelson Prize of the Canadian Mathematical Society, "for her outstanding contributions to research in Number Theory and related areas". She was named to the 2023 class of Fellows of the American Mathematical Society, "for contributions to number theory, including the study of L-functions, and for service to the mathematical community".
References
External links
Home page
Year of birth missing (living people)
Living people
Argentine mathematicians
Argentine women mathematicians
Canadian mathematicians
Canadian women mathematicians
University of Buenos Aires alumni
University of Texas at Austin alumni
Academic staff of the University of Alberta
Academic staff of the Université de Montréal
Fellows of the American Mathematical Society | {
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The Spring Valley House–Sulfur Springs Hotel is a historic former hotel located along Dee Bennett Road in rural Utica Township, LaSalle County, Illinois. Built circa 1849, the hotel is unusually large for a rural hotel of the area. The brick and limestone building, which features Greek Revival elements and vernacular stonework, is four stories tall and in area. Its size is likely a result of it serving two different audiences; due to its proximity to the Illinois River and a major stagecoach line, it hosted travelers passing through the area, but it also functioned as a resort destination due to the area's hot springs. Three such springs are located on the site of the hotel, one of which has a spring house built over it. The opening of the Chicago and Rock Island Railroad through the area doomed the hotel, as stagecoach and river travel declined dramatically, and it closed after 1862.
The hotel building was added to the National Register of Historic Places on November 20, 1987.
References
Hotel buildings on the National Register of Historic Places in Illinois
National Register of Historic Places in LaSalle County, Illinois
Greek Revival architecture in Illinois
Historic districts in Illinois | {
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When writing the last proper post for the proper website, I expressed a sickened frustration at the prospect of a lifetime – I've always got three-score-and-ten ahead of me, no matter how old I am – of being subjected to the trauma of constant updates on the fate of Waterford teams the length and breadth of the land. In retrospect this was a rather maudlin way of looking at it, unworthy of Modeligo and Cappoquin asterling performances in their respective Munster championships. The truth of the matter is that interest in a particular competition will ebb and flow according to the prospect of Waterford success. It's a logarithmic progression, so when (for example) the Waterford ladies football team are a hot prospect at Senior level, interest in them rockets. Let their standards slip, even a little, and interest drops right back down again. This isn't something that is peculiar to myself or Waterford folk. Stephanie Roche will be able to tell you all about the phenomenon as she hangs up her fancy frock and pulls back on a self-laundered shirt.
With that in mind, could interest in the Waterford footballers be about to rocket? While forlornly keeping tabs on Modeligo and Cappoquin's ultimately unsuccessful tilt at All-ireland glory, what should happen but the footballers only go and beat Cork then win the McGrath Cup. I can hear the scoffing at the notion that winning the McGrath Cup or beating Cork on the way to it means anything in the wider scheme of things, and it's fair to say it won't mean much if it doesn't translate into success at bigger dances. Still, we've met Cork many times since the last win over them in 1960. On many of those occasions it would have been a small-time fixture with Cork at one of their habitual low ebbs – the Rebels only seem to have two modes: steely-eyed assassins or in-fighting riddled rabble, with no points to be found in-between. Yet despite that, Cork won every one of those fixtures. So for Waterford to beat them then close out the competition with a win over the Sigerson Cup winners does indeed count for something.
Waterford football has always been an enigma. It's not unfair to say that, in the course of my lifetime, we have been the worst county in the land. Yes, I know Kilkenny have been worse, but given their notorious scorched earth policy towards the big ball game, that's not setting the bar very high. It's not as if the raw materials for some manner of competitiveness are not present. Large swathes of the county are dominated by football, and it's strange to contemplate that those people who are so committed to the game can't get their act together to the point where they can give Clare, Limerick and Tipperary a goon a frequent basis. This is particularly true now the back door is in place. The prospect of being whaled upon by Kerry and Cork, even when the latter would be in-fighting riddled rabble, would have justifiably put off many a generation of Waterford football talent from making the necessary investment to compete at the highest level. Once the back door was introduced though, you would have expected a better showing. Even if progress through Munster only ever ended one way, you could then draw a fresh new challenge from up the country and have a reasonable expectation of beating any of the counties that tend to move between Divisions Three and Four of the National Football League. That's not how it has worked out though. They gave Galway an awful fright a few years back in Salthill, and the high-profile scalping of London was noteworthy, giving us all a good chuckle at seeing it on Sky Sports News. Other than that though, the back door has proven to be just as barren as the provincial championship, and losing last year to Carlow, the Carlow beaten by 28 points in the Leinster championship , the Carlow undergoing much internal angst over the rise of hurling at the expense of football, suggested that Waterford football was going nowhere fast.
Could Tom McGlinchey be about to change all that? No, of course not. The infrastructure impediments that see underage teams thrown together at the last minute and the sense of inadequacy that plagues Waterford teams at all levels in all codes are not going to removed overnight. It doesn't all have to change though to get better. Any improvement is better than none at all, and they might well have taken that first step in such a journey.
This entry was posted in Football, Waterford and tagged Cappoquin, Cork, McGrath Cup, Modeligo on 27/01/2015 by deiseach.
It's been a good couple of weeks for Waterford GAA, what with Modeligo and The Nire reaching their respective provincial finals, and Cappoquin winning theirs. It might not seem like much in the grander scheme of things but if the tweet I referenced last year was correct, i.e. that Ballysaggart's three wins in the Munster championship were more than all previous entrants managed in the Junior competition's entire history, then it's definitely been a good couple of weeks for Waterford GAA. It's an article of faith that the Intermediate and Junior competitions are far less competitive in Waterford than they would be in the larger counties, so any evidence of broadening the base of talent in the county is to be welcomed. As for the footballers, it's always been a curious anomaly that a county with a robust infrastructure for the big ball game cannot even take on the best that Clare, Limerick and Tipperary have to offer with any confidence, let alone those hailing from Cork and Kerry. Add in a savage, if shameful, delight at The Nire taking the wind out of the sails of the supposed Invincibles of Cratloe, thus gaining a measure of revenge for their hurling win over Ballygunner, and it has been a very good couple of weeks for Waterford GAA.
I hope the fundamentals have changed. When Waterford teams of the past were going down like dominoes as soon as they crossed the Suir/Blackwater, it didn't really matter because the first I'd know about it was reading a headline in the local papers or, if I was feeling particularly energetic, a single line in tiny font in the results section of the Monday national paper. In the days since Twitter went supernova (see top of post), it's incredibly easy to keep tabs on the adventures of Waterford teams against mysterious rivals like Bruff, Ballylanders, Feohanagh-Castlemahon or Castlemartyr. Okay, not all rivals are that mysterious. Hammering away at the refresh button on my Twitter feed to see how The Nire were getting on against Cratloe was a surprisingly tense affair. It's not The Nire I care about, it's the Waterford team, and there are going to be six of the them at the various levels in each code to concern myself with. If this becomes habit-forming, and the fundamentals have not changed – the anomaly is the current run of competitiveness and we will soon see a reversion to the mean with frequent 20-point beatings for each of the respective county champions – then there's going to be many a cold winter on Twitter ahead.
This entry was posted in Football, Hurling, Munster, Waterford and tagged Ballysaggart, Cappoquin, Modeligo, Munster, The Nire on 26/11/2014 by deiseach.
This entry was posted in Football, GAA, Hurling, Waterford on 04/10/2012 by deiseach.
One of my enduring benign memories of Croke Park, benign because most of the memories from Jones's Road are anything but, was of going to see Ireland play Australia in what I still think of as the Compromise Rules series in 2000. While Australia won handily enough it was an enjoyable day out, and a real treat to be in a crowd of 57,289 (says Wikipedia) who were all rooting for the same team. Before the game we had the equivalent fixture between Ireland and Scotland in hurling/shinty and when that finished the Jocks, replete with names like Fraser Colqouhoun and Alastair Campbell-McDonald that would have flagged what school they went to, took a lap of honour around the embryonic cathedral. It was impossible not to have a wry chuckle at the contrast with what the equivalent venue in Scotland must be like. You're not in Kansas anymore.
Impossible, but how wrong-headed was such smugness. Quite apart from being a little bit rude, this weekend we'll see what has built Croke Park and it has very little to do with hurling. Ian O'Riordan wrote an article in the 2009 Munster hurling final programme on the occasion of the 125th edition of the match where he noted that the GAA had two objectives when it was established: to revive 1) the Irish language, and 2) the ancient game of hurling. In those terms, the GAA has been a failure as both the teanga and the iománaíocht languish in ghettos. So it's just as well that a lesser objective, that of tearing people away from the pernicious British sports of association football and rugby football that were beginning to put down roots, was so successful.
While researching the results archive, it struck me how the GAA once scrupulously maintained its calendar at inter-county level in such a way as to give everyone the chance to play both sports. Football and hurling never clashed during the League season. That's no longer the case, and in truth it probably wasn't ever that big a deal in a practical sense as proper dual stars were a rare beast. Still, the principle was there and an outsider might wonder why such respect was being accorded by the majority sport to that of the minority pursuit. This is especially true considering the scoffing that hurling supporters frequently come out with about the self-evident superiority of hurling in every sense – skill, excitement, drama, history, even skills with foot to ball after Nicky English's goal in the drawn 1987 Munster final. Much as with the Irish language, it's probably a reflection of the reluctance to abandon those early aspirations of the GAA that the football 80% (approx) of the association hasn't told hurling to paddle yer own bloody canoe, you've got the equipment with which to do it.
We'll see it large this weekend. The tsunami that is going to sweep out of the west upon Dublin is going to be epic. You might argue that mere numbers don't matter, that the excitement will be a question of never mind the quality, feel the width. But this is going to be a truly national experience. Only the most arch of anti-GAA bigots could fail to be intrigued by what is going on, two teams who have cleared multiple difficult hurdles to find themselves 70 minutes away from fulfilling the dreams of generations of their fellow county men and women – or alternately crushing them once again. It's going to be great, and despite being a hurling man first and foremost, it's a pleasure to be a part of it.
This entry was posted in Football, GAA, Hurling, Waterford and tagged Donegal, International Rules, Mayo, Shinty on 21/09/2012 by deiseach.
There are two me's when it comes to the GAA. The online me, the one that fancies himself as the descendant of Déiseach and who has been carrying the online Waterford GAA flame since 1999. At the very least I'd like to think of this blog as being part of an embryonic 32-county community of Gaeldom with me ploughing a lonely furrow for Waterford now that Up the Déise is a shadow of its former glory. And there's no doubt who owns the house that is known by the trees in this notional community – 'Willie Joe' (not his real name) of the Mayo GAA Blog. It's a smashing resource for supporters of Mayo football, and it almost made me weep to see a recent post on Twitter where he said he'd had over 6,000 hits in one day. Speaking of weeping, it's been a tough ride over the years for Mayo supporters – their loss to Meath in the curtain-raiser to our match against Kilkenny in 2009 is still fresh in my mind – so it would be marvellous for them in general and Willie Joe in particular were Mayo to finally land the Big One 61 years after they last won it. Hey, that's how long Ireland went without the Grand Slam! It's meant to be, isn't it?
Well, no. For facing them in the opposite corner is the featherweight that has beefed itself up into a heavyweight. Watching Donegal sweep Cork aside in the All-Ireland semi-final was a gobsmacking experience. Jim McGuinness got a lot of stick last year for the destructive manner of their style of play, but that was just a prelude to the well-oiled machine that Donegal have become. While they're clearly a fit team – I enjoyed the comment of one wag on the GAA Discussion Board that "Chuck Norris was first to puke when he trained with Donegal" – that alone does not explain the bewildering array of angles that each of the Donegal players takes when not on the ball. Any time a Donegal player was in possession he could be confident that there would be two or three team-mates in the vicinity, usually making a beeline for the opposition goal. All the talk on the Mayo GAA Blog and on Twitter about how Donegal are over-confident does not mean that Donegal have nothing to be over-confident about. Everything has to go right for Mayo for them to end that 61-year wait, and luck is not something you associate with Mayo.
Not that feeling Donegal are going to take some stopping is a reason to hope they win. No, it is because of the other me that a victory for Dún na nGall would be a great thing. Note that it is 'Dún na nGall', not 'Tír Chonaill', because Tír Chonaill does not include the Inishowen peninsula. I know this because it was explained to me by my best friend Pól, the best man at my wedding. Were Donegal to win the All-Ireland it would mean so much to him and it probably mean even more to his father, a man whose wool is so GAA-dyed that he saw fit to invite me to see the Donegal Minor footballers take on Derry in a friendly match in Celtic Park on the one occasion I was at the family homestead in Letterkenny – a vote of confidence in me if ever there was one. I know (of) many Mayo people online thanks to Willie Joe. I know one Donegal family in real life thanks to Pól. Will I be rooting for the needs of the virtual many or the substantive few? I'll find out on September 22nd.
What was that? Who will I be cheering for this Sunday? Don't be daft. Come on the Tribesmen.
This entry was posted in Football, Hurling and tagged Donegal, Galway, Kilkenny, Mayo on 07/09/2012 by deiseach.
It's hard enough for the Waterford county football champions to take on whatever team emerges from the Kingdom in the Munster club football championship. But the entire county?
This entry was posted in Football, Munster, Waterford and tagged Kerry, Munster on 03/10/2011 by deiseach. | {
"redpajama_set_name": "RedPajamaC4"
} | 1,347 |
<?php
/**
* Created by PhpStorm.
* User: Hesk
* Date: 14年8月6日
* Time: 上午11:59
*/
defined('ABSPATH') || exit;
if (!class_exists('userRegister')) {
class userRegister
{
private $reg_user, $vcoin_transaction, $titan;
public function __construct()
{
}
function __destruct()
{
$this->reg_user = NULL;
$this->vcoin_transaction = NULL;
gc_collect_cycles();
}
public static function user_reg()
{
add_action("user_register", array(__CLASS__, "new_user_reg"), 11, 1);
add_action("delete_user", array(__CLASS__, "my_delete_user"), 11, 1);
}
public static function my_delete_user($user_id)
{
global $wpdb;
$user_obj = get_userdata($user_id);
$email = $user_obj->user_email;
$headers = 'From: ' . get_bloginfo("name") . ' <' . get_bloginfo("admin_email") . '>' . "\r\n";
wp_mail($email, 'You are being deleted, brah', 'Your account at ' . get_bloginfo("name") . ' is being deleted right now.', $headers);
api_cms_server::enable_account($user_id, false);
}
/**
* register action callback in here
* @param $user_id
* @internal param $ID
*/
public static function new_user_reg($user_id)
{
$user = new WP_User($user_id);
if (is_array($user->roles)) {
if ($user->roles[0] == "appuser" || $user->roles == "appuser") {
if (get_user_meta($user_id, "uuid_key", true) == "") {
$re = new userRegister();
$re->admin_create_vcoin_key_user($user);
}
}
}
$user = NULL;
}
/**
* totally independent function to create new user from the admin panel
* @param WP_User $user
*/
public function admin_create_vcoin_key_user(WP_User $user)
{
$this->reg_user = $user;
$this->create_vcoin_key_for_user();
}
/**
* create a vcoin key for the user
* and create an user for the application
*/
private function create_vcoin_key_for_user()
{
$this->titan = TitanFramework::getInstance('vcoinset');
$this->vcoin_transaction = new vcoinBase();
$data = get_userdata($this->reg_user->ID);
$bind_id = $this->vcoin_transaction->create_new_user($data->user_email);
update_user_meta($this->reg_user->ID, "uuid_key", $bind_id);
$free_v_coin = $this->titan->getOption("vcoin_registration");
if (intval($free_v_coin) > 0) {
$this->vcoin_transaction = new vcoinBase();
$this->vcoin_transaction->setReceive($bind_id);
$this->vcoin_transaction->setSender(IMUSIC_UUID);
$this->vcoin_transaction->setAmount($free_v_coin);
$this->vcoin_transaction->setTransactionReference("new account coins");
$this->vcoin_transaction->CommitTransaction();
}
inno_log_db::log_vcoin_email(-1, 901201,
"new free coin from opening account. added (v)" . $free_v_coin . " to the account user " . $this->reg_user->ID .
" with trace_id" . $this->vcoin_transaction->get_tranaction_reference() . " and the uuid key is " . $bind_id
);
}
/**
* @param $login_name
* @param $user_email
* @param $role
* @param array $extra_fields
* @param $pwd
* @throws Exception
* @internal param array $extrafields
*/
public function newUser($login_name, $user_email, $role, $extra_fields = array(), $pwd)
{
try {
if ($role == "appuser") {
$extra_fields["birthday"] = "1/1/2000";
$extra_fields["country"] = "Hong Kong";
$extra_fields["countrycode"] = "HKG";
$extra_fields["setting_push_sms"] = "0";
$extra_fields["sms_number"] = "";
$extra_fields["gender"] = "M";
$extra_fields["uuid_key"] = "";
$extra_fields["app_token"] = "";
$extra_fields["password"] = $pwd;
$extra_fields["coin"] = 0;
$extra_fields["coin_update"] = "";
$extra_fields["profile_picture_uploaded"] = "";
} else if ($role == "developer") {
$extra_fields["service_plan"] = 100;
$extra_fields["app_coins"] = 0;
}
// inno_log_db::log_vcoin_login(-1, 101222, "new user create_user_account.");
$this->reg_user = $this->create_user_account($login_name, $user_email, $role, $extra_fields, $pwd);
if ($role == "appuser") {
// inno_log_db::log_vcoin_login(-1, 101222, "new user and add uuid to the vcoin server.");
$this->create_vcoin_key_for_user();
}
} catch (Exception $e) {
throw $e;
}
}
/**
* @param $login_name
* @param $user_email
* @param $role
* @param array $extra_fields
* @throws Exception
*/
public function newUserRandomPass($login_name, $user_email, $role, $extra_fields = array())
{
try {
$this->reg_user = $this->create_user_account($login_name, $user_email, $role, $extra_fields, wp_generate_password($length = 12, $include_standard_special_chars = TRUE));
if ($role == "appuser") {
$this->create_vcoin_key_for_user();
}
} catch (Exception $e) {
throw $e;
}
}
/*
public static function UpdateUserMeta($user_id, $data)
{
if (is_array($data)) {
foreach ($data as $key => $value) {
update_user_meta($user_id, $key, $value);
}
}
}
public static function AddUserMeta($user_id, $data)
{
foreach ($data as $key => $value) {
add_user_meta($user_id, $key, $value);
}
}*/
/**
* @param $user_name
* @return string
*/
protected static function get_unique_new_username($user_name)
{
$returnUsername = '';
$check_same_id = 0;
if (!is_null(username_exists($user_name))) {
$check_same_id++;
$returnUsername = $user_name . $check_same_id;
} else {
$returnUsername = $user_name;
}
return $returnUsername;
}
/**
* create a user account in here now
* @param $login_name
* @param $user_email
* @param $role
* @param array $extra_fields
* @param $pwd
* @throws Exception
* @return WP_User
*/
protected static function create_user_account($login_name, $user_email, $role, $extra_fields = array(), $pwd)
{
try {
// $pwd = !$generate_password? wp_generate_password($length = 12, $include_standard_special_chars = TRUE);
// add_action("user_register", array(__CLASS__, "user_reg_action_cb"), 10, 1);
remove_action("user_register", array(__CLASS__, "new_user_reg"));
$namelist = explode(" ", $login_name);
$login_name_final = $role . gformBase::gen_order_num() . join("_", $namelist);
$user_id = wp_create_user($login_name_final, $pwd, $user_email);
if (is_wp_error($user_id)) {
throw new Exception($user_id->get_error_message(), 10129);
}
add_action("user_register", array(__CLASS__, "new_user_reg"));
// remove_action("user_register", array(__CLASS__, "user_reg_action_cb"));
$user = new WP_User($user_id);
foreach ($extra_fields as $key => $val) {
// update_user_meta($user_id, $key, $val, false);
add_user_meta($user_id, $key, $val, false);
}
update_user_meta($user_id, 'display_name', $login_name);
update_user_meta($user_id, "nickname", $login_name);
update_user_meta($user_id, "first_name", $namelist[0]);
update_user_meta($user_id, "last_name", $namelist[1]);
// debugoc::upload_bmap_log(print_r($args, true), 29291);
//wp_insert_user($args);
$user->remove_role('subscriber');
$user->add_role($role);
return $user;
} catch (Exception $e) {
throw $e;
}
}
/**
* Handles sending password retrieval email to user.
*
* @uses $wpdb WordPress Database object
* @param string $user_login User Login or Email or User ID
* @return bool true on success false on error
*/
public static function retrieve_password($user_login)
{
global $wpdb, $current_site;
if (empty($user_login)) {
//
return false;
} else if (is_numeric($user_login)) {
$user_data = get_user_by('id', $user_login);
} else if (strpos($user_login, '@')) {
$user_data = get_user_by('email', trim($user_login));
if (empty($user_data))
return false;
} else {
$login = trim($user_login);
$user_data = get_user_by('login', $login);
}
do_action('lostpassword_post');
if (!$user_data)
return false;
// redefining user_login ensures we return the right case in the email
$user_login = $user_data->user_login;
$user_email = $user_data->user_email;
// do_action('retreive_password', $user_login);
// Misspelled and deprecated
do_action('retrieve_password', $user_login);
$allow = apply_filters('allow_password_reset', true, $user_data->ID);
if (!$allow)
return false;
else if (is_wp_error($allow))
return false;
$key = $wpdb->get_var($wpdb->prepare("SELECT user_activation_key FROM $wpdb->users WHERE user_login = %s", $user_login));
if (empty($key)) {
// Generate something random for a key...
$key = wp_generate_password(20, false);
do_action('retrieve_password_key', $user_login, $key);
// Now insert the new md5 key into the db
$wpdb->update($wpdb->users, array('user_activation_key' => $key), array('user_login' => $user_login));
}
$message = __('Someone requested that the password be reset for the following account:') . "\r\n\r\n";
$message .= network_home_url('/') . "\r\n\r\n";
$message .= sprintf(__('Username: %s'), $user_login) . "\r\n\r\n";
$message .= __('If this was a mistake, just ignore this email and nothing will happen.') . "\r\n\r\n";
$message .= __('To reset your password, visit the following address:') . "\r\n\r\n";
$message .= '<' . network_site_url("wp-login.php?action=rp&key=$key&login=" . rawurlencode($user_login), 'login') . ">\r\n";
if (is_multisite())
$blogname = $GLOBALS['current_site']->site_name;
else
// The blogname option is escaped with esc_html on the way into the database in sanitize_option
// we want to reverse this for the plain text arena of emails.
$blogname = wp_specialchars_decode(get_option('blogname'), ENT_QUOTES);
$title = sprintf(__('[%s] Password Reset'), $blogname);
$title = apply_filters('retrieve_password_title', $title);
$message = apply_filters('retrieve_password_message', $message, $key);
if ($message && !wp_mail($user_email, $title, $message))
wp_die(__('The e-mail could not be sent.') . "<br />\n" . __('Possible reason: your host may have disabled the mail() function...'));
return true;
}
}
} | {
"redpajama_set_name": "RedPajamaGithub"
} | 316 |
Q: how to fix cannot convert int to boolean package com.mime.WorldExplorer.graphics;
import java.util.Random;
public class Screen extends Render {
private Render test;
public Screen(int width, int height) {
super(width, height);
Random random = new Random();
test = new Render(256, 256);
for (int i = 0; 256*256; i++ ) {
test.pixels[i] = random.nextInt();
A: This line:
for (int i = 0; 256*256; i++ )
should be
for (int i = 0; i < 256*256; i++ )
According to Java docs, one way to declare the for loop is:
for (initialization; termination;
increment) {
where:
*
*The initialization expression initializes the loop; it's executed once, as the loop begins.
*When the termination expression evaluates to false, the loop terminates.
*The increment expression is invoked after each iteration through the loop; it is perfectly acceptable for this expression to increment or decrement a value.
So, termination should be a condition that evaluates to a boolean, not an integer.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 7,818 |
Q: Possible code for active div In logged.php:
$TPL->NavBar('active',' ');
In class.template.php:
public function NavBar($home,$about) {
$this->Content('navigator_bar');
}
In navigator_bar.php:
<li class= <?php $home ?> ><a href="home">Home</a></li>
<li class= <?php $about ?> ><a href="about">About</a></li>
Is that possible to link $home and $about variables into a new file.php?
A: Use request methods such as $_GET,$_POST,$_REQUEST to send data to your new_file.php
or
set the variables in session to get it in your new_file.php
IN SESSION:
In Logged.php:
echo $_SESSION['home_val'] = $home;
echo $_SESSION['about'] = $about;
In new_file.php:
$_SESSION['home_val'];//gives $home
$_SESSION['about'];//gives $about
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 3,355 |
As we come to the end of a successful year, we want to thank those who have contributed to our success. Many have asked how they can help or donate this holiday season to Amazing Gracie's Gift Foundation. The holiday season is the perfect time to show those around you how much you care. For those who are hard to buy for, consider making a donation in honor of them or in memory of someone special as a gift this season. In return, your donation will be recognized and a Christmas card will be sent mentioning your gesture.
Include who your donation is in honor/memory of. Please provide a name and address of the person who you would like to receive a card. | {
"redpajama_set_name": "RedPajamaC4"
} | 8,101 |
Amanda Inez Knight Allen (September 8, 1876 – June 5, 1937) was a Mormon missionary and a Utah politician. In 1898, she became one of the first two single women to be missionaries for the Church of Jesus Christ of Latter-day Saints (LDS Church).
Amanda Inez Knight was born near Payson, Utah Territory, to Jesse Knight and his wife Amanda McEwan. She was born the fourth of five children; her siblings included brothers Raymond and J. Will Knight and sisters Jennie Knight Mangum and Ione Knight Jordan. The family moved to Provo and Inez Knight enrolled in Brigham Young Academy (BYA). By the age of 22, Knight had completed her studies at BYA and had moved to St. George, Utah, where she was involved in family genealogical research.
Missionary service in Great Britain
On April 1, 1898, Knight was set apart as one of the first two single women in the LDS Church to be formally selected as full-time church missionaries. The other was her childhood friend Jennie Brimhall. Jennie Brimhall and Inez Knight were missionary companions in England for a year, leaving Provo on April 2 arriving in England on April 28, 1898. As missionaries, Knight and Brimhall were frequently asked to speak at public meetings and distribute missionary tracts on the street. Because Knight and Brimhall were the first, and for a time only, lady missionaries serving Europe, they were often asked to travel throughout England to speak. In a letter to the Deseret Evening News, missionary Joseph S. Broadbent wrote that "Sisters Jennie Brimhall and Inez Knight, both of Provo, Utah, each spoke at some length on Utah and her people and bore strong testimonies on the restoration of the Gospel and the divine mission of Joseph Smith. There were about 800 people present and a pin could be heard drop."
Knight and Brimhall not only traveled extensively in England, but throughout other parts of Europe as well. Knight reported having spent "a month visiting the principal cities of France, Switzerland, Germany, Belgium, and Holland. Knight believed that one of her main purposes as a missionary was to dispel the belief, common throughout Europe, that Mormon women "were downtrodden slaves". Knight and the other missionaries were not always welcome, however. In February 1899, Knight was in attendance at a church meeting in Bristol when all of the windows were broken by anti-Mormon rioters. Knight, her companion, and the other missionaries had to seek protection from the local police. Although Jennie Brimhall returned to Utah in November 1898 due to poor health, Knight continued her mission until 1900 with several other companions, including Liza Chipman and J. Clara Holbrook, both from Utah. Due to the scarcity of lady missionaries, however, at times Knight served alone. She recorded in her journal one meeting in which "I was the only girl. I felt more conspicuous by the elders beginning their remarks; my brethren and sister." Areas in which Knight served included Cheltenham, London, Kent, and Bristol. Knight returned home from Britain in June 1900, after over two years service throughout Britain, Scotland, and Wales.
Personal life and community work
In June 1902, Knight married Robert Eugene Allen, a prominent local banker and community developer, in the Salt Lake City temple. Robert Allen was born on December 21, 1877, in Coalville, Utah, to Mr. and Mrs. Thomas L. Allen. Mr. Allen served an LDS mission in Liverpool, England, in 1905, and attended the Brigham Young Academy where he met Knight. They had five sons, including W. Eugene J. Knight, Robert K. Allen, Joseph Knight Allen, and Mark E. Allen.
After her marriage, Inez Allen was active in various areas within the church and the community. From 1927 until her death (10 years) she was a member of the Relief Society's general board. Allen was also extensively involved with Brigham Young Academy for several years following her mission to Great Britain. In 1900, just a few months after returning home, Allen was named matron for "Missionary Theology for Girls" of the Academy. Allen was the matron of the school for two years despite personal setbacks, which included falling ill with smallpox in October 1900. Allen helped initiate the community welfare department in Provo and was active in the Red Cross organization of Utah County.
Allen was frequently honored for her role as one of the first two single female missionaries for the LDS church. In 1934 she and Jennie Brimhall Knight were honored by Church President Heber J. Grant at a meeting of the Yesharah Society. In addition to her leadership in the Relief Society and membership in the Yesharah Society, Allen participated in various other activities and clubs, including the Nelke Reading Club.
Political work
Allen was also active in the Democratic Party in Utah, serving on various committees and in different offices as early as 1895 at the age of 19 years old. She was named a member of the executive committee of Governor George Dern's advisory council for unemployment relief in 1931. She served four years as a Democratic national committeewoman, during which time she attended two national conventions, one in New York in 1924 and the other in Houston, Texas in 1928. She once ran as a Democratic candidate for State Senate, and was endorsed by William Jennings Bryan and Heber J. Grant for the position. At times, Allen's political beliefs and religious views clashed. As a national committeewoman for the Democratic party, Inez Allen was a supporter of 1932 Democratic candidate Franklin D. Roosevelt. However, Allen opposed the repeal of the 18th Amendment, one of Roosevelt's platform planks. In 1924, Allen was a Utah delegate to the Democratic National Convention in Cleveland, Ohio. Because her husband was a Republican, Allen's political experiences were sometimes unique. For example, in 1924, Allen attended both the Democratic and Republican National Conventions, the first she attended as a Democratic national committeewoman, the second she attended with her husband, who was acting as a delegate from Utah. Additionally, Allen was elected to the National Women's Democratic Committee in 1928. Allen was frequently recognized and honored for her political efforts, and was named Utah's "Goddess of Liberty" at the 1898 or 1900 Provo Fourth of July Celebration.
In 1937, Allen died unexpectedly in her home in Provo, Utah, of gastritis. Her funeral was held June 9, 1937, and speakers included Dr. Franklin S. Harris, then President of BYU, and Stephen L. Richards of the Quorum of the Twelve Apostles (LDS Church). The funeral was large, with members of the Yesharah Society, Relief Society General Board, and faculty of BYU in attendance. She is buried at the Provo City Cemetery.
Legacy
Inez Allen and her husband passed on a legacy of participation in local, state, and national politics to their children. Robert K. Allen served nationally as a U.S. Treasury agent from 1934 to 1945, working both in the United States and at the U.S. Embassy in Paris. He served locally as well, running for Provo City Council in 1961 and for mayor of Provo in 1965. Both Mrs. and Mr. Allen donated generous amounts of money to Brigham Young Academy. Inez Allen began donating as early as 1897. A year before her mission, she donated $10,000 to the institution, the only woman among the ten significant donors that year. As a donor, Allen was asked to give a speech at the 1897 ground-breaking ceremony of the new college building, again being the only woman invited to do so. A men's dormitory hall was named in honor of Mr. and Mrs. Knight in 1937.
Publications
Notes
External links
Inez Knight Allen diary (finding aid), Brigham Young University, Harold B. Lee Library, L. Tom Perry Special Collections
Inez Knight Allen diary (digitized journal), Brigham Young University, Harold B. Lee Library, L. Tom Perry Special Collections
Jeffrey S. Hardy, "Amanda Inez Knight", Mormon Missionary Diaries, byu.edu
1876 births
1937 deaths
19th-century Mormon missionaries
American leaders of the Church of Jesus Christ of Latter-day Saints
American Mormon missionaries in England
Brigham Young Academy alumni
Female Mormon missionaries
People from Provo, Utah
Relief Society people
Utah Democrats
Knight family (Latter Day Saints)
Women in Utah politics
Latter Day Saints from Utah
19th-century American women politicians
19th-century American politicians
20th-century American women politicians
20th-century American politicians
Harold B. Lee Library-related 19th century articles | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 4,716 |
{"url":"https:\/\/zbmath.org\/?q=an:1109.76352","text":"# zbMATH \u2014 the first resource for mathematics\n\nNumerical investigation of 3-D separated viscous incompressible fluid flow past an obstacle on a plane. (Russian. English summary) Zbl\u00a01109.76352\nNumerical investigations of a liquid flow past near an obstacle given by the equation $$y=ae^{-b(x-x_0)^2 - bz^2}$$ are fulfilled. The liquid is considered as a viscous incompressible and the liquid flow is uniform on the infinity. Equations under investigation are written in a form conservation laws ( for the mass and the momentum) by use of the \u201dpressure- velocity\u201d variables. Numerical integration of the equations is carried out by the known method of physical variables splitting generalized for the case of arbitrary curvilinear system of coordinates. The topological structures of the 3-D flow arising near a body surface are studied for different Reynolds numbers.\n##### MSC:\n 76M25 Other numerical methods (fluid mechanics) (MSC2010) 76M27 Visualization algorithms applied to problems in fluid mechanics\nFull Text:","date":"2021-05-08 20:56:14","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.39096149802207947, \"perplexity\": 1014.938266245986}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2021-21\/segments\/1620243988923.22\/warc\/CC-MAIN-20210508181551-20210508211551-00551.warc.gz\"}"} | null | null |
We've captured some of the top Frequently Asked Questions and would be happy to connect with you to answer any additional questions you may have.
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It Is Easy To Be A Member/Owner!
If your debit card is lost or stolen, you can immediately prevent any unauthorized transactions by using Lock'N'Block. Once you've locked your card and blocked any transactions, you will still need to report your card as lost or stolen by calling 1-888-277-1043 or your branch. | {
"redpajama_set_name": "RedPajamaC4"
} | 333 |
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