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Pachons – pierwszy miesiąc pory szemu i dziewiąty miesiąc roku w kalendarzu egipskim. Jak każdy miesiąc w starożytnym Egipcie trwał 30 dni od 16 marca do 14 kwietnia. Po pachonsie następował paini.
Kultura starożytnego Egiptu
Kalendarz egipski
Miesiące | {
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Takudzwa launched a chess club called "The Chess Grandmasters" at his high school in an effort to restore school pride, as well as to help learners to improve their concentration, which would positively impact their academics. His early efforts in garnering support and recruiting individuals to his club was slow, most of his peers didn't understand the point of playing the game. However, over time the chess club grew from having only four players using two boards, to a current membership of over sixteen players.
Takudzwa registered The Chess Grandmasters into the Western Province Chess League and at the end of 2012, the club had won all the games they had played within their league. | {
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{"url":"http:\/\/mathhelpforum.com\/pre-calculus\/49063-composition-functions-print.html","text":"# Composition of Functions\n\n\u2022 September 14th 2008, 03:32 PM\nComposition of Functions\nHello everyone,\n\nI'm having trouble finding the sums of functions.\n\nMy particular problem is,\n\nThey're asking me to solve (f+g)(x).\n\nIf (f+g)(x) is the same thing as f(x)+g(x) then:\n(x-2)+?\n\nCan x2\/x2+1 be simplified so I can add the two functions easier?\n\nI tried simplifying a bunch of things but I can't seem to get anywhere.\nAny help would be appreciated. Thanks in advance!\n\u2022 September 14th 2008, 03:35 PM\nskeeter\n$(f+g)(x) = f(x) + g(x)$\n\n$(f \\circ g)(x) = f[g(x)]$\n\u2022 September 14th 2008, 04:41 PM\n11rdc11\nI'm not sure how your functions look but I'm going to assume it was like this and you just forgot to indicate it was up to a power. Correct me if I'm wrong.\n\n$f(x)=\\sqrt{x^2-4}$\n\n$g(x)=\\frac{x^2}{x^2+1}$\n\nso\n\n$(f+g)(x) = f(x) + g(x)$\n\n$= \\sqrt{x^2-4} + \\frac{x^2}{x^2+1}$\n\nfind common denominator\n\n$= \\frac{(x^2+1)\\sqrt{x^2-4} + x^2}{x^2+1}$","date":"2016-08-29 12:49:00","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\": 0, \"img_math\": 0, \"codecogs_latex\": 7, \"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\": 0.8262787461280823, \"perplexity\": 1069.040592525238}, \"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-2016-36\/segments\/1471982957972.74\/warc\/CC-MAIN-20160823200917-00182-ip-10-153-172-175.ec2.internal.warc.gz\"}"} | null | null |
{"url":"https:\/\/groupprops.subwiki.org\/w\/index.php?title=Conjugacy_class_size_formula_in_general_linear_group_over_a_finite_field&oldid=27365","text":"# Conjugacy class size formula in general linear group over a finite field\n\n(diff) \u2190 Older revision | Latest revision (diff) | Newer revision \u2192 (diff)\n\nThis article gives formula(s) for the conjugacy class sizes in a general linear group of finite degree $n$ over a finite field with $q$ elements, which we denote by $GL(n,q)$.\n\n## Case of semisimple elements\n\n### Elements diagonalizable over $\\mathbb{F}_q$\n\nSuppose $g \\in GL(n,q)$ is diagonalizable over $\\mathbb{F}_q$, with eigenvalues $\\lambda_1, \\dots, \\lambda_k$ having multiplicities $r_1,r_2,\\dots,r_k$ respectively (the $\\lambda_i$s are all distinct). Note that $\\sum_{i=1}^k r_i = n$.\n\nThen, the centralizer of the diagonal representative of this conjugacy class is isomorphic to:\n\n$GL(r_1,q) \\times GL(r_2,q) \\times GL(r_3,q) \\times \\dots \\times GL(r_k,q)$\n\nIn fact, if the diagonal entries are arranged so that all the $\\lambda_1$s occur first, then the $\\lambda_2$s, and so on, then the centralizer is the set of invertible block diagonal matrices with blocks of sizes $r_1, r_2, \\dots, r_k$.\n\nThe size of the conjugacy class is thus:\n\n$\\frac{|GL(n,q)|}{\\prod_{i=1}^k |GL(r_i,q)|}$\n\nThis is the same as the $q$-analogue of the multinomial coefficient:\n\n$\\binom{n}{r_1,r_2,\\dots,r_k}_q$\n\nIn all cases, this simplifies to a polynomial in $q$, and its degree is $q^{n^2 - \\sum_{i=1}^k r_i^2}$.\n\nSome particular cases for the partition of $n$ as a sum of $r_i$s, and the corresponding sizes, are given below.\n\n$n$ Partition of $n$ Size of $|GL(n,q)|$ Size of centralizer of diagonal element Degree of polynomial giving size Size of conjugacy class Degree of polynomial giving size\n1 1 $q - 1$ $q - 1$ 1 1 0\n2 2 $(q^2 - 1)(q^2 - q)$ $(q^2 - 1)(q^2 - q)$ 4 1 0\n2 1 + 1 $(q^2 - 1)(q^2 - q)$ $(q - 1)^2$ 2 $q(q + 1)$ 2\n3 3 $(q^3 - 1)(q^3 - q)(q^3 - q^2)$ $(q^3 - 1)(q^3 - q)(q^3 - q^2)$ 9 1 0\n3 2 + 1 $(q^3 - 1)(q^3 - q)(q^3 - q^2)$ $(q^2 - 1)(q^2 - q)(q - 1)$ 5 $q^2(q^2 + q + 1)$ 4\n3 1 + 1 + 1 $(q^3 - 1)(q^3 - q)(q^3 - q^2)$ $(q - 1)^3$ 3 $q^3(q^2 + q + 1)(q + 1)$ 6\n$n$ $n$ $\\prod_{i=0}^{n-1} (q^n - q^i)$ $\\prod_{i=0}^{n-1} (q^n - q^i)$ $n^2$ 1 0\n$n$ $1 + 1 + \\dots + 1$ $\\prod_{i=0}^{n-1} (q^n - q^i)$ $(q - 1)^n$ $n$ $q^n(q + 1)(q^2 + q + 1)(q^3 + q^2 + q + 1) \\dots (q^{n-2} + q^{n-1} + \\dots + q + 1)$ $n(n - 1)$","date":"2021-06-24 14:49:08","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\": 0, \"img_math\": 51, \"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\": 0.9419727921485901, \"perplexity\": 263.7766422228578}, \"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\/1623488556133.92\/warc\/CC-MAIN-20210624141035-20210624171035-00318.warc.gz\"}"} | null | null |
Or copy and paste, whatever.
This one is a winner my friends.
Just take a minute...soak that picture in.
It's called "spaghetti in garlic gravy".
Uummm, spaghetti and gravy? Sign me up.
- Add all the marinade ingredients into the chicken and marinate for 20 minutes (if making this dish in pronto) or over night (if making this dish the next day… much better).
- Saute the marinated chicken in extra virgin olive oil until cooked (about 4-5 minutes) then set aside.
- Place sauté pan over medium heat and add butter and olive oil.
- Saute garlic until fragrant and soft.
- Add the flour and cook for a minute.
- Add chicken stock and simmer gravy until thickened then add the chopped basil.
- Add the sauteed chicken in the gravy then toss the cooked spaghetti into this sauce.
- Add the cherry tomatoes and finish the dish with the chopped parsley and grated parmesan cheese (serve extra on the side).
It was soooo good. Everyone ate it.
Next time I think I will add even more herbs and maybe a little white wine to the sauce.
yes I do. that looks SOOOOOO good. and "500 grams" of spaghetti. that sounds like alot.
wow that looks sooooo yummy!!!
is this pre or post my fitness pal? i'm feeling like my app wouldn't like this recipe. but my tastebuds would.
thanks for letting us know it exists! | {
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EVERYTHING LISTED UNDER: Spiritual Life
Make a joyful noise
Roger Cook, Topeka Presbyterian Manor chaplain, shares how we can find emotional, spiritual and mental benefits from listening to music and by lifting our voices in song.
Why Your Funeral Director Will Likely Be Female
Funeral director Jan Smith of Flanner Buchanan in Indianapolis guides a casket into a hearse. [Photo credit: courtesy of Jan Smith][/caption]By Kevyn Burger for Next AvenueJan Smith was in the final semester of her training to be a funeral director when her 8-year-old nephew died after a heart transplant.Her family's heartbreak deepened her understanding of the value of the work she was preparing for.
How a Daughter Helped Her Mom Face Death
"I have a question for you, Aim," Mom said from her blue La-Z-Boy. "How did you stay so positive during everything you went through?"This takes me by surprise. "Uh, Prozac?" I joke, and she laughs.
How to Be Supportive to Friends Experiencing Loss
Loss is an inescapable part of life. Whether we've lost someone to death, or are going through a living loss such as divorce, retirement, a life-threatening illness, a debilitating injury or a life-altering condition like dementia or addiction, support can make all the difference in helping us summon the strength, faith and courage to fight our way back into life.
Facing Down the Biggest Fear of All
Our fear of death begins when we're kids. Perhaps we had to face the mystifying idea of impermanence when a beloved pet, parent or grandparent died. The stark reality that this loved one was really gone — and gone forever, was both devastating and terrifying. From early childhood, when we're introduced to the concept of "futureless-ness" — that is, old age and eventually death, there are few things as difficult for us to deal with. Facing down the fear of dying requires great strength, humility and spiritual fortitude. But, as you will see, it's worth the effort. | {
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Confronting violence, Durango Herald, Feb. 15, 2008
Students of the Pagosa Springs High School Drama Club rehearse "Bang, Bang, You're Dead" by William Mastrosimone on Wednesday . The play about gun violence in schools will be performed Saturday. The student in the center is Tyler Carpenter, who plays the lead character. Becca Stephens is standing in the back.
• Heath High School, West Paducah, Ky.
• Westside Middle School, Jonesboro, Ark.
• Lincoln County High School, Fayetteville, Tenn.
• Thurston High School, Springfield, Ore.
• Columbine High School, Littleton.
• Heritage High School, Conyers, Ga.
• Santana High School, Santee, Calif.
• Henry Foss High School, Tacoma, Wash.
These are just a few of the schools across America in which teens have shot and killed their peers at school.
Since 1996, there have been 40 recorded incidents of shootings in and around schools, according to crime data recorded by the Web site infoplease.com.
"Bang, Bang, You're Dead" is a play written by William Mastrosimone in an effort to end violence among teenagers. The play centers on Josh, a teenage boy who shoots his parents and five schoolmates, and is then haunted by physical manifestations of his memories of them.
Josh is based on Kip Kinkel, the 15-year-old who killed his parents and two classmates, and wounded 25 other students at Thurston High School in Oregon.
Mastrosimone's play was performed for the first time April 9, 1999, just 11 days before the Columbine High School shootings. The Pagosa Springs High School Drama Club will perform it again Saturday.
Director Dale Morris said this week that she and the students selected the play believing that the benefits of putting this work out there far outweigh the risks. But she admits it's a difficult production.
Tyler Carpenter, a junior at Pagosa High School, plays Josh. The lanky teen sports a multi-shaded, multi-length punk hair cut and speaks with wisdom beyond his years.
"My character is something I've been trying to distance myself from," Carpenter said at rehearsal Wednesday night. "He's stuck up and ignorant about a lot of what people go through in real life. He doesn't think about how what he does is going to affect others. He has a very twisted view of the universe."
Carpenter said he uses music to help him get into the mode for playing his character. He hears the anger in lyrics. It's the same music he listens to, but the difference comes from his mood. For Carpenter, music is an escape and a release. When getting ready to play Josh, he said: "I can amplify those feelings of hatred and misunderstanding."
The play has touched each of the 14 students in the production.
"I get to breaking points," Hilary Matzdorf said. "The people that do this are normal. It can happen to anyone."
"I don't know," Emmi Greer said. "I don't have any first-hand or second-hand experience with violence. But this production has made me assess myself and how I would face a situation like this. It's intense. It's noxious. It doesn't go away. Things in real life will remind you of things in the play. It's like it really happened."
"You see and take away everything they (the characters) could have been and everything they lost in losing their lives," Ashley Iverson said.
And while they have mixed feelings about the subject matter, all of the students are clear in what they hope the audience will take away from the production, particularly their peers who will attend a performance next week during school.
"We want to get it to be perceived as something real," Jeff Readon said. "Not just as something you can laugh off."
Student Becca Stephens said: "It's not like we are going to end violence. But our hope is that people are reminded of what happened. We can have a lasting impact."
And Rhain Harris said: "I want people to think about this play for more than just the car ride home."
I bet they will.
"Bang, Bang, You're Dead," 7:30 p.m. Saturday, Pagosa High School Auditorium, free but donations appreciated.
artsjournalist@centurytel.netLeanne Goebel is a freelance writer specializing in the arts.
March 16, 2008 in Durango, Pagosa Springs. Tags: Pagosa Springs, theatre
Pagosa actors put on Into the Woods, Durango Herald, Nov. 21, 2009
Pagosa Springs Community Comes Together for New Mural
"Buying Pagosa," Part II originally appeared on pagosa.com, Feb. 25, 2005
← Brothers with Durango roots land NBC series, Durango Herald front page, Feb. 12, 2008
Disturbed and Disturbing, Durango Herald, Feb. 22, 2008 → | {
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{"url":"https:\/\/ipalimanowa.pl\/585x2g\/opfrqz.php?cb9e83=micranthemum-monte-carlo-seeds","text":"# micranthemum monte carlo seeds\n\nWe use cookies to improve your experience, to assess the use of the individual elements on our websites and to support the marketing of our services. Micranthemum Monte Carlo - Tissue Culture Cup. It will creep laterally \u00e2\u0080\u00a6 \u00a9 2020 Arizona Aquatic Gardens. You get 1 Potted Monte Carlo plant. Add to Cart Sale. Remove the plant from the plastic container. \u00e2\u0080\u00a6 Using tweezers, collect the split plants one at a time \u00e2\u0080\u00a6 You can read more about our Privacy Policy here. Very attractive, uniform plants that are extra dark green. The Micranthemum monte carlo seems like a bigger version of Hemianthus callitrichoides aka \u00e2\u0080\u0098Cuba,\u00e2\u0080\u0099 but it also slightly same as to \u00e2\u0080\u0098standard\u00e2\u0080\u0099 Micranthemum umbrosum. 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A low-growing plant with bright green, rounded leaves use of cookies Micranthemum 'Monte Carlo originates., Freshwater aquarium Shrimp, Crayfish & Lobsters a whorl you are happy with it x 1.75 \u201d.! A database and images of herbarium \u00e2\u0080\u00a6 Micranthemum Monte Carlo layout to avoid introducing algaes. Front micranthemum monte carlo seeds the aquarium are happy with it ranging \u00e2\u0080\u00a6 Micranthemum Monte Carlo \/ HC Cuba carpeting plants Liners... Free from snails, algae and pesticides, which makes them completely micranthemum monte carlo seeds delicate...","date":"2021-08-03 07:44:09","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\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.1986784189939499, \"perplexity\": 13973.022844832727}, \"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-2021-31\/segments\/1627046154432.2\/warc\/CC-MAIN-20210803061431-20210803091431-00108.warc.gz\"}"} | null | null |
import sys
from mixbox.binding_utils import *
from stix.bindings import register_extension
import stix.bindings.indicator as indicator_binding
import stix.bindings.stix_common as stix_common_binding
XML_NS = "http://stix.mitre.org/extensions/TestMechanism#Snort-1"
#
# Data representation classes.
#
@register_extension
class SnortTestMechanismType(indicator_binding.TestMechanismType):
"""The SnortTestMechanismType specifies an instantial extension from
the abstract TestMechanismType intended to support the inclusion
of a Snort rule as a test mechanism content."""
subclass = None
superclass = indicator_binding.TestMechanismType
xmlns = XML_NS
xmlns_prefix = "snortTM"
xml_type = "SnortTestMechanismType"
xsi_type = "%s:%s" % (xmlns_prefix, xml_type)
def __init__(self, idref=None, id=None, Efficacy=None, Producer=None, Product_Name=None, Version=None, Rule=None, Event_Filter=None, Rate_Filter=None, Event_Suppression=None):
super(SnortTestMechanismType, self).__init__(idref=idref, id=id, Efficacy=Efficacy, Producer=Producer)
self.Product_Name = Product_Name
self.Version = Version
if Rule is None:
self.Rule = []
else:
self.Rule = Rule
if Event_Filter is None:
self.Event_Filter = []
else:
self.Event_Filter = Event_Filter
if Rate_Filter is None:
self.Rate_Filter = []
else:
self.Rate_Filter = Rate_Filter
if Event_Suppression is None:
self.Event_Suppression = []
else:
self.Event_Suppression = Event_Suppression
def factory(*args_, **kwargs_):
if SnortTestMechanismType.subclass:
return SnortTestMechanismType.subclass(*args_, **kwargs_)
else:
return SnortTestMechanismType(*args_, **kwargs_)
factory = staticmethod(factory)
def get_Product_Name(self): return self.Product_Name
def set_Product_Name(self, Product_Name): self.Product_Name = Product_Name
def get_Version(self): return self.Version
def set_Version(self, Version): self.Version = Version
def get_Rule(self): return self.Rule
def set_Rule(self, Rule): self.Rule = Rule
def add_Rule(self, value): self.Rule.append(value)
def insert_Rule(self, index, value): self.Rule[index] = value
def get_Event_Filter(self): return self.Event_Filter
def set_Event_Filter(self, Event_Filter): self.Event_Filter = Event_Filter
def add_Event_Filter(self, value): self.Event_Filter.append(value)
def insert_Event_Filter(self, index, value): self.Event_Filter[index] = value
def get_Rate_Filter(self): return self.Rate_Filter
def set_Rate_Filter(self, Rate_Filter): self.Rate_Filter = Rate_Filter
def add_Rate_Filter(self, value): self.Rate_Filter.append(value)
def insert_Rate_Filter(self, index, value): self.Rate_Filter[index] = value
def get_Event_Suppression(self): return self.Event_Suppression
def set_Event_Suppression(self, Event_Suppression): self.Event_Suppression = Event_Suppression
def add_Event_Suppression(self, value): self.Event_Suppression.append(value)
def insert_Event_Suppression(self, index, value): self.Event_Suppression[index] = value
def hasContent_(self):
if (
self.Product_Name is not None or
self.Version is not None or
self.Rule or
self.Event_Filter or
self.Rate_Filter or
self.Event_Suppression or
super(SnortTestMechanismType, self).hasContent_()
):
return True
else:
return False
def export(self, lwrite, level, nsmap, namespace_=XML_NS, name_='SnortTestMechanismType', namespacedef_='', pretty_print=True):
if pretty_print:
eol_ = '\n'
else:
eol_ = ''
showIndent(lwrite, level, pretty_print)
lwrite('<%s:%s%s' % (nsmap[namespace_], name_, namespacedef_ and ' ' + namespacedef_ or '', ))
already_processed = set()
self.exportAttributes(lwrite, level, already_processed, namespace_, name_='SnortTestMechanismType')
if self.hasContent_():
lwrite('>%s' % (eol_, ))
self.exportChildren(lwrite, level + 1, nsmap, XML_NS, name_, pretty_print=pretty_print)
showIndent(lwrite, level, pretty_print)
lwrite('</%s:%s>%s' % (nsmap[namespace_], name_, eol_))
else:
lwrite('/>%s' % (eol_, ))
def exportAttributes(self, lwrite, level, already_processed, namespace_='snortTM:', name_='SnortTestMechanismType'):
super(SnortTestMechanismType, self).exportAttributes(lwrite, level, already_processed, namespace_, name_='SnortTestMechanismType')
# if 'xmlns' not in already_processed:
# already_processed.add('xmlns')
# xmlns = " xmlns:%s='%s'" % (self.xmlns_prefix, self.xmlns)
# lwrite(xmlns)
if 'xsi:type' not in already_processed:
already_processed.add('xsi:type')
xsi_type = " xsi:type='%s:%s'" % (self.xmlns_prefix, self.xml_type)
lwrite(xsi_type)
def exportChildren(self, lwrite, level, nsmap, namespace_=XML_NS, name_='SnortTestMechanismType', fromsubclass_=False, pretty_print=True):
super(SnortTestMechanismType, self).exportChildren(lwrite, level, nsmap, indicator_binding.XML_NS, name_, True, pretty_print=pretty_print)
if pretty_print:
eol_ = '\n'
else:
eol_ = ''
if self.Product_Name is not None:
showIndent(lwrite, level, pretty_print)
lwrite('<%s:Product_Name>%s</%s:Product_Name>%s' % (nsmap[namespace_], quote_xml(self.Product_Name), nsmap[namespace_], eol_))
if self.Version is not None:
showIndent(lwrite, level, pretty_print)
lwrite('<%s:Version>%s</%s:Version>%s' % (nsmap[namespace_], quote_xml(self.Version), nsmap[namespace_], eol_))
for Rule_ in self.Rule:
Rule_.export(lwrite, level, nsmap, namespace_, name_='Rule', pretty_print=pretty_print)
for Event_Filter_ in self.Event_Filter:
Event_Filter_.export(lwrite, level, nsmap, namespace_, name_='Event_Filter', pretty_print=pretty_print)
for Rate_Filter_ in self.Rate_Filter:
Rate_Filter_.export(lwrite, level, nsmap, namespace_, name_='Rate_Filter', pretty_print=pretty_print)
for Event_Suppression_ in self.Event_Suppression:
Event_Suppression_.export(lwrite, level, nsmap, namespace_, name_='Event_Suppression', pretty_print=pretty_print)
def build(self, node):
self.__sourcenode__ = node
already_processed = set()
self.buildAttributes(node, node.attrib, already_processed)
for child in node:
nodeName_ = Tag_pattern_.match(child.tag).groups()[-1]
self.buildChildren(child, node, nodeName_)
def buildAttributes(self, node, attrs, already_processed):
super(SnortTestMechanismType, self).buildAttributes(node, attrs, already_processed)
def buildChildren(self, child_, node, nodeName_, fromsubclass_=False):
if nodeName_ == 'Product_Name':
Product_Name_ = child_.text
Product_Name_ = self.gds_validate_string(Product_Name_, node, 'Product_Name')
self.Product_Name = Product_Name_
elif nodeName_ == 'Version':
Version_ = child_.text
Version_ = self.gds_validate_string(Version_, node, 'Version')
self.Version = Version_
elif nodeName_ == 'Rule':
obj_ = stix_common_binding.EncodedCDATAType.factory()
obj_.build(child_)
self.Rule.append(obj_)
elif nodeName_ == 'Event_Filter':
obj_ = stix_common_binding.EncodedCDATAType.factory()
obj_.build(child_)
self.Event_Filter.append(obj_)
elif nodeName_ == 'Rate_Filter':
obj_ = stix_common_binding.EncodedCDATAType.factory()
obj_.build(child_)
self.Rate_Filter.append(obj_)
elif nodeName_ == 'Event_Suppression':
obj_ = stix_common_binding.EncodedCDATAType.factory()
obj_.build(child_)
self.Event_Suppression.append(obj_)
super(SnortTestMechanismType, self).buildChildren(child_, node, nodeName_, True)
# end class SnortTestMechanismType
GDSClassesMapping = {}
USAGE_TEXT = """
Usage: python <Parser>.py [ -s ] <in_xml_file>
"""
def usage():
print(USAGE_TEXT)
sys.exit(1)
def get_root_tag(node):
tag = Tag_pattern_.match(node.tag).groups()[-1]
rootClass = GDSClassesMapping.get(tag)
if rootClass is None:
rootClass = globals().get(tag)
return tag, rootClass
def parse(inFileName):
doc = parsexml_(inFileName)
rootNode = doc.getroot()
rootTag, rootClass = get_root_tag(rootNode)
if rootClass is None:
rootTag = 'SnortTestMechanismType'
rootClass = SnortTestMechanismType
rootObj = rootClass.factory()
rootObj.build(rootNode)
# Enable Python to collect the space used by the DOM.
doc = None
sys.stdout.write('<?xml version="1.0" ?>\n')
rootObj.export(sys.stdout, 0, name_=rootTag,
namespacedef_='',
pretty_print=True)
return rootObj
def parseEtree(inFileName):
doc = parsexml_(inFileName)
rootNode = doc.getroot()
rootTag, rootClass = get_root_tag(rootNode)
if rootClass is None:
rootTag = 'SnortTestMechanismType'
rootClass = SnortTestMechanismType
rootObj = rootClass.factory()
rootObj.build(rootNode)
# Enable Python to collect the space used by the DOM.
doc = None
rootElement = rootObj.to_etree(None, name_=rootTag)
content = etree_.tostring(rootElement, pretty_print=True,
xml_declaration=True, encoding="utf-8")
sys.stdout.write(content)
sys.stdout.write('\n')
return rootObj, rootElement
def parseString(inString):
from mixbox.vendor.six import StringIO
doc = parsexml_(StringIO(inString))
rootNode = doc.getroot()
rootTag, rootClass = get_root_tag(rootNode)
if rootClass is None:
rootTag = 'SnortTestMechanismType'
rootClass = SnortTestMechanismType
rootObj = rootClass.factory()
rootObj.build(rootNode)
# Enable Python to collect the space used by the DOM.
doc = None
# sys.stdout.write('<?xml version="1.0" ?>\n')
# rootObj.export(sys.stdout, 0, name_="Indicator",
# namespacedef_='')
return rootObj
def main():
args = sys.argv[1:]
if len(args) == 1:
parse(args[0])
else:
usage()
if __name__ == '__main__':
#import pdb; pdb.set_trace()
main()
__all__ = [
"SnortTestMechanismType"
]
| {
"redpajama_set_name": "RedPajamaGithub"
} | 856 |
package view;
#
# BUILD CONSTRAINT: all views must return $content, $extension.
# additional return values (as seen below) are optional. However,
# careful use of symlinks and dependency management in path.pm can
# resolve most issues with this constraint.
#
use strict;
use warnings;
use Dotiac::DTL qw/Template *TEMPLATE_DIRS/;
use Dotiac::DTL::Addon::markup;
use ASF::Util qw/read_text_file/;
push @TEMPLATE_DIRS, "templates";
# This is most widely used view. It takes a
# 'template' argument and a 'path' argument.
# Assuming the path ends in foo.mdtext, any files
# like foo.page/bar.mdtext will be parsed and
# passed to the template in the "bar" (hash)
# variable.
sub single_narrative {
my %args = @_;
my $file = "content$args{path}";
my $template = $args{template};
$args{path} =~ s/\.mdtext$/\.html/;
$args{breadcrumbs} = breadcrumbs($args{path});
read_text_file $file, \%args;
my $page_path = $file;
$page_path =~ s/\.[^.]+$/.page/;
if (-d $page_path) {
for my $f (grep -f, glob "$page_path/*.mdtext") {
$f =~ m!/([^/]+)\.mdtext$! or die "Bad filename: $f\n";
$args{$1} = {};
read_text_file $f, $args{$1};
}
}
return Template($template)->render(\%args), html => \%args;
}
# Has the same behavior as the above for foo.page/bar.txt
# files, parsing them into a bar variable for the template.
# Otherwise presumes the template is the path.
sub news_page {
my %args = @_;
my $template = "content$args{path}";
$args{breadcrumbs} = breadcrumbs($args{path});
my $page_path = $template;
$page_path =~ s/\.[^.]+$/.page/;
if (-d $page_path) {
for my $f (grep -f, glob "$page_path/*.mdtext") {
$f =~ m!/([^/]+)\.mdtext$! or die "Bad filename: $f\n";
$args{$1} = {};
read_text_file $f, $args{$1};
}
}
return Template($template)->render(\%args), html => \%args;
}
sub sitemap {
my %args = @_;
my $template = "content$args{path}";
$args{breadcrumbs} .= breadcrumbs($args{path});
my $dir = $template;
$dir =~ s!/[^/]+$!!;
my %data;
for (map "content$_", @{$path::dependencies{$args{path}}}) {
if (-f and /\.mdtext$/) {
my $file = $_;
$file =~ s/^content//;
no warnings 'once';
for my $p (@path::patterns) {
my ($re, $method, $args) = @$p;
next unless $file =~ $re;
my $s = view->can($method) or die "Can't locate method: $method\n";
my ($content, $ext, $vars) = $s->(path => $file, %$args);
$file =~ s/\.mdtext$/.$ext/;
$data{$file} = $vars;
last;
}
}
}
my $content = "";
for (sort keys %data) {
$content .= "- [$data{$_}->{headers}->{title}]($_)\n";
for my $hdr (grep /^#/, split "\n", $data{$_}->{content}) {
$hdr =~ /^(#+)\s+([^#]+)?\s+\1\s+\{#([^}]+)\}$/ or next;
my $level = length $1;
$level *= 4;
$content .= " " x $level;
$content .= "- [$2]($_#$3)\n";
}
}
$args{content} = $content;
return Template($template)->render(\%args), html => \%args;
}
sub breadcrumbs {
my @path = split m!/!, shift;
pop @path;
my @rv;
my $relpath = "";
for (@path) {
$relpath .= "$_/";
$_ ||= "Home";
push @rv, qq(<a href="$relpath">\u$_</a>);
}
return join " » ", @rv;
}
1;
=head1 LICENSE
Licensed to the Apache Software Foundation (ASF) under one
or more contributor license agreements. See the NOTICE file
distributed with this work for additional information
regarding copyright ownership. The ASF licenses this file
to you under the Apache License, Version 2.0 (the
"License"); you may not use this file except in compliance
with the License. You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing,
software distributed under the License is distributed on an
"AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
KIND, either express or implied. See the License for the
specific language governing permissions and limitations
under the License.
| {
"redpajama_set_name": "RedPajamaGithub"
} | 7,341 |
An Unsung
Soldier
**Naval Institute Press**
291 Wood Road
Annapolis, MD 21402
© 2013 by Robert S. Jordan
All rights reserved. No part of this book may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying and recording, or by any information storage and retrieval system, without permission in writing from the publisher.
Library of Congress Cataloging-in-Publication Data
Jordan, Robert S.,
An unsung soldier : the life of Gen. Andrew J. Goodpaster / Robert S. Jordan.
1 online resource.
Includes bibliographical references and index.
Description based on print version record and CIP data provided by publisher; resource not viewed.
ISBN 978-1-61251-279-2 (ePub) 1. Goodpaster, Andrew Jackson, 1915–2005. 2. Generals—United States—Biography. 3. Eisenhower, Dwight D. (Dwight David), 1890–1969—Friends and associates. 4. National security—United States—Decision making—History—20th century. 5. United States. Army—Biography. 6. North Atlantic Treaty Organization—Biography. 7. United States—History, Military—20th century. 8. United States Military Academy—Biography. 9. Cold War. I. Title. II. Title: Life of Gen. Andrew J. Goodpaster.
E745.G66
355.0092—dc23
[B]
2013020592
Photos courtesy of the George C. Marshall Foundation, Lexington, Virginia.
Print editions meet the requirements of ANSI/NISO z39.48-1992 (Permanence of Paper).
21 20 19 18 17 16 15 14 13 9 8 7 6 5 4 3 2 1
First printing
_This book is dedicated to the memories of_
_Dr. Norman H. Gibbs_
_Chichele Professor of the History of War, All Souls College, Oxford University_
_and_
_Dr. Edgar S. Furniss Jr_.
_Professor of Politics, Princeton University; Director, The Mershon Program_ ,
_The Ohio State University_
_Mentors to many students and scholars—especially to a young student who_
_found himself in awesomely unfamiliar academic environments_
Contents
**Foreword**
**Preface**
**Acknowledgments**
**Terms and Abbreviations**
**PART I: A Career in Preparation and Execution**
**Chapter One:** The Professional Foundation
**Chapter Two:** Professional Planning
**Chapter Three:** Goodpaster and the Creation of NATO/SHAPE
**Chapter Four:** Solarium: The Articulation of a National Posture
**Chapter Five:** The "New Look"
**PART II: Goodpaster with Eisenhower**
**Chapter Six:** Presidential Staff Secretary and Counselor
**Chapter Seven:** A Functional National Security System
**Chapter Eight:** National Defense Writ Large
**Chapter Nine:** Eisenhower's Health Crises
**Chapter Ten:** The U-2 and Overflights
**PART III: Arrival at the Top**
**Chapter Eleven:** Deputy Commander and Commander-Designate in Vietnam
**Chapter Twelve:** As NATO Supreme Allied Commander
**Chapter Thirteen:** Returning to West Point as Superintendent
**Conclusions:** The Soldier-Scholar in the National Security Policy Process
**Afterword**
**Appendix:** Contributions to Public and Voluntary Service
**Notes**
**Source Material**
**Index**
Foreword
I am happy to have this opportunity to say a word about my dear friend and sometime colleague, Gen. Andrew Goodpaster. I do this having in mind that I was honored with the Goodpaster Award of the George C. Marshall Foundation. In addition, I was invited to dedicate "Goodpaster Hall" on the campus of St. Mary's College, in nearby Maryland.
I first met General Goodpaster when he became commandant of the National War College—the military's highest institution of professional military education—and I became a student there shortly thereafter. General Goodpaster took me "under his wing" and provided me with invaluable perspectives on leadership, policy and strategy development, and war prevention. While I confess to receiving somewhat special treatment, General Goodpaster so endeared himself to my entire class that they elected him an honorary member of the class at the end of the year. That was an initiation of an increasingly close association, which grew until his unfortunate passing in 2005.
There never is a poor time for a career military person to bring up the subject of leadership. In 1981, when General Goodpaster was superintendent at West Point, he described his concept of leadership: "I thought that the framework [for the Department of Behavioral Sciences and Leadership] had to be leadership, but a deep and broad understanding of leadership. I think that has been the case. And the related disciplines—psychology, for example, and some elements of sociology—would fall within the framework of a sense of how you should give leadership. How does an officer give leadership at the various echelons of responsibility?"
This observation had been earlier reframed thus: "If we wish to know the meaning of behavior, we must know the meanings of the behaver [ _sic_ ]; to remain outside his frame of experience is simply to remain in the dark."
With warfare today relying more and more on high technology, it is noteworthy that General Goodpaster's Princeton doctoral dissertation, written in 1950, anticipated this significant trend before it had become such a dominant aspect of both strategy and tactics. For him, knowledge of engineering (he was commissioned in the Corps of Engineers from West Point) had to be linked to, or partnered with, knowledge of the social and behavioral sciences. He also was convinced that, as the United States had entered the world political-military arena to stay after the great victory of World War II, military officers should obtain a thorough grounding in history and international affairs. I watched him put his ideas into practice when we were both at the National War College.
General Goodpaster's leadership style was understated and quietly focused—he led by persuasion, by rational discourse, and by unfailing courtesy and consideration for others. These traits made him both a successful Supreme Allied Commander in NATO and an essential White House assistant and confidante to President Dwight D. Eisenhower.
In a completely different vein, General Goodpaster joined the board of St. Mary's College of Maryland in 1987. He devoted twelve years to a substantial overhaul of the college's overall progress, curriculum procedures, and faculty compensation to lift St. Mary's to the first tier of liberal arts colleges in the nation.
Policy was as much a part of him as command and combat; in the Army an officer who was outstanding in both was a marked man. This is why Goodpaster rose quickly through the ranks, always being called back into a policy role even as he desired command assignments. He invariably wanted to know _why_ , as well as _what_ and _how_ , when confronted with a policy dilemma. Also, he shared President Eisenhower's insistence on considering the various alternatives when arriving at a decision. Not only was he not a "yes-man," he did not want to be associated with them as he advanced up the career ladder.
Professor Jordan has written a painstakingly researched, yet eminently readable, account of the career and accomplishments of General Goodpaster, for which I, for one, am very grateful.
**Lt. Gen. Brent Scowcroft, USAF (Ret.)**
National Security Advisor to President Gerald Ford and
President G. H. W. Bush
Preface
"It is absurd to make out that the means ever became more important than the end."
—GRAHAM GREENE, _The Lost Childhood and Other Essays_
Few military men of his generation have been both "warriors" and "thinkers," yet Gen. Andrew Jackson Goodpaster Jr. qualifies to be among that select company. To write about so-called action generals who more often than not possessed vivid personalities, although still a challenge, pales against the challenge of writing about a contemplative general who also could be an operational commander in combat or near-combat situations.
General Goodpaster was a dedicated cold warrior throughout his active-duty military career of nearly forty years. He was also a sophisticated observer and commentator on the foreign policy and national security scene for nearly a quarter-century thereafter. In fact, it was said that during the course of his professional and post-military career, "he continued to receive calls from agencies involved with national security affairs for a variety of assignments at the highest and, in the Cold War, most important level of policy—the three-way intersection of presidential politics, military planning, and international relations."
It is difficult to speak of a nonconformist when discussing a very senior military man, but the more Goodpaster's personality is examined, the more difficult it is to simply consider him the consummate "insider." Although he was notably successful at playing by the rules at each level of his career, nonetheless he managed to retain his distinct character and personality. This was true for many of the general officers who came to the peak of their careers either near the end of World War II or during the early Cold War years—Lyman Lemnitzer, Lauris Norstad, and Matthew Ridgway come to mind. Yet none of them in their earlier years came to the attention of the "movers and shakers" who controlled their professional futures in quite the same manner as Goodpaster. Two persons stand out as his mentors: George "Abe" Lincoln, and Dwight D. Eisenhower. George C. Marshall was his model of the "complete officer."
As his career unfolded, Goodpaster could retain the aspect of a detached observer even as—by extension—he was able to relate successfully to those around him within a largely closed yet supportive hierarchical professional environment. From his relatively humble origins, he achieved the highest international military command assignment possible—as the supreme allied commander, Europe (SACEUR), of the North Atlantic Treaty Organization (NATO).
Thereafter, he earned the gratitude of the Army as a whole when he returned to West Point as its superintendent from 1977 to 1981 to help restore integrity to its reputation, which had been sullied by a widespread cadet cheating scandal involving engineering examinations. Along the way, he became one of the first serving Army officers to obtain a doctoral degree in an Ivy League university. He also, of course, became an essential part of the Eisenhower White House entourage relatively early in his military career, often performing essentially civilian responsibilities informally, as well as becoming through his presence not only a trusted aide but also a counselor and friend to the president.
Not resting on his laurels, upon his final retirement and for over a quarter-century thereafter, he was actively involved in both the formal and informal worlds of Washington policy-making, making his mark repeatedly as a respected participant. He identified himself with organizations as diverse at St. Mary's College of Maryland and the Atlantic Council, serving as an officer in both, along with contributing his time and presence to many other worthwhile activities.
**Robert S. Jordan**
Woodbridge, Virginia
December 2012
Acknowledgments
The Eisenhower Presidential Library in Abilene, Kansas, and the George C. Marshall Foundation in Lexington, Virginia (wherein are the Goodpaster Papers), underwrote travel and maintenance costs, and their staffs have been unfailingly supportive. In particular, tribute must be paid to David Haight and to Christopher Abraham of the Eisenhower Presidential Library and to Joanne Hartog for monitoring my research progress, and especially to archivist and assistant librarian Jeffrey Kozak, both of the Marshall Foundation. Jehanne Moharram for the Naval Institute Press painstakingly and patiently copyedited the manuscript. Thanks also to the Association of the United States Army for providing a last-minute subvention.
The late Dr. Stephen Ambrose, an Eisenhower biographer, should also be remembered both as a friend and as a professional colleague in the Eisenhower Center at the University of New Orleans. Dr. J. Kenneth McDonald has consistently supported this endeavor, both as a constructive critic and as a valued friend and former colleague.
Individuals who were encouraging and helpful in a practical sense are David Acheson, Roger Axtell, Stephen Benedict, Edwin A. Deagle Jr., Jay Gatlin, Christian Graff, Matthew Graff, Dr. Gregory Granger, Ambassador Martin Hillenbrand, Ambassador Aubrey Hooks, Ambassador Robert E. Hunter, Brig. Gen. Amos A. Jordan, Dr. Lawrence S. Kaplan, Max Lawver, Caleb Leming, C. Richard Nelson, Professor Robert O'Neill, Dr. Gregory Pedlow, Dr. Wayne Rasmussen and Susan Rasmussen (for both logistic and moral support), Dr. Steven Rearden, Lt. Gen. Brent Scowcroft, Professor John Shy, Dr. Lewis "Bob" Sorley, Nicholas Stratton, Roger Sullivan, Ambassador George Vest, Andrew Ward, Kenneth Weisbrode, and especially my wife, Jane Hatch Jordan.
Responsibility for the outcome rests, of course, with the author.
Terms and Abbreviations
_Note: All agencies listed are U.S. agencies unless otherwise noted_.
**ACDA** | Arms Control and Disarmament Agency
---|---
**ACE** | Allied Command Europe (NATO)
**AEC** | Atomic Energy Commission
**APGA** | Association of Princeton Graduate Alumni (Princeton University)
**ARPA** | Advanced Research Projects Agency
**CE** | Corps of Engineers (U.S. Army)
**CIA** | Central Intelligence Agency
**CID** | Committee of Imperial Defense (UK)
**CINCEUR** | Commander-in-chief, U.S. forces, Europe
**CMH** | Center of Military History
**COMUSMACV** | Commander, U.S. Military Assistance Command, Vietnam
**CORONA** | Code word for a program of strategic reconnaissance satellites
**DCI** | Director of central intelligence
**DDCI** | Deputy director of central intelligence
**DDP** | Deputy director for plans, CIA Operations
**DOD** | Department of Defense
**ELINT-COMINT** | Electronic Intelligence-Communications Intelligence
**IISS** | International Institute for Strategic Studies
**JASC** | Joint Advanced Study Committee
**JCS** | Joint Chiefs of Staff
**JWPC** | Joint War Plans Committee
**MBFR** | Mutual and balanced force reductions
**Memcon** | Memorandum of conversation
**NATO** | North Atlantic Treaty Organization
**NCO** | Noncommissioned officer
**NSC** | National Security Council
**OCB** | Operations Coordinating Board (NSC)
**OPD** | Operations and Plans Division (of the War Department)
**OSD** | Office of the Secretary of Defense
**PfP** | Partnership for Peace
**PPS** | Policy Planning Staff
**PROVN** | Program for the Pacification and Long-Term Development of Vietnam
**PSAC** | President's Science Advisory Committee
**S &P** | Strategy and Policy Group
**SAC** | Strategic Air Command
**SACEUR** | Supreme allied commander, Europe (NATO)
**SALT** | Strategic Arms Limitation Talks
**SCS** | Screening and Costing Staff
**SHAPE** | Supreme Headquarters Allied Powers Europe (NATO)
**START** | Strategic Arms Reduction Talks
**SWNCC** | State-War-Navy Coordinating Committee
**TCC** | Temporary Council Committee (NATO)
**TCP** | Technological Capabilities Panel
**USAF** | U.S. Air Force
**USCINCEUR** | U.S. commander-in-chief, European Command
**USMA** | U.S. Military Academy (at West Point)
**USSR** | Union of Soviet Socialist Republics
**WH** | White House
**WPD** | War Plans Division (later renamed OPD)
**WUDO** | Western Union Defense Organization
Part I
A Career in Preparation and Execution
Chapter One
The Professional Foundation
"During our first two years, my first two years at West Point, we knew about the war in China. We knew that there was war in the world and we knew that the situation in Europe was unstable and becoming more and more dangerous."
—GEN. ANDREW J. GOODPASTER
In demeanor, Andrew Goodpaster was described as being austere yet approachable in a no-nonsense way. He dressed neatly but not stylishly. He smiled readily, was courteous but not obsequious, usually waited for others to speak before interjecting his own thoughts, and except perhaps because of his height, could easily be missed in a crowd.
The Eisenhower historian Stephen Ambrose had this to say: "General Andrew Goodpaster, in Ike's opinion, was not only the best officer in the U.S. Army, but also one of the two or three smartest men in the country. Well over six feet tall, ramrod straight, impeccable in his perfectly pressed uniform, with rugged features, broad shoulders, and a powerful chest, he was graceful in his movements, polite yet firm in his attitude." He seemed more at ease with himself than self-regarding.
An important personality trait that Goodpaster possessed was trustworthiness. He took seriously this observation: "The elements that go into inspiring trust are a style that is not offensive to the majority, a transcending honesty, a high level of intelligence, a willingness to deal with problems that immediately touch people's lives, a sense of patriotism, and public confidence in those to whom presidents lend their prestige and authority."
In sum, he came across as quietly self-confident, not seeking the limelight but not shirking it either. His understated personality enhanced his rapid progression in staff as well as command assignments. Although much his own man, his aptitude as a "facilitator" for the success of others gained him respect and the early attention of important career mentors. Put in sociological terms: "Among leaders there is self-advertising, in which the leader's self-image is advanced by his own posturing; and there are famemakers, others who advance the leader's image."
Specifically, from his days at West Point to his service as President Eisenhower's staff secretary and defense liaison officer, Goodpaster was an excellent illustration of the second—he left the first type to others. Contributing to this was his gift of influencing others in a way that drew them to him—a personality trait that is not learned.
As befitting an ambitious graduate of West Point, he was determined to conduct himself professionally so that opportunities for advancement would be there for him. When command assignments came to him, he grasped them enthusiastically and effectively. In fact, he continually sought them out.
**"Abe" Lincoln and West Point**
Goodpaster's origins were modest. He was born in Granite City, Illinois, in 1915 to Andrew Jackson and Teresa Mrovka Goodpaster. His father owned a small farm, and occasionally worked as a streetcar conductor in St. Louis, Missouri. After wending his way through the public schools of Granite City, with parental encouragement he entered McKendree College in Lebanon, Illinois, where he stayed for only two and a half years, preparing for a career teaching high school mathematics (in those days, he was known as "Jack"). For financial reasons, he dropped out in order to go to St. Louis to work in a meatpacking plant, where he was elected the first president of the company's labor union. The kind of employment opportunities in the St. Louis area that suited his temperament and ambitions were obviously scarce, but even then he showed leadership qualities.
At that juncture, in 1935, upon the nomination of Rep. E. M. Schaefer of the 22nd District of Illinois and after a competitive examination, Goodpaster obtained an appointment to West Point (he was unsuccessful in obtaining an appointment to the Naval Academy). When asked how he adjusted to being a plebe (first-year cadet) at West Point, Goodpaster answered, "I had a vague notion of what it was. It was still quite a shock to go in there. But they left no doubt as to what was expected of you, and I very soon concluded that it was well within my capabilities to do what had to be done."
In this respect, Goodpaster reflected this definition of adulthood: "If the term 'adult' means anything, its meaning must be social. One does not declare oneself adult: one is perceived to be. Unavoidably, the qualities we call adult are on the side of 'sanity,' 'normality,' rationality, continuity, sobriety, responsibility, wisdom, conduct as opposed to mere behavior, the good of the family or group or species as distinct from the desires of the individual."
Goodpaster himself put it well, when he commented on his initial experience at West Point: "When we went into West Point, it was with a four-year commitment to serve after graduation. We didn't think too much about that; but as time went on the whole atmosphere was that this was a calling. That this was one of the great fields of service and then duty, honor, country began to take hold of us and a . . . a feeling that to serve your country in the military was one of the worthiest things that we could do. . . . We saw the officers there, they were fine people."
As the members of the class of 1939 moved through their undergraduate experience, "we had that sense that the world was headed toward war and it was a sobering thought because we had the feeling that we would be drawn into it. The cadets all talked about it." Stephen Ambrose summarized the situation confronting Goodpaster and his West Point contemporaries: "In 1939, on the eve of World War II, the United States had an Army of 185,000 men with an annual budget of less than $500 million. America had no military alliances and no American troops were stationed in any foreign country. The dominant political mood was isolationism."
In fact, Goodpaster's class had been made larger than its predecessors—nearly eight hundred—to accommodate for the expected growth of the officer corps in anticipation of the exigencies of war: "We are the class of 1939, first and largest of the large classes—fledglings untried in the larger game for which we have been preparing. Humbly we hope we may be worthy tools, may carry the Spirit of the Corps out with us into the Service, and yet may leave behind the Corps itself, better than we found it."
Mentoring is a widespread human activity, and especially so within a military setting in which continuity of management is an essential—indeed obligatory—aspect of successful leadership. In Goodpaster's case, the pivotal mentor for him throughout his career was then-captain George "Abe" Lincoln, an instructor in the Department of Economics, Government, and History. During his years on the faculty at West Point, Lincoln was to redefine the role of the officer to conform more closely to the needs of modern and ever-changing warfare. Lincoln had graduated from West Point in 1929 and had proceeded from there to Oxford University as a Rhodes scholar, thus setting the stage for generations of talented West Pointers who went on to win the coveted scholarship. Doubtless conditioned by his own experience at Oxford, Lincoln introduced into the curriculum more courses in the humanities and social sciences. Engineering, for him, could not play its proper role in preparing the cadets for what lay before them without partnering with these other disciplines.
Lincoln was the person who had the greatest influence on Goodpaster while he was at West Point, and this beneficial relationship continued for the rest of their lives. For Lincoln, Goodpaster was emblematic of the type of officer that he envisioned would hold the future of the Army in their grasp. Early on, this mentoring relationship brought an invaluable opportunity to Goodpaster in the late winter of 1939, when Lincoln nominated him to represent West Point in a Council on Foreign Relations–sponsored student conference. This was the first time the academy had sent a delegate.
Goodpaster recalled: "I was sent down from West Point as our delegate to that enterprise. . . . We engaged in three days of debate. . . . At the end of it, three of us were voted to set out our respective views: one, I think from Harvard, supported the continuation of the Neutrality Act. . . . I had taken the position that we should disengage from the Act but maintain, as I put it, freedom of action depending on the course of events without commitment to any particular group or side at that time."
Undoubtedly to Lincoln's satisfaction, Goodpaster left this impression:
The outstanding man of the sixteen [university seniors] was Andrew Goodpaster. This became increasingly apparent as the conference progressed. He was a frequent contributor to the general discussion, never in the sense of talking too much but of speaking up at the right time and in the right way. . . . He thinks clearly and can express his ideas simply and directly. . . . He was one of the three spokesmen for the university men at the Friday night dinner. This in itself is a sign of his ability, for the spokesmen are chosen from the outstanding men of the group. His "speech"—for lack of a better term—was a fifteen-minute description of what he considered to be the most effective foreign policy for the United States during the next half year. It brought a salvo of applause from the Council members present.
Goodpaster also was brigade adjutant, served on the debate team that won a national championship, and served on the Honor Committee, in addition to playing football and swimming. When Goodpaster graduated second in his class, he was already marked as a "comer" possessing natural leadership.
To seal his commitment to an Army career, when Goodpaster was about to enter his first assignment, he married Dorothy "Dossy" Anderson, whom he had met during his first year, when she had been working in the West Point Library, on 28 August 1939. Dossy was the daughter of the academy's executive officer, Lt. Col. (later Maj. Gen.) Jonathan Waverly Anderson. The Goodpasters had two daughters, Susan and Anne, in the course of a satisfying marriage coupled with highly successful military service—not so easily accomplished.
Later on, Goodpaster addressed the question of leadership development at the academy as follows: "The idea of progressive development on which we built the duty concept—it's obedience for the Plebe; it's self-discipline for the Yearling; it's a sense of responsibility and a commitment to the mission as the cadet progresses in his duty sense as he goes through the Military Academy. . . . It is the objective of West Point to nurture both these elements of duty—1) the ability to assess and decide what ought to be done, and 2) the desire to do it. Both rest on well-recognized legal, moral, and social underpinnings."
All of these feelings and attitudes were present in the psychic makeup of this young midwesterner in the early years of a vocation that, to him, seemed selfless as well as self-justified. Put in another context: "It's true it isn't easy to be young in these times. . . . An ethical system based on universal values, you can try to impose it on others. But the meaning one gives to one's own life is another story."
**Early Career Unfolds**
In September 1939, not long after Goodpaster graduated, Germany invaded Poland, and three days later Britain and France had declared war. "In a 'fireside chat' radio broadcast [President Franklin D. Roosevelt] said: 'I cannot ask that every American remain neutral in thought. Even a neutral cannot be asked to close his mind or conscience.'" Goodpaster would have agreed with this presidential observation. He clearly understood that combat would be inevitable; what he did not foresee at that stage of his life and career was that a decade or so later he would occupy a place at or near the seats of political/military power.
After commissioning in the Corps of Engineers, Goodpaster's first assignment was with the 11th Combat Engineers Regiment in Panama, considered at the time a high-priority duty station (under the Neutrality Act, armed forces could only be deployed in defense of the Western Hemisphere). There were few, if any, areas of more hemispheric strategic significance than the Panama Canal. This made the port city of Balboa and its surrounding territory a prime assignment for Goodpaster. At that time, the Pacific side of the Canal Zone was designated the defense priority. The official war-fighting doctrine of the Army was built around holding on to the so-called strategic triangle of Alaska-Hawaii-Panama, along with planning for a war with Japan in the Pacific. To the planners of that time, there was more at stake in the triangle than in Europe, as difficult as it may seem in retrospect. The Pearl Harbor disaster seemed to confirm this planning priority.
Nonetheless, the Panama Canal area was not Goodpaster's first choice: "First of all, the word was around that service overseas had special value, special interest. . . . If I couldn't get the Philippines, then Panama, 'cause I knew about the construction of the canal. . . . The vacancy came the next year in the Philippines and the number one man in the class of 1940 chose the Philippines, went out there, served on Bataan, and died on Bataan."
Goodpaster's unit was charged with building cantonments for the Army ground and air units that were being sent down for training and to assist in the zone's defense. He observed, "When we got to Panama and I joined the Eleventh Engineers, I soon discovered that the ruling requirement was speed and resourcefulness in getting the job done." Here is how Goodpaster described the task: "The cantonment that we built in Panama was about . . . four acres in size. We enclosed it with barbed wire, we put towers at the corners, and then within it, the cantonment included screened-in tents, with wooden floors, screen barracks, screened mess halls, and screen latrines. And this now was a living area for the 1,800 people that we had been instructed to care for. That was a cantonment."
When the post library was being disbanded, Goodpaster related, "one of [the books] turned out to be one of my prized possessions. Its title was _Infantry in Battle_. The author of the book was George C. Marshall, who was then a colonel at Fort Benning. And he had a lot in this book about instances of good command procedure and instances of poor command procedure. . . . I found Marshall's book, and the book on combat orders, extremely helpful in elaborating the process of command decision. . . . This turned out to be, for me, quite a fundamental lead into how to exercise command."
Marshall had already become Goodpaster's model of an officer who could command the respect of those around him by virtue of his force of character. At some point in his career, Marshall had composed his "Rules of Leadership." They are worth recalling, because these rules could apply to Goodpaster as he was just embarking on his career: "1) Learn and benefit from early childhood experiences; 2) Experiment with a variety of challenging life experiences to gain self-confidence; 3) Have a vision for your life and a plan for achieving your vision; 4) Develop close lifelong friendships with people you can trust; 5) Become the 'master of the situation'; 6) Learn the value of self-discipline."
Goodpaster understood by then that getting the job done meant understanding what needed doing and then accomplishing it as speedily as possible. To do this, he acknowledged that the official "specs" for his construction project had to be adapted to the circumstances on the ground without contravening standing orders. By the completion of his tour of duty in Panama, Goodpaster felt he had "earned his spurs" as an Army engineer.
In 1942 Captain Goodpaster was sent to Camp Claiborne, Louisiana, where his task was to help train African-American inductees in the ways of the combat engineers: "They did not want to take instruction from other [African-Americans] . . . they were termed then colored NCOs [noncommissioned officers] that were sent down to form the cadre of our regiment. But we really moved out quickly. We trained them as bulldozer operators, heavy equipment operators, gave them training in the placement of mines, the clearing of mines, demolitions, building hasty bridges, all the things that engineers were involved in."
After only a few months, then-major Goodpaster was assigned to Fort Leavenworth to take the Command and General Staff College course, but in only nine weeks, instead of the usual nine months. From there he took command of the 48th Combat Engineer Battalion at Camp Gruber, Oklahoma. While his battalion was participating in maneuvers in Louisiana, "I got one little piece of experience, unsought, that in going out forward of the general troop area to do a little personal reconnaissance I got captured by the enemy, and I learned what it was like all of a sudden, to be gone from the unit and to be under the control of somebody else." The battalion was scheduled for overseas duty, having been assigned on 1 November 1943 to the 1108th Engineer Combat Group, II Corps, Fifth Army in Italy. The group consisted of the 48th and 235th Combat Engineer Battalions. Concomitantly, in the late spring of 1943 Goodpaster was promoted to lieutenant colonel.
Initially, the Allies had thought that the Italian campaign would be short—especially after the Italian army and government had changed sides. This proved to be wishful thinking because Hitler had ordered his commanders to fight as long and as hard as possible. The mountainous regions of the Italian peninsula north of Rome "had been organized into a series of defensive positions. . . . The Italian campaign is . . . a doughboy's war and an engineer's war and they are the ones who will win it, mile by mile."
Goodpaster recounted his first experience under fire: "As we moved up to the Volturno River, we were charged with building and then the maintenance of a pontoon bridge across the Volturno. And it was at that particular point that I learned what artillery fire was like on the receiving end. I was not damaged, but we began to lose some of our troops. . . . Finally, in early December, we got the mission for which the 48th became rather famous. That was the conversion of what had been a mainline railroad that the Germans had destroyed between Naples and Rome. . . . I think we put in more than a dozen major bridges and a lot of culverts. . . . There we came under quite frequent artillery fire. We had to work both at night and day to get our job done."
The possibilities for incurring heavy casualties were very great. The German general Kesselring had anticipated the Allies' plan: "They were now dug in along the steep escarpment of Monte Cassino. . . . The Germans could kill the British, Americans, and Canadians as easily as if they were shooting fish in a barrel." This put a premium on personal leadership skills, not only to perceive what to do, but also in doing it under withering fire.
Inescapably, the casualty rates were high and the goal proved beyond reach. The Rapido operation was one of the worst battlefield failures of the Italian campaign, which meant that early in his career Goodpaster was exposed to the inglorious aspects of war. One company commander in the 148th infantry reported: "I had 184 men. Forty-eight hours later, I had 17. If that's not mass murder, I don't know what is."
Service as infantry was a second mission of engineers; as the attack unfolded, instead of pulling back, they would convert themselves into ground troops and participate openly in the hostilities. As a result, Goodpaster learned firsthand what it felt like to see troops blown up or strafed. He remarked that he "developed the practice on Sundays of getting a list of where my troops were and going back to see them in the hospitals. That . . . hit [me] harder in a way than when I learned that troops had been killed because this was an actual visit to see how they were, and what their prospects were."
Goodpaster recalled the situation that confronted him and his troops:
To the north side of Route 6 as it went on into Cassino, there was a wide open plain, and the north branch of the Rapido had been diverted [by the Germans] to flood that plain, which was very soft soil. They did quite a job of flooding it. As a result, it was not possible to get tanks up to the area of the stream itself. In this area, the stream must have been about thirty feet to forty feet wide, with very steep banks. Many of the banks had been built with masonry to channel the stream and direct its flow. . . .
I talked to a couple of officers who had reconnoitered up there, and they had come up with the idea that if we could get the tanks down into the streambed, which was gravel and rock bottom because of the speed of the flow of the water, it was now dry or essentially dry. . . .
A small group of us went up and removed the mines that the Germans had put around the obstruction that they had put in, and opened up a way so the tanks could get down into the stream. . . . As we were coming back up the stream the tank battalion commander was leading his tanks down, and he told me later he was never more amazed in his life to see this engineering lieutenant colonel walking up the streambed toward him, and telling him that he could get his tanks into the stream and down the dry streambed, and up the other side. He did that.
Ever mindful of his troops, Goodpaster very graciously sent the following message to them:
During the six days which ended at noon Dec. 21, 1943, this battalion completed the mission of opening up for two-way passage of class 40 motor traffic a five-mile stretch of railroad containing twelve major obstacles, all under observed enemy artillery fire from German "Winter Line" prepared positions, the forward end being under automatic weapons fire. . . . I have served in and with some of the finest units in the army. You men who constitute this battalion can take your place among them; your performance of the last six days, though many of you probably do not realize it yet, matches the proudest accomplishment of the Corps of Engineers throughout its brilliant century and a half history. . . . I am proud to share with you the privilege of serving in this battalion. /s/ Andrew Goodpaster, Lt. Col., 48th Engr Combat Battalion Commanding.
Although at this point, it is very unlikely that Eisenhower would have been aware of Goodpaster, he nonetheless embodied a quality that Eisenhower prized: "I must have those [commanders] who appreciated the importance of morale and had demonstrated a capacity to develop and maintain it."
Afterward, Goodpaster's battalion received a Distinguished Unit Citation for "outstanding performance of duty in action against the enemy, during the period 15 December to 21 December 1943." The citation read:
This unit was assigned the mission of converting the railroad . . . into a two-way highway. The road contained twelve obstacles ranging from craters to destroyed bridges and constituted a high exposed defile. Open throughout to direct German observation and observed artillery fire, which was accurate, continuing, and concentrated, on all work parties and equipment. Obstacle sites, not accessible by road, were reached by routes opened and constructed through mine and trip-wire fields flanking the railroad. . . . The performance of the 48th Engineer Combat Battalion was an inspiration to other units and reflects the highest traditions of the Corp of Engineers.
It was not long thereafter that Goodpaster suffered sufficiently severe wounds to justify his return to the United States for treatment. He took a shell fragment in the upper arm and shoulder. For this, he received the Silver Star. The commendation read:
ANDREW J. GOODPASTER, 021739, Lieutenant Colonel, CE, Headquarters, 48th Engineer Combat Battalion, for gallantry in action. . . . While engaged in this mission, he and one of the Infantry Battalions' Commanders were wounded by the same shell. Lieutenant Colonel Goodpaster rendered first aid to the Infantry Officer and saw to his evacuation, then, in spite of his wound, searched for and found the next in command, and spent several hours with him going over the defensive situation before he made his way back for treatment. His action was above and beyond the call of duty and was in the finest tradition of the Corps of Engineers and of the military service. Entered service from Granite City, Illinois. By command of Major General KEYES.
Chapter Two
Professional Planning
"A hard precipitating factor, encouraging the militarization of policy . . . has been the emergence of a new class of professional warriors."
—ARTHUR M. SCHLESINGER JR., _The Cycles of American History_
In late 1944 the Lincoln-Goodpaster relationship resumed when Lincoln, learning that Goodpaster was in Washington at Walter Reed Hospital recovering from combat, recruited him for the new Operations and Plans Division (OPD) of the General Staff of the War Department. Goodpaster had thought that he was headed into civilian life for medical reasons. Lincoln was chief of the Strategy and Policy Group (S&P), which was established in 1943 within OPD. This placed Goodpaster in the center of Allied wartime strategic planning for Europe and the Far East. Goodpaster recounted: "I was back in the States on convalescence at the time. I joined the Army Staff here in the Pentagon in August of 1944, and a good many of my duties in the Strategy Section of the Operations Division, OPD, involved staff work connected with the conduct of the operations in Europe." Significantly for Goodpaster's future, the Operations Division was known as General Marshall's Command Post.
This was his earliest direct involvement with Eisenhower. "Lincoln's wartime relations with George Marshall, Dwight Eisenhower, and John McCloy enabled him to engage Goodpaster in the new National Security Council (NSC) policy planning for what became the four-decade strategy for the Cold War." What other early career Army officer of those times could claim to be the recipient of such patronage—well earned as it was?
Because Lincoln played such a continuously significant role in Goodpaster's career, it is useful here to trace his own career trajectory. Promoted to brigadier general in November 1944 at the age of thirty-eight, Lincoln formed the "Lincoln Brigade," to which he actively recruited fellow Rhodes scholars to a new unit in S&P, the Strategic Policy Section. The S&P's purpose was to support the work of the State-War-Navy Coordinating Committee (SWNCC), which served as the coordinating agency for the president with respect to national security and foreign policy in World War II.
Lincoln considered a Rhodes scholarship to Oxford University to be a premier recognition of all-around personal excellence. He believed strongly that combining the sharply contrasting educational philosophies and traditions of West Point and Oxford provided officers with an intellectual breadth that would serve them well in senior planning assignments. Goodpaster had aspired to a Rhodes scholarship while at West Point, and would have been considered were it not that he was by then over the age limit. Even so, "[Lincoln's] experience with his first soldier-scholar, Andrew Goodpaster, USMA Class of 1939, from 1944 to 1947, proved to him that his role as mentor could produce very talented soldier-scholars capable of dealing with demands comparable to those [Lincoln] faced as Marshall's strategic planner in World War II."
An example of Goodpaster's usefulness was his inclusion in the early summer of 1945—before Japan's capitulation—in the last long wartime planning trip of OPD to the Pacific. The party visited various places over the course of several weeks. Goodpaster wrote the report. "[Goodpaster] ended with a reminder of the principles that should guide [OPD] in dealing with overseas commands—to give 'every consideration' to theater requests for trained personnel and other stated needs, to 'avoid arguments over generalities,' and, if correspondence failed to 'get down to the specific cases on a complicated subject,' to send out a party of staff officers to talk things over 'before blood pressures begin to rise.'"
**Planning and Planners**
Marshall understood that "plans are useless, but planning is indispensable." An informed observer went further in explaining this catchphrase: "Thinking carefully and deeply about the future does not provide a charted course for policy; the variables and the contingencies are far too numerous. The act of planning does, however, prepare the decision maker to maintain coherence and adjust effectively rather than sink in a sea of chaotic pressures."
Within this context, whereas the Americans brought industrial and logistical expertise to the Anglo-American wartime relationship, Marshall understood that his British ally brought something equally important: how to organize the planning and operational components of the largest international wartime endeavor in history. Specifically, as part of Marshall's reorganization of his planning machinery, he copied important aspects of the British style of administration, known as the cabinet secretariat system. The exigencies of war and the running of an empire during the late nineteenth and early twentieth centuries had been the motivating force for Britain, and it had become likewise for the United States when it entered the world arena during and after World War II. This meant that on the U.S. national side, Marshall created "joint" committees of the services (including the Army Air Force) and, for the Allies, a "combined" chiefs-of-staff committee.
To support this arrangement, one of the first things that Marshall did after Pearl Harbor was to shake up his headquarters staff. On 9 March 1942, "having seen his General Staff grow imperceptibly from 122 to nearly 700, Marshall massively slimmed down the operation, with all the changes coming into effect immediately. . . . Within two months no fewer than six hundred officers had come off the Staff. . . . One of the senior Planners who survived the mass cull, Lawrence Lincoln ["Abe" Lincoln's brother], was to call it 'a matter of evolution, or perhaps almost revolution, effected by necessity.'"
Directly relating to this bureaucratic arrangement, the War Plans Division (WPD)—soon to be renamed the OPD—was given the role of a central command post inside the War Department. "Accordingly, the reorganization assigned to WPD those General Staff duties relating both to the 'formulation of plans and the strategic direction of military forces in the theaters of war.' . . . OPD was itself virtually a complete general staff." Its mandate involved "the recognized primary interest of OPD in regard to all matters affecting overseas operations." For a rising young officer fresh from combat, there could not be a better place for Goodpaster to gain insight into the upper reaches of the higher command functions.
Goodpaster served in OPD until mid-1947, which included a one-year tour with the Joint War Plans Committee (JWPC) of the Joint Chiefs of Staff (JCS). This was an excellent assignment for a "teachable officer," for "the JWPC planning process was very efficient in linking the operational and strategic levels of war. It consisted of formulating a strategic concept . . . [that] then led to a campaign plan for each theater of war." In June 1944—just before Goodpaster arrived—"the JWPC finished its inquiry into Pacific strategy and issued a comprehensive study, JPS 476, entitled 'Operations against Japan, Subsequent to Formosa.' It incorporated the essential point made by OPD's Strategy Section officers about the necessity to develop plans for an early invasion of Japan proper."
Goodpaster's "first duty there was to participate in finalizing a plan for the occupation of Japan. . . . The Joint War Plans Committee considered it, passed it up to the Joint Staff Planners, who passed it up to the Joint Chiefs of Staff. . . . This was the plan that contemplated the division of Japan into four occupation zones. . . . Years later when the Japanese scholars discovered this plan in our archives, they were absolutely appalled."
It was in this assignment that Goodpaster first came officially to Eisenhower's attention: "I suppose the first time I met him was in 1946. The war had ended. He was back as chief of staff of the Army and I was then serving on the Joint War Plans Committee of the Joint Chiefs of Staff and was of course quite familiar with the positions that he and the other chiefs were taking on the flow of business that came before the Joint Chiefs at that time, particularly everything that involved planning and operations for the period immediately following the close of the war."
Goodpaster was assigned to the Political-Military Survey Section: "I worked on a number of things there. One project brought me into contact with General Eisenhower and that was to set up an advance study board of young officers who, on Eisenhower's request, would try to project themselves forward five years, ten years, to look at what the future shape of the Army might be and ought to be." Goodpaster was at the center of this enormous and enormously important undertaking, which gave him valuable staff experience at the highest level.
**Life as a Washington Planner**
In 1950, after three years away at Princeton, Goodpaster was assigned as the Army member to the Joint Advanced Study Committee (JASC), located within the JCS. The JASC was carrying on the work of the JWPC:
General Dwight D. Eisenhower formed the original group in January 1947 with the idea that the unprecedented technological developments of the recent past and near future may have necessitated a thorough re-thinking of all major phases of military activity. He envisioned that a group of officers would be freed from all current demands and would endeavor to develop a basic philosophy of national security and a modern theory of war, determine the nature of a possible future war, what the requirements would be to win that war, and the proper course to attain those requirements. He suggested a time lead of from 10 to 15 years, and emphasized objectivity and imagination as essential to the group's efforts.
It is obvious that the three officers (Army, Navy, Air Force) who were assigned would be of the very highest caliber. They chose to examine how the "bomb" would affect military thinking in the future. Significantly, given the perilous situation then existing in Korea, Goodpaster reported: "An outstanding point which has emerged from a two months' survey of all U.S. atomic weapons activities 'from mine to target' is that the United States is not now in position for immediate atomic action against a class of targets which is of major present importance to U.S. security. Further, current actions to improve this situation are far too slow and incomplete."
He had in mind the conventional thinking that the Chinese entry into Korea represented a "dynamic surge of Soviet Communism." Obviously, therefore, serious consideration as to the employment of tactical nuclear weapons in Korea was on the table. Goodpaster, in fact, recommended to Gen. Alfred Gruenther, then the Army vice chief of staff for plans, "facilitation of the placing of our highest forms of technological power behind our military forces engaged in the UN opposition to Soviet-Communist aggrandizement." He added, "It is apparent that action is urgently required: 1. To facilitate the effective use of atomic weapons against this class of targets. . . . This much must be done regardless of the question of actual authorization of the use of the bombs for this purpose. 2. To develop the necessary psychological readiness to use this weapon where such is indicated on a military basis."
One interesting side effect of this preoccupation with how to use (and therefore justify) the stockpiling of nuclear weapons was speculation as to how these weapons had changed the nature of leadership decision-making—unless they were to be regarded as simply a new form of artillery or aerial bombardment. Not only were there such new considerations as alliance obligations and homeland destructiveness, there were also considerations as to whether there had been an alteration of the very nature of war-making and war-winning decision-making. If this were so, then what about the balance between civilian leadership and military necessity in a democracy? Goodpaster noted, for example, that effective planning for the employment of tactical nuclear weapons would enhance the perceived power of the Presidency in war.
To someone as thoughtful as Goodpaster, the quandary of how to address the nature of atomic/nuclear weapons both strategically and tactically, and from there how to relate this growing weapons arsenal to the nature of representative government, would have been troubling. Could almost instantaneous decision-making on their use be reconciled with the need, in a democracy, to rely as much if not more on persuasion than on compulsion? Indeed, nuclear leadership "must justify itself by its detachment, moderation, and power of analysis." These traits personified Goodpaster.
Goodpaster seemed to have relished conceptual thinking: "I have been undertaking to develop a better understanding of the military component of a nation's life as a system of actions, a system of decisions, and a system of relationships. I am not sure whether this should be an extra-curricular activity or not and have therefore done about half of my work on it in the office and half at home. . . . The reason for reaching for such a framework comes from the fact the whole structure of military activity has been disturbed in a very fundamental way by the introduction of atomic explosives."
Goodpaster remained in this assignment for only the latter six months of 1950. His efficiency report for this period concluded: "His wide knowledge of political matters, his clear understanding of military organization, concepts, procedures, plans, and actions render him particularly well fitted for staff assignments at high command levels. It is quite unusual to find an officer with the exceptional qualifications of Lt. Colonel Goodpaster."
**A Soldier at Princeton**
In 1947 Goodpaster went to Princeton University for graduate study in engineering. As he recounted: "After I and my associates had been in OPD for about three years, the Chief of Engineers renewed his claim on us and said that it was time for two of my colleagues and myself to go get our graduate education in engineering. Lincoln, our boss, said that he would not agree to that, that he wanted us to go to graduate school, but it should be for the study of international relations. . . . We would go and we would get our engineering degrees, to establish our credentials in our branch, and in addition would be able to pursue the kind of broader planning against a broader perspective that we had been engaged in, in OPD."
At that time, it was not at all usual to assign a serving officer full-time to a civilian institution for graduate study in the social sciences (or the arts, for that matter). It is thus noteworthy that Goodpaster himself recognized the desirability of a broader educational experience. For example, he wrote to Dr. Bernard Brodie of Yale University's Institute of International Studies in January 1947: "I am interested both in broader studies of history and political affairs fitted to plans and policy work on the War Department Staff and elsewhere, and in other broad and basic studies which do not have specific application. As a result, I seem to be riding two or maybe three horses at once. . . . There is a need for understanding of the forum in which these matters are determined and for an awareness of the fundamental elements of history, philosophy, and social forces which orient national policies."
Along with Goodpaster, Stanley Joulwan was assigned to Columbia University and Edward L. Rowny went to Yale. Goodpaster summarized: "After I'd been there two years and had completed the studies for a Master of Science degree in Engineering and a Master of Arts degree in International Relations, [his academic mentors] Professor Harold H. Sprout [of the Department of Politics] and Dr. Edward Meade Earle [of the nearby Institute of Advanced Study] proposed to the Army that I stay for the third year. I had done all my course work for a PhD, and all I would have to do is prepare the dissertation during that third year." It was almost a precondition for Goodpaster and his faculty sponsors to aim for the doctorate after he had passed his "Generals." The Princeton doctoral program in politics (which included international relations) was based on the premise that the candidate, although earning a master's degree at the General Examinations stage, was expected to go on to complete the doctorate. Goodpaster was fortunate in having Professor Sprout as his dissertation supervisor, as the latter was famous for going out of his way with students to be helpful.
It is quite clear that Goodpaster adapted readily to the "cloistered" environment of Princeton, and that he earned from the faculty not only the respect that goes to the better students but also their friendship. An example is an exchange in 1955 between Professor Sprout, while he was spending a year at Oxford, and Goodpaster, who was then serving in the White House. Sprout brought to Goodpaster's attention the situation of the recipients of the British-sponsored Marshall scholarships (named for General Marshall and the Marshall Plan) who were in the commissioned reserve but were not given an exemption from their service in order to complete their scholarship years. This was in distinction to the policy for the Rhodes, Fulbright, and Rotary scholarship holders. As Sprout put it, "As you will surmise, I have no personal stake in this issue at all beyond the stake that every American has in promoting cordial relations with Britain and in doing whatever he can to reciprocate the warm welcome which one receives here these days." Through this exchange of letters, an inequality was rectified.
In 1976 the Association of Princeton Graduate Alumni (APGA) awarded Goodpaster its James Madison Medal. The medal's purpose is "to recognize the distinction of alumni of the Graduate School. . . . The Madison Medal recognizes an alumnus or alumna of the Graduate School who has had a distinguished career, advanced the cause of graduate education or achieved a record of outstanding public service." Foreshadowing the writing of this biography, the author, as president at the time of APGA, described Goodpaster as "Soldier, Statesman, Scholar."
**National Technology and International Politics**
Although the "Internet age" has overtaken the "technology age," Goodpaster's dissertation, whose title is above, is worth recalling because the general outlines of what he proposed to examine remain relevant today. He managed to combine in a single topic information and analysis that was both academically sound and professionally relevant.
He recognized the importance of a nation's technology as a component of national power. It was not lost on him, of course, how America's overwhelming industrial strength played such a key role in the victory of World War II. As he wrote: "A nation's technology is one of the factors bearing most strongly upon the domestic and international well-being of its citizenry. A nation's welfare, its internal prosperity, its external security are strongly influenced by the kind and size of its productive activities. From an international standpoint, the role that a nation plays in the world family of nations—the influence that it wields, the pressures and problems that it faces, its powers and limitations, its relative advantages and disadvantages—stem in good part from the processes, the facilities, and the input and output of its own industries and those of other nations. The analyst of international politics, however he defines his field, must take into account the manifold, pervasive influence of technology."
It is interesting to note that in a sense Goodpaster's dissertation presages the pervasive influence of the technology of the Internet and of the various related industries that have been spawned, and how they are transforming the manner in which virtually the entire world arranges its affairs. For an officer who was at that time still just embarking on what would be a lengthy and notable career at the forefront of public affairs, his insights formed while a graduate student served him well. As he put it: "The ever-changing nature of technology has extensive consequences. The products of a particular period, in kind and in quantity, are the _implements_ [Goodpaster's emphasis] with which international action is conducted. The radio, the telephone, and other communication devices tell much as to the tempo of diplomacy, the methods and scale of cultural penetration."
Goodpaster was especially interested in how technology affects international affairs, not surprising since the Cold War was just about to shape every other aspect of American national life. He made this clear at the outset of his dissertation: "The proposition to be investigated might be framed as follows: The characteristics of a nation's technology changes as the result of the interworking of physical, social, and psychological factors external to technology; and these characteristics, and the changes in them that occur, produce the impact which technology has upon international politics."
Technology can, of course, have both good and bad aspects, as the rearmament of Germany prior to World War II revealed. Goodpaster waxed almost poetic in discussing this point: "[Technology] destroys in one place as it builds in another; it weakens here as it strengthens elsewhere; . . . while it raises problems, it provides means by which a capable government can devote to solving them."
Likewise, Goodpaster was wise to note throughout his dissertation that technological innovation can lead to greater or lesser benefits for human-kind. In fact, many of the technologies that are transforming society at an increasingly rapid pace had either their inspiration or their applications generated because of perceived military needs or aspirations. The sophisticated means of communication that exist today—including the use of drones—would not have particularly surprised Goodpaster, but he would have cautioned that they cannot substitute for human judgment both in the abstract and in day-to-day decision-making.
Goodpaster concluded thus:
Upon national capabilities, the products of technology have a rather direct influence; they are the material sustenance of programs of national action. Also, as implements of action, they tend to set the character and tempo—whether in warfare, diplomacy, psychological appeal and subversion or economic action. . . . [Yet] technology is itself but a single, passive factor in the resolution of such problems; the resolution can only be achieved through the efforts of analysis and statesmanship.
After the successful oral defense of his dissertation, Goodpaster gossiped about it like any graduate student would, concluding in a letter to a friend: "All in all the experience gave meaning to the old adage about the professors knifing each other through their students." Likewise, he also appraised his experience, concluding, for example: "I was embarrassed to admit that my fundamental ideas on technology did not change very much as a result of the year's work. I do feel, however, that my understanding of what was implied in those general ideas was considerably improved."
Chapter Three
Goodpaster and the Creation of NATO/SHAPE
"The willingness of proud sovereign states to entrust their precious armed forces to the command of a foreigner in time of peace was a measure of their willingness to subordinate their national interests to the common weal."
— LORD HASTINGS ISMAY, _The Memoirs of General Lord Ismay_
It is easy, almost facile, to claim that the treaty commitment of 1949 to create the North Atlantic Treaty Organization (NATO) was only a restoration of the World War II winning coalition. In fact, this represented the first time in American history that the United States had committed itself formally in this way while not actually at war. Although in retrospect it seems almost ineluctable that the democratic states of Western Europe, along with those in Scandinavia and the Mediterranean, would be linked through the formation of the broader "Atlantic" concept, this was not assured at the time. Visionary leadership combined with hard-boiled intra-Washington and cross-Atlantic bargaining accompanied every stage of this historic realignment of Euro-Atlantic relationships.
After the outbreak of the Korean War in 1950, there was widespread fear that the Korean "feint" was a preliminary to full-scale war in Europe. As it was put: "Rather than retreat from Europe, American policymakers envisioned the North Korean invasion of South Korea as part of the global Communist assault against the West. . . . The United States embraced the alliance and intended to fortify it and reshape it as a military organization." This was Eisenhower's challenge when he was invited by President Truman with the concurrence of the North Atlantic Council to become the first supreme allied commander, Europe (SACEUR), charged with creating a multinational force-in-being.
Goodpaster played a central role in swiftly bringing about this "militarization" of the erstwhile political alliance. In fairness, Goodpaster and his colleagues benefited greatly from the plans, headquarters, and personnel of the pre-existing Western Union Defense Organization (WUDO), which was created in 1948 and was the military arm of the Brussels Treaty. WUDO was incorporated directly into the newly formed Allied Command Europe (ACE). Thus, it was possible within only a few months for Goodpaster and his colleagues to lay down the basic structure of ACE.
Although it seems in retrospect to be only a footnote in American history, at the time the transformation of the alliance from being primarily political in nature to possessing a military component was a dramatic departure from the manner in which the United States had conducted itself politically and militarily since its emergence on the global stage.
**Creating a Multinational Headquarters**
Goodpaster's career took an unexpected but very exciting turn when, after six months back in Washington, where he had been enmeshed in the intellectual as well as the practical aspects of defensive nuclear war, he found himself alongside Eisenhower, who became the central figure in the creation of the military structure of NATO.
Initially, Eisenhower considered morale to be his biggest problem. Europeans just did not want to think about fighting—or building the forces to fight—another war. Goodpaster put it retrospectively: "A militarily denuded Europe stood momentarily transfixed by the fear of a Soviet invasion." Eisenhower, as the symbol of victory, was well equipped both actually and symbolically to counter this attitude, understandable as it was. The appointment of Eisenhower and the formation almost immediately of his supporting staff gave tangible evidence that the United States was firmly committed to resist what was perceived at the time as a "clear and present danger" from the Soviet-dominated East.
Eisenhower's insistence on an integrated command structure—in distinction to one "international" in form—reassured all of the member nations that they would have a "presence" in the headquarters. It was very important, therefore, that the American supporting staff officers, such as Goodpaster, possess the ability to work effectively alongside officers from a different linguistic and cultural, as well as military, tradition. Goodpaster said, "Eisenhower gave us very clear instructions, working through Gruenther. And both of them of course, had had experience with this—that the headquarters would be . . . completely integrated so far as services were concerned . . . [and] that the headquarters itself would operate on a completely international basis."
Eisenhower once exclaimed in frustration that "devising an organization that satisfies the nationalistic aspirations of twelve different countries or the personal ambitions of affected individuals is a very laborious and irksome business." It was obvious that "[Eisenhower] and members of the SHAPE [Supreme Headquarters Allied Powers Europe] Planning Group could not draw up an organization solely based on military considerations. Of equal importance were questions of personalities, politics, and national prestige." Goodpaster recalled:
My first connection with NATO came on 16 December 1950. It came at a time when the world situation seemed to be deteriorating rapidly. . . . Then serving in Washington, I received a request from Col. R. J. Wood, until then an instructor at the National War College, later to be the Staff Secretary at SHAPE, to leave for Paris at noon the next day. . . . I found [myself] late on 18 December comprising the initial contingent of what was to become the European headquarters of the NATO Allied Forces. Gen. Alfred M. Gruenther . . . had instructed us to establish an Advanced Planning Group and to develop plans and proposals for the organization and buildup of the headquarters and the command structure of the Allied forces.
Eisenhower came over just three weeks later. The abruptness that accompanied this new assignment is exemplified in this exchange between General Gruenther, who had moved from Army vice chief of staff to deputy supreme allied commander, and Goodpaster's JCS superior, Admiral A. C. Davis: "General Eisenhower asked me to check with you to ascertain whether or not it would be agreeable to you to have Lt. Colonel Andrew J. Goodpaster assigned to him on a period of 30 days temporary duty to assist in studying problems incident to the establishment of SHAPE. I recognize that there is the danger of losing Goodpaster, and I do not want to promise that he would not be kept on permanently at the end of the 30-day period."
For a rising officer who possessed skills both in battlefield leadership and in staff planning, this newly created cockpit of the Cold War seemed made to order. As events were to prove, for both Goodpaster and Eisenhower, such indeed became the case.
When Eisenhower arrived in Paris, he quickly set to work with the Advanced Planning Group to devise a structure for the new command, ACE, and its new headquarters, SHAPE. There could be no more convincing example of Goodpaster's identification with SHAPE than the fact that he was the staff officer who drafted General Order Number 1, which activated the headquarters.
Suffice it to say, Goodpaster worked in close proximity to Eisenhower during these eventful weeks. As he recalled: "I had been a staff officer at SHAPE when then-General Eisenhower set up the headquarters. I had worked very, very closely with him on matters of security policy, of course with the direct relation to military planning, but in the context of what were then called the political and economic capabilities of the member nations."
One of Goodpaster's tasks was to assist Eisenhower in forming the political and military guidelines for the new treaty organization, and thus, he was Eisenhower's liaison to the various national diplomatic and political personalities who were closely involved. He recalled that between January and April "[we were] getting quite close to the point now of actually operating the apparatus we have constructed with the end in view of increasing our military capability through creation of forces improved in quality, quantity, and readiness, and development of improved ideas on how they might be employed." Fortunately, many, if not most, of the senior officers at SHAPE had been with Eisenhower in World War II, so their working relationships fell more easily in place.
As to his personal staff, Eisenhower said to Gruenther: "By having an American staff [that reported directly to him], it is solely for the good of the NATO organization (give them the example of a Congressional committee). After all, there are relatively few American officers engaged in this kind of thing. . . . Goodpaster and one or two others are the principal ones." This was not an idle observation, for those officers were hand-picked. Gruenther implied as much in a speech at West Point, during which he referred to several officers who were academy graduates as making "a very fine impression on everyone with whom they come in contact. We have . . . a lieutenant colonel who is probably the most brilliant and most respected officer in the entire headquarters."
Goodpaster, of course, phrased the relationship differently:
[General Gruenther] would take the broad principles and the main lines of effort that General Eisenhower laid down on how to solve or resolve or satisfactorily meet the defense need, the security need there in Europe, and he then would convert that into proposals for our staff organization, for the organization of our command and so on. I was invited to come over as one of the initial planners. And in those early days I would work on the plan for the organization of our headquarters and the plan for the organization of the command, the terms of command authority, and things of that kind, submit them to General Gruenther and he would then take them up with General Eisenhower. We would have the guidance from Eisenhower to go on and, of course, he drew very heavily on his experience as the Supreme Commander during World War II.
Goodpaster also assisted in establishing SACEUR's parallel command structure for the American national military contingents assigned to NATO. Eisenhower's national role was titled U.S. commander-in-chief, European command (USCINCEUR). Under his successor, Gen. Matthew Ridgway, this other (and perhaps militarily more important) responsibility increased in importance. In this other "hat," as an American commander, CINCEUR would report directly to the JCS, bypassing the NATO chain of command. In reality, on most matters the deputy USCINCEUR would primarily be involved.
A good illustration of Goodpaster's being at the center of not only the military but also the formation of the civilian side of the alliance was his being delegated to represent the SACEUR in the work of the so-called Temporary Council Committee (TCC). This high-level committee of national representatives of the North Atlantic Council was created in September 1951 "to reconcile the military needs of the Alliance with the member nations' capacity and/or willingness to support these needs with money and material." Here is how the situation was described:
As the military side of NATO grew, it became increasingly apparent that the administrative organs of the alliance were unable to handle effectively the attendant military, political, and financial problems; further reorganization was necessary. . . . At the Ottawa Conference in September 1951, the council created the Temporary Council Committee (TCC). The TCC, although primarily concerned with the preparation of a comprehensive plan for production rates of military equipment and for force buildups, also examined the structure of the alliance. The TCC's report in December 1951 offered specific proposals for force targets and military standards for adoption by the alliance. It also underlined the need for improving and strengthening the nonmilitary structure of NATO.
The committee—known as the "Twelve Apostles"—was asked to render a report to the North Atlantic Council at the Rome Council meeting, scheduled for the end of November. From the larger committee, an executive bureau—known as the "Three Wise Men"—was composed of the chairman, W. Averill Harriman of the United States, with Sir Edwin Plowden of the United Kingdom and Jean Monnet of France as vice chairmen. The TCC's actual work was delegated to these three men.
Goodpaster observed: "I went over and was a staff officer, assistant to the chief of staff, General Gruenther, but I worked very closely with General Eisenhower particularly on something called the 'Three Wise Men Report' . . . a study which would correlate military needs with political-economic capabilities of the member nations and come up with a force program. . . . In this I was General Eisenhower's representative to the committee and its supporting staff, part of which [the Screening and Costing Staff (SCS)] was headed by General [Joseph] McNarney and again General [Abe] Lincoln was detailed from West Point to come over and work with us."
There could be no other assignment that could prepare Goodpaster, as a mid-level serving officer, for higher alliance command because it not only gave him a broad cross-alliance sense of needs and wants, it also brought him into contact with the major political-military figures of the other member-states as well as his own. For example, "as the replies [to the questionnaires] came in, the staff of the Executive Bureau studied them and assembled them into a form useful for further individual and comparative study. Then each country had its reply appraised by a committee of experts and by the Bureau. When a particular country's programme was considered, the representative of that country on the TCC sat with the Executive Bureau. . . . This examination was characterized by a frankness on the part of the delegations which was unusual in such delicate matters, invading as they did the innermost recesses of a nation's national existence."
This was so because the report also dealt with the civilian structure of the alliance. Goodpaster had, perforce, stayed in close touch with Eisenhower during this time "because that was kind of a make or break operation. And he was determined it would be a make operation." That Goodpaster contributed effectively to the jointness of the TCC enterprise is attested by this note from Ambassador Harriman to Eisenhower: "It has been my good fortune, and the good fortune of the U.S. Delegation and the Executive Bureau to work closely with Lt. Colonel Andrew Goodpaster. We have all been impressed by his wide knowledge, his fine judgment in the difficult areas of international security in which we have been dealing, and the depth and precision of [his] thinking, which has many times assisted us in moving forward with our work. You were good enough to lend him full time to assist in the preparation of the final report and his contribution thereto was substantial."
Goodpaster wrote to his friend "Abe" Lincoln, commenting on how to deal with wrapping-up the work of the TCC: "[W]e have done a little preparatory work toward the final action on the reports contemplated for the Lisbon ministerial meeting of the North Atlantic Council. In addition, I started some work ten days or so ago aimed at outlining a course of action in connection with the FY '53 aid program, and working out some of the relationships and assignments both for us and the U.S. agencies concerned."
Goodpaster's appraisal of the whole TCC enterprise was thus:
The TCC operation wound up somewhat above the minimum standard I had set for it. The minimum standard was simply that it should avoid doing any real harm. Above that, everything would be velvet. In actual fact, it will have one or two accomplishments to its credit—some progress on the further infrastructure development, and a firmer statement of exactly what we will wind up the year with in the way of forces, budgets, etc. The operation has been extremely interesting to me in showing in what elements of our over-all problem representatives of military, economic, political, etc., lines of thought can (and frequently cannot) make a contribution.
SHAPE chief of staff Gruenther added this note, commenting specifically on Goodpaster's role: "I cannot let this occasion go by without expressing my gratitude for the tremendous help you were to SHAPE in reporting so faithfully the details of progress of the [TCC] meetings you attended. I am confident that this important project would not have turned out as well had you not done so much to be in two places at once, giving advice both to them and to us. General Eisenhower and I are both grateful for this invaluable assistance."
Goodpaster's mind had ranged over virtually the entire gamut of SHAPE's organizational effectiveness; he thus displayed a capacity for analysis that few officers possessed. Goodpaster could both be intimately involved in some daily problem-solving activity and at the same time be able to step back and view the problem analytically, which probably was an important reason why he stood out from his contemporaries and had captured the attention of his superiors.
An example of this trait is his lengthy commentary to a correspondent from the RAND Corporation—Goodpaster was by this time firmly ensconced in the "think tank" world:
As you know, I am very much interested in this question of the timing of decision-making. I think you have something quite fundamental in this point. I have a small collection of observations regarding the view of this matter taken by some people whose abilities in this field I respect very highly. Mr. Churchill says he follows the line of "keeping options open" for future choice whenever possible. Marshall was quite vigorous in his views at one time on "post-war planning," which was reaching and implementing a host of firm conclusions at a time when major, basic elements of information were still unknown. Colonel Lincoln has the expression "let us temporize until we see how events develop." General Gruenther has a more operational technique, which he calls exposing oneself to the pressures of a given problem. I think I discern in General Eisenhower a tendency to put problems in the broadest possible frames of reference, recognizing that uncertainty and flexibility must be (and can be) introduced. While I don't count myself in this galaxy, I have a little rule which I at least consider from time to time and that is to reach no decision before it is necessary if it significantly limits future choices.
In virtually all of his staff assignments, he seemed to have been left alone to do his analytic best, while also helping solve the day-to-day problems connected with guiding the postwar United States into uncharted waters. Already by this point in his career, Goodpaster had established a network of friends—both personal and professional—that any officer of his rank would have envied.
Looking back over a span of over thirty years, Goodpaster commented in 1971 that "as we note the achievements of Allied Command Europe—a vital arm of the military instrument of NATO—we must view those achievements in relation to the objectives of the Alliance which NATO's military instrument is charged to serve." The objectives of deterrence and defense had been recognized, but in his estimation, solidarity and détente remained elusive. Goodpaster went on:
The traditional objective of deterrence—preventing war and making peace secure—must be today, as it was in 1951, the paramount route by which we provide for our security while maintaining our freedom. . . . The second traditional objective is defense. For deterrence to be effective, we must make unmistakably clear to any potential aggressor that the peoples of the Atlantic Community have the collective will and means to defend their territories and to make aggression unprofitable. . . . The third objective of our military instrument is solidarity—collective action and unity in the Alliance.
This has proved to be a strikingly successful means for the NATO nations to rise above the quarrels and conflicts of the past which have exhausted them and twice this century nearly destroyed them. . . . A final objective in the military instrument of NATO is détente—a relaxation of tensions. To be meaningful and durable, a détente must be based upon reducing and removing the _causes_ of tension—rather than merely the _symptoms_ of tension [Goodpaster's emphasis].
Goodpaster came out of this earlier NATO assignment with a reputation as "an honest broker, a man to be trusted, one who was fair and discreet and enjoyed Eisenhower's total confidence." He was already providing the high level of performance, in staff work and dealing with political as well as senior military figures from throughout the alliance, which was to be a hallmark of his entire career, and which subsequently led him to service in the White House.
His next assignment, in July–October 1954, was as chief of the San Francisco Engineer District. As he said: "Well, I went out to San Francisco, and at the end of two months, a man who had served with me in SHAPE, General Paul T. Carroll, who was serving in the White House as Eisenhower's Staff Secretary and Defense Liaison Officer, died of a heart attack. And General Eisenhower, by then President, asked that I come into the White House to take up that duty. . . . And my stay in the White House with General Eisenhower and then for two months with President Kennedy was to last for six and a half years."
A minor-appearing matter is worthy of note because it illustrates how carefully rank and status is calibrated at the most senior levels of the government. Goodpaster was impelled to write the following memorandum at the ascension to power of the Kennedy entourage: "I will need some kind of designation by President Kennedy to cover my status while I continue here, since the previous designation has terminated. I mentioned to the President this morning that, with Ralph Dungan as Staff Secretary, I could have some designation like 'Staff Assistant to the President' and he thought that would be fine."
**A Brief Foray into Nobel Speechwriting**
While at NATO, Goodpaster experienced an unusual opportunity to be of direct service to General Marshall. This occurred in 1953, when Marshall was en route to Oslo, Norway, to receive the Nobel Peace Prize. He fell sick and had to interrupt his travel to stay briefly with General Gruenther (who was by then the SACEUR) at SHAPE. Goodpaster recounted the episode in 2003: "[Marshall] landed in Europe with a few central ideas in his head but nothing on paper. . . . I knew his thinking, however, having worked with him previously, and by our third meeting, his health had improved greatly—and his speech was all but finished."
In the speech, Marshall acknowledged the place of military strength in world politics, but he also inserted a caveat: "The maintenance of peace in the present hazardous world does depend in very large measure on military power, together with allied cohesion. But the maintenance of large armies for an indefinite period is not a practical or a promising basis for policy. We must stand together strongly for these present years . . . but we must, I repeat, must find another solution."
What Goodpaster did not mention was that "Colonel Andrew Goodpaster . . . got down on the floor in Marshall's bedroom and put the various sections of the dictated bits together." It is doubtful that Goodpaster would have been drawn into this writing crisis if his own credentials in written composition were not already well established. Goodpaster's reputation in this respect had doubtless already spread throughout the headquarters.
By the same token, Eisenhower would not have been tapped for similar staff positions if he had not possessed similar skills. For example, during the invasion period of liberating Europe, Eisenhower had written to Marshall: "Dear General: Please do not look upon any communication I send you as a defensive explanation. Not only do I refuse to indulge in alibis but frankly, I feel that you have given such evidence of confidence in me that I never experience the feeling of having to defend my actions. My communications, therefore, whether in letter or in telegraphic form, spring simply from my belief that in higher echelons the common understanding of problems is the most certain way to insure smooth functioning."
Chapter Four
Solarium: The Articulation of a National Posture
"Out of the crooked timber of humanity nothing straight was ever made."
—IMMANUEL KANT
An indication of Eisenhower's regard for Goodpaster can be seen at the very outset of his presidency, before Goodpaster joined the White House staff. The occasion was Eisenhower's desire to examine the parameters and possibilities of refashioning the Truman administration's foreign and national security policies to suit the existing global situation. This was distinct from Eisenhower's campaign promise to "go to Korea." Rather, it was an attempt to discern what the situation would be after a settlement in Korea and after the death of Stalin. The main adversary was still the Soviet Union, and the main hostile ideology was still the Soviet version of the Communist state.
Thus, the basic "strategic dilemma" was the same for both Truman and Eisenhower—in spite of nominal disagreement. As it was put: "The clear determination of the Soviet Union to reject American proposals for a new world order, to defy American demands for liberalization in Eastern Europe, and to insist on the [United Nations] Security Council veto gradually pushed the Truman Administration toward the realization that international control was pointless and unattainable in any event as long as the two postwar great powers were unwilling to collaborate."
Goodpaster described the setting: "You had the death of Stalin in early 1953. And there were a lot of ideas back then about what should be done. People around the president, high up in the government, wanted to capitalize on it. A lot of people brought a lot of agendas to this issue and tried to push them on the president. He didn't take too well to that kind of pressure, and he did not want to get swept up in a political wave." He wanted a grand strategy that "called for, not so much the emotional and transitory sacrifices of a crisis, but rather those which enable us to carry forward, steadily, surely, and without complaint the burdens of a prolonged and complex struggle—with liberty at stake." The nuclear dimension came into sharp and alarming focus when, at this same time, the Soviet Union detonated its own nuclear bomb.
**Truman's Containment: A Cold War Antidote?**
Before the outbreak of the Korean hostilities in 1950, the JCS had come to share Ambassador George Kennan's view of the Cold War as being "a state of international tension, wherein political, economic, technological, sociological, psychological, paramilitary, and military measures short of overt armed conflict involving regular military forces are employed to achieve national objectives." How to define and refine this broad generalization was the de facto primary policy debate as between the Truman and Eisenhower administrations. Certainly one of the dilemmas in that search for definitions was that in the mind of some, Kennan's own view of what he meant by containment was initially over-generalized and, as will be seen, thereafter shifting in emphasis.
An observation of the Oxford social historian Theodore Zeldin is apropos: "When, in the past, people have not known what they wanted, when they have lost their sense of direction, and everything appeared to be falling apart, they have generally found relief by changing the focus of their vision, switching their attention. What once seemed all-important is suddenly hardly noticed any more. . . . In the course of history, humans have repeatedly changed the spectacles through which they have looked at the world and themselves."
Kennan resigned as director of the State Department's Policy Planning Staff (PPS) in 1949 to be replaced by his deputy, Paul Nitze. This presaged a "harder" line toward the Soviet Union as America's chief adversary and a greater emphasis on military force to counteract the perceived Soviet threat. Nitze had been the principal author of the famous (or infamous) National Security Council report NSC-68, which advocated a more aggressively militant stand toward the presumed threats posed by the Soviet Union to a weak and divided Europe.
Kennan recalled: "One of the reasons for my leaving the staff at the end of 1949 was my disagreement with NSC-68. I had the very strong feeling that the Russians were not going to attack us, but that on the other hand the strength of their armed forces, the disparity between theirs and ours, was a reality and would not go away; it would remain a reality for an indefinite time; and that our plans ought not be laid toward an ostensible 'peak of maximum danger'; they ought to be laid, in the military sense, in such a way as to endure for many, many years into the future as a permanent fixture of our policy."
"A central issue in the postwar debate over service roles and missions was the question of how future wars would be fought, and, in particular, the role of atomic weapons in military strategy. . . . In an age becoming accustomed to rapid advances in military technology, nuclear weapons loomed far larger and more ominous than all other instruments of warfare. . . . For the majority of military planners, nuclear weapons represented chiefly a dramatic enlargement of existing military capabilities that might or might not eventually revolutionize warfare."
The story of this unusual document, NSC-68, is thus worth recounting at some length:
In April 1950, the secretariat received a seventy-page typescript from the Department of State stamped TOP SECRET and given the label NSC-68. It was distributed to the president and the council's statutory members and advisors, the vice president, the secretaries of state and defense, the chairman of the National Security Resources Board, the chairman of the Joint Chiefs of Staff, and the director of Central Intelligence.
Entitled "United States Objectives and Programs for National Security," the paper analyzed the ongoing cold war and courses of action open to the United States. After reviewing arguments for continuing on the current course, turning to isolation, or deliberating opening war on the Soviet Union, NSC-68 made a case for an alternative, described in its table of contents as "A Rapid Buildup of Political, Economic, and Military Strength in the Free World." To appreciate this document, you should keep in mind that the cold war was still new. . . . The cold war had come as a surprise.
NSC-68, in spite of Kennan's forebodings, had not attracted much attention until the outbreak of war in Korea. Goodpaster recalled: "What it called for was a major upgrading of American military forces. . . . It was then pulled off the shelf and used as the framework of the expanded military program." He also suggested that NSC-68 was used as a budgetary ploy to convince Truman to raise the defense budget.
Another point of departure from Truman to Eisenhower was the idea of a period of "maximum danger," which the Truman administration had placed at 1954–1956. This served as a guidepost for planning the rapid buildup of countervailing military forces. Instead, Eisenhower favored Kennan's notion of the "long haul"—the stretched-out notion of an almost interminable situation of threat and counterthreat. Eisenhower seemed to agree that "containment meant you were counting on forces of change, natural forces, nationalism, internal social change, and the like."
Whether Goodpaster agreed that the Truman administration "militarized" Kennan's notion of containment by pushing more rapid rearmament is probably irrelevant, because Goodpaster would have been more concerned, in his career assignment, in carrying out whatever conception of the Soviet threat that Eisenhower adopted. Nonetheless, Goodpaster found himself involved in the debate over what should become the guiding policy prescription for those troubled and dangerous times.
The journalist Barton Gellman summarized: "The broad strategy of containment had three ends: to restore a balance of power and build up war-stricken allies, to exploit tensions in the then-monolithic Communist International and thereby to reduce Moscow's means of projecting power, and (in the long run) to moderate and to negotiate Soviet global behavior."
**The Solarium Initiative**
Goodpaster's Princeton friend, Edward Meade Earle, put the situation thus: "Strategy is the art of controlling and utilizing the resources of a nation—or a coalition of nations—including its armed forces, to the end that its vital interests shall be effectively promoted and secured against enemies, actual, potential, or merely presumed. The highest type of strategy—sometimes called grand strategy—is that which so integrates the policies and armaments of the nation that the resort to war is either rendered unnecessary or is undertaken with the maximum chance of victory."
Reflecting this concept, Eisenhower, with Secretary of State John Foster Dulles' agreement, decided to initiate a systematic overview of the possible courses of action that the United States might take in response to the sharply changing circumstances of the Cold War. This was especially important given that both superpowers were arming themselves with nuclear weapons of all sorts. It was widely known that Eisenhower was preoccupied with the nightmare of a Soviet nuclear surprise attack on the United States or its allies. This, to his way of thinking, was the primary threat against which America's scientific resources should be devoted.
The first reassessment step was taken on 8 May 1953, when
Eisenhower held an off-the-record meeting from 5:00 to 6:45 in the afternoon with the Dulles brothers, [Secretary of the Treasury George] Humphrey, [Under Secretary of State Gen. Walter Bedell] Smith, [publicist and speech writer] C. D. Jackson, and [National Security Advisor Robert "Bobby"] Cutler in the White House solarium for the purpose of generally discussing the state of East-West relations. "It is difficult to conclude that time is working in our favor," the secretary of state began the discussion. . . . It was evident that the "course" mapped out by Truman is "a fatal one for us and the free world." Unless "we change this policy, or get some break, we will lose bit by bit the free world, and break ourselves financially."
Viewed from this rather dramatic angle, the eresult was not so much a radical departure as an updating and refining of the Truman administration's notion of containment. Therefore, the story as to how Eisenhower's idea—which was dubbed the "New Look," even if it was not entirely new—was implemented is worth recounting in detail, especially as the listing of the participants reads like a Who's Who of Washington's power brokers:
A working committee comprising Cutler, Smith, and Allen Dulles supervised the organization, which included the appointment of a panel, chaired by General James Doolittle and including Robert Amory, Lt. General Lyman Lemnitzer, Dean Rusk, and Admiral Leslie C. Stevens . . . to draft "precise and detailed terms of reference for each alternative." Among the factors each task force would be asked to consider were: "forces needed, costs in manpower, dollars, casualties, world relations, intelligence estimates; time-table; tactics in every other part of the world while actions were being taken in a specific area; relations with the UN and our Allies; disposition of an area after gaining a victory therein; influencing world opinion; Congressional action required."
The criteria for selecting the task force participants were as follows:
Members of Task Force A were to have an "intimate understanding of the past policies and actions of the United States, the rest of the free world, and of the USSR, and broad-gauge political, military, economic, and psychological planning for the future." The requirements for inclusion on Task Force B were an "intimate knowledge of Communist reactions and methods; sound political and military judgment both regarding the Communist orbit and the free world; knowledge of United States military capabilities to wage general war, including the use of unconventional [i.e., nuclear] weapons; [and] ability to evaluate the economic capabilities of the United States and the rest of the free world to support the alternative." The qualifications for working on Alternative C included "imaginative military, political, psychological and subversive planning experience; profound experience on Soviet-Communist actions and reactions; knowledge of the military situation in Korea and Soviet satellite areas; and ability to evaluate the economic resources required to follow such a course."
Kennan, the leader of Task Force A, commented later: "I was very fortunate in the [task force members] that I had around me. They were drawn from different departments of the government, and some of them were even outsiders. . . . It is my impression that we were not asked to take that [working] paper as something that had been approved and that we had to recognize as valid. We were, however, to approach it critically ourselves. But we were to take off from that paper; where we disagreed with it, to say that we disagreed; or where we were in accord with it, to say so and to base our paper accordingly."
**The Process**
Robert "Bobby" Cutler, the special assistant for national security affairs, also described what the goal and process were:
The solarium was a small penthouse on the White House roof. . . . General Smith's earnest positive voice explained our one-page proposal of three task forces, each with a leader. . . . The President began suggesting names for members of the task forces (each with seven men of varied backgrounds under a chairman). "Put Andy Goodpaster on your list, and be sure to get him." . . . The leaders were General Lemnitzer, later chairman of the Joint Chiefs of Staff and Supreme NATO Commander; Major General James McCormack, later Administrative Vice President of the Massachusetts Institute of Technology; and George Kennan, former United States Ambassador to the USSR. . . . The Council assembled an elite group.
Goodpaster described Eisenhower's method: "The three teams were: a) To provide the argument for the existing policy of containment to prevent Soviet expansion in Europe, hopefully without engaging in a general war; b) Within containment, to move from an essentially passive stance to one more actively responsive to any Soviet aggression which would lead to general war, emphasizing American and allied retaliation with all means at their disposal; c) To confront Soviet military expansion, and to force the Red Army to withdraw from the occupied territories of Eastern Europe in particular. . . . Eisenhower put each of these men in charge of a group of seven or eight people, each charged with making the very best case they could for that particular line of policy. I was still serving with NATO in Europe at the time and he brought me back to participate in the 'rollback' group. And he told me later, he said, 'Well, I wanted to be sure that I had one man that I could at least hope had some common sense participating in the rollback study.'"
Later, Goodpaster recounted:
I had occasion to come back to the States with General Gruenther who was testifying before the Congress and seeing then-President Eisenhower in it would have been April, perhaps early May, of 1953. While I was there, I went around to the White House to visit with some of my friends who had been at SHAPE, General Paul Carroll in particular who was a staff assistant to Eisenhower at that time. I had lunch with him. And joining our table was Brigadier General Bobby Cutler, a Boston lawyer and banker who by that time was serving as Eisenhower's special assistant for national security affairs.
The moment Pete Carroll introduced me to Bobby Cutler, Cutler's eyes opened up and I could tell there was really something on his mind. We had an interesting conversation but he did not reveal what was on his mind. He told me in June when I came back to participate in the Solarium exercise, that at the time of the luncheon he had just come from a talk with Eisenhower, who was assigning individuals to each of these task forces by name and giving his reasons for doing so. And as Bobby Cutler told me: President Eisenhower had put me on Task Force C.
As it turned out, Goodpaster must have followed through as desired, for later on he commented wryly: "The rollback option . . . 'sank without a trace except for propaganda and covert operations.'" Goodpaster identified more specifically Eisenhower's motives:
At the end of it, I would say that it was very clear that rollback was dead and that something in the area of containment or areas of interest would be pursued. Rollback sank, it was finished as of that day. It had been very much in the rhetoric of the campaign and, to some degree, in the early months of the Eisenhower administration. But he used this, and in my belief he did it very intentionally and deliberately, as a means of forging a single controlling idea that would dominate his administration. Having done that, it was no longer necessary for him then to try to influence every particular decision, every particular action that was taken. He could look then to the Secretary of State, to the Secretary of Defense, to others to act within that broad, defined policy.
Eisenhower used the Solarium method—which came to be considered as an exercise unique in the history of U.S. national security policy-making—for several purposes: (1) to demark his outlook on how to deal with the Soviet threat; (2) to use this method to "bring on board" his newly assembled national security configuration; (3) to ensure that a coherent argument could be made for both the American public and the NATO allies that the United States knew what it wanted to accomplish to avoid both a superpower nuclear exchange and a conventional war in Europe.
Another aspect of Eisenhower's attitude toward the nonmilitary features of the Cold War was his consistent interest in psychological warfare, disinformation, and liberation (or "rollback") propaganda. Without going into detail, it can be safely noted, for example, that "Eisenhower's staff secretary, Colonel Andrew J. Goodpaster, later recalled that the president had 'never ridded himself of some feeling that our government, elements in our government—and specifically the CIA—had gone beyond their authority and in fact had carried out a line of propaganda of their own which was not in accord with his policy.'" After the Hungarian uprising of October 1956, much of these efforts were left to die a slow bureaucratic death. By 1958 the administration had embraced a less didactic evolution strategy.
On a more pragmatic level, one of Eisenhower's purposes in organizing this review was to widen the circle of participants in the exercise, thus enabling them, at its conclusion, to "buy in" to what Eisenhower had wanted in the first place. Goodpaster later speculated as to why Eisenhower took such a personal interest in the project: "I'm sure, from later discussions, that one of his purposes was to deepen the understanding of these matters on the part of the principal advisors, some of whom had had very limited experience in these fields."
As to the efficacy of the position papers, Kennan observed: "I cannot judge from this distance how useful [my] paper was or how useless. It probably had less importance than we thought at the time; perhaps greater importance today historically. . . . What emerged in the end was something not too different from what had existed before we came into the picture, but with a greater stamp of presidential approval than had existed before."
All of these considerations lend some credence to the view that Eisenhower knew all along what he wanted the outcome to be. "Whether Eisenhower actually altered his own thinking as a result of these deliberations is impossible to determine. Goodpaster says Project Solarium did not tell Eisenhower 'anything that he hadn't thought through before.'" If Goodpaster understood what was afoot as far as Eisenhower's motives were concerned, it is very likely many—if not most—of the other participants did as well.
The new administration wanted to emphasize an intellectual departure from the Truman legacy as well as create a strategic synthesis. Solarium effectively laid to rest any lingering sentiments for Truman's strategy for dealing with the Soviet threat; it also justified Eisenhower's (and John Foster Dulles') concept of how to adapt America's Cold War stance to the rapidly changing circumstances, both domestically and abroad, which confronted Eisenhower at the outset of his presidency.
As will be described shortly, this synthesis was to last for only a limited time because of the changing nature of warfare as ever-more lethal new weapons were being introduced, along with the political and psychological needs of coalition warfare. The pressures of decision-making—both tactically and opportunistically—had begun to sink in. Just as the so-called limited Korean conflict had, by the early 1950s, come to overhang all other political/military considerations—and budgetary, as well—so indeed did the increasingly ever-present "brush wars" of the latter 1950s that accompanied decolonization (Suez being the linchpin), even if they did not necessarily directly involve the United States militarily. They began to take on a life of their own—Vietnam, of course, was the overarching example, but not the only one.
To summarize:
Debate over whether or how the United States won the Cold War will continue for decades, but it is certain that Eisenhower's [Solarium] synthesis made survival possible. He transformed an ambivalent doctrine of containment into a workable policy of deterrence. Kennan's preference for propaganda, covert action, and political pressure was insufficient. Nitze's plan was too risky and inexact. The two approaches required a synthesis that deterred Soviet aggression while maintaining a common front with U.S. allies and limiting the domestic costs of a long and expensive struggle. The strategy put forth in NSC-162/2 struck such a balance and proved enduring, not least because the diverse Solarium participants took part in a process designed for "each," as Eisenhower liked to say from his days at NATO, "in the presence of all."
This unique example of presidential leadership foretold one of the techniques that Eisenhower employed throughout his presidency to get things done—stand back, set the tone and define the issue, and then let others step into the limelight. This was, equally, Goodpaster's natural instinct, which is one important reason why he was consistently successful as he moved from one staff assignment to another.
Chapter Five
The "New Look"
"[The New Look] fundamentally I think came from the conviction on Eisenhower's part that we were in the nuclear age and that the nuclear complement of war had really already, even then, become a dominant component—we're talking large-scale war."
—GEN. ANDREW J. GOODPASTER
On 29 October 1953, Eisenhower approved NSC-162/2, and thus the "New Look," which "called for development and maintenance of:
1. A strong military posture, with emphasis on the capability of inflicting massive retaliatory damage by offensive striking power;
2. U.S. and allied forces in readiness to move rapidly, initially to counter aggression by Soviet bloc forces and to hold vital areas and lines of communication;
3. A mobilization base and its protection against crippling damage adequate to insure victory in the event of general war."
Of equal importance, it is worth noting, NSC 162/2 stressed the need for "a sound, strong and growing economy."
The term "New Look" is attributed to Eisenhower's chairman of the JCS, Adm. Arthur W. Radford. Eisenhower himself—and presumably Goodpaster—did not intend to imply an abrupt change from the Truman notion of containment. Nonetheless, it was no secret that the administration was seeking for a way to reduce the military budget by minimizing conventional forces and by maximizing nuclear forces. Accompanying this was more reliance on covert operations against unfriendly regimes. Thus, by placing maximum reliance on nuclear weapons, the budgetary emphasis benefited the Strategic Air Command (SAC), at the expense (or so the Army thought) of the ground conventional forces.
This meant that all was not well between the senior Army leadership and the White House. Eisenhower's "New Look" strategy depended on the concept of "massive [nuclear] retaliation" if there was a direct and immediate threat either to the NATO area or to the continental United States, thus reducing the need for maintaining large conventional ground forces. Eisenhower recognized that the United States' capacity to fend off a real or imagined nuclear threat amounted to the same thing, which required preparing to act on the worst threat assumption.
This was interpreted by the senior Army leadership as reducing the role (and hence the budget) of the forces that the Army felt were still needed to fend off a Soviet ground attack in Europe. Admiral Radford summarized it thus: "The logical thing to do was to emphasize America's nuclear striking power and to rely on indigenous ground forces as a first line of defense against local aggression. American forces should be redeployed to the United States where they would be reorganized to form a small, highly mobile strategic reserve that could come to the aid of our allies in the event of a war."
Goodpaster interpreted it this way:
Now the institution, the Pentagon and its major component elements, were far from having made the adjustment to that kind of a concept. But he had no doubt in his mind. [Eisenhower] expressed it in highly simplified terms that, for example, any major war in Europe was bound to become an all-out war and a nuclear war. There were many for whom that was too simple, and that was very harsh medicine, but that was a conviction on his part, and the attempts to preserve forces as they had existed in a previous time simply cut very little ice with him.
**The Distribution of Administrative Influence**
PPS director Paul Nitze's major contribution in 1949 was to link Kennan's essentially pessimistic view of the Soviet Union's peaceful intentions to a more aggressive notion as to how to win should conflict erupt between the two nuclear-armed powers.
A Report to the National Security Council by the Executive Secretary on United States Objectives and Programs for National Security, April 14, 1950. This celebrated study, which remained classified until 1975, was the first major project that Nitze supervised after becoming director of the State Department's Policy Planning Staff on January 1, 1950. Coauthored by Nitze and members of a joint State-Defense study team, NSC-68 proposed a course of action that followed logically in the wake of earlier efforts to contain Soviet expansion. However, it differed from most previous assessments in that it viewed the Soviet threat as not only political but increasingly military in nature. . . . NSC-68 urged significantly increased U.S. military preparedness, especially in nonstrategic and nonnuclear capabilities.
We should note, however, that for Eisenhower the use of nuclear weapons would govern the use of all other weapons systems. "By 1957, the United States had nearly six thousand nuclear bombs and over two thousand medium- and long-range bombers. This destructive capability, coupled with research programs to develop new weapons technologies, seemed more than sufficient to the president." This is why Eisenhower's notion of deterrence could be summarized as prepare for a war so terrible that it should never be fought.
The phrase "massive retaliation" was introduced by John Foster Dulles as a counter to the Truman administration's use of the term "containment." The latter was criticized as being too passive to sloganize a credible deterrent, yet when it came time to retaliate "at times and places of our own choosing" (to paraphrase Dulles), the Eisenhower administration was no less willing to engage in warfare on such a scale than was its predecessor. As explained:
The possibility that the United States might convert local wars into a general nuclear war alarmed U.S. and allied opinion, and this in turn led Dulles into a series of efforts to clarify his meaning in a more specific and moderate direction. He was not entirely successful in this respect, and indeed could not afford to be. For massive retaliation was primarily a declaratory policy intended to deter various kinds of aggression against members of the free world. Dulles and Eisenhower used the threat of massive retaliation as a means of warning a would-be Soviet or Chinese Communist aggressor that the United States would not allow it the choice of conditions for combat.
By the end of the Eisenhower years, it was evident that the New Look doctrine of massive retaliation was either not credible or had achieved its purpose. As Eisenhower proudly pointed out in his final State of the Union address: "For the first time in our nation's history we have consistently maintained in peacetime, military forces of a magnitude sufficient to deter and if need be to destroy predatory forces in the world." In addition, of course, and in the meantime, countering nuclear war with nuclear war—strike-counterstrike—therefore seemed to Eisenhower the most reassuring way to allay his surprise-attack anxiety.
He went on to list the various types of weaponry that had been either developed or introduced during his presidency. For example, Eisenhower cited the following: "Today we spend ten times as much each day on these [long-range ballistic missile] programs as was spent in all of 1952. . . . The explosive power of our weapons systems for all purposes is almost inconceivable . . . and either our B-58 Medium Range Jet Bomber or our B-52 Long Range Jet Bomber can carry more explosive power than was used by all the combatants in World War II—Allies and Axis combined. . . . Sea warfare has been revolutionized, and the United States is far and away the leader." Therefore, for the future, conventional forces would need building up to address low-level or non-European conflicts that might or might not involve either of the two Communist powers.
In fact, arguing that there existed in the late 1950s and early 1960s a "Sino-Soviet bloc" carried the concept way beyond any notion of its reality. This resulted in a misdiagnosis of the nature of the Communist threat in Indochina, and this led eventually to the disaster of Vietnam. As Kennan observed, "The Chinese would, in the normal course of things, become more and more nationalistic and less and less available as a puppet for the Soviet Union." So much for the so-called domino theory, which was gaining policy credence.
There is no doubt, however, that Eisenhower brandished the prospect of using nonconventional weapons in a "battlefield" sense, if the Soviet Union tried to invade Europe. Goodpaster recalled that when Eisenhower was SACEUR, he drew attention to the so-called
nuclear cannon, a 280-mm gun bearing an atomic projectile; it was very clumsy, cumbersome, very difficult to handle on roads over in Germany. . . . But it still represented a capability, a devastating capability, insofar as the other side was concerned. The thought of their troops being hit by an atomic round would be very sobering, and I think Eisenhower was well aware of the way that the Soviet Union would think about the possibility of this being used against them. It was a deterrent in his mind, and not just a deterrent to war of their initiation, but a deterrent also to their attempting to use pressure tactics or threats to force concessions. They faced the problem that if they tried to back that up with military action, they could very well have a nuclear attack against them, against their forces in the field or against their airfields, and so on.
Contributing to this preoccupation, Eisenhower had been carrying in his mind a strong dread, his so-called Pearl Harbor nightmare, that if the conditions seemed favorable, the Soviet Union would mount a nuclear surprise attack on the American homeland or on the allies. "[Eisenhower] was convinced . . . that modern weapons had increased the danger of such a surprise attack on the nation and wanted [the newly appointed Technological Capabilities Panel (TCP)] to suggest measures through which science and technology might reduce the peril." This panel was dubbed the "surprise attack panel" and was led by Dr. James R. Killian, president of the Massachusetts Institute of Technology. The panel was a subcommittee of the President's Science Advisory Committee (PSAC).
Unlike other commissions, which issued reports that were ignored, the TCP recommendations (at the personal insistence of President Eisenhower) accelerated the development of advanced weapons and intelligence collection systems that became vital to America during the Cold War. . . . One of the most significant recommendations came from the TCP's intelligence subcommittee, directed by Edwin Land, . . . which called for the Central Intelligence Agency to develop an advance reconnaissance aircraft proposed by the Lockheed Corporation, the U-2.
In the pivotal meeting of 7 February 1958, Land and Killian discussed the program that became CORONA. In his memorandum summarizing this meeting with Eisenhower, Goodpaster recorded his observations as follows:
Subsequently, because of my feeling that there might not have been full understanding between the President on the one hand and Dr. Killian and Mr. Land on the other, I met with the latter two and then talked further with the President. They [Land and Killian] clarified that what was really intended was that General [Bernard] Schriever and the Air Force would be in charge of the program. I told them that I did not think the President had that understanding or intention. I then talked to the President who stated emphatically that the project should be centered in the new Defense "space" agency [Advanced Research Projects Agency (ARPA)] doing what the CIA wanted them to do. I then informed Dr. Killian.
Eisenhower had thus made clear that CORONA should be run by civilian leadership rather than by the Air Force or other military agencies. This anecdote is an illustration that, throughout his career, Goodpaster was intimately involved in these kinds of covert, off-the-books operations.
In fact, the work of Killian and Land, among others, gave the United States a significant boost in its research activities dealing with space flight, aerial intelligence-gathering, long-range missile development, weather observation, and so forth. Furthermore, given Goodpaster's already proven interest in, and knowledge about, the possibilities of technology in the cause of maintaining peace or prosecuting war successfully, his involvement in this aspect of presidential concern was naturally congenial to him. He was at the heart of these activities both as presidential liaison and as a knowledgeable observer.
**Deterrence and Détente**
Many books have been written about the meanings of the terms "deterrence" and "détente"—as was true also for "containment" as we have just seen. The central role of deterrence and détente was to rein in the nuclear arms race, while at the same time retaining a creditable threat posture in the event of a Soviet attempt to "blackmail" the United States. Calculations of "throw-weight" and other attempts to draw comparisons between dissimilar stockpiles became the stuff of agonized analysis and heated debate. Goodpaster would have been aware of these goings-on, of course, throughout his career, and especially while he was serving as NATO's supreme allied commander later on. Nevertheless, his assignments (and presumably interests) lay more in the implementation side of the debate, rather than in strategically conceptualizing.
Goodpaster had this to say about deterrence: "The proper question was not whether NATO could have defended successfully; it was whether the USSR could have attacked successfully. . . . A calculus of deterrence today—by almost any concept of rationality that can be imagined—must inevitably lead to a quick rejection of the vast bulk of conceivable conflicts between the super powers." In a way, this was a reformulation of Eisenhower's use of the deterrent. As Goodpaster put it: "You knew that in due time, the Soviets were going to build the same kind of capability. But Eisenhower had a great sense of how these things would be viewed by the other side, in other words, of the deterrent as a strategy. He just comprehended that. He thought in those terms—how does this affect the other man—and he saw that as a very powerful deterrent."
It is possible that this was intentional, for, as Kennan commented, in the context of Solarium: "The President . . . spoke about the whole range of these problems. He spoke, I must say, with a mastery of the subject matter and a thoughtfulness and a penetration that were quite remarkable. I came away from it with the conviction (which I have carried to this day) that President Eisenhower was a much more intelligent man than he was given credit for being."
In contrast, a narrow definition of détente was used by one scholar: "Some have taken the word 'détente' to mean a state of near-bliss between Washington and Moscow. It simply means 'the easing of strained relations, especially in a political situation.'" In fact, the term became a propaganda instrument directed not only at each other, but also by each with their respective domestic audiences. In other words, the term had both policy relevance and emotional relevance, depending on the circumstances and purposes for which it was employed. Analytically, as well, "deterrence" and "détente" are linked together.
Furthermore, Goodpaster mentioned in discussing Solarium: "In assessing the Soviet threat, there was a flat statement that there was very little chance of any deliberate Soviet attack or any desire of the Soviets for a general war, that the only way that was likely to happen was by mistake or miscalculation. It was assumed, however, that the Soviets would try all the other things which were possible to try to expand their area of influence."
Another way of looking at it would be to consider détente in terms of its possessing an ideological component: "The President was arguing that, because the Soviet menace was basically ideological, or 'philosophical,' it was also indivisible and thus posed a threat everywhere in the world. . . . But Eisenhower's approach led to confusion, for it blurred over the fact that the ties between Communist ideology and other types of Communist power varied greatly in different parts of the world."
The United States learned later on, to its regret, that pasting the same label of "Communist" on every form of anti-American or anti-Western self-government emerging throughout Asia and Africa (and also for that matter, Latin America) imposed simplicity on an extremely complex and diverse historical evolution.
It is safe to say that after the Suez crisis of 1956, in which the United States sided with a newly independent (and anticolonial) government in Egypt against its erstwhile NATO allies, Britain and France, the stage was set for America's entry into competition for the "hearts and minds" of the new nations of Asia and Africa, as well as the ongoing cultural rivalry in Europe.
Goodpaster summarized Eisenhower's concept of how to adjust American policy in the face of rapid decolonization (some of which was unexpected): "His idea concerning Third World nations was to work with them on development, to show them the opportunities for self-government and tell the story of what the West had to offer and what has been achieved by Western civilization. He was always one who tended to put things in positive terms—that we should tell the story, that we should provide the assistance to them so that they could begin to better the life [ _sic_ ] of their farmers and improve their industry and trade and so on. This would give a more reliable and more rewarding basis for development than the so-called shortcut of Communism."
It is useful to recall here, however, that when it came to Southeast Asia, the picture was muddled. There was one military faction in Washington that advocated what has been termed the "all-or-nothing" approach—meaning to settle the ideological ambiguities through military means, at least initially by the use of airpower. The dilemma was put starkly when the French were facing defeat at Dien Bien Phu in 1954. Harkening back in disapproval as to how the Korean "police action" was settled, this group favored either intervening in order to achieve an unequivocal victory or remaining out. Eisenhower favored this approach, as did General Ridgway, the Army chief of staff at the time, even though he had succeeded General Douglas MacArthur in Korea precisely to bring about a negotiated settlement at the 38th parallel. In any event, "sobered by this hard-boiled cost-benefit analysis, Eisenhower rejected military intervention altogether and decided to try to deal with the consequences of the now certain French defeat through diplomacy."
In contrast, in the 1958 crisis over the offshore islands of Quemoy and Matsu, Eisenhower recognized the danger of a local conflict escalating out of control, when he disagreed with his JCS by refusing to pre-delegate to them the decision to use tactical nuclear weapons if it seemed necessary to forestall a Communist Chinese invasion. But this did not imply that these weapons would absolutely not be used—only that the president reserved to himself that decision based on the circumstances at the time. Fortunately, the invasion never occurred.
In any event, even though Eisenhower had hinted broadly that if the Chinese did not accept a negotiated settlement in Korea, nuclear weapons might be used, by then it was clear that no president would delegate what would have been a fateful decision as to whether or not to introduce nuclear weapons of any kind in any crisis other than a direct Soviet attack in Europe. Simply stated: "It was the possession of atomic bombs by America and the possible intention to use them which brought about the Armistice, not the conventional military operations in which UN fire power was counterbalanced, to a large extent, by Communist manpower. This was possibly the only time that nuclear weapons could have been used without causing World War III. The Communists probably knew this but the West was not so sure."
The danger of escalation was simply too great. The nuclear arms race would continue in the "what-if" mode. During the Eisenhower years, the nuclear stockpile grew both larger and more diversified, which implied that, in the opinion of some observers, automatic escalation was not necessarily a foregone conclusion. As it was put: "The smaller atomic weapons, the tactical weapons, in a sense now became the conventional weapons."
Goodpaster elaborated on why, as a consequence of the dangers of an endless nuclear arms race, a policy of détente made sense. For the United States and USSR, it placed constraints on the size and capabilities of each nations' nuclear arsenal. In Goodpaster's opinion, the "détente process shap[ed] and constrain[ed] U.S. and USSR military capabilities," especially "the size and composition of strategic nuclear forces" of each nation. Additionally, multilateral organizations like NATO and the Warsaw Pact used the umbrella of détente to find common ground to reduce conventional forces. Beyond European, Russian, and U.S. soil, Goodpaster observed,
Détente manifests itself in further ways in such areas as the Mid-East and the Far East and particularly on such issues which are of high interest in the United States and the Soviet Union but which do not, however, touch directly and vitally on the question of their national survival. . . . In these so-called "third areas" of the world, it is an important military implication of détente that, short of issues involving the most vital interests of the United States and Soviet Union—on which each will feel constrained from challenging the other—threats to peace and order must be expected to continue to occur, and it must be expected that these will from time to time occasion intervention and conflicting measures of many kinds by both powers.
Ultimately, he concluded, with détente came the very real possibility that "peace and security may derive through 'linkage' to other détente-related agreements in which the Soviet Union has interests that are of value to it."
If there was a time when the post–World War II world appeared to be permanently divided into two "camps," it was during these Eisenhower years. In an earlier but similar period, the nomenclature was different but the attitudes were alike: "From an individual struggle, a struggle of families, of communities, and nations, the struggle for existence has now advanced to a struggle of empires." The biggest single diplomatic challenge for Goodpaster, and for the Eisenhower administration in its first term, was how to reconcile the policy of détente—seeking negotiable areas of mutual interest between the United States and the Soviet Union, and which would result in a lowering of tensions—with the concurrent maintenance of the highest stage of readiness.
By his second term, Eisenhower de facto adjusted his overall strategic concept to take account both of "means other than war" vis-à-vis the Soviet Union and of the relevance to America's national security of so-called peripheral wars. It was not understood generally that, as Goodpaster put it, Eisenhower was "slow to pick up the sword." "He repeatedly sought negotiations with the Soviets on the reduction of arms. Ike avoided involvement in 'brush fire wars' that could escalate into a nuclear confrontation. He ended the war in Korea in 1953, declined to intervene militarily in Indochina in 1954, and, above all, refused to support his World War II allies in their attack on Egypt in 1956. Eisenhower was the least interventionist of any modern president, although he approved activist covert operations in places like Iran and Guatemala."
Part II
Goodpaster with Eisenhower
Chapter Six
Presidential Staff Secretary and Counselor
"The old soldier is accustomed to well-staffed work."
—ROBERT CUTLER
When "compared to the rest of government, the White House barely qualifies as an organization at all, if the term organization implies the existence of a fixed plan that is likely to look about the same tomorrow as it did yesterday. The very vibrations of the place differ markedly from president to president." Nonetheless, first it must be said that the White House chiefs of staff, first Sherman Adams and then Wilton Persons, were definitely the men "in charge" of the Eisenhower White House. How could a former military commander have it otherwise?
Not far behind was Goodpaster: "Goodpaster was [Eisenhower's] Staff Secretary, a position akin to today's National Security Adviser, and took part in nearly every meeting the President had, in addition to serving as his chief liaison to the foreign policy bureaucracy. It was not without justification that Goodpaster was known as 'Ike's alter ego.'"
Furthermore,
The dozen members of the top-echelon of the White House staff were men with whom Eisenhower had recently worked. Among them were his wartime associates, Walter Bedell Smith, Wilton "Jerry" Persons, and Andrew Goodpaster; others were Bryce Harlow, Gabriel Hague, and C. D. Jackson, men from government, academia, and business whom he had met during the postwar period. The responsibilities of these presidential assistants were grouped under four headings: domestic affairs (cabinet secretariat, departmental liaison, congressional liaison, state and local relations); foreign affairs (defense, national, and mutual security, intelligence); special projects established by order of the president or Congress; and routine scheduling and coordination. Like everyone else, members of the White House staff had access to the president through a single person: Sherman Adams. . . . He gave and withheld permission to enter the Oval Office on the basis of whether the information was vital and the president receptive.
Vice President Richard Nixon figured into this, of course, but more in a collateral way. Eisenhower had made his vice president more aware of what was going on than did any of his predecessors. Nixon's biographer Stephen Ambrose captured the situation: "He was by no means privy to all of Eisenhower's secrets, but he knew more than anyone else. This is not to say that he was the closest to Eisenhower, because he was not—Andrew Goodpaster, Foster Dulles, George Humphrey, Jim Hagerty, and some others were closer."
As far as National Security Council affairs were concerned, "the NSC was also subjected to White House staff procedures by the appointment of Robert Cutler and later Gordon Gray as its secretariat. These men had been Eisenhower's associates in wartime and postwar defense policy assignments; he trusted them and knew they were capable and conscientious. Cutler and Gray were included in the NSC inner circle along with Generals Andrew Goodpaster and Walter Bedell Smith, two former military aides now in mufti as presidential assistants. Eisenhower relied on these four men when sudden foreign crises called for an immediate decision rather than a full-scale council discussion."
Their style was to convene an inner group after the weekly NSC meeting to go over the more important and relevant matters that were on Eisenhower's mind. Press Secretary James Hagerty reported, for instance, on a 9 December 1954 meeting: "Comparatively quiet day. . . . After the NSC meeting broke up I attended a meeting at two o'clock in Jerry Person's office with Fred Seaton, Jerry Morgan, Jack Martin, Andy Goodpaster, and Murray Snyder on the military plans, which the NSC discussed this morning."
Later in his administration, recognizing that the NSC meetings were becoming unwieldy, Eisenhower began the practice of assembling, a half hour before a regular meeting, a smaller planning group to identify the most significant matters needing decisions. As reported: "Staff Secretary Andrew Goodpaster worked closely with Gordon Gray in coordinating these meetings as an adjunct to formal Council meetings."
**Goodpaster as Staff Secretary**
In his memoir, Eisenhower described the functions given to Goodpaster's immediate and only predecessor:
To look after all communications of a top-secret character from or to the White House, I selected an outstanding young Army officer, Brigadier General Paul T. Carroll, who had served in World War II with distinction and had been with me both in the Pentagon and in SHAPE Headquarters in Paris. . . . His successor in 1954 was another Army officer of exceptional capability, Colonel (later Brigadier General) Andrew J. Goodpaster.
In this position, Goodpaster served officially as an observer at all NSC meetings. Besides carrying out what Eisenhower euphemistically called "communications," the main feature of the new position, that of "staff secretary," was maintaining total confidentiality. Eisenhower wanted "to have close substantive liaison on official matters of all kinds with the departments involved in international affairs. And that was a special duty of mine, with the State Department, the CIA, the Defense Department, the AEC [Atomic Energy Commission], and I think that was about the extent of it, but international activities of all of the departments."
Goodpaster and his immediate colleagues were also on hand to record the substance of presidential communications—especially memoranda of conversations, or "memcons." These would "cover defense and space programs, strategic planning, nuclear testing and disarmament, intelligence matters, foreign policy, budgetary problems, government organization, and administrative subjects."
Furthermore, "the staff secretary (and the chief of staff if need be) will subject papers for the president to a tough procedural scrutiny. Are memoranda verbose? Are they larded with extraneous details? Has the author slanted the options? . . . The staff secretary is the funnel for papers coming back out of the Oval Office. If a decision is marked or notes scribbled on briefing papers, he scoops up the inscribed documents, notifies those concerned of the chief executive's action, and builds the archival record."
One important reason for Eisenhower's strong desire for confidentially was that, in his public diplomacy, "Ike employed hints rather than threats, and always succeeded in keeping his options open." The British parallel, although not by any means exact, shared some significant characteristics:
The immediate circumstances, however, which gave rise to the formation of such a group of civil servants came from the war-making responsibilities of the British government. . . . A secretary who performed a coordinating role had always to maintain unobstructed channels to all the governmental bodies, groups, and leading individuals in the policy-making process. While he might be asked his opinions on some issue—and he often was [as was Goodpaster]—he should not, according to the tradition which was being built up, have taken stands on issues in such a way as to interfere with his access to and his credibility with those political persons and organs that he was serving.
To interpret further this statement, self-effacement and discretion came to be hallmarks of the position, and Goodpaster's temperament fitted this requirement perfectly. "Improving on procedures he had learned from the British, Ike created a White House secretariat, headed first by General Paul Carroll and after 1954 by General Andrew Goodpaster. Other administrative changes were also made. The most important was to promote the National Security Council (NSC) to become the central forum for making cold war policy, though in practice the president and the secretary [of state] determined significant matters."
Even more to the point is this observation about the role of Sir Maurice Hankey (later Lord Hankey), who was the key individual in adapting the British secretariat method to the machinery of the Paris Peace Conference, which settled World War I: "It would be inaccurate to infer from this that either the CID [British Committee of Imperial Defence] secretariat or its successor international secretariats had little power just because they were to behave in a politically neutral manner in policy-making."
As far as Eisenhower's staff is concerned,
whereas the talents of the staffs under Roosevelt and Truman were to be found largely in their possession of highly sensitive political antennae, their overarching loyalty, or their creativity, the top echelon of Eisenhower's staff was noted for its functional professionalism. . . . A newly created staff secretariat . . . kept track of all pending presidential business and ensured the proper clearances on all papers that reached the Oval Office. A two-man operation within the secretariat prepared daily staff notes for the president, giving him advance notice of actions to be taken by the departments and agencies. [Chief of Staff Sherman] Adams coordinated White House work through early morning staff meetings, generally three times a week. The sessions also were used for briefings by the CIA and preparation of suggested answers to questions that might be asked at presidential press conferences.
Also involved in these activities were the office of Executive Branch Liaison and the legislative liaison team. All of these entities were designed to avoid misstatements and departments working at cross-purposes, to keep in touch with key congressional leaders, fact-check speeches, prepare background briefs and summaries, and so forth.
**The Influence of Personality on Bureaucratic Relationships**
As defense liaison officer, Goodpaster "would give the daily CIA briefing to President Eisenhower, and also the exchange of messages, the overnight exchange of messages from the State Department, and a report of activity in the Defense Department as well. And out of that, he would very often ask for additional information or ask for something to be looked into. And I would communicate that back to the responsible departments. So that's the way we began to work." Goodpaster, in fact, was the person from whom "Eisenhower had no secrets . . . something that could be said of no other man, not even the Dulles brothers. . . . He gave Eisenhower a 30-minute briefing every morning, because he . . . had the information and knew how to present it the way the president wanted it."
For example, Allen Dulles sent a classified report on a private dinner meeting he had at the German embassy with Konrad Adenauer, chancellor of West Germany, when the latter was in Washington for the funeral of Dulles' brother John Foster. His note read: "Dear Andy: I would appreciate it if you would kindly show the attached to the President and then it can either be destroyed or retained in your file."
Nevertheless, there were limits to what Goodpaster could do. He described an incident that occurred when he was fresh on his job. It involved drafting a stiff letter from the president to his secretary of defense, Charles Wilson, which was intended to assist Wilson in curbing the chiefs' tendency toward parochialism rather than putting together an integrated budget. Goodpaster inserted some language in the draft that softened what Eisenhower had said orally in a meeting with the secretary and the chiefs. "And that's when he looked up at me and said, 'Now Andy,' he said, 'ultimately this can either be done your way or my way and I guarantee you that ultimately it's going to be done my way.' And I said, 'Yes sir, Mr. President.'"
Earlier in this chapter, Goodpaster has been described as fulfilling a communications function; then it was said he served as an "advisor"; now he is being described as virtually a third extension of the president in matters of national security policy formulation _and_ implementation. Perhaps this ambiguity is a necessary adjunct of the kind of largely unobserved—and unobservable, except to a few—role that Goodpaster performed.
If anyone doubted the multiplicity of roles that Goodpaster played, note this assertion:
Andrew J. Goodpaster played a significant role in the development and implementation of U.S. national security policy in the Cold War years from the late 1940s through the 1970s. His formative impact in such key areas as nuclear strategy, military modernization, and the maturing of NATO as a politically and militarily integrated alliance is largely obscure, however. He avoided the limelight and preferred the position of the loyal and expert assistant who gave substance to the leadership and direction of others. As President Dwight D. Eisenhower's principal White House aide on national defense issues, he enjoyed an especially close and influential working relationship with Eisenhower on virtually every foreign and military decision of that administration.
In one respect, Goodpaster's role was not too complicated, because "Eisenhower's argument for the New Look was not sophisticated, but he believed it and insisted that others believe it. His feeling was that the economy was the pillar of U.S. strength and security, and unbalanced budgets threatened that pillar."
It might at first glance appear useful to compare Goodpaster's role with that of Colonel House as he served President Woodrow Wilson at the Paris Peace Conference of World War I. This, however, does not seem apt because historians have concluded that House was more a de facto secretary of state. However, a comparison with President Franklin Roosevelt's "man Friday," especially in Harry Hopkins' wartime role, might be a closer fit. In personality, Goodpaster and Hopkins could not have been more different. Roosevelt's ghostwriter Robert Sherwood "met this bright-eyed, intrepid, and deeply loathed and deeply loved man. . . . Plainly he was 'a master of the naked insult,' and no less plainly his fervor shone out in spite of his frailty." What a contrast to Goodpaster! Where they were similar is in the trusted relationship that each had with his respective president.
Here is a description of Hopkins' role: "The fact is that by 1940 Roosevelt valued the peculiar kind of service rendered and the companionship provided by Hopkins to such an extent that he converted his friend to war purposes." It is this uncanny ability of two persons to be drawn to each other in trust and even affection that stood both Roosevelt and Hopkins apart from most of their peers. Something similar was said of Goodpaster: "He played the role of envoy, and confidante and managed to do so without inflaming potential rivalries with other members of the [White House] team."
Trust is a trait that military persons understand readily, since there is no place where trust between or among the participants is more decisive than on or near the battlefield. Literature is replete with narratives of the kind of male "bonding" that occurs under such circumstances. What often is not generally understood is that the same expression of human behavior can also occur between two persons who share over time great responsibility. The loneliness that accompanies high office—or high command—is one reason; another is simply that physical attraction stimulates trust, and conversely, mistrust almost naturally accompanies feelings of repellence between two persons.
Just as Roosevelt needed Hopkins' companionship so badly that Hopkins moved into the White House during the war, Eisenhower came to rely on Goodpaster's companionship almost as much as on his executive skills. As far as Goodpaster was concerned, Eisenhower possessed an "inner power," a sense of being "necessary." These were the same traits that had attracted Goodpaster very early in his career to Abe Lincoln and to Marshall.
Goodpaster's obituary described him thus:
Later, President Eisenhower asked General Goodpaster to serve as staff secretary in the White House. He became known as the president's alter ego for his ability to carry out orders in his wide-ranging national security portfolio with minimal need for instruction. His mandate included work on the so-called Solarium Conference to plan for the American role in a post-Stalin Soviet Union. Some called him "the man with the briefcase" for his silent but essential backstage role in practically all military matters. General Goodpaster, wrote one reporter for the _New York Herald Tribune_ , "looks like a business executive and hides his White House importance behind a quiet façade that lends itself neither to anecdotes nor stuffiness."
One of the ways that Eisenhower employed Goodpaster in a national security/foreign policy dimension came up in February 1955, during the heated emotions of the crisis with Communist China over the islands of Quemoy and Matsu in the Formosa Strait, which had been occupied by the Chinese Nationalists. Eisenhower explained: "To get further information and a sensing of the problem, as it appeared to an observer firsthand, I should ordinarily have called in at such a moment the Commander-in-Chief of the Pacific Fleet. But in a time of such tension, with the enemy scrutinizing our every move, I could not possibly call Admiral [Felix] Stump back to Washington. I therefore sent Colonel Goodpaster, the brilliant and trusted White House Staff Secretary, to Pearl Harbor to confer with Admiral Stump. On March 15 Colonel Goodpaster's report was in my hands."
Eisenhower also gave this profound reply to a reporter's question as to whether he would use atomic weapons if the islands were directly challenged by the Communist Chinese: "I said that I could not answer that question in advance. The only thing I knew about war was two things: the most unpredictable factor in war was human nature, but the only unchanging factor in war was human nature."
Further examples, from _The White House Years_ , of Goodpaster's usefulness are:
1. On July [1957], I discussed with Under Secretary [Douglas] Dillon and General Goodpaster a message from Chris Herter at Geneva. In it the Secretary expressed the opinion that the conference seemed to have reached a stalemate. [p. 406]
2. I next landed at Okinawa [in 1960], the most important of the Ryukyu chain, seized at fearful cost by the Americans in World War II. . . . The chief representative of the Ryukyuan people was Mr. Seisaka Ota. . . . Mr. Ota earnestly protested a cut of about a million and a half dollars in the United States' appropriations for economic support of the Ryukyus. . . . So I asked General Goodpaster to make a transpacific call to General [Wilton] Persons in Washington with instructions to mobilize all possible effort for the restoration of the money. [pp. 565–566]
3. As Phoumi [Vongvichit] proceeded [in 1960] to retake Vientiane [Laos] General Goodpaster reported the events to me. "Two points are giving me concern: the fact that Phoumi has not yet taken the airport at Vientiane, which is of great importance to the Soviets' airlift; and the fact that the pro-Communists are probably advancing on Luang Prabang—the royal capital." He then posed several questions: "First, should we seek to have Thai aircraft transport supplies into the area. Second, if the Thais can't do the job, should we use United States aircraft? Third, should we suggest that Thai forces seize the airfield at Vientiane and hold the one at Luang Prabang? Finally, should we support reconnaissance of Laos by Thai aircraft and of North Vietnam by United States aircraft?" [p. 609]
4. My assistant, General Goodpaster, once showed me, in a state of complete exasperation, a press account on the subject of presidential functioning that ran about as follows. . . . Goodpaster was so perturbed at such a distortion of fact that I laughed aloud. "Andy," I said, "let's not worry about how decisions are made, let's just be sure they are right." [p. 632].
An unhappy example of misapprehensions that not even Goodpaster could have corrected was the Suez crisis of 1956, which occurred during the run-up to the presidential election. This "shooting" crisis appeared to take the White House by surprise, and yet, for months prior to the Anglo-French invasion, Eisenhower had been deeply involved in trying to settle differences—especially the concerns of the British—with the Egyptian government. At the Bermuda Conference of France, Britain, and the United States in December 1953, Eisenhower had already made clear to Churchill that "any attempt by European powers to sustain by force their dominant positions in these territories would have long since resulted in furious resentment, unrest, and conflict."
Notwithstanding, British prime minister Anthony Eden, in spite of an opinion by his own legal staff that Gamal Abdel Nasser's seizure was legal as long as he did not close the canal to traffic, planned to reoccupy the canal. As to the United States, "He was not really worried. . . . When it came to the crux, Eisenhower was in charge of the United States—and Eisenhower would not let him down. After all, he was an old friend and comrade, and he knew about war. As Macmillan kept on saying, once Great Britain took action Ike would 'lie doggo' and let them get on with it, and that was all they needed. It was the costliest miscalculation the British had ever made."
Although Eisenhower's aides, as well as the State Department, claimed that the events of the Anglo-French-Israeli military action were unexpected, the United States had in fact received ample short-run notice. Goodpaster, in his official role as White House liaison with the CIA, must have been "witting"—in CIA terminology. He also would have learned from Department of Defense (DOD) sources that the U.S. Sixth Fleet in the Mediterranean was observing the Anglo-French invasion force as it assembled on Malta and then sailed toward Suez.
There is some room for attempting, in hindsight, to understand the situation. Not only was Robert Murphy, the American special envoy sent to London to calm Eden, unsuccessful, but even Secretary of State John Foster Dulles went to London to try to do it and did not succeed. There was, in fact, a sense of alarm among both the British and American senior diplomatic community in London. The following episode underscores why:
The well-known military expert, Captain [Basil] Liddell-Hart, had come to see the prime minister at 10 Downing Street. Eden had asked him for an outline of how a military campaign should be fought in Egypt, and Liddell-Hart had written one for him—only to have it sent back, with curt demands for alterations, no less than four times. Finally, rather than do a fifth revision, he had sent in the original outline and decided to leave it at that. Eden summoned him and said: "Captain Liddell-Hart, here I am at a critical moment in Britain's history . . . and it takes you five attempts—plus my vigilance amid all my worries—before you get it right." "But sir," Liddell-Hart said, "it hasn't taken five attempts. That version, which you now say is just what you wanted, is the original version."
There was a moment's silence. Eden's handsome face went first pale and then red. He looked across at the long, languid shape of Captain Liddell-Hart, clad in a smart off-white summer outfit, then he reached out a hand, grasped one of the heavy, old-fashioned Downing Street inkwells, and flung it at his visitor. Another silence. Liddell-Hart looked down at the sickly blue stains spreading across his immaculate linen suiting, uncoiled himself, picked up a government-issue wastepaper basket, and jammed it over the prime minister's head before slowly walking out of the room.
The United States could hardly support an intervention in the Suez against Egypt, and then point the finger at the Soviets for their actions. In any event, only propaganda support was given to the Eastern Europeans, while active opposition through the United Nations as well as bilaterally placed the United States in open disapproval of its two NATO allies. In CIA circles, the fact that the United States offered only verbal support while Hungary was following Poland in rising up against their Soviet masters underscored the futility of any notion of "rollback."
**Goodpaster's Formal and Informal Influence**
It was observed: "Not all defense matters came to the president through the NSC. If a defense issue did not involve the formulation, revision, or clarification of an NSC policy, then it was not part of the NSC system. These matters were handled by the Staff Secretary (who was also the defense liaison officer) directly with the president. The procedures might involve informal briefings by Brigadier General Andrew J. Goodpaster on operational or intelligence matters or meetings with cabinet level officials and others, which Goodpaster normally attended."
In recognition of this role, in July 1956 Gen. Maxwell D. Taylor, the Army chief of staff, recommended Goodpaster for promotion to brigadier general. Taylor reported: "He has demonstrated superior performance of duty in the very sensitive area in which he has operated, thereby reinforcing past indications that he is an exceptional officer, entitled to promotion ahead of his contemporaries. I request [the adjutant general] that this letter be transmitted personally to the president of the Brigadier General Selection Board to inform the board that I strongly recommend that Colonel Goodpaster be selected for promotion to brigadier general."
There is no doubt that Goodpaster's influence went beyond the strict confines of his formal title. In fact, "I knew from my service with Eisenhower at SHAPE that he had confidence that I could analyze and provide advice and recommendations on serious issues of policy." It is quite clear, in fact, that Goodpaster was involved in foreign affairs generally, and not just acting as the White House liaison with the Department of Defense and the CIA.
Here is how Goodpaster put it: "On many occasions the President and I talked about his views—the views he was developing regarding nuclear weapons and what to be done about them. . . . And we often talked about what could be done to head off and reduce the possibility that this would ever occur. . . . He asked me to follow closely the work of Harold Stassen whom he had appointed as his first disarmament advisor. . . . I talked to him many, many times about proposals for crash programs. . . . He wanted an orderly program rather than, as he said, stops and starts that just waste money."
One of Eisenhower's biographers, in fact, described Goodpaster's role in the White House as that of "adviser." An example was Eisenhower's decision to appoint Gen. J. Lawton Collins to assist in the 1954 crisis in Vietnam: "The president's staff secretary, Colonel Andrew J. Goodpaster, suggested Collins for the Vietnam assignment." Then: "In view of [the] pessimistic outlook contained in National Intelligence Estimate 63-7-54, November 23, 1954, and pessimistic cables received from Collins, OCB [NSC Operations Coordinating Board] agreed on December 8 to request early review by NSC of the U.S. position in Indochina. Collins has been requested to submit an appraisal on the prospects of achieving U.S. objectives in Indochina on or prior to January 15. NSC will be requested in light of further report to review U.S. program and position in Indochina."
Goodpaster also would have understood how Eisenhower manipulated the public media to serve his own purposes. A good instance is the famous "Open Skies" proposal made at the 1955 Geneva Summit, from which neither side expected much.
But it was the president who, on 21 July, put forward what came to be known as his "open skies" plan. He had, in fact, discussed it with his advisers but, according to his later account, he "extemporized some of the proposal" and "just threw it right in [the Russians'] faces." . . .
Declaring that he had been "searching my heart and mind for something that I could say here that could convince everyone of the great sincerity of the United States in approaching the problem of disarmament," . . . he proposed that they should "give each other a complete blueprint of our military establishment" and provide "facilities for aerial photography to the other country." Then, "as Ike finished his earnest and impressive peroration, in which he pleaded for peace with security, there was a great clap of thunder like some cosmic round of applause and all the lights went out.
The drama of the occasion could not, however, conceal the fact that the Soviet leaders who were present—and especially Khrushchev—looked upon this more as a propaganda stunt than as a serious proposal. The reason was obvious:
As Ike recorded in his memoirs, the American "plan was to keep the Soviets on the defensive" by proposing measures of general appeal. This was certainly true of the "open skies" plan, which had the additional advantage that the open United States would gain by it more new information about the closed Soviet Union than vice versa. On the other hand, one of Ike's closest confidants, his staff secretary Colonel (later General) Andrew J. Goodpaster, asserted that the proposal was not disingenuous or made for propaganda purposes. . . . On balance, it seems, Ike was hoping to have it both ways. He wanted a propaganda advantage that would also reduce the risk of nuclear war and might just lead to some form of agreement that would clearly benefit the United States.
In fairness to Eisenhower, it could also be argued that he perceived, in order to avoid what seemed during those times a catastrophic nuclear war, that "a form of behavior becomes out of date only when something else takes its place, and in order to invent forms of behavior that will make war obsolete, it is a first requirement to believe that an invention is possible." Was arms control leading to disarmament achievable? Disregarding the overwhelming body of skeptics surrounding them, to their credit Eisenhower and Goodpaster—along with Stassen—considered disarmament worth a try.
One of Goodpaster's notable traits was that he combined the sometimes abstract nature of diplomacy as practiced by the professional diplomat with the practicality of the professional soldier. Few general officers of his generation could manage to achieve this blend. In describing the problem, he inadvertently described himself in both his national and multinational roles, which is one important reason why his career took the form that it did:
The national security environment is also a complex one, in which relationships are intricate, often unstable. Below the President, participation is widely diversified into strongholds vested with particular interests, values, and responsibilities. Viewing security problems from the White House, one has the ineluctable impression that only on the President's desk does everything come together. The big issues affecting national security arise, in particular, between the departments of Defense and State. Not only in dealing with security problems but also in framing them, the military and the diplomatic approaches are inherently different.
Still, it remains necessary to draw them into some coherent combination. There is nothing diplomatic about a machine gun, nor can an aide memoire of itself stop subversive infiltration and terror; yet, in the modern world it is clear that both must be employed in some higher security context if security and safety are to be served. . . . The interest of the State Department is to limit the scale and extent of violence, while that of the professional military man, once higher authority has decided to resort to force, is to seize and hold the initiative and to gain quick preponderance over the adversary, employing force decisively and aggressively to accomplish the mission with minimum loss of life and minimum risk to the United States.
For example, on 18 July 1958, Allen Dulles wrote to Goodpaster: "Dear Andy: I enclose for your files, a copy of the Briefing Notes which I used at the meeting which the President had with Congressional Leaders, July 14, 1958, 2:30 p.m., in connection with the Middle East crisis. These notes were closely followed in my presentation, but with some additions and there was, of course, a question-answer period not included in these notes."
Another example is this memorandum from Goodpaster to the State Department:
Memorandum for: Mr. John A. Calhoun, Director, Executive Secretariat, Department of State, 26 May 1959. The President today indicated general acceptance of the recommendations in Secretary [Douglas] Dillon's memorandum to him of May 22nd concerning the Baghdad Pact Council session this fall. In so doing, he indicated that the State Department should prepare for him a short speech of welcome rather than anything amounting to a major address. He also said that before any move is made in this matter, the State Department should consult very carefully with appropriate Congressional leaders concerning the proposals. A. J. Goodpaster, Brigadier General, USA, Staff Secretary.
All of the foregoing suggests that one scholar's appraisal of Eisenhower as a "figurehead president" is not accurate—in fact, it is a complete distortion of the reality. As reported: "[Richard] Neustadt presents an account of a leadership style that, by relying extensively on delegation, renders the president ill-equipped to advance his policies." A contrasting view was put forth by another scholar, who titled his study of the Eisenhower period, _The Hidden-Hand Presidency: Eisenhower as Leader_. Where to strike the balance between "hands-on" and detached is impossible to determine because administration comes down to matters of human temperament and bureaucratic culture.
The amount of detail that Eisenhower could consume is reflected in this note to an assistant secretary of state: "A man named Henry A. Kissinger has just written a very provocative book entitled 'Nuclear Weapons and Foreign Policy.' The book was brought to my attention by Cabot Lodge. . . . I have not read the complete book, but I am sending you herewith a copy of a fairly extensive brief made by General Goodpaster of my office."
Furthermore, drawing on this as a parallel, Eisenhower's public discourse and private commentary projected sharply different images: "His remarks in press conferences were colloquial and folksy. His speech rhetoric was dignified, but simple and direct enough 'to sound good to the fellow digging the ditch in Kansas.' In private, particularly when he conveyed his thoughts to his aides on paper, his prose was crisp and detached, revealing a cognitive style in which deductive clarity played a central part."
Eisenhower, like all presidents before and after him, could not possibly achieve what they initially expected was possible. "It is never long enough to do any real planning, to think about where the country ought to be, even in the next decade, and to design programs to get from here to there. . . . He never really ran the government as he had expected. Rather, he found that the job was to try to keep the social fabric intact; to keep the peace if possible; to defend the nation from aggressors; to maintain the nation's place in the world, even by force; to attempt to balance economic growth and stability; and at best to make some new initiatives that the history books would record as his." In doing all of this, Goodpaster was, quite literally, at his side.
Eisenhower confirmed this in his 1956 efficiency report on Goodpaster: "Colonel Goodpaster is Staff Secretary at the White House and serves also as Department of Defense Liaison Officer. He has the full responsibility for the operations of the 'Secretariat' in the White House Office, a department that during the past year has taken over increasingly important duties. Colonel Goodpaster sees me frequently during the day; all military, diplomatic and intelligence matters are brought to me by him, as well as many additional important problems. He participates in Cabinet, National Security Council, and other high-level meetings, and sits in on intimate meetings in my office with top-level military, intelligence and State Department personnel. His post is one of highest importance."
Even when not at his side, Goodpaster was in the picture. This excerpt of 11 February 1955 from Press Secretary Hagerty's diary illustrates the point: "At the press conference Wednesday, Joe Harsch of the _Christian Science Monitor_ . . . [asked]: 'Mr. President, is that invitation to General [Georgy] Zhukov still open?' . . . Goodpaster told me Thursday morning Harsch had received a call from the third secretary of the Russian Embassy. The third secretary said he would very much like to talk to Harsch and they made a luncheon engagement at the Metropolitan Club. . . . The sounding out of Harsch by the third secretary was a very interesting development and, of course, Harsch confidentially reported it to the CIA. Goodpaster was sure that the President would want to hear of this."
Thus, during the Eisenhower years, both in theory and in practice, the staff secretary's role grew because "of its position at the intersection between politicians and the military." As Goodpaster described: "Here was a senior executive working with his immediate subordinates but supported by a staff system which took care of the flow of paperwork and information. And we the staff people were charged with the follow-up on meetings in the president's office, where decisions were made, to check to see that they were indeed carried out and to keep an eye on operations and activities within the department, and if there was a discrepancy between them and the policy guidance that had been given, to bring that back in to the president."
Eisenhower firmly believed that the NSC machinery should operate as intended, which meant that it was advisory rather than a decision-making body, and he regularly attended the Thursday meetings. As reported: "Eisenhower hoped that the NSC would become a 'corporate body' of top officials, who would act as personal advisers to the president. Moreover, he wanted the NSC planning board to serve as the council's 'planning arm' by providing 'sound security policy recommendations.'" He was actively interested in attempts to rein in the three services' attempts to "go around" him to lobby Congress for their needs, especially if they ran against the official set of priorities, meaning in particular the Army.
The same could be said of the JCS's Joint Staff, on which Goodpaster also served. Later, in the Johnson presidency, then-JCS chairman Gen. Maxwell Taylor hoped that he could consolidate the authority of the JCS into the single office of the chairman, thus bringing under control the constant interservice rivalries that hampered the military establishment from insisting on a larger policy-making role in national security affairs. Although he was unsuccessful, this is what he envisioned (viz. Goodpaster's role):
Taylor thought Congress should "dissolve the JCS" and replace it with a single "Defense Chief of Staff" and a "Supreme Military Council." The defense chief of staff would have "great authority" and report directly to the secretary of defense and the president. Now that he was chairman, Taylor thought that he could become a de facto "defense chief of staff." In an effort to centralize authority, he gave his special assistant for policy, Maj. Gen. Andrew Goodpaster, formerly President Eisenhower's national security assistant, unprecedented responsibilities and latitude. Goodpaster became, in effect, a deputy. Previously, in the absence of the chairman, the senior service chief presided over important sessions as acting chairman. When Taylor was out of town, Goodpaster as his "deputy" attended White House and other high-level policy and planning sessions in place of another [Service] Chief. . . . Taylor tried to formalize Goodpaster's position and make it permanent. He wanted him promoted to lieutenant general and his title changed to Assistant Chairman, Joint Chiefs of Staff, a maneuver that required considerable political support.
Certainly, the efficiency report that Eisenhower wrote on Goodpaster in 1958 could apply as well to this later period of Goodpaster's service: "He handles the most delicate and sensitive material that ultimately comes to my attention. He is an invaluable assistant. It follows that I have in him the utmost confidence. In character, ability, performance, and dedication he is of the very highest classification."
Chapter Seven
A Functional National Security System
"The military policy to be adopted by the nation would have a significant bearing on the courses of action open to it in the area of foreign policy."
—DONALD F. BLETZ, _The Role of the Military Professional in U.S. Foreign Policy_
Goodpaster's upward career trajectory rested in large part on both the conceptual and the accompanying bureaucratic evolution of the "national security" dimension of presidential leadership. Both dimensions suited Goodpaster's temperament as his career unfolded along a parallel trajectory.
To begin at the beginning: it seems difficult to comprehend in hindsight, but during most of the first half of the twentieth century, when the United States had become a world power, there was no systematic scheme in place to coordinate within the government what later came to be known as national security policy. General Marshall recognized this deficiency early in World War II when he asked the War Department General Staff to create a unit "solely responsible for thinking and planning improved methods of warfare." He thus used a "think-tank" approach to develop a global vision and strategy for the army.
Marshall said at one point: "You should organize in your division a small planning and exploring branch, composed of visionary officers, with nothing else to do but think out improvements in methods of warfare, study developments abroad and tackle such unsolved problems as measures against armored force, night bombardment, march protection, and the like." This certainly was a step in the right direction, and was one that, undoubtedly, both Abe Lincoln and Goodpaster would have welcomed.
When the United States entered World War II, it "did not have a politico-military body such as the British War Cabinet or our present National Security Council. . . . It was not until December 1944 that a politico-military body was created. It was the State-War-Navy Coordinating Committee (SWNCC), composed of assistant secretaries of the represented departments. . . . It was the direct ancestor of the National Security Council."
The SWNCC advised President Roosevelt "regarding military strategy, military relations with our allies, the allocation of munitions and shipping, requirements of all kinds—including the manpower needs of the armed forces—and matters of joint army-navy policy." Goodpaster served on the staff of SWNCC in the early postwar period. As he said: "I . . . saw [Eisenhower as Army chief of staff] during that spring of 1947 when I was working with the State-War-Navy Coordinating Committee in preparation for what became the Marshall plan, reporting to him on the work that our group was doing."
An example early in his career of how close to the seat of power Goodpaster was: in 1945, he helped resolve a disagreement between Secretary of War Henry Stimson and then–Army Chief of Staff George Marshall. It had to do with the visit to Washington of President Sergio Osmana of the Philippines, who was very interested in knowing if the United States was going to honor its wartime commitment to grant full independence. Goodpaster was working at that time for Lincoln in the Strategy Section. Secretary Stimson wanted a general statement, whereas General Marshall wanted a more detailed statement. As Goodpaster recounted:
At that point, Mr. Stimson came through the door between their two offices, the door that was never closed, and here these two men stood side by side, two men who revered each other, greatly respected [each other]. . . . At about that time, General Marshall turned to the three of us with a kind of frosty twinkle in his eye and said, "Well, I think we've given you all the help we can, it's time for you to go to work." And so we did. . . . We prepared a third solution. . . . And at ten o'clock, as President Truman had required, Mr. Stimson brought it over and the document was signed by the two presidents. . . . [Marshall] would say, don't bring me a problem, bring me a problem with your best solution. And, of course, that was why he was as successful and able as he was.
It flows from this anecdote that one of Marshall's traits that appealed to Goodpaster (and to Eisenhower) was his insisting "that his principal assistants should think and act on their own conclusions in their own spheres of responsibility." It was observed: "The former army general was a man who believed in both an orderly process and planning."
It was in this assignment that Goodpaster came to admire Marshall firsthand. Goodpaster would have agreed with this statement: "On leaving Washington for the last time, that craggy veteran of seven administrations, Secretary of War Henry L. Stimson, said to Marshall, 'I have seen a great many soldiers in my lifetime and you, sir, are the finest soldier I have ever known.'"
Marshall was working at that time, along with George Kennan, on developing the Truman Doctrine of aid to Greece and Turkey. In June 1947 Marshall delivered his famous speech at Harvard about the United States taking responsibility, in tandem with counterpart war-shattered nations of Western Europe, to rebuild their economies, thus removing them from the threat of Soviet Communism. The idea was soon dubbed the Marshall Plan.
**The National Security Council**
In tracing the evolution of what has come to be known as "national security," it is useful to recall that the creation of the NSC is usually considered the starting point. This is important for this biography because the NSC played an important role in Goodpaster's responsibilities as the president's defense liaison officer in the White House, and then later when he was involved in the NSC's activities. Its formation in 1947 was contained in the same legislation that unified the armed services. The enabling statute "provides a council 'to advise the President with respect to the integration of domestic, foreign, and military policies relating to the national security.' To do this, the council is to 'assess and appraise the objectives, commitments, and risks of the United States in relation to our actual and potential military power.' The council has no statutory function and operates with a staff appointed at the discretion of the president."
One of the problems—both bureaucratic and political—in creating a new function, and especially if it involves the president, is that there is always maneuvering either to enhance its role or to sublimate its role. In the case of the NSC, Truman tried to have it both ways. He wanted to keep it in check, but at the same time, the legislative provisions meant that it could not be ignored entirely. So he appointed a fellow Missourian, Adm. Sydney Souers, to the post of executive secretary to the NSC.
To minimize intra-administration politicizing, "Truman, in one of his first assignments for his new assistant, had Harriman draft a presidential order limiting attendance at NSC meetings to members, plus others explicitly invited by the President himself. Nevertheless, a new power center in Washington would over the years evolve from Harriman's circumspect beginning as the first presidential assistant for national security affairs."
Eisenhower also did not want to vest too much authority in the NSC, and in particular any policy-making role. The small staff could coordinate, facilitate, monitor, and so forth. Eisenhower did, however, create a position in the White House of special assistant to the president for national security affairs. Some years later, in response to a request for his opinion as to whether the special assistant should be confirmed by Congress, Goodpaster responded:
I recognize that [today] when the functions of the office go beyond a purely "staff" character a problem of assuring appropriate accountability to the Congress arises. During the Eisenhower administration with which I was associated as a staff assistant in this area to the President, this difficulty did not exist. By specific instruction of the president, positions such as mine and that of the Special Assistant for National Security Affairs were limited to "staff" responsibilities, and were denied executive authority, the line for which ran directly from the president to the secretaries of the departments concerned, and the heads of the agencies concerned. In addition, our functions did not involve direct contact with the press and other media, those being reserved to the President himself and his press secretary. Moreover, it was not his practice to have members of his staff like myself engage in negotiations, or official discussions, with foreign authorities: this function was reserved to the State Department or, within their respective areas, to other departments and agencies of the government.
No one would argue against the fact that the actual policy-making took place in the Oval Office: under crisis conditions, Eisenhower would meet with his principal advisers, using NSC staff for coordination purposes. In this respect, Goodpaster could play a useful role, moving both inside and outside the formal chain of command. The so-called NSC process, like Solarium, became Eisenhower's method of engaging or creating a sense of participation and commitment with the various foreign and national security–related constituencies. He also "had a penchant for careful staff work, and believed that effective planning involved a creative process of discussion and debate among advisers compelled to work toward agreed recommendations."
The Special Assistant was made responsible for determination, subject to the President's desires, of the Council agenda, for briefing the President in advance of Council meetings, and for presenting matters for discussion at the Council meetings. As Chairman of the Planning Board he was responsible for scheduling Planning Board work and for the manner of presentation and quality of such work. He was to appoint (subject when necessary to the President's approval) such ad hoc committees, such consultants from outside the Government and such mixed governmental-nongovernmental committees as might be required. He supervised the work of the NSC Staff through the Executive Secretary.
The Operations Coordinating Board (OCB), which monitored the implementation of NSC decisions, derived its authority from Executive Order 10483, which provided:
Section 2. The National Security Council having recommended a national security policy and the President having approved it, the Board shall (1) whenever the President shall hereafter so direct, advise with the agencies concerned as to (a) their detailed operational planning responsibilities respecting such policy, (b) the coordination of the inter-departmental aspects of the detailed operational plans developed by the agencies to carry out such policy, (c) the timely and coordinated execution of such policy and plans, and (d) the execution of each security action or project so that it shall make its full contribution to the attainment of national security objectives and to the particular climate of opinion the United States is seeking to achieve in the world, and (2) initiate new proposals for action within the framework of national security policies in response to opportunities and changes in the situation. The Board shall perform such other advisory functions as the President may assign to it and shall from time to time make reports to the National Security Council with respect to the carrying out of this order.
Overall, NSC 162/2, which was the official statement of the NSC authority, only partially filled Eisenhower's wishes, but it did enough so that he could be pleased publicly with the result. There were, for instance, reservations about when and under what conditions troops could be withdrawn, and it failed to state clearly how and when nuclear weapons would be used. Furthermore, "the armed services did not yet have unencumbered access to nuclear weapons. . . . The lack of weapons in sufficient quantity and appropriate design was a constant impediment that the services said hindered them from carrying out the President's desired changes in policy and strategy."
In 1953 President Eisenhower adopted a reorganization plan for the Department of Defense and the JCS that enhanced the powers of the secretary of defense and the chairman of the JCS at the expense of the separate services. The chairman of the JCS, Adm. Arthur W. Radford, became the principal military adviser to the secretary of defense and to the president (he replaced Eisenhower's wartime colleague, Gen. Omar N. Bradley).
A few years later, in a further consolidation of power, the Defense Reorganization Act of 1958 removed the service secretaries from the chain of command leading from the president to the operational forces, and authorized the president, with the advice of the Joint Chiefs, to create unified and specified commands that took their orders directly from the secretary of defense. In addition, the chairman of the JCS gained increased influence in JCS deliberations and greater control over the Joint Staff.
Goodpaster described the law's intended and unintended consequences:
The Act of 1958, in clarifying the authority of the Secretary of Defense, has had a result not anticipated or consciously intended by those who participated in its formulation. With regard to operational planning and the military and tactical advice that is offered to decision makers, the intent of the legislation was to concentrate responsibility in the Joint Chiefs of Staff, thus ending the situation in which the individual services, acting separately, extended operational influence over field commands. The Secretary of Defense and his immediate office would exert policy direction and control. But in the application of the Act, a further shift has occurred, resulting in a more detailed treatment of a wider range of matters at the civilian level of the Office of the Secretary of Defense than was then foreseen. . . . Where the act visualized fixing the responsibility for military operational matters in the Joint Chiefs of Staff and assigning the conduct of combat operations to the unified commands, there has evolved in practice a sharing of the Joint Chiefs of Staff role and a retention of operational decisions on a more centralized basis at the Secretary of Defense level of control than was anticipated in 1958.
Eisenhower's first national security assistant, Bobby Cutler, described Eisenhower's approach: "President Eisenhower used the National Security Council as a vital mechanism to assure that all sides of an issue could be known by him before coming to his decision. He wanted a skilled planning arm to gather from informed sources the material relevant to each issue, to winnow and to test that material in the crucible of argument, and to bring the integrated, exactly phrased result before the Council for debate in his presence." Cutler further enthused: "The National Security Council has emerged as a mechanism of the executive branch . . . equal in importance to the Cabinet. . . . Out of the grinding of these minds comes a refinement of the raw material into valuable metal, out of the frank assertion of differing views, backed up by preparation that searches every nook and cranny, emerges a resolution that reasonable men can support."
**Goodpaster's National Security Role**
All told, Goodpaster, living up to Eisenhower's expectations, described his role
while Bobby Cutler was there, then Dillon Anderson, then Bobby again, and then Gordon Gray. They would deal with the policy papers that would come via the NSC route, broad plans, major programs, things of that kind. I would get the day-to-day flow of things that involved the president. If these matters came to the White House for coordination but did not require the president's attention, they would oftentimes go to the Operations Coordinating Board, which was part of the structure that was under Cutler's and then Gray's supervision.
One feature that distinguished the Eisenhower administration's approach to "national security" from that of the Truman administration was precisely the role that Goodpaster played:
Beyond State and the NSC, Ike also had a third resource for foreign policy management: his staff secretary Andrew Goodpaster. The formal job was created in 1954 when Eisenhower lost his temper over mismanagement of White House paperwork—"Andy's" initial task was to be sure it flowed smoothly to the right people. But once Goodpaster solved that problem, he was available to do much more. Quietly and efficiently, he handled much of Eisenhower's most critical national security and intelligence business. He sat in the West Wing, down the hall from the Oval Office. He organized and took notes for the president's many informal meetings with senior advisers on international matters.
He smoothed communications between Eisenhower and Dulles, and perhaps even more between the president and Dulles's successor, Christian Herter. . . . He did not provide independent substantive advice, nor was his stature equal to that of Eisenhower's formal national security assistants, Bobby Cutler and later Gordon Gray. But he played a key operational coordination role. And Eisenhower trusted him totally—he would remark that every man would want his son to be like Andy Goodpaster.
Furthermore, acting just barely within the formal operational structure of the NSC—if formalities were to be employed—Eisenhower would regularly meet alone with Goodpaster. "These informal meetings accomplished precisely what contemporary critics of Eisenhower's foreign policy-making took the NSC to task for not accomplishing—rapid, flexible decision-making by the president himself. . . . Goodpaster was not just the note-taker in the informal policy-making meetings in Eisenhower's office: his role was like a combined Planning Board and OCB. He saw that critical participants were not frozen out of discussion and that Eisenhower's decisions were carried out. In this sense, his duties paralleled those of Cutler. Indeed, their two positions came to be combined in later presidencies."
After leaving the White House, Eisenhower deplored the dismantling by the Kennedy administration of the elaborate NSC committee structure, and the de facto downgrading of the NSC in highest-level decision-making. "I explained to [Kennedy] in detail the purpose and work habits of the Security Council, together with its two principal supporting agencies—the Planning Board and the Operations Coordinating Board. I said that the National Security Council had become the most important weekly meeting of the government." Nonetheless, one observer recalled: "The elaborate organizational staff reforms of the Eisenhower White House were stripped away with an almost evangelical glee; in particular the downgrading of Eisenhower's cherished National Security Council (NSC)."
Later, witnessing the Bay of Pigs debacle, Eisenhower would observe that Kennedy and his principal advisers might have avoided their mistakes if they had had Eisenhower's less impulsive national security decision-making apparatus. Goodpaster agreed wholeheartedly with Eisenhower, having himself been a product of the more hierarchical system of policy formation and decision.
**John Eisenhower's Role**
Whether Goodpaster welcomed the presence of the president's son at his elbow can only be an object of conjecture. A hint, however, shows in a handwritten note that Goodpaster wrote to himself:
President asked, on my first day back from leave, how long I had been here, indicating he was wondering whether I wouldn't be thinking I should leave in another year or so (he thought I had been here about 2 years—was surprised when I told him 3). I told him I had no definite period in mind—that when I was ordered in I accepted idea of serving here if my service were thought to be needed, and as long as they were thought to be needed [ _sic_ ], recognizing but disregarding the possibility of adverse effect on my future in the military service.
He then said he had thought about this in relation to the possibility of bringing John in as my replacement as Staff Secretary and Defense Liaison Officer (in which post he had been serving during my leave).
I told him my only thought was to serve here if, in such capacity, and so long as needed. He said John should be available in early 1959 (after he finishes Armed Forces Staff College), and that, if he comes here shortly after that, I would be available for other duty. He said he had in mind that I might continue to serve here as a special assistant, or military adviser, unless for some reason I should be returned to Army duty.
I told him any of these actions would be all right with me—that I was hoping, on leaving here, to get an assignment such as Asst Div Comdr or CG of one of the missile commands, such as the one in Italy.
Goodpaster recalled: "In 1958 John Eisenhower came aboard as an assistant to me and he worked on the international side of the house. And this was a great help to me because he and I could substitute for each other in taking these meetings and writing up the results of the meetings and then following them up in the government." John Eisenhower described his duties: "I spent about a month, a little more than a month, between stations and the White House in '57 filling in for General Goodpaster while he was gone on leave. Then, in October of '58, I came on a permanent basis for the rest of the administration. I was General Goodpaster's assistant and our functions were paper flow: to make sure that every action that came to the president's attention had everybody's contribution to it. We were a device for insuring that the last one in the office was not the one who got his way. That when something was brought to the president's attention, everybody had a chance to comment on it first."
Other assistants would monitor follow-up to the various presidential meetings. "It was an informational channel and it was really quite helpful in keeping a flow of specific information of particulars of what was going on in the government, getting down below the kind of broad generalities and major programs which could be reflected in, say, budget and the money provided, to knowing some of the quite specific things that were going on which did or did not conform to and support the line of policy that the President had in mind. . . . This helped to discipline the system and keep it aligned with the policy directions that the President gave."
Furthermore, John Eisenhower recollected:
My particular functions were daily intelligence briefings. I sat in on them and made records of quite a few of the meetings that Dad had in his office. We tried to arrange it so that there would be no meeting of any importance that was not recorded. The great exception to this, which is too bad historically but I guess it was certainly the way they wanted it, was John Foster Dulles. Nobody was in the room with Dad and Dulles so that what they've said has just been lost except for what Dad recorded from his own memory.
When [Christian] Herter took over, General Goodpaster and I would sneak in one at a time. We would go in and see if we were thrown out! And we weren't! So, from that time on we were able to record the private conversations between the president and the secretary of state.
Thus, "it was necessary for us to work very closely together and to pass tasks or topics back and forth, to check with each other to see that each was informed of any significant thing that the other was concerned in." What this implies—almost asserts—is that Goodpaster and then later also John Eisenhower, were intimately involved at the presidential level, in virtually all matters of a "national security" nature, even though not technically charged with the responsibility to do so.
Chapter Eight
National Defense Writ Large
"War is the most controversial strategy that great powers can employ to increase their share of world power."
—JOHN J. MEARSHEIMER, _The Tragedy of Great Power Politics_
It is useful here to recall, in capsule form, Eisenhower's notion of national defense, made in 1954. Both houses of Congress had shifted to the Democratic Party, and therefore more challenges would be forthcoming to Eisenhower from various military-related interests.
[Eisenhower] said that the controlling thought that the leaders must keep in mind was that the United States was really never frightened about enemy attack until the advent of atomic bombs and the long-range bomber. . . . But the invention of the A-bomb and nuclear weapons and the long-range bomber to carry them has caused us all to take a different look at the world. "It seems to me that the great emphasis that we now should put on national defense should be centered on two main objectives: (1) massive retaliation, which simply means the ability to blow hell out of them in a hurry if they start anything and (2) a system of advance warnings developed through our radar system to minimize any such attack. . . . Now, everything points to the fact that Russia is not seeking a general war and will not for a long, long time, if ever. Everything is shifting to economic warfare, to propaganda, and to a sort of peaceful infiltration. . . . What we want to do is to lessen the priority we have been keeping on Army ground troops and those parts of the Navy that do not deal with air and with submarines. I want you to know that this judgment is my own."
Goodpaster explained, although a bit eloquently, why the national security process is important: "The first and overriding characteristic of national security affairs is that . . . the stakes are high. They concern the continued existence of the United States as a free nation, with free institutions. What is really involved is self-preservation, the first law of life. In this sense—and to this degree—military and security needs take priority over almost all other considerations. While these are not of themselves primary goals of a national society—as are the freedom and self-government, and the education, health, economic well-being, and the cultural and moral advancement of its people—without the protective shield of the power and readiness to defend itself, it is not likely that these others could be attained."
**The Overall Political Framework**
More important is the observation that "the final characteristic of the national security environment is the fundamental fact that the conduct of policy and action occurs within an over-all political framework. The framework is political both internationally and domestically. Internationally, it is evident that considerations of security guide both the foreign policy activities of peace and the warfare that continues foreign policy by other means."
This leads to the question of what is meant by having the best men assigned to the Joint Staff. Obviously, the best way to insure that the Joint Chiefs of Staff provide thorough, well-reasoned, professional military advice, particularly in times of crisis and war, is to make sure that only the best officers are selected to head their Services. . . . What is meant by the term "best-qualified"? Of course, there are all sorts of ways one could measure qualifications. However, when it comes to the Joint Chiefs of Staff providing military advice in times of crisis or war, the best-qualified individuals are those highly professionally adept, combat-experienced (if possible), tough-minded, and willing to state the bald-faced truth as they see it. Such officers must be bright (and few rise to that level unless they are), but need not be intellectuals. And while at least a modicum of diplomacy and tact is essential, it is neither necessary nor desirable—in such times—for such men to be military diplomats (politicians).
This definition fit Goodpaster, although perhaps the term "scholar" could also be appended to him, given his lengthy list of correspondence, articles, and speeches after his retirement. It is a credit to both Eisenhower and his close colleague Gen. Alfred Gruenther that they saw in Goodpaster the qualities that Brig. Gen. George Lincoln recognized, and which led to Lincoln first drawing Goodpaster into the planning world of the Pentagon, then bringing him to Paris to participate in the creation of SHAPE, and then bringing him to the White House itself.
Overall, Goodpaster, in furtherance of his responsibilities, was a model of the officer corps of his day. "A study of the alumni of the National War College in 1969 revealed a surprising acceptance of political-military emphasis on the part of the graduates. 'The study of our national strategy, to include the integration of military and foreign policies . . . is clearly seen as the most important base of study for the course, regardless of year of graduation, service, branch of government or rank of the respondent.'" What is also most interesting here is that Goodpaster was commandant of the National War College in 1967–1968.
To summarize: "Eisenhower introduced a variety of staff entities and roles that hitherto had been absent from the presidency, among them a White House chief of staff, Cabinet and National Security Council (NSC) staffs, and a special assistant for national security affairs. . . . [There also was] his informal national security policy-making operations, which involved such fluid procedures as daily consultations between Eisenhower and Secretary of State John Foster Dulles, informal meetings in the Oval Office between Eisenhower and core aides, and one-to-one meetings of the president and an extensive network of public and private advisors."
There were strong pressures from both Congress and the administration for reducing the Pentagon's budget, and this in turn introduced into the situation the continual bickering among the services over their respective budgetary justifications. Thus the confusion was twofold: (1) a president confronting the most basic concept of how to fight and win the most likely (at least it seemed then) kind of warfare (i.e., nuclear); (2) a JCS that bickered and competed among themselves over how to equip themselves and for what war-making purpose. Overall, the "ultimate absurdity"—as Herbert York termed it—was that with increasing expenditures on armaments, American security was in fact declining. Thus, any hope of an orderly system of war planning fell by the wayside because of this situation, which had taken on a dimension that was more than just a "roles and missions" dispute.
To make matters even more confusing, the chiefs would air their complaints before Congress, to Eisenhower's intense displeasure. However,
One Chief who, over the course of several years managed to attain a closer than normal relationship with President Eisenhower, was Admiral Arleigh Burke. Years later Burke recalled: "'He'd call me up on the white phone . . . maybe four-thirty, five o'clock and say, 'Could you come over for a discussion or a cocktail or something?' 'Yes, sir. Of course.' And I went over. And he might ask me a question . . . on the Army. I said, 'Mr. President, I don't know a damn thing about that.' He was an impatient man. 'I know you don't know anything about it, damn it. I want to get your views.'"
It is a safe bet that Goodpaster was on hand during these occasions.
**Concepts of "National Security"**
There have been criticisms, from time to time, that the chairman of the JCS had either too much authority to speak out or too little. "Critics of the system seem to have forgotten that one of the complaints about the Joint Chiefs in the mid-1950s . . . was that Admiral Arthur Radford had too much influence with President Eisenhower, not too little." In fact, the Army's chiefs of staff at the time, Gen. Matthew Ridgway and then Gen. Maxwell Taylor, claimed that Eisenhower's massive retaliation strategy and his reduction in the Army's size represented an excessive dependency on the military advice of Chairman Radford.
Moreover, "Part of the problem of the service Secretaries has been the Joint Chiefs of Staff channel to the Office of the Secretary of Defense [OSD], the National Security Council, and the President; part of it is OSD; part also is the nature of centralized military planning in an armed service department. . . . [The service secretaries] . . . were not permitted to participate in the discussions . . . of the top management—i.e., the National Security Council and the Secretary and Deputy Secretary of Defense—by whom policies affecting [their] enterprise were considered and determined."
Goodpaster recalled that "some of the changes introduced by the Act of 1958 clearly reflected dissatisfaction at the higher levels of the government with the form and degree of service rivalry then manifest. The act took steps to eliminate such sterile rivalry. It created a chairman with statutory powers, and emphasized corporate responsibility. It strengthened the role of the Vice Chief in each service, to enable him to shoulder a larger part of the burden of service operations, thus clearing the agenda of the Chief and allowing him to spend more time on his corporate responsibility."
Eisenhower delegated downward, letting the various issues clinging to a large issue of policy either fall away or become more clearly defined.
Given his leadership style, Eisenhower preferred not to deal directly with the military—that was [Secretary of Defense Charles] Wilson's job. Recognizing Wilson's lack of a military background, Eisenhower tried to buttress the secretary's position when he reorganized the Pentagon on July 1, 1953. Wilson's authority was strengthened, as the number of assistant secretaries increased from three to nine. In a bow to the military, the president also gave the chairman of the Joint Chiefs the authority to manage the joint staff and approve the selection of those who were to serve on it. Eisenhower wanted the chairman to recruit officers who would focus not just on the interests of their own service, but on "national planning for the overall common defense."
He was only partially successful in this endeavor, however, undoubtedly placing a burden on both his own chief of staff and on Goodpaster to monitor happenings at the higher echelons in the Pentagon. Goodpaster, inevitably, was always in danger of being caught in the middle of a contretemps. He had worked for Army Chief of Staff Ridgway at SHAPE when Ridgway was SACEUR, and now Ridgway was the "bad boy" in Eisenhower's eyes for vigorously advocating an increase in conventional forces.
Furthermore, to the skeptic, massive retaliation was nothing more than a slogan to use as a budgetary axe rather than signaling a sharp change in grand strategy. So-called peripheral actions were still taking place with no open consideration of using the "nuclear option"—at least since the Korean truce.
The enunciation by John Foster Dulles in January 1954—before Goodpaster had arrived—that "local defenses in many areas . . . were inadequate against aggressors who could strike without warning, and therefore these defenses 'must be reinforced by the further deterrent of massive retaliatory power.' America's shield would be its 'capacity to retaliate instantly, by means and at places of our choosing.'" However, in Berlin, in Korea, in Indochina (including Vietnam), and in regard to a so-called Sino-Soviet bloc, Eisenhower and Dulles could not move American public opinion beyond what the _Economist_ termed "a spectacle of vociferous inaction" to favor more fighting, even if they had wanted to. Even the Communist Chinese claims and threats regarding the offshore islands of Quemoy and Matsu did not trigger any military response. In fact, instead of "unleashing" Chiang Kai-shek, he was in effect "leashed."
This debate over the efficacy of deterrence over offense—or vice versa—raged especially vigorously during the Eisenhower period of the Cold War. "Massive retaliation" was partly a declaratory policy and partly a justification for sharply increased expenditures on both nuclear warheads and the means of delivering them. Furthermore, "many have argued against reliance on deterrence alone, since the adversary could punish the United States in return for any strike we might deliver."
This brings to mind some contradictory elements to any notion of a nuclear "grand strategy." First, it is easier to articulate a strategy than it is to identify the circumstances under which it can assist the tactician. Thus, "new technology, even when properly integrated into weapons and systems with well trained and highly motivated people, cannot erase the difficulties that impede strategic excellence. A new device, even innovative ways to conduct war, is always offered as a poisoned chalice. . . . Every new device and mode of war carries the virus of its own technical, tactical, operational, strategic, or political negation." That, in essence, is massive retaliation, if it is to be considered an operational guide rather than merely a political slogan.
Goodpaster, having studied the nature and impact of technology on both military strategy (trying to reduce the unknowable to educated guesswork) and weapons innovation (the unforeseeable setting), would have taken this for granted. Many of his civilian and military colleagues, however, even if they had known better, would have sidestepped this reality in the interests of furthering budgetary or career ambitions.
**The "Arms Race" That Wasn't**
One area of national security that virtually paralyzed Eisenhower was the persistent assertions, by both some of his more right-wing Republican colleagues and virtually all of the Democratic political opposition, that he had neglected to keep abreast of the Soviet Union missile for missile. After all, in the minds of the public, that was what the arms race was about. Nevertheless, because of _how_ he obtained his information, he felt he could not reveal _what_ that information contained as to any notion of a superpower "balance." Not only was there no balance, there was a lopsided advantage in the Americans' favor.
A particular thorn in Eisenhower's side was his former Army chief of staff, Gen. Maxwell Taylor, and his notion of "flexible response." Taylor, when chief of staff, had lobbied aggressively for an increase in the Army's conventional war-making capability, arguing that the "nuclear option" had cancelled itself when both the Soviet Union and the United States had achieved a kind of parity. Goodpaster appeared to have supported the Taylor argument, observing: "In the latter part of his administration, probably under the impetus of Foster Dulles, Eisenhower was almost driven to recognize that there was more to it than just the nuclear weapons, that problems were arising in the so-called 'third world' that [required] conventional military strength and a conventional military position. . . . The President was reluctant to acknowledge that. I think part of that reluctance came from a concern that he would lose the ability to keep a limit on the buildup of military forces."
For example, "Dulles's reconsideration of Massive Retaliation symbolizes the turmoil within the Eisenhower administration as different actors attempted to challenge with new ideas and new bureaucratic alliances the prevailing commitment to the strategic nuclear deterrent." The intra-administration debate had even spilled over into congressional politics. As it was reported:
Eisenhower also contemplated ways to control the testimony of the active-duty chiefs. In a White House meeting on 25 January 1960 with Joint Chiefs of Staff chair [Nathan] Twining, and his staff secretary Army Col. Andrew Goodpaster . . . General Twining admitted that he too had become tangled up on the "argument over intelligence based on intentions v. capabilities." . . . Twining was troubled by [the] Preparedness Committee's practice of requiring the members of the Joint Chiefs of Staff to testify under oath. . . . The president had a simple solution for such situations: "Any military man who appears before the group and is required to take an oath," he said "should refuse to give opinion and judgment and limit his testimony strictly to facts."
Eisenhower had to endure many more partisan attacks during the forthcoming presidential election, and since the electoral outcome between Nixon and Kennedy was so close, this lingering, apparently irresolvable issue may have tipped the scales in Kennedy's favor. It is easier, for example, to cry wolf than to make an appeal based only on the assertion "believe me because of who I am." The embarrassment and moral confusion of the U-2 incident further weakened the argument.
Note should be taken here that Eisenhower took very seriously the third "leg" of his concept of national security—arms control and disarmament. It was easy for the skeptics (or the disillusioned) to dismiss this aspect, but according to Goodpaster, this was not, in fact, the case.
Goodpaster ordered Eisenhower's security-related priorities as follows: (1) defense capability; (2) deterrence; (3) arms control. He explained that "[Eisenhower] had, of course, just been over in NATO. And in NATO, they formulated the security policy as being a dual policy of defense and deterrence, deterrence being linked primarily to superpower nuclear parity. . . . But he was one of the first to see that control of armaments was really a third main line of policy. . . . Eisenhower, interestingly, had a very great interest in this and he felt—and I speak of this because I spoke to him many times, we had long talks about this—and I shared with him, I think, a view that action in the field of disarmament was really a third major link or line of our policy at the time. I discussed this with him and, over the years, it has seemed to me that he was one of the first to see it in those terms."
Nonetheless, "since an acceptable treaty for controlled disarmament was not realized, we continued to build an overpowering military establishment as the only feasible defense against the menace and probing of international Communism and as the indispensable platform from which to continue negotiations for a peaceful world." Eisenhower commented: "It seems a wry and sad commentary on human intelligence that the development of a unique weapons system [the Polaris submarine-launched missile] did more to restore a feeling of Western confidence in a stable future than had all the disarmament talks conducted over a period of years."
As to any contradiction between the New Look and disarmament, Goodpaster felt that, to the contrary, Eisenhower recognized that embracing the New Look almost demanded a careful examination of the possibilities of disarmament. The destructive potential of nuclear weapons had changed the character of war to such an extent that, without linking an evolving nuclear arms race to an equally evolving nuclear arms reduction effort, the world would be left as a hostage to the superpower rivalry. The overarching danger was that this rivalry could spin out of control at any time. For this reason, Eisenhower felt that the superpowers would recognize the need to engage in arms reduction negotiations, difficult as they might be.
Even so, Eisenhower left a noteworthy legacy, especially because—as the Cold War persisted and eventually collapsed—negotiations did in fact produce results that would have pleased him. To quote: "The Arms Control and Disarmament Act (P. L. 87–297, 75 Stat. 631) was landmark legislation designed to entrench arms control as a key component of United States national security policy during and after the Cold War. Congress achieved three main tasks: it set ambitious goals and purposes for coordinating disarmament with other defense strategies; it created the U.S. Arms Control and Disarmament Agency (ACDA), a body that would make the country's commitment to arms control a part of its governing institutions; and it established standards and procedures for integrating all aspects of security policy."
The new agency was to have four principal tasks:
1. To conduct, support, and coordinate federal research on arms control issues
2. To prepare for and manage U.S. participation in international arms control negotiations
3. To inform the American public about arms control
4. To prepare for and operate or direct "control systems" that might be useful in monitoring and enforcing compliance with international arms control agreements
The agency's director became "the principal adviser to the secretary of state and the president on arms control and disarmament matters." This double responsibility—reporting to both the president and the secretary—was often referred to as a "dual-hat" mechanism. The director was an "independent voice" in the most senior-level national security debates, while not straying too far from the secretary of state's leadership in international diplomacy. Obviously, the more closely the director was tied to the top national leadership, the greater the agency's influence.
The act made arms control a legitimate tool of U.S. policy. The concept of seeking enhanced security through negotiation, rather than solely through arms procurement, became an accepted feature of the political landscape, and even national leaders who were not inclined to value diplomatic approaches were frequently nudged in that direction by the arguments and information provided by ACDA. Although it was only after the demise of the Soviet Union that credible and binding international disarmament treaties were negotiated, the administrative framework was set in place shortly after Eisenhower left office.
Incoming president John F. Kennedy recognized Goodpaster's value by requesting from President Eisenhower that Goodpaster be held over in the White House beyond the transition period, even though he already had his orders for the command assignment that he coveted.
Eisenhower reported:
Senator Kennedy was very much concerned with the activities of General Goodpaster, and said he would like to hold Goodpaster for two months into the new Administration. I told him that I thought a better solution would be for him to appoint a man right now who could take Goodpaster's post (the duties of which I detailed at some length) and allow Goodpaster to leave with the rest of us on January 20th. He said he would be handicapped unless he had Goodpaster for a month or two, really favoring the second. Of course I had to say that he would soon be the Commander-in-Chief and he could _order_ [Eisenhower's emphasis] General Goodpaster to do anything, and those duties would be efficiently performed; but told him also of Goodpaster's great desire to go to active line duty and that a particular spot was being held for him. I asked the Senator if he would assure me that that spot would be held. (That evening I called [Army Chief of Staff George] Decker and told him the details of this conversation and asked him, as a personal favor to me, to make it his business to protect Goodpaster's future to this extent. He said there would be no trouble about this.)"
Subsequently Eisenhower wrote: "Dear Senator Kennedy: I have now heard from both Secretary [Thomas] Gates and General Decker regarding your desire to retain General Goodpaster temporarily after your inauguration. They have arranged, as you asked, for him to stay on in your office for a period ending sometime in February or March, the exact date to be determined later. At the same time, they have taken steps to see that, as we agreed, when he ends his service here he will be sent to the same assignment that is now planned for him."
When Kennedy immersed himself in plans to oust Cuba's Castro, "though the President's initial orders seemed restrained, Kennedy proceeded to rob himself of the machinery that Eisenhower had created to exercise close control. . . . More than ever before business was transacted directly with the new NSC staff, yet Kennedy showed little interest in consulting Ike's White House staff secretary Andrew Goodpaster, who had most of the relevant information at his fingertips." Significantly, Goodpaster was not privy to Richard Bissell's tightly held plans, nor were the agency's Cuba experts.
This was unfortunate because, although the Kennedy administration suffered the opprobrium of failure in its anti-Castro Cuba policy, the seeds had been planted earlier during the Eisenhower administration, and Goodpaster was at the center. "On November 9, Andrew Goodpaster informed [Secretary of State Christian] Herter of the approval [to disrupt Castro's regime]. At the White House, knowledge of the action was to be restricted to Goodpaster himself, Ike's son John S. D. Eisenhower, and one confidential secretary."
No greater compliment could be paid to Goodpaster than this: "Transition aide Richard Neustadt stressed repeatedly . . . the need for 'a Personal Assistant to the Commander in Chief-Elect' to handle duties that 'roughly corresponded to (and expanded upon) the work now done for Eisenhower by General Goodpaster. . . . When Kennedy saw the President on December 6 he extracted Eisenhower's reluctant assent to Goodpaster's staying on for a month after inauguration day, deferring his transfer to the active-duty post that Eisenhower was instrumental in holding for him."
During this "interregnum," Goodpaster received many notes from well-wishers; one in particular stands out because it captures Goodpaster's personal as well as professional traits. It read: "Dear Andy: This word of appreciation to our Staff Secretary, one of the most able, most influential, and most anonymous men in the United States Government. And one of the most congenial and considerate. The value, to the President and to the country, of your knowledge, judgment, and loyalty is great—beyond estimation."
In April 1961 Goodpaster became, as promised, commander of the Eighth Infantry Division in Germany. But just a year later, in April 1962, he was recalled to Washington to serve as assistant to the chairman of the Joint Chiefs of Staff, and in 1967 as director of the Joint Staff. These assignments are mentioned to show how much Goodpaster was valued in and around the uppermost echelons of the Pentagon after his service in the White House.
Somehow, Goodpaster had, over the six years that he worked in the White House as staff secretary and defense liaison officer, moved among the "movers and shakers" of the Eisenhower administration without attracting unwanted attention or controversy. He was trusted, even admired for qualities that appeared contradictory to persons in and around the seat of power. By not seeking to enhance his personal influence in an intensely competitive bureaucratic environment, Goodpaster made himself an essential part of the policy process.
As Eisenhower's staff secretary, he occupied an all-important position that had relevance to this observation: "In government, as in every institution, information is blood. Clamp it off from any part and the member cannot function. At the White House, the national security assistant [and staff secretary] is a carotid artery to the president."
Chapter Nine
Eisenhower's Health Crises
"The effect—of the fearless leader, the happy warrior, the father figure on whom the nation relied—was as central to his own equilibrium as it was to the country's."
—H. W. Brands, _Traitor to His Class_
As his presidency unfolded, an unanticipated—but understandable—situation arose concerning the state of Eisenhower's health. The persons around him and in the White House writ large found themselves distracted during significant periods of time while Eisenhower was recuperating from several serious maladies. There also was the brooding possibility that, if Eisenhower had been fully healthy, or even able to give concentrated attention during a specific incident, the outcome might have been for the better. This did not mean that during his two terms of office he ceased to function effectively, but these events had an inevitable unsettling mood on those in his immediate circle as well as in the larger world.
**The Heart Attack**
The first crisis came in September 1955, while Eisenhower was vacationing in Denver prior to engaging in pre-election activities. He recounted: "I went to bed at about 10 p.m. and slept. Sometime later—roughly 1:30 a.m., I think—I awakened with a severe chest pain. . . . [Mamie] urged me to lie down and promptly called the White House physician, General [Howard] Snyder. She thought I was quite sick. . . . I was helped into a car and taken to a hospital . . . but never after that night did I feel any pain or any other symptoms connected with the attack."
Following custom, Eisenhower wrote a "Dear Dick" note to Vice President Nixon, saying: "I hope you will continue to have meetings of the National Security Council and of the Cabinet over which you will preside in accordance with the procedure which you have followed at my request in the past during my absence from Washington." Thus, Eisenhower made a situation appear routine when it was anything but! Although other efforts were made to show that, with Nixon acting for the president in Washington, matters were going forward "as usual," in fact, there was considerable maneuvering taking place among the administration's chief players. John Foster Dulles took the helm, shutting out Nixon; instead he relied on Sherman Adams to be in Denver to coordinate matters. The truth was: "Eisenhower simply did not like Nixon."
As an example of Dulles' control at this stage, note the following: "During the subsequent Geneva conference of the four foreign ministers between 27 October and 16 November 1955 . . . in a letter to the president, who was recuperating in Fitzsimons army hospital in Denver after his September heart attack, Dulles wrote that Molotov had delivered 'one of the most cynical and uncompromising speeches which I have ever heard,' when the Soviet foreign minister completely rejected any discussion of the reunification of Germany except on Soviet terms."
Goodpaster had to have been privy to all of this as he continued to perform his functions from the Denver "White House." He also, along with the president's personal secretary Ann Whitman, was constantly monitoring his moods. As she put it, "The doctors do not think (and perhaps this is partial guess work on my part) that any serious decision would upset him, but the little minor crises do upset him and worry me so terribly."
In a memorandum to Sherman Adams in December, Goodpaster wrote: "When the President returns, it would be of great value, I suggest, to have a generally understood pattern for appointments, etc. While not rigid, such a pattern would make for a better organized, more orderly use of the President's time and energy. . . . As the above indicates, it would appear that there would be, at most, an opportunity for eight appointments with the President, on official matters . . . in a week—and this number might be as low as three." The cabinet, the National Security Council, and such were expected to step in.
When Eisenhower went to his Gettysburg farm for further recuperation, Goodpaster was readily at hand there also. "We would fly up to Gettysburg after he went up there for his recuperation, either every day or every other day. Adams would fly up once a week. We would transact all of our business. We, by that time, had the secure telephone put in there and I could work with him in that way. So that's the way we worked it out."
However,
access to the president became more of a problem than it had been previously. . . . Dulles had access to the President. . . . But there was no Dulles in the Pentagon, and in the period after the heart attack, access was not easy for either Secretary Wilson or Chairman Radford. . . . There was, however, one individual of lesser military rank who did have access—Brigadier General Andrew J. Goodpaster. Goodpaster was both staff secretary under Adams (subsequently under Persons) and defense liaison officer. In this latter role, he was pretty much on his own. Eisenhower considered Goodpaster's work in national security affairs as more important than his other functions and viewed it as overlapping the role of the special assistant for national security affairs.
Also, to provide a private place near the Oval Office where Eisenhower could rest during the day, "he ought to have a little room where he could just relax, read, even do any painting that he wanted to do. . . . I [Goodpaster] designed a way to cut off part of the room that was used by his scheduling secretary, and make use of that space and a space just across the walkway so that he could use that as a place to go and spend a little time just relaxing and taking off the pressure."
During the reelection campaign, Eisenhower recalled, "First I reiterated the decision to accept the Republican nomination (should it be tendered to me). Then, because five months earlier I suffered a heart attack, I explained the latest findings of the doctors—optimistic findings, by and large. There was no denying that in view of my illness I was more of a risk than a normal person of my age, but not great."
**Ileitis**
Not too long after the heart attack, Eisenhower suffered another illness that also came during the reelection campaign. John Eisenhower reported: "The blockage had been in the ileum, a small tube which connects the small and large intestines." His ileitis required surgery, which was successful; nonetheless, it "had wide repercussions. First of all, it intensified the health issue for the 1956 political campaign. . . . And with a temporary loss of stomach muscles, he walked slowly and hunched over."
As Sherman Adams recounted,
Shortly after midnight, Andy Goodpaster called me from his home and told me that the President was about to undergo surgery. "I am leaving right now to go to Walter Reed," Goodpaster said to me. "For what purpose?" I asked. "To observe his competency should any military decisions become urgent," he said. . . ." Goodpaster was already at the hospital when I reached there a half-hour later. Hagerty joined us and the three of us stood in the corridor at the door of the operating room and watched the surgeons as they worked on the body of the President of the United States. . . . Goodpaster said something about how we would have to change the office routine again.
Eisenhower commented: "Strangely enough, although I was truly miserable for several days I was never disturbed in this instance by the doubts that beset so many others. My current ailment was something acute which was corrected by immediate surgery; and once I was conscious again and in possession of my faculties, I did not bother with the question of full recovery."
This was not the first time that Eisenhower had been afflicted with ileitis. While president of Columbia University, he had suffered an attack. "His doctor, Howard Snyder . . . told Eisenhower to stop smoking. He did so immediately. . . . When asked how he did it, he said he had simply given himself an order to quit."
As to the latter medical emergency, "it was also not noted that the unexpected illness had required a postponement of a meeting with the heads of the Latin American states: 'The original dates had been set for June 25–26, 1956, but it was rescheduled after my ileitis operation.'"
Eisenhower insisted that more, rather than less, information should be given to the press and general public as his recuperation advanced. Goodpaster would have been consulted about what to say and what not to say when it came to matters of state. Otherwise, health details were left to others. For example, this is an exchange in a press conference dealing with his heart attack, arranged at Walter Reed Hospital for the president's personal physician, Dr. Howard Snyder. After reporting that the president had walked around his room, the question was asked whether he had some support: "Would you describe it as less support than yesterday or about the same?" Dr. Snyder: "About the same." The next question was: "Just one elbow?" and so forth. The idea was that with this kind of detail, the people at large could grasp the general state of affairs while Eisenhower was hospitalized.
This leads to a consideration of the overall effect of illness on presidential leadership. With the memory of Woodrow Wilson's disabling illness having been covered up by his wife and others around him—including Colonel House—as a negative example, Eisenhower was determined that the general public should not be left in the dark about his own health maladies. Wilson had been experiencing "cerebral episodes" as early as 1896, and in April 1919 he suffered what a neurologist termed a "a stroke so destructive as that it made of him a changeling with a very different personality and a markedly lessened ability." To claim that illness did not alter the running of the presidency would be an obvious misstatement. Nevertheless, to say that the effective running of the presidential office was disabled would also be inaccurate and misleading, because the "office," as distinct from the incumbent, was an ongoing agency of government.
This is where persons such as Goodpaster enter the scene, for their tasks become more complicated, decisions become more tentative, coordination more imperative, and overall (including the morale of the spouse and family) a different situation obtains. Goodpaster understood this and adapted himself accordingly. He possessed the gift of being able to subordinate himself to his chief executive's wishes, while at the same time making sure that the running of the office—and for lengthy periods of time this would mean from, literally, a hospital bed—did not suffer more than was necessary. Put another way, what would have been seen as an inconvenience to Eisenhower—albeit a serious one—would have been in fact a major alteration of procedures and scheduling to those persons immediately around him.
Added to this was the fact that Adams was determined that Nixon not be considered primus inter pares among those with direct access to Eisenhower. One of the fears of presidential bureaucratic loyalists is that their chief, in times of crises, would be cast in the shadows by overweening aides, and that would include the vice president. For example, the instruction was that "3. For most items, departments will bring problems to attention of White House Staff before contacting the Vice President. 4. Staff members should take particular care to assure that matters they send for President's attention or signature really require it. 5. Material intended for President's attention or signature should be submitted through Staff Secretary to Governor Adams. 6. Staff members should let Staff Secretary know when they expect to be absent from the city." Furthermore, during the Denver period, Goodpaster penned a note: "On basis guidance from Gov. Adams . . . I will select from State Daily Summary and material sent by CIA (which will be sanitized) material for Denver, and I will send it out over WH [White House] facilities." Clearly, Goodpaster had almost a "choke hold" on communications for the president.
Understandably, it would come as no surprise that those persons closest to Eisenhower would have been thinking what Goodpaster expressed:
"Still, in the back of our minds, there was always the unmentionable dread of a next attack." However, something even more unexpected and less amenable to purely medicinal control occurred.
**The Stroke**
Goodpaster had to perform a different, and perhaps more delicate, form of diplomacy when Eisenhower had what was termed a mild stroke in November 1957. Eisenhower recalled that after experiencing some dizziness,
I sat down quickly and rang for my secretary. As Mrs. Whitman came to my desk I tried to . . . I could not express what I wanted to say. . . . Actually my performance must have been worse than I suspected, for Mrs. Whitman . . . became thoroughly alarmed and called for General Goodpaster.
Andy Goodpaster wasted no time asking questions or making any attempt to diagnose the difficulty. He knew something was wrong and concentrated on getting me to my room in the Mansion. . . . I responded without protest to Goodpaster's grasp of my arm and his urgent, "Mr. President, I think we should get you to bed." . . . Goodpaster helped me to undress and lie down.
John Eisenhower recalled that "on that Monday afternoon, Ann Whitman came into my office on the verge of tears. 'The President has gone back to the house,' she said. 'He tried to tell me something but he couldn't express himself. Something seemed to have happened to him all of a sudden.' When she had called Dr. Snyder the President refused to leave his desk. 'Go away from me,' he tried to say. But Goodpaster had been able to persuade him to leave the office and had walked back to the living quarters with him. . . . 'And just now [Eisenhower] gave up and went home,' she said. 'I can't imagine what's wrong with him.'"
Looking toward the future, Adams
called Nixon on the telephone and explained the situation to him. . . . Then I asked Goodpaster to accompany me while had a talk with Mrs. Eisenhower. . . . While we were talking the President walked casually into the room. He was wearing a long robe over his pajamas and his feet were in bedroom slippers. He smiled at us, as if to let us know that nothing was wrong with him. He started to say something. "I suppose you are dis-" but he stammered, hesitated and then struggled on with the rest of the sentence: ". . . talking about the dinner tonight." We saw that he was trying to talk about the plans for the evening but he was frustrated and getting angry at his inability to form words. "There's nothing the matter with me!" he said finally with effort. "I am perfectly all right!" . . . Flushed and upset, he shook his head abruptly and said, "If I cannot attend to my duties, I am simply going to give up this job. Now that is all there is to it." Then he turned away from us and walked out of the room.
Eisenhower probably came to rely even more on Goodpaster, because "even today, occasionally I reverse syllables in a long word and at times am compelled to speak slowly and cautiously if I am to enunciate correctly. This is not, I am told, particularly noticeable to anyone else, but it certainly is to me."
Goodpaster informed Gen. Lauris Norstad, then NATO supreme allied commander, that "by now you will have seen the reports on the President's condition. To preclude undue concern on your part, let me say that the doctors indicate he is in no danger whatsoever, his general condition is excellent, and he is resting easily and has already improved tremendously. We are much heartened. It is clear, however, that one must assume that he would not attend a NATO meeting in December. Accordingly, the arrangements about which I wrote you must be put in abeyance at least temporarily. I would like to stress that, except for the impairment of speech—which is rapidly decreasing—there is no other impediment whatsoever that is perceptible." Eisenhower's entourage, including Goodpaster, respectfully disagreed. The problem with the aftereffects of a stroke is precisely that they can be imperceptible yet consequential.
Another kind of aftereffect would be Eisenhower's desire to calm down the public (and political) uproar when _Sputniks I_ and _II_ were suddenly launched, thus appearing to give the Soviet Union an edge in the space race. He asked Goodpaster and his speechwriters to craft a series of three addresses to the nation on the general subject of space science, but the third speech had to be cancelled because of his stroke.
Even up to the very conclusion of his presidency, Eisenhower's health remained on everyone's mind, and this included emotional considerations. Immediately after hearing the disappointing results of the 1960 election, Eisenhower recalled: "As I wrote to a friend several weeks later, when I heard the outcome, I felt as though 'I had been hit in the solar plexus with a ball bat,' as though eight years of work had been for naught. It was a low moment, and about all I remember of November 9 is that when I began debating whether to cancel my previously planned trip to Augusta, my staff—and my son in particular—objected violently, almost shoving me aboard the plane. At the moment, I had little spirit to argue. (The doctors, I later learned, had been concerned in the last days that I had temporarily used up all my available earlier reserves in the closing weeks of the campaign.)"
Personality, temperament, opportunity, and competence all play a role in the "mix" of relationships in the hotly competitive and pressure-cooker environment of the White House. Eisenhower, with insight, once remarked, "After a bit of cool reflection, I realized that the cause of the difficulty lay more in my own failure to make myself unmistakably clear than in the failures of others to understand me."
It may be too much to say that as a consequence of these serious illnesses, the relationship between Goodpaster and Eisenhower was gradually evolving into one of at least partial dependency, but it probably isn't too much off the mark.
As for international politics, if the cause for the misalignment of international conferences at the highest level can be attributed to the health of the participants, then perhaps even vital interests might be compromised for reasons having little or nothing to do with the actual negotiating postures.
To put it rhetorically: "In a summit conference the health of the negotiator becomes a significant factor. Could someone suffering from a heart condition withstand the labors of a prolonged summit conference or one hastily called in a dangerous crisis? An upset stomach could leave a president in a poor state to negotiate. If an illness should suddenly strike, will it be considered a diplomatic affliction by others? Dare the statesmen risk postponement after there has been so much preconference publicity?"
Goodpaster would recognize immediately the relevance of this line of consideration to his responsibilities coping with Eisenhower's illnesses.
**Post-Presidency Health Issues**
In the nine years after his presidency, before his death in early 1969, there were several "ups and downs" to Eisenhower's health. In almost every case, Goodpaster was on hand in one way or another, whatever and wherever his assignment.
In Eisenhower's final illness, this story is recounted by Eisenhower's grandson David: "Eisenhower . . . had long ago resolved never to reveal weakness to his wife. With her now, he refused to concede that he was failing. He tried, futilely, to persuade the doctors to withhold news from her about his situation and strictly forbade his wife to speak morbidly. Finally, he conceded. Prone, under the 'bulldozer' life support machine and flanked by [the Surgeon General, Dr. Leonard] Heaton, . . . and several nurses, Eisenhower scolded her for any remorse about their life together. 'Now Mamie,' he growled, 'don't forget that I have always loved you.'"
He asked that the tubes and machines be removed and shortly thereafter, on 28 March 1969, Eisenhower died with his family gathered around or near him. He wanted to end the suffering, which by then appeared to be for no appreciable purpose. Thus concluded Goodpaster's nine years of formal and informal liaison with three of Eisenhower's successor presidents. But Goodpaster's advisory role to future presidents continued well beyond his retirement from active duty.
Finally, it is important to note that Goodpaster's relationship with the president's personal secretary, Ann Whitman, was warm and trustful. They probably bore the burden of most of Eisenhower's lesser day-to-day indispositions as well as his major health setbacks. Behind that ruddy, famous, and endearing grin lay a temperament that was prone to outbursts of irritable frustration and anger. In closing this chapter, offered here is an example of how the three of them shared a concern for each other:
Andy,
This is a perfectly miserable thing to have happen on Christmas day. I am so sorry. [She is referring to the death of Goodpaster's father.]
I'm sure you aren't in the mood to be thanked for everything just now, but I do—mostly for your understanding, for your broad shoulder, and—for the gay and handsome scarf that lifts me out of the two hundred letters that lie ahead of me.
If you don't know, our leader decided to drive to Gettysburg, and for the first time in their history, the secret service had to beg for additional time. He gave them, reluctantly, ten minutes more to produce a driver. He is charged up within an inch of his life and off in a cloud.
Ann
Chapter Ten
The U-2 and Overflights
"For the first time since Independence, the United States government had publicly admitted that it had committed espionage in peace-time and deceived the world about it."
—MICHAEL R. BESCHLOSS, _Mayday: Eisenhower, Khrushchev, and the U-2 Affair_
Without a doubt, the technological innovation of the U-2 spy plane, which promised to help break the American impasse with the Soviet Union over the problem of inspection and verification of its nuclear arsenal, ended in a diplomatic disaster. To put it mildly, it ruined Eisenhower's hoped-for triumphal conclusion to his presidency. In many books recounting this episode, the word "incident" is used—a euphemism if ever there was one.
**The Justification**
Eisenhower's reason for initiating research on both aerial reconnaissance and photography was to "give us information about what the Soviets had, and to some extent, what they did not have. And also it would be very useful to see if there was any massing of troops that could be used for surprise attack." Then, the president continued: "When the Soviets rejected my Open Skies proposal in 1955 I decided that more intelligence about their war-making capabilities was a necessity. So I directed that we would begin aerial reconnaissance, making use of the then relatively invulnerable, high-flying U-2 aircraft. . . . From 1956 onward its basic mission was to provide us with current information on the status of the Soviet missile and armaments programs."
As usual, Goodpaster was at the center of things. In 1954 he had penned: "Authorization was sought from the President to go ahead on a program to produce thirty special high performance aircraft at a cost of about $35 million. . . . The President directed those present to go ahead and get the equipment, but before initiating operations to come in for one last look at the plane." It was his job to coordinate this highly secret spying activity with the CIA, which had the operational responsibility. Goodpaster explained, "I served as Eisenhower's liaison with the CIA with regard to the whole U-2 program, and assisted him in considering the proposals for each of the flights. When the final flight went down, I just have to say that we handled the situation in a very miserable and unsatisfactory way. We had not thought through the use of a cover story, looking at all the what-ifs that we should have considered." This was odd, considering the stakes involved.
Eisenhower gave full support to the work of the CIA, which also meant, of course, that Goodpaster as the White House liaison with the CIA was fully in the picture as well. "In fact, because the administration focused heavily on covert operations, countless conversations took place behind permanently closed doors." To recall: "To the extent that their busy schedules permitted, [Eisenhower and John Foster Dulles] ended the day by meeting in the Oval Office, mostly alone but sometimes joined by Central Intelligence Agency (CIA) director Allen Dulles, or one or two others." It can safely be inferred that Goodpaster was one of those "other" persons who were present, although he was excluded from the sessions of just the two of them because Dulles preferred that no notes be taken. When Christian Herter succeeded Dulles as secretary of state, Goodpaster became a regular attendee.
To illustrate how central Goodpaster was: "In a meeting Eisenhower held with Secretary of Defense Neil McElroy, Richard Bissell of the CIA, and Goodpaster on 7 April 1959, covering various reconnaissance flights and related matters, Goodpaster recorded: 'Earlier the President had discussed this matter [reconnaissance flights to gather information on the Soviet missile program] at length with me. In response to his request for my advice, I analyzed the proposal as to the importance of possible costs and possible gains.'" How more central to presidential decision-making could he have been?
Eisenhower always kept in mind the budgetary outlays and the consequences. One of his motives was to use the information obtained from the U-2 to verify the various alarmist claims being put forth by the armed services to justify ever-larger budgets and weapons acquisitions. For each flight that was approved, Eisenhower insisted on knowing what were the reasons for doing it and how useful was the information, both in terms of knowing what the Soviets were doing, and how it would affect the many pressures that were being exerted by the military establishment.
Goodpaster as a West Point Cadet
In a brace
With NATO's first supreme allied commander
SACEUR with the family
Secretary of State George C. Marshall in his office
With "The Boss"
With Eisenhower at London dinner for Churchill (Goodpaster at top right)
Maj. Gen. Goodpaster receiving parachutist's badge
As NATO SACEUR, reviewing the troops
Official photo as SACEUR
With Mrs. Goodpaster (second from right) in the Marshall Foundation Library
Goodpaster later pointed out that when an overflight was brought in for approval, "we kept necessary informal notes, but my recollection is that we did not write up an official permanent record on those. Those were regarded as too sensitive and the knowledge of those was very, very closely restricted." In addition, Eisenhower assembled a small consultative group, which had as its members the secretaries of state and defense, the JCS chairman, the CIA director, and Richard Bissell.
**Bureaucratic Momentum**
Secretary of State Dulles considered that "Richard Bissell Jr. was one of the rising stars of the CIA. A tall, amiable, cultivated man, with an interest in ornithology, sailing, and ecology—all pursuits that the top echelons of the Agency strongly approved—he had previously worked for the Marshall Plan in Germany and the Ford Foundation in Washington. He had known Allen Dulles since 1948, was a friend of Frank Wisner, and had first met Foster when Eleanor threw a party at McLean for her brothers, Vice President Nixon, Bob Bowie, and other members of the administration."
Bissell, who believed that covert operations should be the prime function of the CIA, was appointed deputy director for plans (DDP) in 1958, replacing Wisner (who had suffered a mental breakdown). Bissell's deputy was Richard Helms. In other words, the person who had been placed in charge of developing and operating the most technologically superior instrument of aerial espionage—the U-2—was virtually a novice in the business. Furthermore, by that time, DDP reportedly controlled over half the CIA's budget and was responsible for what was known as the CIA's black operations.
Even more puzzling, if not alarming, "part of Bissell's job description was to develop new espionage technologies, including the authority to give a bureaucratic jolt to promising projects through funding and management support. His office became a hothouse for ideas and was responsible for the U-2 spy plane and, later, spy satellites." Even with all of this bureaucratic energy devoted to the technology of spying, Eisenhower believed that "only spies, not gadgets, could tell him about Soviet intent to attack."
After the plane—little more than a jet-propelled glider—had proven airworthy, arrangements were made to base it in Wiesbaden.
They were now ready to go. Bissell alerted Allen, who in turn informed his brother. A meeting was held in the White House in the spring of 1956 at which Bissell laid out his plans for a number of flights over Russia. He was told to wait outside while the President discussed them with Allen, Foster, and his military secretary, General Andrew Goodpaster. Presently, Goodpaster came out and said to Bissell, "Well, you've been authorized to conduct overflights for two weeks." "I hope that means fourteen days of good weather," Bissell said. "In other words, bad days don't count." "It doesn't mean anything of the kind," Goodpaster said. "It means two weeks. You're free to go for two weeks."
Eisenhower also could draw upon his military background and experience in war to shape his attitude toward these very expensive as well as diplomatically dangerous overflights. Bissell, for example, noted that "Andy Goodpaster sees Eisenhower's military background—his experience as a field commander and the importance of intelligence when he was supreme allied commander—as influencing his interest in and active management of the U-2 project. His understanding of the various intelligence disciplines made him acutely sensitive to the critical role U-2 intelligence could play in maintaining national security. . . . Almost every morning, Goodpaster used the CIA's overnight intelligence report to brief him. . . . He would then take this information and fit it into a worldview that had been shaped by years of 'reviewing and studying and pondering.'"
**The Ill-Fated Flight of 1 May**
The rationale was: "Eisenhower approved another U-2 flight even though the summit conference could be endangered. There was fear lest a détente be reached at the Paris [four-power summit] meeting which might lead to a permanent grounding of the U-2 planes. Because this might be the last flight, one more mission ought to be attempted. The Central Intelligence Agency had information that a new Soviet rocket rested on its launching pad near Sverdlovsk. [Francis Gary] Powers's mission would be to photograph this rocket." As the world came to learn, Powers' plane was shot down; he parachuted to the ground and was captured. No amount of dissimulation could hide the fact that the United States had been caught publicly engaging in aerial espionage over the Soviet Union (and China) for several years.
It should be no surprise that in 1960 "the president and Dick Bissell were locked in an increasingly intense struggle over the control of one of the biggest secrets of all—the U-2 spy plane. Eisenhower had not allowed any flights over Soviet terrain since his talks with Khrushchev at Camp David six months earlier. Khrushchev had returned from Washington praising the president's courage in seeking peaceful coexistence. Eisenhower wants the 'Spirit of Camp David' to be his legacy." That legacy was soon to be destroyed.
Along the way, this entire matter of testing and verification was causing deep discomfort at the highest levels within the administration—and particularly between the State Department and the Atomic Energy Commission. This was especially so in regard to the notion of ceasing testing altogether, including underground. As the journalist Arthur Krock recounted, Eisenhower held a meeting on Thursday, March 24, 1960. "Secretary of the Air Force James H. Douglas, and Gordon Gray, Eisenhower's special assistant on national security matters, and other insiders [presumably including Goodpaster]" along with Christian Herter, the secretary of state, were all in attendance. In an already tense atmosphere, John A. McCone, the chairman of the Atomic Energy Commission, "strongly argued" for continuing the U.S. "show me" policy when it came to inspections and the dangers associated with an extended moratorium on underground nuclear testing. The president, however,
pounded the table and said he intended to follow Herter's counsel in favor of taking these ventures. Later he calmed down, but his rebuke to McCone scared the Pentagon also into silence.
At the same meeting, the President directed that any speeches on the subject be approved by Herter's department. McCone, who was flying that afternoon to make such a speech in Los Angeles, left his transcript behind for Herter's inspection. When he got to Los Angeles an AEC aide informed him Herter had flatly vetoed the whole speech. McCone got Herter on the telephone, but the Secretary would say only that he had sent the speech to the White House and would have no more to do with it.
McCone then got in touch with Col. Goodpaster of the White House staff who told him the speech was "out." Then, inquired McCone, does this mean we have changed our test policy entirely? McCone's reaction must have induced second thoughts at the White House, because soon afterward Goodpaster phoned McCone to say that if he would put in one sentence estimating the Soviet proposal as "hopeful," the remainder would be acceptable. McCone put in the sentence and delivered the speech as written.
This was hardly the first time that dissension had arisen over the risks and benefits of overflights over the Soviet Union. For example, after the U-2 flights had been suspended, the Air Force pushed for using the RB-57D in its stead. After receiving assurances that the Russians would not detect such flights, Eisenhower agreed. When this assurance proved misplaced, "Eisenhower, according to Allen Dulles, was furious . . . he said he was going to 'order a complete stoppage of the entire business.' He instructed Colonel Goodpaster to call Secretary of Defense Wilson, JCS chair Radford, and DCI [Director of Central Intelligence] Dulles and inform them that, effective immediately, there were to be no flights of U.S. reconnaissance aircraft over Iron Curtain countries. Each man confirmed that he understood."
As later events confirmed, the pressure to overfly did not diminish. After the downing of Powers and its attendant embarrassments, the overflight procedures were changed but the flights themselves had not been discontinued:
One of the most important changes in the overflight program after the loss of Francis Gary Powers's U-2 was the institution of more formal procedures for the approval of U-2 missions. During the first four years of U-2 activity, very few members of the Eisenhower administration had been involved in making decisions concerning the overflight program. The President personally authorized all flights over the Soviet Union and was consulted by Richard Bissell and either the DCI or the DDCI [deputy director of central intelligence] about each proposed mission. In addition to CIA officials, the President's discussions of individual U-2 missions or of the program as a whole generally included the Secretary of State or his Under Secretary, the Chairman of the Joint Chiefs of Staff, the Secretary of Defense or his deputy, and the President's secretary, Colonel (later General) Goodpaster.
The approval process under President Eisenhower was thus very unstructured. There was no formal approval body charged with reviewing overflight proposals; the President kept this authority in his hands and simply consulted with selected cabinet officials and advisers before reaching a decision.
Eisenhower had anticipated this situation as early as 1956:
After the election he authorized additional flights. The Soviets protested privately but strongly. On November 15, Eisenhower met with Herbert Hoover [II], [Admiral] Radford, and Allen Dulles to discuss the flights. Eisenhower thought that they were beginning to "cost more than we gain in the form of solid information." Hoover pointed out that "if we lost a plane at this stage, it would be almost catastrophic." Eisenhower agreed, and added "Everyone in the world says that in the last six weeks, [because of its reaction to the Suez crisis] the [United States] has gained a place it hasn't held since World War II." The country had to "preserve a place that is correct and moral."
**The Overall Setting**
Building on "the Spirit of Camp David," Eisenhower agreed to attend a four-power summit in Paris in May 1960. It was to be the crowning achievement of his foreign policy, even if there were no dramatic breakthroughs over such a thorny question as Berlin. Consequently, "never was there a worse time for the President to be forced to take responsibility for an espionage affair, no matter how many may have been informed of the mission. . . . [Allen] Dulles considered that one more flight was so important that it should take precedence over foreign policy. . . . In Washington, the U-2 no longer served American foreign policy. Instead, national policy was endangered for the sake of the U-2. Intelligence gathering had become important for its own sake." In contrast: "In a revealing moment, [Eisenhower] remarked that nothing would make him 'request authority to declare war more quickly than violation of our air space by Soviet aircraft.'"
By this time John Foster Dulles had died and was replaced by Christian Herter. Bissell commented later that "I would have thought that, if they wanted, they could have got the maximum propaganda advantage out of shooting down the plane. . . . It was a misreading of the situation which, one suspects, Foster Dulles would never have made. . . . A more percipient man than Eisenhower would have guessed that they would try to get out of the summit. A more experienced Secretary of State would have warned him that there were crises coming. A more alert Director of Central Intelligence would have warned his deputies to stay away from all anti-Soviet provocations until the summit was over."
Before Eisenhower left Washington for Paris, word had come in that Powers was shot down on the Communists' celebrated May Day. Eisenhower was at his Gettysburg farm when the unfortunate event took place, so it was left to Goodpaster to pass the bad news to him.
Bissell's hindsight was better than his foresight. Both symbolically and propagandistically, the timing could not have been worse. It seems obvious that sending Powers aloft posed an excessive risk, unless the summit itself was considered expendable, which from all appearances appeared unlikely. As mentioned, summits in general are surrounded with skepticism, even cynicism. Yet for Eisenhower, this one—if for no other reason—would be an occasion to celebrate the culmination of his extraordinary career of wartime and subsequent public service. To be caught up in such a major embarrassment had to be devastating for him as well as for those persons closest to him, Goodpaster in particular.
History had not yet given its initial assessment of Eisenhower's handling of the Cold War as president. But his ability to use his personality, or public persona, to engage adversaries as well as allies in mutually rewarding endeavors was already well-recognized. There is a photograph of Eisenhower taking leave of his official French hosts after the failure of the summit. Goodpaster, famous briefcase in hand, is exiting along with him, illustrating why Goodpaster's near-constant presence had come to be taken for granted, and thus rendering him even more effective as the end of their official time together drew closer.
John Eisenhower recalled: "Monday morning, May second, General Goodpaster told me about the plane going down. He and I both were cleared for the U-2 project. Our only reaction was just feeling sorry for the pilot, and that was about all there was to it because we were assured that nobody would ever be taken alive." Later, President Eisenhower commented: "My acknowledgment of responsibility for espionage activities was practically unprecedented in history, but so were the circumstances." On 5 May, during a meeting of the Security Council, "General Goodpaster, with the missing U-2 very much on his mind, got up and left the meeting to arrange for the complete text [of Khrushchev's statement to the Supreme Soviet] to be sent to us by secret teletype."
The consequence was that "[Eisenhower] knew that at such a summit there would be no sign, even on the surface, of geniality. . . . By no means did I intend, at the forthcoming conference, I told them [President Charles de Gaulle and Harold Macmillan, the British prime minister], to raise my hand and swear that we would never again do anything in the field of espionage. I would not permanently tie the hands of the United States government for the single purpose of saving a conference."
This sounds a bit self-serving, as the United States had just been caught dissimulating over an intelligence activity, so why could not Eisenhower have made the promise, which would not have tied the hands of his successor, who would be in place in a matter of months? Goodpaster would not, in his oral interviews, claim that "plausible denial" dictated that covert operations carried on during the Eisenhower years were not specifically authorized by the president. The flights of the U-2 were an exception, where Eisenhower, after tentatively trying to employ plausible denial, took personal responsibility (as did President Kennedy over the Bay of Pigs covert disaster). As Richard Helms commented, in testifying before Congress: "I just think we all had the feeling that we're hired out to keep those things out of the Oval Office."
The timing of the U-2 crash could not have been worse, for virtually all the senior members of the administration, including Eisenhower, were going through an emergency exercise in case of a direct attack on Washington. They were gathered at a "secret command center dug deep into Mount Weather in the Blue Ridge Mountains and built on a series of giant nuclear shock-absorbing steel springs. Its code name was High Point, but members of the president's inner circle also called it simply 'the hideout.'"
This inner circle gathered at the bunker to decide how to handle Chairman Khrushchev's claims. After five days of silence from Moscow, "the Soviets were not only taking credit for blasting the spy plane out of the sky with a missile, they were pointing the finger of responsibility directly at the president." Assuming that all Khrushchev had was a dead pilot and 'a stack of scrap metal,' the men in the bunker decided to stick with the NASA weather plane story, especially given that Allen Dulles had given the White House 'absolutely categorical' assurances that a U-2 pilot would never survive a crash." Later, "top Eisenhower aide Andrew Goodpaster [commented] that 'we had an understanding . . . that the plane would be destroyed and that it was impossible for the pilot to survive.'"
A "wall of lies" now began to be constructed to shield Eisenhower from confessing to direct responsibility, and this must have been agonizing to Goodpaster. He had had to pass the word that "the president wants no specific ties to him of this particular event." After all, career officers had been taught from their earliest days to "stick to the facts" and leave the interpretation to others. Unfortunately, it was the facts that were being reinterpreted, until finally the façade could no longer be sustained when Powers was produced and parts of the downed plane were placed on display in Red Square.
Khrushchev observed: "It was as though the Americans had deliberately tried to place a time bomb under the meeting." Before he left for Paris, Eisenhower met with Herter and Goodpaster in his office and "told them in no uncertain terms that all further U-2 overflights of the USSR would cease. 'Inform Allen Dulles,' he said abruptly. The next day Eisenhower was to depart for Paris and a long-awaited summit conference with Khrushchev. He wanted no more surprises."
It also turned out that, ironically, Eisenhower's method of dealing with problems—through indirection rather than otherwise—worked to his disadvantage in this, possibly the greatest embarrassment for the United States in the Cold War period. His style was described thus:
Visible leadership on the outside, persistent and continuing presidential pressure on the inside. . . . But this was not the way Eisenhower operated. His approach was successful in maintaining his public popularity and in retaining the loyalty and respect of senior officials within the government. It prevented, presumably, any number of unwise actions. It contributed, however, to his administration's disappointing conclusion. Eisenhower relied upon an organizational approach to addressing issues of a national security nature, and on the whole it served his purposes well. But he also understood that flexibility was needed to address both complexity and unexpected events.
Allen Dulles defended the use of the U-2 as an espionage tool:
It is extremely difficult for me to sum up in words the significance of the effort to our national security. I do not wish to exaggerate, nor do I wish to belittle other vital intelligence programs. The photographic coverage and the data derived from it are an inseparable part of the whole national intelligence effort. But in terms of reliability, of precision, of access to otherwise inaccessible installations, its contribution has been unique. And in the opinion of the military, of the scientists, and of the other senior officials responsible for our national security it has been, to put it simply, invaluable.
Just as the Eisenhower administration was winding up its affairs, another spy scandal involving the Soviet Union broke out. The Strategic Air Command had been flying reconnaissance flights using the RB-47H. On 1 July 1960 an electronic intelligence-communications intelligence (ELINT-COMINT) flight was shot down near the Soviet Union, although the United States claimed it was over international waters. The crew of six, from the 55th Strategic Reconnaissance Wing, were captured. Only two crew members survived. "The Soviets' immediate protest of an incursion infuriated President Eisenhower. He ordered an investigation to see if the plane had actually crossed into the Soviet Union as the protest note indicated. The initial investigation revealed that the flight was over international waters about seventy miles north of the Soviet border when it was shot down. . . . Khrushchev refused to return [the two survivors] as a protest of the U-2 and other overflights."
John Eisenhower, as assistant staff secretary, forwarded to the president a joint memorandum from the secretaries of state and defense that delineated the American response to this further embarrassment: "Following State-Defense study of the problem, we have concluded that the unilateral military measures listed in the enclosure might be effective in obtaining the release of the RB-47 officers if diplomatic measures continue to be unavailing. We have rejected as unpromising at this time economic and cultural measures and measures involving cooperation of our allies. . . . We think that our efforts to date have had some success in impressing upon the Soviets the connection between the release of the officers and the prospects for improving relations with the U.S. or indeed of entering into negotiations with us."
Partly as a consequence, "on August 9 the president summoned Allen Dulles, [Ambassador] Livingston Merchant, General [Nathan] Twining, Gen. John Persons, Gen. Robert Breitweiser, General Goodpaster, and Col. John Eisenhower to discuss the resumption of COMINT-ELINT flights. . . . Before he left office, he decided to pull all the Air Force, Navy, and special reconnaissance activity together under the Joint Chiefs of Staff to provide effective and unified operational control and coordination of all flights. . . . The Joint Reconnaissance Center became operational before Eisenhower left office on January 16."
It is worth noting here, however, that the American and Soviet conceptions of "negotiations" had become very divergent. Whereas Eisenhower and his foreign policy advisers conceived of heads-of-state conferences as a useful diplomatic tool to help narrow the differences between the superpowers during the Cold War, the Soviet Union under Khrushchev had a different motive.
These conferences all too often were purposely used by Khrushchev as occasions to discredit the "warmongering" Americans and to propagandize the Soviets as "peace advocates." Generally speaking, "in the postwar summit meetings too little attention has been paid to purpose and content; the conferences tended to become charades that would save the world. . . . At the Paris Summit Conference of 1960, four statesmen could not negotiate because of one U-2 plane that had been shot out of the sky."
Above all else, it was indeed wretched for Eisenhower that he had to defend the clumsy U-2 espionage failure as his presidency drew to a conclusion. As his science adviser, Dr. George Kistiakowsky, remarked: "Eisenhower began to talk with much feeling about how he had concentrated his efforts the last few years on ending the cold war, how he felt that he was making big progress, and how the stupid U-2 mess had spoiled all his efforts. He ended very sadly that he saw nothing worthwhile left for him to do."
Part III
Arrival at the Top
Chapter Eleven
Deputy Commander and Commander-Designate in Vietnam
"Having fought the fight, lost 50,000 of our young people . . . having in hand a situation that could be sustained in much the same way as Korea . . . all of that was cast away. . . . And that's the ultimate tragedy of Vietnam in my view."
—GEN. ANDREW J. GOODPASTER
Like most of his contemporaries, Goodpaster viewed experience as a combat commander as the true measure of his capabilities as a career Army officer. The fact that early in his career he jumped from the usual assignments as a junior officer to occupying the ultimate staff position of his generation in the Eisenhower White House did not sway him from that belief.
Although his tour was brief in terms of his overall career assignments, Goodpaster regarded being promoted to four-star rank and assigned as deputy commander in Vietnam in 1968, with the clear prospect of becoming commander, as the true consummation of his career. Before this, having served as director of the Joint Staff under the aegis of the Joint Chiefs of Staff, along with other JCS-related assignments, had made him very much professionally engaged in the planning aspects of that unfortunate war.
For example: "At this point, the Joint Chiefs of Staff were tasked by [Robert] McNamara to come up with a comprehensive strategic review of the Vietnam situation to determine what assurance the United States could have of winning the war 'if we do everything we can.' Lt. Gen. Andrew J. Goodpaster was put in charge of an ad hoc staff group to conduct the study. The resulting 'concept and appraisal,' completed in less than two weeks, indicated that victory was possible given the establishment of a military force capable of seizing and retaining the initiative." Goodpaster then inserted this significant caveat: "Within the boundaries of reasonable assumptions . . . there appears to be no reason we cannot win if such is our will . . . and if that will is manifested in strategy and tactical operations."
Goodpaster in particular must have been reminded about Eisenhower's advice to him: "The United States was 'not going to be run out of a country we helped to establish.' Since the President [Lyndon Johnson] had 'appealed to force,' the United States 'must win.'"
Eisenhower, from Gettysburg, was not reluctant in expressing his thoughts concerning the ebb and flow of a conflict that defied an easy definition or a simple solution. For example: "Through General Andrew Goodpaster, now secretary of the Joint Chiefs of Staff, Johnson kept Eisenhower informed in advance of bombing halts and troop level increases and his efforts to enlist allied support and to open conversations with the communists." Eisenhower urged Johnson not to give away gratuitously the option of negotiating an end to a war that seemed to be becoming crippled more by domestic than purely military conditions.
Goodpaster and his JCS colleagues had defined the Vietnam problem as a military problem, requiring a military solution, thus favoring escalation as a means toward a negotiated victory. They promised that escalation could bring victory nearer. There was also the opinion that the JCS should have been more aggressive in advocating its views as to how to conduct the war, rather than leaving the policy initiative to the McNamara "Whiz Kids." In their defense, the JCS claimed with some justification that they were shut out of the policy debate. It was reported that "the president's deep distrust of his senior military officers manifested itself in exclusive advisory forums that limited JCS access to the president."
In any event, Goodpaster's JCS role placed him squarely among the often bitter clashes of policy, whether among the military leadership or between the military and the civilian leadership. He ultimately came down on the side that drew the conclusion that "the Vietnam War had been lost at home by incremental policy decisions and mismanagement." Goodpaster shared the previously unthinkable realization that "few would deny that the United States was a vastly more powerful state than North Vietnam, yet the weaker state was able to defeat the stronger in the Vietnam War (1965–72) because non-material factors trumped the balance of power."
The seemingly endless escalation on the battlefield had brought with it, in the American public's eyes, an escalation in the perception of what constituted an acceptable (or even "honorable") victory. Complicating matters was that by the time Goodpaster took up his command in 1968, to accept a stalemate would have been tantamount to humiliating failure; to the enemy it would have represented a stepping-stone to complete success.
**A Battlefield Commander**
Goodpaster succeeded Gen. Creighton Abrams as deputy commander, U.S. Military Assistance Command, Vietnam. Abrams, in turn, had replaced Gen. William Westmoreland as commander, U.S. Military Assistance Command, Vietnam (COMUSMACV), when Westmoreland became Army chief of staff. As deputy, Goodpaster would serve as acting COMUSMACV in Abrams' absence. Goodpaster's most noteworthy action was to implement the order from Washington to halt the bombing campaign. "By that time," Goodpaster said, "we'd come to the judgment . . . that we could accommodate this, that the situation of our military operations had gone far enough so that this would not have any damage to us that we couldn't manage quite well."
Goodpaster might have felt that way, but Washington was by no means completely convinced. Clark Clifford, who had succeeded a self-doubting Robert McNamara as secretary of defense, had by then turned against the war. In a private meeting of senior officials in March 1967, Clifford "had called for a 'reduced strategy' of a bombing halt or a reduction in bombing of the north, abandonment of isolated military positions, and a new ground strategy that used U.S. troops as a shield around populated areas in order to give the South Vietnamese time to assume the burden of the war." "When asked by Clifford if a military victory could be won, [Ambassador Philip] Habib answered, 'Not under the present circumstances.' 'What would you do?' Clifford asked. 'Stop bombing and negotiate,' Habib replied."
Furthermore, Johnson's self-imposed war-making limitations had skewed a central strategic aspect of war. Goodpaster recognized this as the enemy's center of gravity. "We had adopted a strategy that focused on none of the possible North Vietnamese centers of gravity—their army, their capital, the army of their protector, the community of interest with their allies, or public opinion. . . . Instead, by seeing the Viet Cong as a separate entity rather than as an instrument of North Vietnam, we chose a center of gravity which in fact did not exist. The proof that the Viet Cong guerrillas were not a center of gravity was demonstrated during Tet-68, when, even though the enemy had incurred huge losses, the war continued unabated."
At the operational level, Goodpaster described where the friction lay: "In Vietnam, the relationship between the civilian leadership there under Ambassador Ellsworth Bunker and a couple of really very able assistants that he had and our military leadership was very close and very positive. The division was between those who were out there on the ground and the high leadership back in Washington."
Goodpaster had experienced firsthand the taste of this division when, before taking up his Vietnam assignment, he was a member of the American delegation to the ill-fated Vietnam peace talks in Paris. The incident is worth reporting in full:
Harriman did indeed get the Paris assignment, being posted there in May 1968 with Cyrus Vance as his deputy, Phillip Habib as political advisor, and Lieutenant General Andrew J. Goodpaster as JCS representative. Potential problems surfaced as early as the plane ride to Europe—indeed, even before the mission began—recalled Goodpaster. "From the outset, Governor Harriman tried to get approval for offering a 'scaling back' of our military operations in Vietnam as a negotiating gambit with the North Vietnamese, hoping they would reciprocate. I opposed this at all times, beginning with our delegation's meeting with President Johnson, who disapproved Governor Harriman's proposal, and approved my position."
But Harriman apparently had no intention of being constrained by anything as mundane as instructions from the President. Soon after the delegation's aircraft departed Washington, he offered the view that "now it's our job to end this war—to get the best terms we can, but to end the war." Goodpaster immediately objected. "That's not my understanding," he retorted, recalling LBJ's statement that the delegation was to negotiate, but not in any way compromise, the "maximum pressure" he wanted put on the enemy. "That's not right, General," Harriman countered. "I think it's clear what our position is—what the president ordered."
In this instance, true to form, Goodpaster insisted that the president's instructions be closely adhered to: "Goodpaster would not be intimidated. 'No, sir,' he shot back. 'The president would not want us to endanger American lives. We have not been instructed to end the war on the "best terms we can."' By this time the autocratic Harriman, not accustomed to being contradicted, was angry. 'We're going to end this war,' he insisted. 'That's what the president said we should do.' Goodpaster had the last word. 'Sir,' he said in acid tones, 'that is not what the president said. Those are _not_ [Goodpaster's emphasis] our instructions.'"
**What Is "Victory"?**
In sharp contrast, Goodpaster and Abrams were in complete harmony as to the strategic concept. As Goodpaster said—reflecting the Army view: "We did not have clear guidance from the national level but we worked up our own overall strategic plan. . . . My ideas coincided completely with those of General Abrams. . . . I found that the situation was extremely well assessed."
This is not surprising, because in 1965 their strategic concept had been developed in the Pentagon by Goodpaster and his colleagues. Their study influenced the thinking of senior Army leaders. A variation, known as PROVN (Program for the Pacification and Long-Term Development of Vietnam), was then being implemented. Also noteworthy was that Goodpaster's approach was at variance with General Westmoreland's notion of "search and destroy." PROVN became an inspiration for village-level pacification efforts intended to ensure that the South Vietnamese could resist the constant pressure from the Vietcong.
The concept essentially argued that the "Vietnamization" of the war was a realistic objective, given enough consistent American support. South Vietnam was divided into four zones, with each zone adapted to the local conditions. Overall, this meant attacking the supply routes both within and outside of the country. Within the four zones, air support, including in particular logistics for both the South Vietnamese as well as the American forces, depended upon CIA air drops and secure landing areas. Thus, the CIA was playing an important role in attempts to gain control over the supply routes of the North Vietnamese, and in particular the Ho Chi Minh Trail that led through Laos.
This was a matter of great concern to Goodpaster, given that his specific duties were twofold. One was to travel to the units to observe through briefings how the situations in both the American and Vietnamese areas of responsibility (i.e., combat areas) were going; he would report on what he saw and heard in his weekly meetings with Abrams. Goodpaster's other major responsibility was the training of the South Vietnamese local and regional forces, upon which hinged the success of Vietnamization.
Overall, Goodpaster felt that the "conduct of the war was going well"—referring to Vietnam, however, and not Washington. It was estimated that "the successful pacification program, one repeatedly cited in enemy communications as a threat that had to be countered, was extending not only security but also elected government, trained hamlet and village officials, and economic gains to most of the population."
A related argument could be made that just when the Abrams-Goodpaster strategy was being implemented to bring about a favorable resolution of the conflict—which meant putting in place a pro-Western democratically elected government—the domestic political situation in the United States further hampered such efforts. The split between the civilian and military leadership cadres was getting deeper, with a growing doubt that the war, even assuming it could be won, would result in a victory worth the expenditure, not only in troops and matérial, but also in national honor. For example, Dean Acheson, responding to a statement from JCS chairman Gen. Earle Wheeler that "the Pentagon was not bent on a 'classic military victory,' . . . but only helping the Vietnamese to avoid a Communist victory," declared that Wheeler was simply using semantics to justify the presence of a half million American soldiers.
In other words, the term "victory" had itself lost much of its currency as a justification for continuing the war, and this situation was increasingly compatible with general domestic public opinion. "The American public's attitude seemed to be, 'Either get in or get out,' and there was little taste for negotiations, which appeared to be either useless or a betrayal of how the war had been displayed during the earlier years of escalation."
The level of frustration both politically domestically (win or get out) and militarily in Vietnam (give us the means and the time) had never been higher than while Goodpaster was deputy commander. Even though the "clear and hold" concept had replaced Westmoreland's "search and destroy" concept as to how to conduct the war in the countryside, it could not be a war-winning strategy; it could serve by then only as a basis for a negotiated "honorable" withdrawal. Although the transition in strategy from Westmoreland to Abrams was symbolized by these two terms, to the American public it simply appeared that one dubious slogan had been substituted for another. Regrettably for the historical record, Goodpaster's approach appeared to be catching hold under Abrams, but by then it was too late, politically speaking.
How Goodpaster could still draw a conclusion that his mission was achievable, after having demonstrated in his previous assignments that he could "think strategically" as well as tactically, is puzzling. Surely, analytically, he could recognize that
the difficulties of fighting the war on terms disadvantageous to the United States' real military strengths reflected a larger political problem—the discrepancy between the means and ends (as Clausewitz might have put it). The North Vietnamese and the Vietcong were fighting for what they believed in very strongly; those who were not were undoubtedly subject to the discipline of a totalitarian, passionately nationalistic regime. The South Vietnamese governing system, by contrast, appeared corrupt, unpopular, and in a distinct minority, opposed by the Buddhist monks, unsupported by a frightened, exploited, and war-weary peasantry; those native units loyal to the regime and who often fought well were not sufficient to compensate for this inner corrosion.
Fortunately, Goodpaster was not directly involved in Vietnam long enough to have his career tarred by the Vietnam brush of perceived failure. "In Vietnam, General Fred Weyand reported for duty as deputy to Abrams. 'What's the mission?' he asked. 'Who the hell knows?' Abrams retorted. 'You know what has to be done. I know what has to be done. Let's get on with it.'"
Battlefield conditions did not rattle him any more than did service in staff assignments. It is worth recalling an interesting episode reported by the military historian Lewis Sorley: "At a Harvard lecture series given in 1967 by McGeorge Bundy, Bundy asked Dr. Edwin Deagle [who later was to write about Abe Lincoln] what he thought should have been General Westmoreland's assignment after Vietnam. Deagle responded: 'You should not make General Westmoreland Chief of Staff of the Army, as he will have to go to great lengths to justify his record. Make him the new NATO commander, where he will have no responsibility for Vietnam policy. The chief of staff should be General Andrew Goodpaster, who is brilliant and wise in the ways of Washington.'" Instead, of course, Westmoreland went to Washington, where his professional integrity was in doubt, and Goodpaster went to NATO, with his integrity intact.
Clearly, Goodpaster was caught up in the almost total national fixation on the use or misuse, or the unilaterally conditional employment, of American political-military power in Southeast Asia, which was at that time serving as the cockpit for the Cold War superpower rivalry. In American eyes, this meant a rivalry with a Sino-Soviet "bloc," which in fact had been rapidly deteriorating into its own form of Great Power competition. In contrast, the European "front" of the Cold War had been largely stabilized by the late 1960s, and the Afro-Asian "third world" was still evolving out of its recent decolonization.
Chapter Twelve
As NATO Supreme Allied Commander
"For human activity is complex, human motives exceedingly mixed."
—ALDOUS HUXLEY, _Ends and Means_
The two most coveted assignments before retirement for the most senior
Army officers were chief of staff and NATO supreme allied commander. How and why Goodpaster came to the NATO position rather than the other post was linked to the fact that in the years since his time as a lower-ranking officer in the Eisenhower White House, he had become, willy-nilly, a widely respected "wise man" and adviser to presidents.
**Goodpaster Arrives at SHAPE**
Goodpaster became SACEUR on 1 July 1969. As was customary, he first became U.S. commander-in-chief, European command, in his national role, and thereafter he assumed his multinational command as SACEUR. There was also a third "hat" called Live Oak that was not talked about openly.
As SACEUR, he worked within the framework of multinational institutions to the extent considered compatible with American foreign policy and national security interests. Certainly Eisenhower believed in this approach. His own experience commanding a multinational army in World War II and in initiating similar principles of political cooperation in the formation of NATO's military arm had inescapably defined the position.
Likewise, Goodpaster also had had extensive exposure to the multilateral approach to framing American military policy, having served at different times at the United Nations as well as at NATO in its formative years. In summary, Goodpaster had already played a role that was compatible with both his beliefs (peace is preferable to war under defined circumstances) and his career interests.
He seemed to embody the best aspects of leadership, as expressed in their different ways by his two immediate predecessors, Gen. Lauris Norstad and Gen. Lyman Lemnitzer. Norstad was handsome, innovative, and sensitive to public relations. Lemnitzer was solid, reliable, cautious. Goodpaster was tall, trim, gray-haired, and spectacled, and in addition, he appeared to have a more reflective temperament than most generals. He had a quietly persuasive manner; bellicosity was not his style.
Goodpaster also understood very well this observation by Gen. Alfred Gruenther, an even earlier SACEUR: "I am not really worried about governments. They believe in NATO, and have no thought of scuttling the organization. However, no government does much about keeping the subject alive with the people. That takes effort and imagination, and a lot of time." Further, Goodpaster was quick to recognize that the SACEUR's effectiveness depended on political factors as much as military expertise. He was already aware, of course, having served so many years in and around the political leadership in Washington, that to realize fully the role of SACEUR would require from him adroit political talents. He certainly understood that "consultations with Europe are neither simple in execution nor a panacea for our deeper differences: the process is fraught with as many complexities as are the issues."
The general setting would have been obvious to Goodpaster—especially given his close ties with Nixon and Kissinger: "It was geopolitical decline that preoccupied the architects of U.S. foreign policy especially in the early 1970s."
**The Tasks Ahead**
Goodpaster's greatest immediate challenge as SACEUR was dealing with the strong antiwar sentiment fueled by the frustrations of the war in Vietnam, not only among the European allies, but also in North America with the Canadians. Put succinctly: "There was uncertainty about the future of Europe. The attitude to the common defense was a curious mixture of unwillingness to augment European efforts and fear of American withdrawal." Ever since taking office, the Nixon administration had been searching for ways to balance increasing domestic discontent over war expenditures, brought on partly by a conflict situation in Vietnam that seemed to be endless, with the need to convince the European allies that the real battlefront of the Cold War remained the division between East and West in Europe.
This was indeed a challenge given that opposition to the war in Vietnam had forced Lyndon Johnson to step aside in the 1968 presidential election, enabling Nixon to win by promising an "honorable" conclusion to the war. Goodpaster no doubt understood, having just come from Vietnam, that the weaker party in the military confrontation could not dictate the terms of the conflict. The facts on the ground defined the outcome, and the Europeans, no strangers to inconclusive wars, understood this.
The state of affairs that Goodpaster faced can only be described as alarming, "because of both the demands of the war in Vietnam and the turbulent social conditions at home. . . . This resulted in units that were grossly understrength, wracked by continual massive turnover in those who were assigned, plagued by widespread problems of drug abuse, racial disharmony, dissent, and indiscipline, and thus not only much reduced in operational capability but also poor examples for the NATO Allies that the U.S. was trying to contribute more and better forces to the Alliance." The United States had reduced its forces in Europe from 408,000 to 300,000 between 1963 and 1969.
Goodpaster later recounted that "the crumbling of support from the United States couldn't be stopped but it could be controlled, and I think that the focus then shifted to Kissinger's negotiations, most of which were extremely secret. I helped him on occasion keep them secret." This is another example in which Goodpaster's proximity to Nixon (and later to President Gerald Ford) showed itself.
It was Goodpaster's responsibility to urge the Europeans to do more while America was doing less. This was a challenge indeed! Nonetheless, he had some support among the allies, especially in the Federal Republic of Germany, which was on the front line of the East-West standoff. "There is nothing surprising in a professional soldier asking for the forces to which he belongs to be taken seriously. But when at a semi-official meeting in Bonn, General Goodpaster, the highest officer in the Atlantic Alliance, does not shrink from making a drastic comparison of the military forces in Europe that is clearly unfavourable to NATO, the whole public must take notice, because normally the outspokenness of a military leader diminishes with the importance of his post. . . . What Goodpaster indicated without saying it in so many words is that a military balance does not at present exist and will only come back if the Soviet Union reduces its forces."
One of the most frustrating aspects of the situation in which Goodpaster found himself was that, to make a policy of détente credible, the forces of the two opposing sides must be roughly equal. This equality—or "equivalence"—can be calculated in some combination of ground troops and tactical nuclear retaliatory forces, but essentially this translates into some sort of stalemate between East and West. Paradoxically, it was just such a battlefield stalemate that the United States was unable by then to achieve in Vietnam, and this was weakening Goodpaster's hand in his attempt at a diplomacy of détente in Europe.
Another of Goodpaster's immediate responsibilities was to attempt to counter the strong sentiment both in the United States and in Europe favoring withdrawal, rather than a further buildup, of forces. This included congressional attempts to reduce the American forces in Europe in the face of pressures from Vietnam. Goodpaster did not need to be reminded that "as a minimum, allies represented wartime capabilities, denied to an adversary. Moreover, allies not only contributed in a psycho-political sense to a state's ability to deter conflict, but also to its military potential for immediate combat."
An example that further contributed to Goodpaster's frustration was when President Nixon was faced with how to counter the Mansfield Amendment, offered by Senator Mike Mansfield of Montana in 1971. The amendment called for the number of U.S. troops stationed in Europe to be halved. Goodpaster recalled, "President Nixon had his people call me one night and asked if I could immediately come back and work with him in trying to block that. And I came back and my helicopter landed on the White House lawn. The meeting had just begun and I came in and participated." Fortunately for Goodpaster, on 19 May 1971, the Senate defeated the amendment by a vote of 61–36.
One innovation that Goodpaster introduced "was [to] set up a program called Alliance Defense in the 1970s. The idea was to use every means we could to improve the effectiveness and efficiency of the military funds and budgets that were being provided. And we shifted the accent to looking for those improvements and putting them into effect to get better use of our funds and our efforts. . . . We shifted the accent from fending off cuts to making the forces that we had more effective, using the funds in a better way."
Even at that, no commander would have been satisfied with this state of affairs, but fortunately, for Goodpaster, as he exhorted the allies to do better than the Americans themselves could, his personal standing was not affected. One reason was that he did not lecture his NATO partners; rather, in his speeches he adopted a "conversational" mode of address, which tended to disarm any personal resentment for the American general.
For example, in a speech to the Royal United Service Institution in London, he opened his remarks thus: "We live at a time when a valid understanding, broadly shared, of security problems is of tremendous importance. These problems are complex, difficult, burdensome—even irksome—and they are in important areas, obscure and hard to define and to grasp. . . . Yet public understanding and interest in security issues are truly indispensable if there is to be the support and confidence, widely based throughout our countries, on which the future strength and effectiveness of our military forces depend."
This enabled Goodpaster to play a more effective role in stemming this combination of antiwar and anti-American sentiment and, in general, widespread opposition to increasing military expenditures for a conflict that they all hoped would never occur. For example, a Munich paper editorialized: "We cannot expect a general to bother about who will pay for his army. This is a matter which the political leaders must take up. But General Goodpaster did not hesitate to reiterate the call for a 'considerable' intensification of Europe's defense efforts, a call which is becoming louder and louder in the United States. . . . Nor should General Goodpaster overlook the fact that Europe merely is the front line of the United States. . . . And last but not least, playing a leadership role costs money." What this implies is that the war in Vietnam was a constant drag on Goodpaster's efforts to increase the European members' contributions.
One way to achieve this goal was to engage in negotiations with the Soviet Union to bring about mutual and balanced force reductions (MBFR). The MBFR negotiations were extremely complicated because it was not easy to arrive at an agreed-upon definition of what was "mutual" and what was "balanced." Goodpaster, quoting Nixon, held: "Our objective should be to create a more stable military balance at lower levels and at lower cost." Goodpaster went on to observe that "I have long felt—as did my predecessor, General Norstad, more than fifteen years ago—that such a pattern of reduction is a valid theoretical and logical possibility—that in principle, it should be possible to provide the same level of security as now exists for both sides at lower levels of forces. But to get from the theory to the realization is, we already know, a difficult and time consuming business of great complexity, just as it is of great importance and consequence."
Goodpaster explained his approach to shaping NATO's grand strategy: "There are three intricately interlinked components of military power that give reality to our strategy. They are conventional forces, tactical nuclear weapons, and strategic nuclear forces. The conventional military forces provide much more than what some have called a 'symbolic presence.' Rather, when properly manned, equipped, and trained, they afford an essential means to meet any aggression at the level it occurs. The second element is tactical nuclear weapons; these provide the flexibility in firepower required by the strategic concept. And the third element is strategic nuclear forces; these constitute the ultimate deterrent and, should it ever be necessary, the ultimate defense."
The dilemma was that "no militarily acceptable and apparently negotiable MBFR scheme has been discovered which successfully compensates for the Warsaw Pact advantages in existing forces, geography, and initiative." Goodpaster observed, trenchantly, that "equal reductions in unequal forces could result in forces that are even more unequal." Goodpaster also commented: "The Mutual and Balanced Force Reductions (MBFR) negotiations . . . are testing whether the process of mutual forces limitations developed in SALT [Strategic Arms Limitation Talks] can be in some way applied to military forces below the strategic nuclear level."
Another of Goodpaster's responsibilities as SACEUR was to keep a careful eye on SALT as the negotiations unfolded. Put succinctly: "The most demanding game that the Americans played during the last weeks of 1969 was the game of arms control." Goodpaster pointed out: "In the SALT negotiations on the size and composition of strategic nuclear forces, the détente process shapes and constrains U.S. and USSR military capabilities that, by any standard, are in a class by themselves. . . . The effect will undoubtedly be to narrow the strategic options for their employment, as well as the kinds of missions and objectives that may be assigned to them."
Perhaps even more important, and by implication referring to the notion of "linkage," Goodpaster observed that "I have long felt that one of the collateral effects of strategic nuclear parity has been to narrow the range of issues over which the strategic nuclear forces can be relied upon to provide an effective deterrent. . . . Reliance must not be placed on expectations that détente consultations and negotiations will have enough motivation behind them on the part of the Soviets to keep them from challenging U.S. objectives and interests."
**The End Approaches**
Career-wise, Goodpaster's reputation is often linked to his service in the Eisenhower White House as the president's staff secretary and defense liaison officer. However, in terms of influence and prestige at the highest international level during the Cold War, there could be no assignment more coveted than that of NATO's SACEUR. Quite naturally, therefore, when the news surfaced in October 1974 that Goodpaster was about to be replaced as SACEUR by Gen. Alexander M. Haig Jr., it created some interest and even consternation internationally as well as in Washington. As is generally true for four-star generals, this event was not without its underlying political narrative. Yet the politics at this time was well beyond what might be called normal.
The political environment in post-Watergate Washington was in extreme flux, with a disgraced Richard Nixon having resigned in August before his second term had ended and a largely unknown Gerald Ford having ascended to the presidency under circumstances without precedent in American politics. The immediate problem at hand was what to do about Haig, who had served as Nixon's chief of staff and had ably helped engineer Nixon's resignation. Haig was a senior general and yet still too young to be retired without implying dissatisfaction with his performance. This had created a dilemma in that there were few appropriate assignments for Haig. Complicating matters was the fact that the Army hierarchy did not want such a controversial "politicized" officer returned to its highest ranks.
Conversely, Goodpaster had had some reason to think that his position as SACEUR was still secure in spite of the major political earthquake that had occurred in Washington. Earlier that year he had written to one of his career mentors, General Gruenther: "Whether we look at Washington, which is swamping itself in Watergate and related activities, or at NATO, which is having a rough passage on the fundamental issue of Alliance solidarity, things are far from good. . . . While I was on a brief visit to the States two weeks ago, I had the opportunity to meet with President [Nixon] and discuss a good deal of this. Interestingly, he remains strong for NATO, while insisting that the Allies not gang up in opposition to the U.S."
This presidential relationship was well established, not only because both had been involved in the Eisenhower White House, but also because immediately after Nixon had won the 1968 election, Goodpaster was drawn into the post-election transition. As he said, "I spent a number of weeks, I think probably four weeks or more, at the Hotel Pierre as he was getting his administration organized. I worked closely with Henry Kissinger during that time."
According to one observer, "Although Goodpaster is a close friend of President Richard Nixon he was not appointed as [Army] Chief of Staff during Nixon's tenure because the President felt he was irreplaceable at NATO." Goodpaster had another explanation: "One reason Nixon wanted me to go [to NATO] was to keep closer to Washington and come back and meet with him from time to time and discuss the European situation but more broadly, the whole—his whole approach worldwide . . . issues of security. And I did that. Initially perhaps in his first year, several times and then I would come back to the United States probably twice a year while I was serving as SACEUR and always have conversations with Nixon."
Nonetheless, to his dismay, Goodpaster discovered (or perhaps rediscovered) that at the highest level in the nation's foremost political-military alliance—NATO—virtually nothing is "nonpolitical." Hence, nothing and nobody is irreplaceable. In a White House meeting that included Secretary of State Kissinger and National Security Advisor Brent Scowcroft with the new President Ford to discuss what to do about Haig, they examined various alternatives and then decided to move Haig to NATO as SACEUR. The dilemma was that this would require cutting short Goodpaster's tenure. Ford suggested that Kissinger should inform him, and Kissinger in turn looked squarely at Scowcroft, who then picked up the telephone and called his good friend Goodpaster, who, of course, was not at all pleased with the news. Goodpaster explained:
I had talked with Abrams, who was chief of staff of the Army by that time, about my own tenure and he said they would like to think of a retirement in the spring of 1975. And I said that would be fine with me. . . . And then suddenly . . . I got a call saying that the Americans would like to terminate my assignment and assign General Haig—who had, of course, served with President Nixon—to the post. This clarified something that had occurred.
I had had a call from a couple of my senior European commanders, military heads of their forces, saying that they had just heard that I had requested retirement. And I said well I haven't requested retirement and then I got this call. And what had happened was that the White House had sent out a message saying that I had requested retirement and that General Haig would take over. So it was a little embarrassing and awkward and it was a clumsy affair.
**The Change of Command**
So now, here he was, suddenly devalued by a new and unexpected presidency, within months of ending a truly remarkable career. He was justifiably annoyed and perhaps also somewhat embarrassed after being asked, even ordered, to step aside for what obviously was an arrangement for political convenience. To illustrate why, this statement describing how Haig rose nearly to the top could never be said _under any circumstances_ about Goodpaster:
From the start, he used his position as NSC military aide to become Kissinger's indispensable, across-the-board assistant. . . . Less than three weeks into the administration, Haig wrote a memo to Kissinger urging that he appoint a deputy. "I am not volunteering," wrote the not-so-subtle officer, but "would be honored" to serve. It was 1970 before Haig was given this formal designation, but in the meantime, he employed his assiduous service to Kissinger and his perceived political loyalty to Nixon to build up his role. The fact that other [NSC] Council members did not respect Haig intellectually actually helped in his rise, for it meant they did not perceive him as a threat.
All of this goes a long way in explaining Goodpaster's unusual behavior at the change of command ceremony. It was reported: "The ceremony at which General Haig assumed command was one of the rare occasions where the private General Goodpaster became involved in a public dispute. In a break with custom, he was not present at the ceremonies. Some said he was resentful at being retired; others said he had stayed away because of recent minor surgery. The general did not say." Nevertheless, he did appear alongside Haig at a subsequent news conference on 15 December 1974.
The sensitivity of the episode was such that on 16 December the Associated Press reported: "General Goodpaster explained that he was not at the previous ceremony because he needed to convalesce from a minor operation. . . . 'It is a point of principle and a point of honor with me—I have never turned down an assignment and I have never asked to be relieved of any task.'"
Even earlier, he had sent a message to his NATO commanders: "Apparently some of the messages and letters that were sent out by U.S. authorities stated that I had requested (repeat requested) retirement. This is untrue, and I am deeply troubled at the implication, which is erroneous of willingness on my part of continuing to serve the Alliance as SACEUR. I have not now or previously requested retirement or relief from my duties. I wanted you to know this from me personally." But he was not alone in being disgruntled; some months after Goodpaster had relinquished the command, there was grumbling in NATO circles about the United States sending a "political general."
It is interesting, if not significant, to note that, notwithstanding a particular SACEUR's background and career inclinations, at least through the time of Haig the officers so designated appeared to be appropriate to their respective times and circumstances. For such disparate personalities as Norstad, Lemnitzer, Goodpaster, and Haig, every one of them were experienced in the international political as well as the purely military arenas. Persuasiveness, combined with almost endless patience, were among the hallmarks of their success.
Eisenhower put it well during World War II. In a letter to General Marshall, Eisenhower commented with obvious frustration: "The sooner I can get rid of all these questions that are outside the military scope, the happier I will be. Sometimes I think I live ten years each week, of which at least nine are absorbed in political and economic matters." Ten years later, of course, Goodpaster found himself back in the same situation that Eisenhower was deploring earlier, and, as the record shows, no SACEUR can avoid the political and economic aspects of NATO defense.
Furthermore, as CINCEUR (most of whose day-to-day duties were delegated to the deputy), these generals actually had some troops under their direct national command. This provided a psychological as well as a material backup to their efforts as international commanders. Without a doubt, Goodpaster, with his long experience at or near the top of the national political-military policy-making and execution apparatus, could rightfully be considered almost an ideal choice for Nixon—notwithstanding his proximity to the president as counselor.
Chapter Thirteen
Returning to West Point as Superintendent
"This art [of war], like all others, is founded on certain and fixed principles, which are by their nature invariable; the application of them can only be varied: but they are themselves constant."
—Henry Humphrey Evans Lloyd, in _The Theory and Practice of War_
Upon retiring in 1974, and after a year and a half in Washington at the Woodrow Wilson International Center for Scholars and then membership on the faculty of The Citadel in South Carolina, Goodpaster found himself contemplating an unexpected assignment. It was one that would enable him to leave a lasting mark on the next generation of young officers to graduate from West Point.
As he put it:
They had had this really large-scale cheating scandal. . . . They asked me, in general terms, what would I think of calling a retired officer back to active duty to do that. And I told them I thought that might be a good idea. And they said, "Well if we ask you to come back at the grade of three-star general, would you consider it?" I said, "Of course I would." . . . I said, "Well, I'd like to talk to the secretary of the Army to see that we have a full understanding, before I come back." I said, "I'd be happy to come and do the things I believe in to restore the academy to what it should be."
**Goodpaster's Welcome**
At the time of his appointment as superintendent, a military man who had served with him said: "'This guy's just a brilliant guy without being domineering.' He said that the general gave the impression of being 'just a quiet guy' at first until it became clear that he had 'a few brain cells to rub together.'"
This demeanor of modesty yet firmness of purpose showed itself in regard to one of the most sensitive aspects of a career officer's self-image—recognition of his rank. It is worth recalling here again that when Goodpaster returned to active duty in 1977 to be superintendent, he was reminded that the position was for a three-star lieutenant general and Goodpaster had by then achieved four-star rank. The administration offered to go to Congress for a special legislative act authorizing an exception to this rule, but Goodpaster demurred. He did not want to embark on an especially difficult leadership challenge, in which ethical behavior played such a prominent part, carrying the baggage of his own preferential treatment.
Goodpaster could still recall the last major cheating scandal at West Point, in 1951, involving the football team. He had this to say at that time:
What I have seen to date has made it clear to me that the action and intent of the cadets involved was such as to constitute full culpability on their part warranting action of the kind taken. It strikes me, however, that some rather intensive soul searching is indicated on the part of those who bear responsibility for creating and maintaining the pattern and system within which the violation occurred. I am not thinking of the business of giving the same writ on successive days. I think that a sound honor situation could take a relatively minor test like this in its stride. . . . Those who gave the tremendous emphasis to football did not, I am sure, foresee this as one of the consequences turned up by the wheel of time. . . . I hope . . . that this athletic binge and its unsavory morning after will be enough to return West Point football teams to the Ivy League where they belong.
Goodpaster also perceived in 1951 that the honor system was being applied indiscriminately to offenses, large and small, and that the offenders thought of themselves apart from the corps of cadets and its standards. The same proved to exist in the current scandal.
In the engineering episode, mirroring the football scandal, Goodpaster quickly discovered that he needed to not only determine how to deal with the scandal but also demonstrate that there was a scandal to be dealt with. As he said: "Initially I found people really saying that a cheating scandal of the kind that had occurred couldn't occur. I said let's agree it did occur and it wasn't two hundred [cadets]. It was probably four hundred and there may have been eight hundred. And that's the challenge we have and that's what we're going to set out to correct. And we did."
The scale of the cheating could never be exactly determined, but it seems that "eventually 152 members of the class of 1977 were dismissed for violation of the school's Honor Code by cheating, or toleration of cheating, on a take-home electrical engineering (EE-304) examination."
He went even further when he observed: "You know, there is a lot of nostalgia for the old days, but that's not this decade, that's not when we are living. Now, we've got to live in terms of the kind of country and the kind of Army that we have." This remark would not have gone down well with what Goodpaster termed "the elite."
This "elite," however, could not be taken lightly. This was especially true concerning the Honor Code and System. It was intended to give life to the phrase "Duty, Honor, Country," by allowing the Corps of Cadets to discipline themselves. In the football cheating scandal, for instance, much consideration was given to explaining to the alumni exactly what had occurred (and what had not occurred). For example, in the football scandal, a carefully crafted letter addressed to the "Brothers" was sent to all alumni, pointing out that "the publicity on this affair cannot be said to have been foresighted and well planned." Goodpaster would have been well aware of this earlier example.
In fact, cheating was a source of concern as early as 1970, when the Army War College produced a report on the general state of the officer corps that said: "The findings of this study surprised and, in some cases, shocked many of the Army's senior leaders. . . . In general, it discovered that the majority of the Officer Corps perceived a stark dichotomy between the appearance and reality of the adherence of senior officers to the traditional standards of professionalism, which the words duty, honor, and country sum up. Instead, these officers saw a system that rewarded selfishness, incompetence, and dishonesty."
Knowing the ways of Washington, Goodpaster asked for a letter giving him complete authority to make changes. In addition, he wanted "an understanding that I'm here for an extended but indefinite period, so that the elite guard cannot wait me out. And that was part of the agreement that I had with the Secretary [Martin R. Hoffmann of the Army]. The other part was that I'd said to him and to Army chief of staff General [Bernard] Rogers, any time you want to do something different from what I believe in, you let me know . . . who my successor is, because if this is to be done, it has to be done systematically. And that's what I really intend to do."
"Soon after he became Superintendent in 1977, General Andrew Goodpaster provided what might well serve as the best capsule explanation of the Honor Code's origins and evolution. 'The code, derived from the "code of honor" of the officer corps of the late 1700s,' he told a congressional committee, 'after many changes in statement, application, and interpretation evolved into the present code.'" Further, and noteworthy, given changing public attitudes toward the use and abuse of authority: "The honor system has evolved to include greater respect for due process and the defendants' rights."
To grasp a sense of how far the notion of appropriate behavior had advanced, note this comment by Gen. Fox Connor, of the class of 1898, who considered Eisenhower his most accomplished protégé and who also mentored Gen. George Patton and Gen. George Marshall—thus in direct line to Goodpaster: "In theory, cadets were governed solely by the regulations of the Commandant and his Tacs [tactical officers]. In practice, the upper-class cadets developed their own norms and values and enforced them physically. Cadet discipline took the form of bare fist boxing. Fourth-class cadets, or freshmen, are known as plebes. A plebe suspected of an infraction against the upper-class was required to square off against an upperclassman of similar weight. The fight continued until one of the parties couldn't stand."
**Implementing a Leadership Concept**
Goodpaster was able to build on the steps already taken by his immediate predecessor, Lt. Gen. Sidney Berry, and by General Rogers, who had convened a study board to assess "what the situation was in terms of academics, the military side of cadet life, and the whole complex of activities there." Goodpaster regarded the report as helpful in what he termed "an orientation of objectives."
Thus, when he arrived at the academy, he made a statement in which he recalled that "West Point exists to provide to the cadets of the corps academic, military, physical, athletic and [a] moral ethical experience of such high quality that it can serve as bedrock on which they as future military leaders can build their capabilities over time to make their contribution to the safety and well-being of our country."
Being a pragmatist as well as an idealist, after assessing the situation, he decided that a radical reformation was unnecessary but that a clarification of the purpose of the academy was badly needed. He doubtless bore in mind that by the 1970s the cadets were coping emotionally with the social and ethical turmoil brought on in part by the war in Vietnam, which was also being reflected in the behavior of the troops themselves.
One of the objectives that Goodpaster highlighted was to rekindle a sense of duty. "For the last year, efforts have been under way to foster cadet development of a military sense of duty. Discussions with cadets and members of the staff and faculty have helped to produce the attached paper, which seeks to give focus and direction to this essential aspect of becoming an officer." As superintendent, he obviously was talking about taking the entire military academy, and not just the cadet corps, back to "first principles."
This reveals how Goodpaster realized the importance of forming or changing attitudes, both institutional and personal. Here is an example:
What is "duty" in this sense? Though an understanding of its full meaning can only be approached through a lifetime of study and experience, its basic principle is well and simply conveyed in "doing what ought to be done." An unremitting internal urge to act in all things in this way is the first requirement and serves as a distinguishing mark of the exemplary officer and officer-to-be. But given even this strong desire, the individual quickly confronts a second essential: to know where duty lies; that is, to know how to assess and decide what it is that "ought to be done."
An example of how Goodpaster altered the outlook, rather than discrediting outright an undesirable practice, is the matter of competition. "As I put it, rather than emphasizing the competition with each other, think about it like a game of golf where you are going up against the course, competing against the course, not against each other. The whole idea is to do as well as you can with the tasks at hand and not to elbow your way ahead of this fellow officer or that fellow officer. . . . The role of senior leadership is to decide where that dividing line—dividing area—begins to occur, where the thing begins to get corrupted as we know it had been corrupted."
Goodpaster explained how he approached his task of restoring integrity to where the nation's core Army leadership is nurtured as well as educated:
First, [the program] centers on cadets. Cadets are the product of West Point and they measure the value of the contribution of the institution. Second, it is purpose-oriented, because there has to be a clear concept of purpose, which everyone at West Point can recognize and work toward. It emphasizes a combined experience, one that is a combination of intellectual, military, physical, and moral-ethical experience. It is need-oriented because West Point must look at what the Army requires and to what our nation needs in the way of security and defense activities, which these officers-to-be will be responsible for directing and leading.
In his remarks when he assumed command at West Point, Goodpaster concluded by saying: "We will face our problems with confidence and resolution, with integrity, justice, and human understanding and, not the least, with good humor and good will. Our common standard will be excellence. Our common inspiration will be duty, honor and country."
One especially delicate task with which Goodpaster had to deal was the introduction of women into the cadet corps. He addressed and rejected the idea of putting the women in a separate barracks. Instead: "The real point is that if we are going to have an Army with women in it—and we have and we are going to continue to have—then officers in their pre-officer training should learn how to work in an Army which integrates the services of men and women. It becomes very important to do that during this preparatory period."
It is not necessary to recount every change in procedures or in emphasis that took place during Goodpaster's four-year tenure, except to point out that he simplified the chain of command so that the senior officers in the administration became responsive to cadet self-governance to the extent that this was possible. Another area that he emphasized was that academics were as important as athletics—it seemed that the offending cadets would not have cheated on the playing field, yet they did in the classroom. Goodpaster viewed this as an erosion of values.
Even though the institution of the "military academy" was preserved, the glamour of West Point had lost some of its burnish. Tradition without substance—in other words, an empty shell—was worse than nothing. Goodpaster would have been painfully aware that the cheating scandal had drained the substance out of the tradition—at least temporarily.
In a way, this was mirrored in the perennial debate over football at West Point: is achieving fame and athletic respect by winning on the football field a useful symbol of military leadership—the true payoff of which would be winning in war? Conversely, would losing continually convey another kind of symbol, one that would not be congenial to Goodpaster and his contemporaries, who had graduated just at the eve of the greatest war ever fought?
To every superintendent, honorable conduct in the classroom was a vital aspect of leadership; dishonor, inversely, would discredit this effort to teach personal responsibility by example and deed. As it was affirmed, "The strength of the system . . . is that it belongs to the Corps of Cadets; it is theirs to manage; it is as good as they collectively and individually wish to make it." Put another way, it doesn't take much to turn a positive symbol into a most undesirable symbol.
This was at the core of Goodpaster's tenure as the academy's chief executive and chief symbol of leadership and command behavior. He recognized this responsibility when he declared that "no one will take the Honor Code away from the cadets and this should be known to them. The Honor Code and its well-being is a shared responsibility. One of my prime responsibilities is to look after the well-being of the Honor Code. But this responsibility cannot be accomplished without the wholehearted support of the code by the cadets."
Finally, on a more personal note, returning to West Point held special meaning for both Andy and his wife, Dossy Anderson Goodpaster—they had met there when she was living on the post with her father while he was a member of the staff and Goodpaster was a cadet. They married soon after he graduated, and the marriage truly unfolded in the best traditions of an Army family.
Conclusions
The Soldier-Scholar in the National Security Policy Process
"The increasing role of the American professional military officer in the foreign policy process has presented unique problems for the foreign policy planner and for the professional military officer as well."
—DONALD F. BLETZ, _The Role of the Military Professional in U.S. Foreign Policy_
The mix of presidential politics, wartime exigencies, and personal ambition can possibly trip up promising young officers serving either in or near the White House. They become more engrossed in their personal ambitions than the circumstances warrant. Yet there are other talented young officers, among whom was Andrew Goodpaster, who can enter into this particular career situation and emerge not only unscathed, but also even for the better, both career-wise and personally.
**An Unambiguously Professional Officer**
Goodpaster had received assignments at the international level from the very beginning of his career. He assisted in the formation of NATO, the most formidable military alliance in history, even crafting the general order creating its military component. From there, he moved in and out of national, international, and multinational assignments, developing an outlook that served him well both as staff secretary and defense liaison officer to President Eisenhower in the 1950s, and as NATO's supreme allied commander, Europe, in the 1970s.
Although Goodpaster had worked closely with Republican presidents, he steadfastly maintained his political neutrality concerning his own personal ambitions. He saw himself as, first and foremost, a serving officer in the U.S. Army. In this respect, he was reflecting the professional values of George Marshall. An example of Marshall's careful integrity was when he went out of his way to protest, when accepting the appointment as President Truman's secretary of state, that "I am assuming that the office of Secretary of State, at least under present conditions, is non-political and I am going to govern myself accordingly."
Goodpaster could look back on his years with Eisenhower—and his career in general—with sincere satisfaction. He had played a substantial role in enabling Eisenhower to declare in his last formal report to Congress:
On January 20, 1953, when I took office, the United States was at war. Since the signing of the Korean Armistice in 1953, Americans have lived in peace in highly troubled times. . . . The nation can ill afford to abandon a national policy which provides for a fully adequate and steady level of effort, designed for the long pull; a fast adjustment to new scientific and technological advances; a balanced force of such strength as to deter general war, to effectively meet local situations and to retaliate to attack and destroy the attacker; and a strengthened system of free world collective security.
Because Goodpaster entered the White House as a junior colonel and left it as a brigadier general, he could not cope at times on a completely equal footing with the various three- and four-star officers who had dealings with the White House, and especially those flag officers who were engaged in the sometimes fierce debates over the New Look and its budgetary implications. It could have been especially awkward for him in regard to those senior Army generals disaffected by Eisenhower's definition of "roles and missions." Even though he was close to Eisenhower on a day-to-day basis, Goodpaster appraised the nature of the dissent not as acts of disloyalty to the commander-in-chief, but rather as part of ongoing and ever-changing interservice deliberations. Eisenhower, in contrast, was openly more than annoyed with his former Army colleagues.
Perhaps more significantly, Goodpaster was, in his unfolding relationship with Eisenhower, engaged de facto in the formation of what is today an extensive White House–based national security policy-making apparatus. In contrast to many of his successors, who achieved their White House status in part because of their political ties, Goodpaster regarded political considerations to be largely irrelevant to the successful execution of his duties. This does not mean, however, that he was insensitive to the kind of politics that of necessity must be ever present at this highest level of government. Eisenhower commented on this point in his final report to the secretary of the Army regarding Goodpaster: "In his post of White House Staff Secretary he handles, quite naturally, exceedingly important, delicate and sensitive material, most of which ultimately comes to my attention."
**A Practitioner of Strategy and Policy**
Goodpaster's success in maintaining his professional and service-oriented integrity while in the White House is exemplified by the fact that thereafter both Republican and Democratic presidents sought his advice. As it was put: "No longer adviser to the commander in chief, Goodpaster contributed to national security policy during these years as a troop commander, planner, and negotiator." In fact, he was "on call" ever after.
For example, when McGeorge Bundy, first Kennedy's and then Johnson's national security advisor, organized an important mission to Saigon in February 1965, he included Goodpaster in the party. He was at that time assistant to the chairman of the JCS. This trip coincided with the Vietcong attack on the airfield at Pleiku, which meant that these important participants in the formulation of Vietnam war policy witnessed a huge propaganda victory for their enemy. "A barrage of mortar rounds caused explosions that killed eight American servicemen, wounded more than one hundred others, and set fire to twenty aircraft on the airstrip. Goodpaster and Bundy accompanied General Westmoreland to the site of the attack. The airfield was in shambles."
How Goodpaster felt about this is not clear, but he was always inclined to measure battlefield events from the twin assessments of whether success was possible, and what price would be exacted to achieve that success. He understood the complexity and the tentativeness of decision-making at the highest level of government. In this sense, his innate modesty served him well.
Although President Johnson had already decided to bomb North Vietnam, Pleiku brought home the destructive reality of the war—it was no longer just a matter of quantitative assessments from within the orderly confines of the White House or the Pentagon. Not only were strategic decisions being made within the tight political circle around Johnson, without input from the JCS, the JCS were being given only token acknowledgement of their responsibilities. This is one reason why Goodpaster believed that the military did not "lose" Vietnam—his view was that, under Johnson, there was no real opportunity to pursue the war as the military planners would have wished. He tended to agree with the school of military thought that argued for an all-out effort to achieve victory, rather than adopting a posture of "graduated response."
In contrast to Eisenhower (and Goodpaster), "[Kennedy] would refuse to consider or even to acknowledge the consequences of his decisions, and thus still imagined that he could pursue a policy of gradual escalation without involving the United States in a major war."
Goodpaster's honesty took precedence over pandering to the prevailing public sentiment, such as when Gen. Earle Wheeler, then chairman of the JCS, asked Goodpaster "to establish what the United States would have to do to win the war in South Vietnam 'if we do everything we can.' Goodpaster's lengthy report envisioned the possible need for seven to thirty-five American battalions above and beyond the thirty-four American battalions called for in the forty-four battalion request." The additional troops were not, of course provided, and this lay behind Goodpaster's feeling that the United States lost its "will" rather than its means, to achieve its war aims in Southeast Asia.
Goodpaster's unassuming manner, quiet courteousness, and serious yet not heavy demeanor fitted in well with whatever professional situation in which he found himself. This is why he was so highly regarded in all quarters. Perhaps not coincidentally, at every stage in Goodpaster's military career, he attracted the support of persons influential in furthering his interests. These associations also enabled Goodpaster to continue to participate in foreign and military policy discussions during his many post-Army years of unofficial and semiofficial activity.
While on active duty, he was able to inspire the confidence and even admiration of his troops at whatever level of command, and as a civilian, he was able to articulate policy issues persuasively at the highest political level. There were four areas of the security environment, according to Goodpaster, that were especially important. First was the " _paramount importance of national security_. Self-preservation is the first law of life," he argued. As a result, "government," he believed, "should be organized and run so as to place national security in the highest order of priority." The second key element was " _the dynamism of the security environment_ , the constant change that is encountered with new technology, the rise of new nations, new factions, new leaders, the changing of old alliances and power arrangements, the rise of new interests, the secular shifts which take place as new generations mature which have not been marked by the problems of their predecessors." These forces naturally contributed to the third aspect, " _the factor of complexity_." Nothing was simple when it came to matters of national security, which only are achieved through an intricate and inherently unstable process. "The fourth point to remember," declared Goodpaster was that, "in the security environment is that _it takes place within a political framework on both the domestic and international sides_. This [domestic] arena is rarely one in which the military officer will feel comfortable. . . . These are the issues in which the military is most likely to run afoul of the so-called 'politicization' of their advice and support. . . . The military man is an _advisor_ [Goodpaster's emphasis here; author's emphasis in other instances above]."
Goodpaster successfully carved out for himself a notable niche in America's Cold War history, and even beyond. Geoffrey Blainey observed, referring to Britain's Lord Palmerston and Germany's chancellor Otto von Bismarck in an earlier Great Power period: "It is vital to enquire how much of their influence came from their personalities and policies, how much from the contemporary international situation, and how much from their superior military backing." In Goodpaster's case, his personality dovetailed with the manner in which he performed both as a trusted aide to and as a collaborator with Eisenhower.
**A Final Comment**
The purpose in writing this biography is to place Goodpaster where he belongs among the annals of the soldier-scholars of his historical period. Goodpaster excelled at (1) command at the highest military level; (2) command in combat; (3) leadership at the highest political levels; (4) cogent analysis of men and events. There are military figures who have excelled in one or another of these accomplishments, but few who excelled in all four.
The histories of the Cold War that have been written—and those yet to be written—may not necessarily have Goodpaster listed in their indexes, yet he was one of the key figures during that ongoing crisis—one who remained behind the dominant personalities of those times, whether military or political (or both). Then later, he stood at the forefront himself, not only in regard to Vietnam and NATO, but also in restoring the integrity of West Point during a major ethical crisis. His presence on the Washington scene was always welcome, even in those instances in which he was be a dissenting voice in some policy debate.
Given the strains to the national fabric that warfare can impose on a society, and given that in his time the Cold War appeared to be endless, Goodpaster and his contemporaries in the governing process were fortunate to conduct their affairs "[largely] under a set of conditions in which an able civilian government maintained national interests by effective diplomacy [and] closely supported by a capable military who were willing to remain in their proper place." Goodpaster witnessed this process almost daily before, during, and after his years in and around the White House and the Pentagon.
In conclusion, the military historian Donald Kagan observed that "Thucydides . . . understood war as the armed competition for power . . . 'by a necessity of their nature [human beings] rule as far as their power permits.' . . . In the struggle for power, whether for a rational sufficiency or in the insatiable drive for all the power there is, Thucydides found that people go to war out of 'honor, fear, and interest.'" Gen. Andrew Jackson Goodpaster was a modern-day soldier who understood the human motivations that underlie the persistence of armed warfare in human affairs, even while engaging in a career that embraced the technological complexities of contemporary war.
This biography intends not to celebrate an era; rather, its purpose is to celebrate a noteworthy figure of that era. Even so, as the historian Robert Conquest, put it: "I am well aware that there is much more to be said on the themes I have covered; and that there are important issues which I have passed by, or barely touched on."
Afterword
Gen. Andrew J. "Andy" Goodpaster, USA, was a person who defied the cliché "soldier statesman" by actually being one; he was also a consummate organizer, diplomat, humanist, and friend to so many.
I met him late in his career and regretted all those lost years and experiences, but I had known of him for decades, as the quiet, unassuming man who was "present at the creation" so many times, and who was both adviser to and steadying influence for many of modern American history's more famous leaders. For so long, if one of these leaders, with a sense of the nation's destiny and of the need to get the job done and done right, was in need of the best possible counsel, he would call upon Andy Goodpaster to do what had to be done, to bring along those who had to be engaged, to smooth down ruffled feathers, and to apply good old-fashioned integrity to the most difficult and challenging of situations.
It was not for nothing that Ike, himself one of the superb political talents in uniform, called on Goodpaster to organize and operate the apparatus in the White House that was needed to enable the president to be president in his commander-in-chief hat. It was not for nothing that Goodpaster was sent to Europe as supreme allied commander at a time when the allies needed reassurance that America was truly "over here" and the rock-solid provider of security for Europe. It was not for nothing that he was called to straighten out unfortunate goings-on at the U.S. Military Academy, and that, in his semiretirement, he was called upon to make something of the Atlantic Council of the United States—and while there saw the glimmerings of possibilities in working with the Soviet Union; not just in containing it, but in building new relationships in security that have, indeed, stood the test of time through the period of the USSR's collapse and some new and hopeful—though as yet unfulfilled—prospects in a NATO-Russia relations.
Some of America's premier leaders, in and out of uniform, have believed that they have had to raise their voices in order to be heard, much less to be obeyed. Andy Goodpaster was the opposite. He always carried with him a "zone of quiet" that was infectious in calming the most troubled spirits and the most difficult circumstances. He spoke under the turmoil, not over it, with his precise, understated logic, taking apart the complexities of argument and then reassembling the key elements with clarity and coherence; and he was listened to, always.
In the process, he never stood on ceremony, or invoked his rank, or traded on his comprehensive array of people known or jobs held or results achieved (while making sure that the credit got spread around, himself avoiding the limelight rather than trying to hog it). He always had time for those whom the world might regard as unimportant but in whom Andy would see potential, who could and should be nurtured, and who would make a signal contribution to the nation's well-being, if not today, still being so junior, surely tomorrow.
Isaac Newton said, "If I have seen further it is by standing on the shoulders of giants." Andy Goodpaster did often "see further," but never claimed the credit for doing so. But unimpeachable is the fact that he was surely in the company of those "giants" with unassuming but strong shoulders that helped others to see what had to be done and have the courage to do it. And he set a style and lived a life of character that may have too much faded of late, but still forms the bedrock of the best that is in the American soul, always has been, and always will be if this great nation is to persevere and prosper.
We are all better off that the newly minted Army second lieutenant Andrew J. Goodpaster took the oath on the plain at West Point in 1939 and then served, and served, and served his nation and the Western Alliance for so long and so well. Those of us who had the chance to know and work with him and to benefit from his unforced, unpretentious wisdom have gained an "increased devotion" to do those things that matter most because of the trust, and kindness, and counsel, and friendship of this good man, this great American.
**Ambassador Robert E. Hunter**
U.S. Permanent Representative to the North Atlantic Council
The RAND Corporation
Appendix
**Contributions to Public and Voluntary Service**
_I. Voluntary Service: St. Mary's College_*
General Andrew Goodpaster was appointed to the St. Mary's College of Maryland Board of Trustees in 1987. He was reappointed in 1992, serving for a total of twelve years. He served as Vice Chair of the Board of Trustees and Chair of the Academic Affairs Committee, as a member of the Committee on Historic St. Mary's City, and as Chair of the Task Force on St. Mary's Programs of Study Abroad in the aftermath of an attack on students and faculty in a College sponsored study tour to Guatemala in January 1998. The Task Force worked in parallel with a criminal suit brought by the College against perpetrators of the crime in Guatemala.
As Chair of the Task Force, General Goodpaster oversaw a comprehensive appraisal of the College's programs, reviewing in particular the policies and procedures safeguarding students' health and safety. The membership of the Task Force included faculty, staff, students and trustees of the College, as well as the parents of the students attacked.
The Task Force began its work in March 1998 and completed its report to the Board of Trustees and the St. Mary's Community the following May, recommending several changes to improve safeguards. The Task Force advanced the community's confidence in study abroad programs and underscored the College's willingness to review and revise procedures to anticipate and meet risks.
As Chair of the Academic Affairs Committee, he established the system for faculty compensation based on reaching the mid-point of salaries for a select group of peer institutions. The system also is applied to staff salaries as well. The application of this method has created an expectation of fairness for compensation and, although disputes arise from time to time, discussions are rooted in objective criteria and focused on data that is collected, analyzed, and distributed regularly.
The College's faculty leave of absence program was also a product of the Academic Affairs Committee during General Goodpaster's tenure, and this program has been particularly important to the scholarship opportunities awarded to St. Mary's faculty for career development and renewal.
As Vice Chair of the Board, he chaired the Presidential search of 1996, which attracted Dr. Jane Margaret O'Brien to the College. Under her leadership, the College rose in national rankings to within the first tier liberal arts colleges, and a period of student, residential and academic expansion was undertaken that included the development of a new General Education curriculum with international programs available for students in England, Italy, Gambia, Thailand, Vietnam and China.
During the College's $40 million Heritage Campaign, the College developed a close relationship with neighboring Historic St. Mary's City. General Goodpaster served with Ben Bradlee, Vice President at large of the _Washington Post_ and Chair of the Historic St. Mary's City Commissioners, to resurrect interest in the shared missions of the College and St. Mary's City and to encourage cooperation and collaboration. Governor Parris Glendening and the Maryland General Assembly subsequently committed $60 million to the Maryland Heritage Project in support of the College's and the City's joint planning initiatives. The Heritage Project enabled the College to reorganize its residential and academic campus, which led to the spatial restructuring of the historic campus to accommodate a new visitor's complex on land adjoining and including a portion of Historic St. Mary's City.
The College gained national attention as a public honors college largely due to the courage and prescience of the Board of Trustees, which in 1992 proposed St. Mary's College as Maryland's Public Honors College. General Goodpaster, Johns Hopkins University President Emeritus Steven Muller, Senator Benjamin Cardin, Ambassador Paul Nitze, Terry Meyerhoff Rubenstein, Ben Bradlee, Harry Weitzel, Tom Waring and Governor William Donald Schaefer were among the key Trustees leading the College's initiative to create this unique public-private model of higher education that has been a model for many other States.
In 1998, the College established the Andrew J. Goodpaster Endowed Leadership and Honor Lecture Series in General Goodpaster's honor. The first lecturer was General Goodpaster's close friend and fellow Presidential advisor, Lt. General Brent Scowcroft, who said in his opening remarks what many at the College also felt, that General Goodpaster was his hero. This sentiment was deeply felt by all who served alongside General Goodpaster as Trustees. He inspired the Board to do its best and the College flourished in many ways under his gentle guidance and careful direction.
Before his death in 2005, the Trustees announced that the new academic building would be named in his honor. He was deeply appreciative of the honor. The Andrew J. Goodpaster building at St. Mary's College houses psychology, education and several important lecture halls. It was dedicated a year after General Goodpaster's death, with Lt. General Scowcroft serving as the invited speaker for the dedicatory remarks.
General Goodpaster's granddaughter Sarah Nesnow was exceptionally helpful in providing for the Heritagescapes story that graces the grand foyer and tells the story of General Goodpaster's dedication to his country, to West Point, and to the College he helped launch in to its finest hours as a public honors college for the State of Maryland.
In summary, General Goodpaster was the undisputed conscience of the Board during his tenure and helped to assure the College's rise in stature as it sought to define a new level of achievement for a model of public-private partnership in higher education.
_II. Public Policy Participant: The Atlantic Council_*
_Chair, 1985–1997_
The two areas of foreign policy that Goodpaster cared most about—his own "blue chips"—were nuclear weapons and Russia. It was in these areas that he made his greatest contribution during the final two decades of his life.
**On Nuclear Weapons**
Goodpaster thought that it was not helpful to lump nuclear, chemical, and biological weapons in the same category as "weapons of mass destruction" because each posed quite different threats and called for different responses. Deterring conventional, biological, or even chemical attacks should be left to other, non-nuclear means, while the main function of nuclear weapons still was to deter the use of nuclear weapons by others. Such deterrence had to rely on a credible capacity for instant, devastating response.
His thinking on nuclear weapons was based on personal experience in more than a dozen high-level strategic, policy, and command positions spanning most of the Cold War. For Goodpaster, thinking about nuclear weapons was not merely an intellectual exercise; he was often faced with thinking through the consequences of their use in a wide variety of specific situations, from the time he served with Eisenhower when nuclear weapons became the definitive dimension of the Cold War, to his own tenure as Supreme Allied Commander in the early 1970s, when he had several thousand such weapons under his command.
It once was common to think of nuclear weaponry as just one more tool in the arsenal of modern warfare. But it became increasingly clear to Goodpaster, and to his boss Eisenhower, that the tremendous destructive power of such weapons, particularly with the advent of thermo-nuclear weapons, made it very difficult to conceive of using nuclear weapons as a rational instrument for the pursuit of any national objectives other than survival.
Setting Goodpaster apart from many other military thinkers was his ability to place problems in a global and longer-term context. He often found himself arguing against more simplistic thinking that more weapons are better, especially if they were enhanced with the latest technology. Using this logic, there would never be enough, given the dynamics of Cold War competition. By contrast, Goodpaster persistently pressed the issue of clearly defining the proper roles and limitations for nuclear weaponry.
Goodpaster continued to insist after the collapse of the Soviet Union that nuclear weapons were not useful in war-fighting and that the existing inventories could be safely reduced. The challenge was to determine by how much and how fast this could happen.
Much of his thinking in this area was presented in a series of Atlantic Council Papers known collectively as the _Further Reins on Nuclear Arms_ series. In these papers, Goodpaster developed the criteria that would be necessary to reduce safely nuclear inventories of the United States and Russia to successively lower levels. He said that he could not foresee for the indefinite future ever reducing beyond a few hundred weapons, because this would require such a radically different and safer security environment, one inconceivable in his lifetime. Nevertheless, he encouraged analyses that addressed the requisites of a nuclear weapons–free world, because this remained the desired objective of the international community.
In addressing the prospects for a "zero level" of nuclear weapons, Goodpaster took a middle road between the nuclear "abolitionists"—whose ultimate goals he shared—and the skeptics, whose prudence he respected. He concluded that the international stability and confidence required for abolition to work had to be built and sustained before the levels of stockpiles reached zero. Drawing down arsenals on a pragmatic, negotiated, multilateral basis could go a long way toward building that trust, while hedging against the possible breakout by one or more nations.
Goodpaster never denied that states could reconstitute nuclear weapons capabilities rather easily. In order to counter that likelihood, and to take advantage of a once in a lifetime opportunity presented by the end of the Cold War, Goodpaster advocated a five-power nuclear agreement to reduce stockpiles down to the lowest acceptable levels. He feared that, absent such an agreement, Cold War–era restraints on nuclear proliferation would give way to new strategic arms races in volatile regions, notably the Middle East and East Asia.
Goodpaster would probably say that it is not too late to stem the tide again. Indeed, he kept working on this issue up to the very end of his life.
**On Post-Soviet Russia**
Goodpaster knew several of the Soviet military leaders personally from his tenure as NATO SACEUR, and he continued those associations after the Cold War. He was also one of the first Americans to take seriously the changes proposed by Mikhail Gorbachev and was instrumental in convincing the Reagan administration to embrace them. He later believed that it was essential for the United States to understand the problems facing Russia, and to accord its leaders proper respect at a time when cooperation with the United States was highly controversial. In particular, he was concerned about the Russian military and with transforming _its_ thinking about NATO.
Five years before the collapse of the Soviet Union, Goodpaster initiated a series of semiannual meetings between Atlantic Council representatives and leading Soviet strategic thinkers. This exchange was expanded to include Ukraine after 1991. These dialogues were useful in assuaging the feelings of isolation and humiliation of many former Soviet leaders. The exchanges addressed nuclear weapons, missile defense, conventional forces in Europe, and other issues that were important in promoting a more stable, peaceful environment. They treated security in a broad sense, including creating a more favorable climate for foreign investment, tax reform, fighting corruption, commercial codes, intellectual property, privatization, and other issues. Their efforts forged new ties in the direction of greater prosperity, democracy, and peaceful relations.
Early in these exchanges, Goodpaster noted that while Russia still had the rights of a Great Power, it also had responsibilities. (To a lesser extent, this was true of Ukraine as well, and the Goodpaster meetings contributed directly to the Ukrainian government's decision to remove its nuclear warheads to Russia.) He urged Russians to participate in NATO's Partnership for Peace (PfP, a program he helped to originate), so that Russia's voice would be heard within as well as outside NATO. This was a difficult case to argue because many Russian leaders still saw NATO as the great enemy. To help make his case, Goodpaster sought to establish an "overarching framework" of friendship and cooperation between the United States, NATO, and Russia.
Although Partnership for Peace was eclipsed by NATO enlargement and the interventions in Bosnia and Kosovo—actions that produced in Goodpaster feelings that were mixed, to say the least—it nevertheless laid the groundwork for a post–Cold War European security system that showed every sign of succeeding in the long run.
**On Public Service**
One of Goodpaster's favorite quotations was one he attributed to his former boss, General Marshall, "You'd be amazed to see how much a man gets done if he doesn't seek credit." Goodpaster probably envisioned himself as a conveyor or facilitator of ideas rather than as the emblematic "soldier-intellectual." He would urge his staff to forgo labeling this or that idea, saying, "The important thing is just to get it out there." Goodpaster sought results over posturing. For him, ideas were not sufficient unless they were translated into actions.
To the unfamiliar observer, Goodpaster's writings and thoughts may sound rather conventional or dry. With the exception of his public call in 1996 for the elimination of nuclear weapons, few made headlines or sent shock waves through the bureaucracy. This was the secret of their success. His was a form of constructive, independent thinking for action. As a result, he moved the debate forward on many key issues with a steady, yet subtle, persistence. His impact was measured in decades, not news cycles.
**Notes**
1. Goodpaster noted that just after World War II, military leaders thought a handful of nuclear weapons would be sufficient.
2. See Andrew J. Goodpaster, _Further Reins on Nuclear Arms: Next Steps for the Major Nuclear Powers_. Atlantic Council Policy Paper, Consultation Paper Series, August 1993.
3. Ibid., p. 21.
4. The quotation has also been attributed to Dwight Morrow and Jean Monnet.
_III. International Public Policy: The International Institute for Strategic Studies (IISS)_*
_An Appreciation from Abroad_
I came to know General Goodpaster through the International Institute for Strategic Studies (IISS), of which we were both members. He, of course, was a very senior member of the Institute and I, a generation younger, had yet to make my mark. But the Institute had a broad span of members, not only in international terms—some eighty countries were represented in its membership in the late 1970s—but also in terms of age and profession. These were great strengths, and they helped to propel the Institute from very humble beginnings as a British research and discussion group in 1958 to one which, by the mid-1960s, spanned the NATO membership but also included several other closely associated countries, such as my own Australia.
The Institute was well suited to the kind of discussions in which General Goodpaster shone. There was no doubting his professional standing as a man with a distinguished record of military service during the Second World War and the Cold War. Moreover, he had what many of his contemporaries lacked at that time: serious intellectual credentials in the form of a PhD from Princeton.
He was used to the cut and thrust of debate that challenged basic assumptions, such as the utility of nuclear weapons for the defense of Western Europe. He did not tighten up when under challenge from his juniors, or rely on his seniority to buttress a point that others did not hold. He was well-informed, not behind the times in terms of what was appearing in leading journals, books and newspapers. He was skeptical about much of what others claimed to be the right approach to this issue or that. Furthermore, he respected the rights of others to be skeptical about positions that he held, or had to defend publicly because of the official position he held as Supreme Allied Commander, Europe (SACEUR). Continuous study was part of his life and had been for decades.
There can be no doubt that Goodpaster's impact on others was reinforced by his appearance and his engaged but relaxed nature. His height and figure revealed a man who kept himself physically fit. His penchant for wearing tartan trousers certainly won him favorable attention from those of us of Scottish descent. And in conversation he displayed a ready sense of humor and was quick to appreciate a lighter point made by others to whom he was talking.
As I came to know the views of other generals of other NATO countries I could see that several, but far from all, of them were basically skeptical about the pillars on which western security rested in the middle and later decades of the Cold War. And of course later, as we know, General Goodpaster came out publicly in advocating the elimination of nuclear weapons. One wonders how early he came to espouse this view, and whether the kind of fundamental debates that sometimes were held by the IISS at its conferences had contributed to this direction in his thinking?
Certainly, he advocated the development of strong conventional forces by NATO members as the best way to maintain security against any possible Warsaw Pact move against the West. In doing this he recognized that several NATO governments would resist his arguments to make a greater contribution of conventional forces for the common good. Nonetheless, he sustained his beliefs and policies, even when in discussion with allies whom he regarded as free-riders. For myself, having been a Captain in an Australian infantry battalion in the Vietnam War, I found his emphasis on conventional force development and operational methods very welcome. The Vietnam War at least had some good effect in giving a wide range of U.S. and allied soldiers cause to lift their standards both in terms of operating against an enemy and in the delicate process of relating with a civil population over which the war was being fought.
I did not know much about General Goodpaster while I was in Vietnam because our periods of service there did not overlap. Also, he was too far above me, while not in the public eye in the way that Generals Westmoreland and Abrams were. Nonetheless, it was apparent that, by the early 1970s when I first had contact with him _via_ the IISS, Goodpaster was not happy with some of the approaches to counter-insurgency taken by the Johnson Administration. He felt that Johnson was trying too hard to perform a political juggling act and was thereby failing to devote sufficient resources to winning the war.
Goodpaster was a maximalist rather than a "light-touch" counter-insurgent. At the same time, he could see that it had become very difficult for the U.S. to provide a massive increase in its forces on the ground in Vietnam because of the needs of other theatres, especially Europe. He seemed to be glad that his period in Vietnam as General Abrams' deputy was only a year. The top military post in NATO was much more to his taste than fighting the Vietnam War.
After his first retirement in 1974, Goodpaster was able to utilize the links with the university and think-tank community that he had begun to build up while he was SACEUR. My former mentor and friend Norman Gibbs at Oxford spoke highly of Goodpaster's contributions to the annual NATO conference that Gibbs and others at Oxford ran each spring or summer. He was a frequent participant in the major research institute conferences on international security on both sides of the Atlantic. By the late 1970s, there were many security intellectuals in Europe and North America who thought that a general with a PhD was a great asset and that there should be more of them! General Goodpaster set a career example for many of us in the security analysis business, both military and otherwise. Briefly put, he did the standing of the United States in this community a great power of good.
In 1981, General Goodpaster was elected a Vice-President of the IISS, and he attended Council meetings until he stepped down at his own request in March 1989. I was the Director of the Institute from 1982 to 1987, and was very grateful to have had the General's advice and encouragement throughout this period. He made a remarkable contribution in so many ways to rational thinking on international security questions for over fifty years.
**Notes**
1. General Goodpaster was also affiliated at times and in various ways with the George C. Marshall Foundation, the Woodrow Wilson International Center for Scholars, The Citadel, The Institute for Defense Analyses, and the Center for Strategic and International Studies. There is also the Andrew J. Goodpaster Prize and Lecture awarded by the American Veterans Center, and the Andrew J. Goodpaster Award of the George C. Marshall Foundation.
* Prepared for C. Richard Nelson by St. Mary's president Margaret O'Brien, dated 2 June 2010. Used with permission.
* This is adapted and edited from a larger tribute to General Goodpaster, written shortly after his death in 2006, by C. Richard Nelson and Kenneth Weisbrode, who were associated with him at the Atlantic Council. Used with permission.
* Written by Dr. Robert O'Neill, Chichele Professor of the History of War, Emeritus, All Souls College, Oxford University; former Director, International Institute for Strategic Studies (London).
Notes
**Foreword**
1. A. J. Goodpaster, "Oral History of the Superintendency of Gen. A. J. Goodpaster, USA (Ret.)," interviewed by Lt. Col. James M. Johnson, USA (Ret.), Department of History, U.S. Military Academy (USMA), n.d., p. 93.
2. Floyd W. Matson, _The Broken Image: Man, Science, and Society_ (New York: Anchor Books, 1966), p. 236.
**Preface**
1. William B. Pickett, "General Andrew Jackson Goodpaster: Managing National Security," in _The Human Tradition in America since 1945_ , ed. David L. Anderson (Wilmington, DE: Scholarly Books, 2003), p. 26.
**Chapter 1. The Professional Foundation**
1. Stephen E. Ambrose, _Ike's Spies: Eisenhower and the Espionage Establishment_ (Jackson, MS: University Press of Mississippi, 1999), p. 307.
2. Stephen Hess, _Presidents and the Presidency_ (Washington, DC: The Brookings Institution, 1996), pp. 17–18.
3. Hans Gerth and C. Wright Mills, _Character and Social Structure: The Psychology of Social Institutions_ (New York: Harcourt, Brace and World, 1953), p. 412.
4. Andrew J. Goodpaster, Oral History interview, by Dr. Maclyn P. Burg, 20 August 1976, Eisenhower Presidential Library, p. 23.
5. Wallace Stegner, "The Writer and the Concept of Adulthood," in _Adulthood_ , ed. Erik H. Erikson (New York: W. W. Norton, 1978), p. 227.
6. Andrew J. Goodpaster, transcript of filmed interview by Ken Mandel and James McCall, Great Projects Film Company, Atlantic Council, 31 July–1 August 2001; 15–16 January 2002; 11–12 February 2004, George C. Marshall Foundation.
7. Ibid.
8. Stephen E. Ambrose, _Rise to Globalism: American Foreign Policy, 1938–1980_ , 2nd rev. ed. (New York: Penguin Books, 1980), p. 13. There were U.S. troops in overseas dependencies, such as Alaska, Hawaii, and the Philippines.
9. _Howitzer_ (USMA Yearbook), 1939, p. 339.
10. See Edwin A. Deagle, "General George A. Lincoln: Architect of American National Security" unpublished manuscript. Used with permission.
11. Goodpaster, Mandel and McCall interview.
12. Edgar P. Dean, Secretary of Study Groups, Council on Foreign Relations, to Lt. Col. Herman Beukema, USMA, 23 February 1939, George C. Marshall Foundation Research Library, Lexington, VA.
13. During his post-Army years, they maintained a townhouse in Alexandria, Virginia, and a weekend home at Swan Point, Maryland. He tried to divide his time and energies thus: one-third employment, one-third pro-bono activities, and one-third recreation (which included salmon fishing in Labrador each year). I am grateful for the cooperation of Susan Goodpaster Sullivan and granddaughter Sarah Nesnow.
14. Quoted from the paper "Concept for Duty Development," which was transmitted in a memorandum of 16 April 1981, signed by Lieutenant General Goodpaster as superintendent.
15. Ibid. For an interesting background summary of life at West Point over the years, see Edward Cox, _Grey Eminence: Fox Conner and the Art of Mentorship_ (Stillwater, OK: New Forums Press, 2011).
16. Simone de Beauvoir, _The Mandarins_ (New York: The World Publishing Co., 1956), p. 275.
17. Quoted in David Dimbleby and David Reynolds, _An Ocean Apart: The Relationship between Britain and America in the Twentieth Century_ (New York: Random House, 1988), p. 133.
18. Gordon L. Rottman, _U.S. Combat Engineer, 1941–45_ (Long Island City, NY: Osprey Publishers, 2010), pp. 38–50. As an illustration of the state of the Army's unpreparedness for global combat, consider: "In mid-1939, the U.S. Army Corps of Engineers numbered less than 800 officers and 6,000 enlisted men in active Regular Army service."
19. Michael Matloff, "The American Approach to War, 1919–1945," in _The Theory and Practice of War_ , ed. Michael Howard (London: Cassell, 1965), p. 221.
20. Goodpaster, Mandel and McCall interview.
21. Matloff, "The American Approach to War 1919–1945."
22. Ibid.
23. Ibid.
24. Joseph P. Hobbs, _Dear General: Eisenhower's Wartime Letters to Marshall_ (Baltimore: The Johns Hopkins University Press, 1971), pp. 84–85. Marshall was meticulous in his dealings with his professional colleagues, as the following anecdote illustrates. "Then, on January 30 [1944] Eisenhower referred to a rug he had given to Mrs. Marshall: 'So far as I can recall I have never before in my service given a personal present to my superior or to a member of his family, and I assure you that I regard this as a real privilege.' He discussed the present again on June 26 because Marshall had given the rug to Mrs. Eisenhower as a present from her husband."
25. Stewart W. Husted, _George C. Marshall: Rubrics of Leadership_ (Carlisle Barracks, PA: Army War College Foundation, 2006), p. 13. This inclusion was both undated and without a citation, but Husted attributes it to Marshall and it serves as the subtitle to his very readable biography.
26. Goodpaster, Mandel and McCall interview. It is worth noting that these engineers helped build the famed Burma Road. It was part of the 48th Engineer Combat Regiment, which was activated on 25 July 1942 at Camp Gruber.
27. Goodpaster, Mandel and McCall interview, p. 14.
28. Ibid.
29. Capt. Mark Reardon, CE, _The Battalions: History of the 1108th Engineer Combat Group_ (publisher unknown, 1945), p. 29. "Demolitions and minefields blocked every avenue of approach; machine gun and mortar positions were well-dug-in—many blasted out of solid rock—and camouflaged to disappear into the rugged scenery. German artillery had registered on all roads, trails, and possible sites for bivouac and assembly area." See also Fifth Army Historical Section, _From the Volturno to the Winter Line 6 October–15 November 1943_ , American Forces in Action series (Washington, DC: U.S. Army Center of Military History, 1990), CMH Pub 100–8.
30. Goodpaster, Mandel and McCall interview.
31. Mark Perry, _Partners in Command: George Marshall and Dwight Eisenhower in War and Peace_ (New York: The Penguin Press, 2007), p. 231.
32. One of the most fascinating accounts of this operation, as told from the German side, is _Neither Fear nor Hope: The Wartime Career of General Frido Von Senger Und Etterlin, Defender of Cassino_ , trans. George Malcolm (London: MacDonald, 1963).
33. Rick Atkinson, _The Day of Battle: The War in Sicily and Italy, 1943–1944_ (New York: Henry Holt, 2007), p. 348. This is a dramatic recounting of the entire Rapido operation, in which Goodpaster was deeply involved.
34. For a description of the multiplicity of functions for combat engineers, see Rottman, _U.S. Combat Engineer_ , _1941–45_ , pp. 38–50.
35. Goodpaster, Mandel and McCall interview.
36. Ibid., pp. 17–20. Goodpaster was serving as both the commander of the 48th Division and the 1108th Group. The author has done minor editing of the literal oral interview text. The Fifth Army had initially attacked across the Volturno River on the night of 12 October. The Germans skillfully used the terrain, which was favorable for defense, and retreated to the next line north (the Barbara Line), which the Allies reached by 2 November.
37. Lt. Col. Andrew J. Goodpaster, "A Message to the Men of the 48th Engineer Combat Battalion," 23 December 1943.
38. Dwight D. Eisenhower, _Crusade in Europe_ (Garden City, NY: Doubleday, 1948), p. 210.
39. Reardon, _The Battalions_ , p. 31.
40. U.S. Army, Headquarter II Corps, 2210.5/193-SS (AG).
**Chapter 2. Professional Planning**
1. Andrew J. Goodpaster, interview by Ed Edwin, 25 April 1967, Eisenhower Presidential Library.
2. Goodpaster, Mandel and McCall interview, 15 January 2002, pp. 5–6.
3. Deagle, "General George A. Lincoln," ch. 14, p. 1. Portions of this section, slightly revised, are drawn with permission.
4. Lincoln remained in Washington until 1947, when he became deputy head of West Point's soon-to-be-renamed Department of Social Sciences. In order to return to West Point, he had to accept a two-rank demotion to colonel (having been promoted to major general), which he willingly did. As recalled: "Lincoln's friend and mentor, Colonel Herman Beukema, convinced him that the powerful strategy for intervening in the education of general officers was to equip them for handling political and military high command matters at West Point—not at the military war colleges." Beukema had been head of the department when Goodpaster was a student.
5. Deagle, "General George A. Lincoln."
6. See Ray S. Cline, _United States Army in World War II, The War Department, Washington Command Post: The Operations Division_ (Washington, DC: Center of Military History, U.S. Army, 1951), p. 309.
7. Niall Ferguson, Charles S. Maier, Erez Manela, and Daniel J. Sargent, _The 1970s in Perspective_ (Cambridge, MA: The Belknap Press of Harvard University Press, 2010), p. 13.
8. See Robert S. Jordan, "The Influence of the British Secretariat Tradition on the Formation of the League of Nations," in _International Administration: Its Evolution and Contemporary Applications_ , ed. Robert S. Jordan (New York: Oxford University Press, 1971), pp. 27–50. This same tradition, first introduced into the League of Nations (under Sir Eric Drummond), was incorporated into the NATO International Staff/Secretariat under the leadership of the first secretary-general, Lord Ismay.
9. Andrew Roberts, _Masters and Commanders: How Four Titans Won the War in the West, 1941–1945_ (New York: HarperCollins, 2009), p. 114.
10. Cline, _United States Army in World War II_ , pp. 94–95.
11. Maj. Jeffrey J. Tierney, USA, "Campaign Planning: A Missing Piece in the Joint Planning Process," Executive Summary, _GlobalSecurity.org_, 1992, <http://www.globalsecurity.org/military/library/report/1992/TJJ.htm>.
12. Cline, _United States Army in World War II_ , p. 337. With the atomic bombing of Hiroshima and Nagasaki, war-fighting planning speedily gave way to postwar planning, including the JWPC: "Only the existence of the State-War-Navy Coordinating Committee and the experience of staff like Colonel Bonesteel's political-military group in the Policy Section made such speed possible" (Ibid., p. 350).
13. Ibid., p. 17.
14. Gen. Andrew Goodpaster, interview by Dr. Thomas Soapes, Oral Historian, 11 October 1977, Eisenhower Presidential Library, p. 63.
15. Ibid.
16. "Information Sheet on the Joint Advanced Study Committee, Office," Joint Chiefs of Staff. The committee was expected to engage in "intensive analysis." See also Memorandum No. 10–15–1, "Advanced Study Group, Plans and Operations Division," War Department General Staff, dated 1 May 1947.
17. Untitled JASC memorandum, 29 November 1950, p. 1.
18. Andrew J. Goodpaster, "Basic Considerations," JASC memorandum, 30 November 1950, p. 1ff.
19. Ibid.
20. Ibid., p. 2; Goodpaster to Col. R. W. Porter, 7 November 1950. Goodpaster also observed: "Because atomic explosives are due, before long, to become a factor in nearly every kind and phase of military activity, some penetrating influences are going to be felt on such matters as balance of forces, 'strategic' vs. 'tactical' courses of action, etc., extending to dispersion of troops on the battlefield, and problems of communications and control, as well as concentration."
21. For a thorough analysis of this dilemma, see the Rockefeller Panel Report, _Prospect for America: The Problems and Opportunities Confronting American Democracy—in Foreign Policy, in Military Preparedness, in Education, in Social and Economic Affairs_ (New York: Doubleday and Co., Inc., 1961). Goodpaster's mentor, Abe Lincoln, served on the panel. Goodpaster was assigned to serve as an aide to the vice resident.
22. Goodpaster to Lincoln, p. 4. Goodpaster also noted, wryly: "I am beginning to have some impressions about the military establishment. I can perhaps express them best by stating the extremes, which bound the range within which the truth probably lies. The most striking features to me are the 'diffuseness' . . . and the low current level of intellectual honesty in the sense of willingness and freedom to re-open basic questions."
23. Ibid., p. 3. The British military historian John Keegan termed it "post-heroic" leadership.
24. Goodpaster to Professor Harold Sprout, 8 November 1950.
25. JCS Memorandum: Efficiency Report (Letter), Lt. Col. Andrew J. Goodpaster Jr., 0 21739, CE [Corps of Engineers], period 24 June 1950 to 4 January 1951.
26. Goodpaster, Mandel and McCall interview, 31 July–1 August 2001.
27. Goodpaster to Brodie, 7 January 1947.
28. Goodpaster, Mandel and McCall interview, 31 July–1 August 2001.
29. For example, even though the author had not taken a seminar from him, when it came time to choose where to write his doctoral dissertation—Harvard or Oxford—Professor Sprout stepped forward with an introduction to two key Oxonians, Professor Norman Gibbs of All Souls College, and Sir William Deakin, the warden of St. Antony's College. The author became a member of St. Antony's College, and Professor Gibbs became his dissertation adviser, and later, with the intervention of Professor Max Beloff of All Souls College, the Oxford University Press published the dissertation.
30. Goodpaster may have noted that the warden of Princeton's Graduate College had stones from the garden walls of both Cambridge and Oxford Universities embedded in the wall of his private garden. Also, when he would "dine in," Goodpaster would have worn the black commoner's gown similar to those worn at these two venerable British universities.
31. Letter, Sprout to Goodpaster, 20 March 1955, and reply, Goodpaster to Sprout, 28 March 1955. It took only this one week to get the policy changed.
32. The author was president of APGA at that time, and so conveyed to Goodpaster his medal.
33. Andrew J. Goodpaster, "National Technology and International Politics" (unpublished doctoral dissertation, Department of Politics, Princeton University, May 1950), pp. 1–9.
34. Robert Heilbroner has stated it in similar terms: "Technological determinism is peculiarly a product of a certain historic epoch . . . in which the forces of technical change have been unleashed, but when the agencies for the control or guidance of technology are still rudimentary." Quoted in Charles W. Yost, _History and Memory: A Statesman's Perceptions of the Twentieth Century_ (New York: W. W. Norton, 1980), p. 199.
35. Goodpaster, "National Technology and International Politics," pp. 1–9.
36. Ibid.
37. Ibid.
38. Ibid., pp. 376–377. This conclusion also shows how Goodpaster could combine his engineering work while at Princeton with his increasing interest in international and national security affairs and the social sciences generally.
39. Goodpaster to Lt. Col. James L. Cantrell, 20 September 1950, p. 2.
40. Ibid., p. 1.
**Chapter 3. Goodpaster and the Creation of NATO/SHAPE**
1. See, for example, Robert S. Jordan, _The NATO International Staff/Secretariat, 1952–1957: A Study in International Administration_ (London: Oxford University Press, 1967).
2. For a general background, see Kenneth Weisbrode, _The Atlantic Century: Four Generations of Extraordinary Diplomats Who Forged America's Vital Alliance with Europe_ (Cambridge, MA: Da Capo Press, 2009). For a more NATO focus, see Gustav Schmidt, ed., _A History of NATO: The First Fifty Years_ , vol. 1 (New York: Palgrave, 2001).
3. Lawrence S. Kaplan, _NATO Divided, NATO United: The Evolution of an Alliance_ (Westport, CT: Praeger, 2004), p. 9. Dr. Kaplan's numerous writings on the alliance have become an informal NATO library.
4. Stephen E. Ambrose, _Eisenhower: Soldier, General of the Army, President-Elect, 1890–1952_ (New York: Simon & Schuster, 1983), 1:506.
5. John V. Wahlfeld, _Eisenhower and the Second Crusade in Europe_ (master's thesis, University of North Carolina, 1975), p.11n12.
6. Timothy P. Ireland, _Creating the Entangling Alliance: The Origins of the North Atlantic Treaty Organization_ (Westport, CT: Greenwood Press, 1981), p. 183.
7. Goodpaster, Mandel and McCall interview.
8. Ibid.
9. Gregory W. Pedlow, "The Politics of NATO Command, 1950–1965," in _U.S. Military Forces in Europe: The Early Years, 1945–1970_ , ed. Simon W. Duke and Wolfgang Krieger (Boulder, CO: Westview Press, 1993), p. 18.
10. Andrew J. Goodpaster, "The Development of SHAPE: 1950–1953," in _Generals in International Politics: NATO's Supreme Allied Commander, Europe_ , ed. Robert S. Jordan (Lexington, KY: The University Press of Kentucky, 1987), p. 1. On 18–19 December, the North Atlantic Council formally requested that Eisenhower be appointed SACEUR.
11. Ibid., p. 2.
12. Memorandum for Admiral Davis from Lieutenant General Gruenther, 15 December 1950.
13. Jordan, _Generals in International Politics_ , p. 122. On 2 April 1951, Eisenhower signed the activation order for ACE and SHAPE. On the same day, ACE's subordinate headquarters in Northern and Central Europe were activated, with the Southern Region following in June. In July, SHAPE moved to Rocquencourt.
14. Goodpaster, "The Development of SHAPE: 1950–1953."
15. Ibid. Goodpaster's specific responsibilities in the planning groups were monitoring the creation of the plans and operations, the training, and the intelligence headquarters units. He also recognized early on the importance of establishing an historical section to chronicle the evolution of this new multinational military entity.
16. _The Papers of Dwight David Eisenhower_ , ed. by Louis Galambos et al., vol. 12, _NATO and the Campaign of 1952_ (Baltimore, MD: The Johns Hopkins University Press, 1989), p. 663.
17. Gen. A. M. Gruenther, "The Mission of SHAPE and NATO in Furthering the Security of the Free World" (speech at West Point, 21 April 1952, p. 6).
18. Goodpaster, Soapes interview. Also see Galambos et al., _The Papers of Dwight David Eisenhower_ , p. 594: In a letter to his son John, in regard to John's joining SHAPE, Eisenhower commented: "Some time ago, I casually asked General Gruenther whether there was a place in his General Staff for a man of your qualifications, giving as my reason that I thought you would have a great experience to work with a group of young American officers we have, all of them really brilliant. They are men named . . . Goodpaster."
19. Jordan, _Generals in International Politics_ , pp. xiv–xviii. By the mid-1950s the two "hats" were accompanied by a third "hat," called Live Oak, which involved the SACEUR in the planning for the use of nuclear weapons in Europe. For more, see Robert S. Jordan, _Norstad: Cold War NATO Supreme Commander, Airman, Strategist, Diplomat_ (New York: St. Martin's Press, 2000), chap. 7. See also George C. Mitchell, _Matthew B. Ridgway, Soldier, Statesman, Scholar, Citizen_ (Mechanicsburg, PA: Stackpole Books, 2002).
20. Jordan, _Staff/Secretariat_ , p. 26.
21. Robert S. Jordan, _Political Leadership in NATO: A Study in Multinational Diplomacy_ (Boulder, CO: Westview Press, 1979), p. 13.
22. For a thorough description of the methods employed and the results obtained, see Jordan, _Staff/Secretariat_ , pp. 202ff.
23. Goodpaster, Mandel and McCall interview.
24. Jordan, _Staff/Secretariat_ , pp. 204–205.
25. Goodpaster, Mandel and McCall interview.
26. Harriman to Eisenhower, 18 December 1951. Goodpaster's friend and mentor Abe Lincoln was in Paris representing Secretary of Defense Lovett to the TCC's "Three Wise Men," which would have pleased Goodpaster.
27. Goodpaster to Col. G. A. Lincoln, 14 January 1952.
28. Goodpaster to William Burnham, 15 February 1952.
29. Gruenther to Goodpaster, 21 December 1951.
30. Goodpaster to H. Igor Ansoff, 17 July 1952. His particular letter ran to four typewritten, single-spaced pages. He also was coauthor of an article in the August issue of the academic journal _International Organization_ and speculated at length on coalition theory.
31. Gen. Andrew J. Goodpaster, "SHAPE and Allied Command Europe: Twenty Years in the Service of Peace and Security, 1951–1971," _NATO's Fifteen Nations Magazine_ , April 1971, pp. 11–12.
32. Quoted in Jordan, _Generals in International Politics_ , p. 122.
33. Goodpaster to Flood, 25 April 1951.
34. Andrew J. Goodpaster, memoranda for Mr. William J. Hopkins; and Mr. Ralph Dungan, 21 January 1961.
35. Andrew J. Goodpaster, "George Marshall's World, and Ours," _New York Times_ , 11 December 2003.
36. Quoted in Husted, _George C. Marshall, Rubrics of Leadership_ , p. 1.
37. Forrest C. Pogue, _George C. Marshall: Statesman 1945–1959_ (New York: Penguin Books, 1987), p. 505.
38. Quoted in Hobbs, _Dear General_ , p. 104.
**Chapter 4. Solarium: The Articulation of a National Posture**
1. George F. Kennan, ("X"), "The Sources of Soviet Conduct," _Foreign Affairs_ , July 1947. Kennan wrote his famous "X" article in the journal _Foreign Affairs_ in 1947, suggesting that pressure applied consistently, over time, would result in the Soviet system collapsing from within.
2. Campbell Craig and Sergey Radchenko, _The Atomic Bomb and the Origins of the Cold War_ (New Haven, CT: Yale University Press, 2008), p. 131.
3. David J. Rothkopf, _Running the World: The Inside Story of the National Security Council and the Architects of American Power_ (New York: Public Affairs, 2005), p. 69.
4. Tyler Notting, _Once and Future Policy Planning: Solarium for Today_ (Washington, DC: The Eisenhower Institute, January 1993), p. 1.
5. Quoted in Donald F. Bletz, _The Role of the Military Professional in U.S. Foreign Policy_ (New York: Praeger Publishers, 1972), p. 42.
6. Theodore Zeldin, _An Intimate History of Humanity_ (New York: Harper Perennial, 1996), p. 14.
7. John Foster Dulles Centennial Conference (also called "'Project Solarium': A Collective Oral History"), "The Challenge of Leadership in Foreign Affairs," Princeton University, 27 February 1988, pp. 18–19. Hereafter referred to as Princeton Conference.
8. Steven L. Rearden, _The Evolution of American Strategic Doctrine: Paul H. Nitze and the Soviet Challenge_ (Washington, DC: Westview Press, 1984), p. 423.
9. Ernest R. May, _American Cold War Strategy: Interpreting NSC 68_ (New York: Bedford/St. Martin's, 1993), pp. 1–2.
10. Andrew J. Goodpaster Jr., transcript of oral history interview by Malcolm S. McDonald, 10 April 1982, Eisenhower Presidential Library, p. 2.
11. Princeton Conference, p. 19.
12. Ibid., p. 23.
13. Nonetheless, Goodpaster remained a "hawk" vis-á-vis the Soviet threat throughout his post-Army career, cochairing, for example, the Committee on the Present Danger in 1974.
14. Barton Gellman, _Contending with Kennan: Toward a Philosophy of American Power_ (New York: Praeger, 1984), p. 131.
15. Quoted in Paul Kennedy, ed., _Grand Strategies in War and Peace_ (New Haven, CT: Yale University Press, 1991), p. 2.
16. Robert R. Bowie and Richard H. Immerman, _Waging Peace: How Eisenhower Shaped an Enduring Cold War Strategy_ (New York: Oxford University Press, 1998), p. 124.
17. Ibid.
18. Ibid., pp. 126–127. The authors are quoting from the original documents. See also Meena Bose, _Shaping and Signaling Presidential Policy: The National Security Making of Eisenhower and Kennedy_ (College Station, TX: Texas A&M University Press, 1998), pp. 29–41.
19. Goodpaster, McDonald interview.
20. Robert Cutler, _No Time for Rest_ (Boston: Little, Brown and Co., 1966), p. 309.
21. Quoted in Rothkopf, _Running the World_ , p. 70.
22. Princeton Conference, pp. 9–10.
23. Quoted in Lewis Sorley, _Honorable Warrior: General Harold K. Johnson and the Ethics of Command_ (Lawrence, KS: University Press of Kansas, 1998), p. 112.
24. Ibid.
25. For more on this point, see Bowie and Immerman, _Waging Peace_ , pp. 123–138.
26. Ibid.
27. Ibid., p. 137. Much of this aspect of the Cold War is chronicled in David Caute, _The Dancer Defects: The Struggle for Cultural Supremacy during the Cold War_ (Oxford: Oxford University Press, 2003).
28. James Marchio, "The Planning Coordination Group: Bureaucratic Casualty in the Cold War Campaign to Exploit Soviet-Bloc Vulnerabilities," _Journal of Cold War Studies_ 4, no. 4 (2002): 28. As it was described: "The violent suppression of the popular rebellion in Hungary in November 1956 convinced the president and his top advisers [which would have included Goodpaster] of the dangers of political war. . . . The bloodshed in the streets of Budapest helped force the Eisenhower administration to abandon its strategy of 'conflicting approaches.'" See also Kenneth A. Osgood, "Hearts and Minds: The Unconventional Cold War [review essay]," _Journal of Cold War Studies_ 4, no. 2 (Spring 2002): 85–107.
29. Andrew J. Goodpaster, interview by Ed Edwin, 25 April 1967, Eisenhower Presidential Library.
30. In an aside, during the Princeton Conference, Kennan commented: "Foster Dulles sat at my feet and was thus instructed on what the policy ought to be toward the Soviet Union. Since it was only three months since he had fired me from the Foreign Service, this gave me a certain satisfaction. I could talk, and he had to listen, for about a half an hour." (Princeton Conference, pp. 5–6.) In this respect, the following comment is apt: "Kennan gave modern meaning to a role for intellectuals in high politics." (Bruce Kuklick, _Blind Oracles: Intellectuals and War from Kennan to Kissinger_ [Princeton, NJ: Princeton University Press, 2006], p. 41.)
31. Bose, _Shaping and Signaling Presidential Policy_ , p. 41.
32. Kenneth Weisbrode, "A Tale of Three Cold Warriors," _NATO Review_ (Spring 2006).
**Chapter 5. The "New Look"**
1. Steven L. Rearden, _The Formative Years, 1947–1950_ (Washington, DC: Office of the Secretary of Defense, 1984), p. 36.
2. Quoted in Dale R. Herspring, _The Pentagon and the Presidency: Civil-Military Relations from FDR to George W. Bush_ (Lawrence, KS: University Press of Kansas, 2005), p. 93.
3. Goodpaster, Soapes interview, p. 104.
4. This is in reference to NSC-68.
5. Kenneth W. Thompson and Steven L. Rearden, eds., _Paul H. Nitze on National Security and Arms Control_ (New York: University Press of America for the Miller Center of the University of Virginia, 1990), p. 5n.
6. Marc Trachtenberg, _History and Strategy_ (Princeton, NJ: Princeton University Press, 1991), p. 138. Trachtenberg observed: "His thinking was right out of the first few pages of Clausewitz: war has an innate tendency to become absolute. 'In such a war,' [Eisenhower] said, 'the United States would be applying a force so terrible that one simply could not be meticulous as to the methods by which the force was brought to bear.'"
7. David Callahan, _Dangerous Capabilities: Paul Nitze and the Cold War_ (New York: HarperCollins, 1990), p. 176.
8. There are several variations of this paradoxical thought in the literature of the time.
9. Gordon A. Craig and Alexander L. George, _Force and Statecraft: Diplomatic Problems of Our Time_ (New York: Oxford University Press, 1995), pp. 259–260.
10. Contained in White House Office of the Staff Secretary, 1952–61, Eisenhower Presidential Library, Box No. 24, p. 4.
11. Ibid.
12. Princeton Conference, p. 13.
13. Goodpaster, McDonald interview, p. 3.
14. Neil Sheehan, _A Fiery Peace in a Cold War: Bernard Schriever and the Ultimate Weapon_ (New York: Random House, 2009), p. 273. Sheehan discusses through the lens of Schriever's career the full scope of the government's efforts at reconciling these new technologies with the more traditional roles-and-missions posture of the three services.
15. National Reconnaissance Office, "A National Imperative (1945–1955)," <http://www.nrojr.gov/teamrecon/res_his-NationalImp.html>.
16. David Haight to Robert S. Jordan (n.d.).
17. This observation is attributable to Steven Rearden in a private, undated memorandum.
18. Andrew J. Goodpaster, _For the Common Defense_ (Lexington, MA: Lexington Books, 1977), pp. 62–63.
19. Goodpaster, McDonald interview, p. 5.
20. Princeton Conference, p. 7.
21. Michael R. Beschloss, _Mayday: Eisenhower, Khrushchev and the U-2 Affair_ (Boston: Faber and Faber, 1986), p. 6n.
22. Ibid., p. 23.
23. Walter LaFeber, _America, Russia, and the Cold War, 1945–1966_ (New York: John Wiley and Sons, Inc., 1968), p. 151.
24. See, for example, Francis Stonor Saunders, _The Cultural Cold War: The CIA and the World of Arts and Letters_ (New York: The New Press, 2001); also Cord Meyer, _Facing Reality: From World Federalism to the CIA_ (New York: Harper and Row, 1980).
25. Goodpaster, McDonald interview, p. 10.
26. Craig and George, _Force and Statecraft_ , p. 262.
27. Edgar O'Ballance, _Korea: 1950–1953_ (Malabar, FL: Robert E. Krieger Pub. Co., 1985), p. 147.
28. Rearden, _The Evolution of American Strategic Doctrine_ , p. 39.
29. Gen. Andrew J. Goodpaster, "Interests and Strategies in an Era of Détente: An Overview," Foreword to _National Security and Détente_ (New York: Thomas Y. Crowell, 1976), pp. x–xiii. The policy of détente could only make sense, if a concession by one of the parties was "linked" to a related concession by the other party. A good example was the seemingly endless negotiations over Berlin.
30. Lord Ampthill, quoted in Graham Wallas, _Human Nature in Politics_ , 4th ed. (London: Constable, 1948), p. 290.
31. David A. Nichols, _Eisenhower 1956: The President's Year of Crisis—Suez and the Brink of War_ (New York: Simon & Schuster, 2011), p. 278.
**Chapter 6. Presidential Staff Secretary and Counselor**
1. Stephen Hess, _Organizing the Presidency_ , 3rd ed. (Washington, DC: Brookings Institution Press, 2002), p. 187.
2. Weisbrode, "A Tale of Three Cold Warriors."
3. Elmo Richardson, _The Presidency of Dwight D. Eisenhower_ (Lawrence, KS: University Press of Kansas, 1979), p. 26.
4. Stephen E. Ambrose, _Nixon: The Education of a Politician, 1913–1962_ (New York: Simon & Schuster, 1987), p. 611.
5. Ibid., p. 63.
6. Robert H. Ferrell, ed., _The Diary of James C. Hagerty: Eisenhower in Mid-Course, 1954–1955_ (Bloomington, IN: Indiana University Press, 1983), p. 1131.
7. Phillip G. Henderson, _Managing the Presidency: The Eisenhower Legacy—From Kennedy to Reagan_ (Boulder, CO: Westview Press, 1988), p. 115.
8. Dwight D. Eisenhower, _The White House Years: Mandate for Change, 1953–1956_ (Garden City, NY: Doubleday, 1963), p. 117. According to Goodpaster, Eisenhower invented the title.
9. See memo for record, Robert Cutler, Special Assistant to the President for National Security Affairs, "Attendees at National Security Council Meetings," 30 November 1954.
10. Goodpaster, Mandel and McCall interview, 16 January 2002, pp. 5–6.
11. "President Eisenhower's Diary," Scope and Content Note, DDE Diaries, p. 1, <http://www.ibiblio.org/lia/president/EisenhowerLibrary/finding_aids/DOE's_Diary.html>.
12. Bradley H. Patterson Jr., _The Ring of Power: The White House Staff and Its Expanding Role in Government_ (New York: Basic Books, 1988), pp. 298–299.
13. Piers Brendon, _Ike: His Life and Times_ (New York: Harper and Row, 1986), p. 236.
14. Robert S. Jordan, "The Contribution of the British Civil Service and Cabinet Secretariat Tradition to International Prevention and Control of War," in _The Limitations of Military Power: Essays Presented to Professor Norman Gibbs on his Eightieth Birthday_ , ed. John B. Hattendorf and Malcolm H. Murfett (New York: St. Martin's Press, 1990), pp. 99–100.
15. Brendon, _Ike_ , p. 235.
16. Hattendorf and Murfett, _Limitations_ , p. 100. Hankey kept extensive diaries, whereas Goodpaster did not, unfortunately for his biographer. See Stephen Roskill, _Hankey, Man of Secrets_ , vol. 2, _1919–1931_ (London: Collins, 1972). For more, see Ismay, Lord Hastings, _The Memoirs of General Lord Ismay_ (New York: The Viking Press, 1960). Ismay was Hankey's deputy and later chief aide to prime minister Winston Churchill; later Ismay was the first secretary-general of NATO. In many ways, Ismay served at the highest level of government in a role similar to Goodpaster's: the self-effacing emissary and coordinator who was trusted by all parties.
17. Brendon, _Ike_ , p. 235.
18. For an elaboration on this point, see Henderson, _Managing the Presidency_ , ch. 2.
19. Great Projects, Oral Interview, 16 January 2002, pp. 5–6.
20. Quoted in Pickett, "General Andrew Jackson Goodpaster: Managing National Security," p. 29.
21. Allen Dulles to Goodpaster (with enclosure), 2 June 1959.
22. Goodpaster, Mandel and McCall interview, pp. 10–11.
23. Pickett, "General Andrew Jackson Goodpaster: Managing National Security," p. 25.
24. Douglas Kinnard, _President Eisenhower and Strategic Management: A Study in Defense Politics_ (New York: Pergamon-Brassey's, 1989), p. 135.
25. For an authoritative discussion, see Margaret MacMillan, _Paris 1919: Six Months That Changed the World_ (New York: Random House, 2001).
26. John Mason Brown, _The Worlds of Robert E. Sherwood: Mirror to His Times, 1896–1939_ (New York: Harper and Row, 1965), pp. 385–386.
27. Robert E. Sherwood, _Roosevelt and Hopkins: An Intimate History_ (New York: Harper and Row, 1948), p. 11.
28. Rothkopf, _Running the World_ , p. 68.
29. This is a transposed version of a remark made in Colin Wilson, _Beyond the Outsider_ (New York: Carroll and Graf, 1991), p. 213.
30. David Stout, "Andrew J. Goodpaster, 90, Soldier and Scholar, Dies," _New York Times_ , 17 May 2005.
31. Eisenhower, _Mandate for Change_ , p. 477.
32. Ibid., p. 478.
33. Dwight D. Eisenhower, _The White House Years, Waging Peace, 1956–1961_ (Garden City, NY: Doubleday, 1965). Pages indicated.
34. In this respect, see Ibid., pp. 150–159.
35. Ibid., p. 247.
36. Leonard Mosley, _A Biography of Eleanor, Allen, and John Foster Dulles and Their Family Network_ (New York: The Dial Press, 1978), pp. 406–407.
37. Ibid., p. 409.
38. For a readable account of Eisenhower's reactions at this time, with Goodpaster in the background, see Donald Neff, _Warriors at Suez: Eisenhower Takes America into the Middle East_ (New York: Simon & Schuster, 1981).
39. Douglas Kinnard, _The Secretary of Defense_ (Lexington, KY: The University Press of Kentucky, 1980), p. 46.
40. Gen. Maxwell D. Taylor to the Adjutant General, Department of the Army, "Promotion to Brigadier General." Taylor's enthusiastic language was tantamount to a direct order.
41. Great Projects, Oral Interview, 16 January 2002, p. 2.
42. Ibid., p. 6.
43. Stout, "Andrew J. Goodpaster, 90." It is also on the Arlington National Cemetery website, <http://www.arlingtoncemetery.net/ajgoodpaster.htm>.
44. David L. Anderson, _Trapped by Success: The Eisenhower Administration and Vietnam, 1953–1961_ (New York: Columbia University Press, 1991), pp. 87–88.
45. Briefing Notes on OCB Activities of Possible Presidential Interest, 17 December 1954 [copy to Goodpaster].
46. Brendon, _Ike_ , p. 308.
47. Ibid.
48. Roy L. Prosterman, _Surviving to 3000: An Introduction to the Study of Lethal Conflict_ (Belmont, CA: Duxbury Press, 1972), p. 153.
49. Amos A. Jordan Jr., ed. _Issues of National Security in the 1970s_ (New York: Praeger, 1967), p. 227–228.
50. Allen Dulles to Goodpaster, 18 July 1956, Doc. 76, "White House: Office of the Staff Secretary—International Series," p. 426.
51. Memorandum, Goodpaster to Calhoun, 26 May 1959, Doc. 99, "Papers as President (Anne Whitman Files)—Administration Series."
52. See Richard E. Neustadt, _Presidential Power: The Politics of Leadership_ (New York: The Free Press, 1961), and Fred Greenstein, _The Hidden-Hand Presidency: Eisenhower as Leader_ (Baltimore, MD: The Johns Hopkins University Press, 1994).
53. Recounted by Henderson, _Managing the Presidency_ , p. 179.
54. John P. Burke and Fred I. Greenstein, _How Presidents Test Reality: Decisions on Vietnam, 1954 and 1965_ (New York: Russell Sage Foundation, 1989), p. 11.
55. Hess, _Presidents and the Presidency_ , p. 32.
56. Dwight D. Eisenhower, Enclosure to Efficiency Report on Colonel Andrew J. Goodpaster Jr., from 6/1/55 to 5/31/56, Item #10, Goodpaster Papers, Marshall Foundation.
57. Ferrell, _Hagerty_ , p. 189.
58. _JCS Reform: Proceedings of the Conference_ (Newport, RI: Naval War College, n.d.), p. 62.
59. Goodpaster, Soapes interview, pp. 92–93.
60. Saki Dockrill, _Eisenhower's New-Look National Security Policy, 1953–1961_ (New York: St. Martin's Press, 1996), p. 23.
61. This is described at length in Michael D. Pearlman, _Warmaking and American Democracy: The Struggle over Military Strategy, 1700 to the Present_ (Lawrence, KS: University Press of Kansas, 1999).
62. H. R. McMaster, _Dereliction of Duty: Lyndon Johnson, Robert McNamara, The Joint Chiefs of Staff, and the Lies That Led to Vietnam_ (New York: Harper Perennial, 1997), pp. 54–55.
63. Dwight D. Eisenhower, Memorandum for the Secretary of the Army: Re: Brigadier General Andrew J. Goodpaster Jr., 3 June 1958, Goodpaster Papers, Box 18, Folder 14, Marshall Foundation Library. Also Cutler to Eisenhower, with copies to Army chief of staff and secretary of the Army, 10 July 1958: In 1958 Robert Cutler, when he was leaving the White House, sent a letter to Eisenhower in which he wrote: "I don't think I ever knew a fellow who could get to the heart of a subject quicker, retain so much of its substance in his mind, work at such top speed, and all the time keep his good humor and sense of proportion. To share the doing of a task with him was always a delight. His opinions and judgments are as sound as they are frank. The serenity of his intellectual processes is fortified by his integrity and courage."
**Chapter 7. A Functional National Security System**
1. Husted, _George C. Marshall: Rubrics of Leadership_ , pp. 130–131.
2. Ibid.
3. Bletz, _The Role of the Military Professional in U.S. Foreign Policy_ , p. 82. This is a quotation attributed to Samuel Huntington. See also Steven L. Rearden, _The Formative Years, 1947–1950_ (Washington, DC: Office of the Secretary of Defense, 1984), pp. 125.
4. Jordan, _Issues of National Security in the 1970s_ , p. 222.
5. Goodpaster, Mandel and McCall interview, 15 January 2002, pp. 14–15.
6. Ibid., p. 13.
7. Hobbs, _Dear General_ , p. 9.
8. Ibid., p. 3.
9. Ed Cray, foreword to _General of the Army George C. Marshall, Soldier and Statesman_ (New York: Cooper Square Press, 2000). Goodpaster claimed that Eisenhower regretted the incident, in which he did not defend Marshall from McCarthyite attacks on Marshall's patriotism while campaigning in Wisconsin. He said, "When I joined President Eisenhower in the fall of 1954 . . . I learned that this was a matter of deep chagrin to Eisenhower. He felt he had got himself mouse-trapped and . . . I think he took to his grave the regret that he had not done right by General Marshall. He told me one time, 'You keep your eye out for anything we can do that will show our respect and regard for General Marshall,' and we did." (Goodpaster, Mandel and McCall interview, 15 January 2002, p. 17.)
10. "National Security Council: The Truman and Eisenhower Years," in _Encyclopedia of the New American Nation_ , ed. Paul Finkelman (Boston: Charles Scribner's Sons, 2005), p. 1.
11. Rudy Abramson, _Spanning the Century: The Life of W. Averell Harriman 1891–1986_ (New York: William, Morrow and Co., Inc., 1992), p. 444.
12. Goodpaster to Frederick Tipson, Senate Foreign Relations Committee, 3 April 1980, in _Letters and Statements of Former Secretaries of State and White House Advisers_ (Washington, DC: Government Printing Office), p. 315. See also Senate Foreign Relations Committee, "Comments on the National Security Advisor," article 31, in _Decisions of the Highest Order: Perspectives on the National Security Council_ , ed. by Karl F. Inderfurth and Loch K. Johnson (Pacific Grove, CA: Brooks/Cole, 1988).
13. For a summary of the evolution of the NSC, see Patterson, chap. 7 in _The Ring of Power_.
14. Judson Knight, "NSC (National Security Council), History," _Encyclopedia of Espionage, Intelligence, and Security_ (2004), <http://www.encyclopedia.com/doc/1G2-3403300554.html>.
15. See James S. Lay, _Organizational History of the National Security Council during the Truman and Eisenhower Administrations_ , p. 26, for a detailed description/discussion of the NSC. In the postelectoral period, Robert Cutler had conducted a wide-ranging study of how national security affairs had been handled during the preceding Truman administration, with recommendations for changes.
16. For more about the OCB's "role and mission," see OCB, Memorandum to the Operations Coordinating Board, sub: "Recommendations to Improve the Effectiveness of the OCB—A Report from the Executive Officer of the Board," 3 January 1955.
17. This observation is attributable to Steven Rearden in a private, undated memorandum.
18. Lay, _Organizational History_ , p. 176.
19. Ibid., p. 1198.
20. Jordan, _Issues of National Security in the 1970s_ , p. 225.
21. Cutler, _No Time for Rest_ , p. 366. Curiously, Cutler hardly mentions the nature and extent of his relationship to Goodpaster, although it was considerable, as the record shows.
22. Inderfurth and Johnson, _Decisions of the Highest Order_ , p. 44.
23. Goodpaster, Soapes interview, p. 74. There was also William J. Jackson, in addition to Cutler and Gray. For an elaboration of the NSC adaptations, see Memorandum for the National Security Council: "The Structure and Functions of the National Security Council, 3 July 1957." Relevant is: "Many changes since [17 March 1953]—particularly the bringing within the NSC structure on July 1, 1957, of the Operations Coordinating Board—have required revision of the above-mentioned memorandum."
24. Ivo H. Daalder and I. M. Destler, _In the Shadow of the Oval Office_ (New York: Simon & Schuster, 2009), p. 6. The person who came closest in the Truman administration in temperament and career development was George Elsey. See George McKee Elsey, _An Unplanned Life_ (Columbia, MO: University of Missouri Press, 2005).
25. Greenstein, _The Hidden-Hand Presidency_ , p. 134.
26. _The Papers of Dwight David Eisenhower_ , ed. Louis Galambos et al., vol. 13, _NATO and the Campaign of 1952_ (Baltimore, MD: The Johns Hopkins University Press, 1989), p. 2191.
27. David Eisenhower with Julie Nixon Eisenhower, _Going Home to Glory: A Memoir of Life with Dwight D. Eisenhower, 1961–1969_ (New York: Simon & Schuster, 2010), pp.16–17.
28. Goodpaster, note (handwritten) for the record, 19 August 1957, Eisenhower Presidential Library.
29. John S. D. Eisenhower, interview by Carol Hegeman, Supervisory Park Ranger, 26 January 1984, pp. 2–3.
30. Goodpaster, Soapes interview, p. 77.
31. John S. D. Eisenhower, interview by Hegeman, p. 4. He also commented that on the frequent weekends when the president was at his Gettysburg home, "I was his 'eyes and ears' to the staff."
32. Goodpaster, Soapes interview, p. 74.
**Chapter 8. National Defense Writ Large**
1. Ferrell, _Hagerty_ , p 133.
2. Lt. General Andrew J. Goodpaster, "The Role of the Joint Chiefs of Staff in the National Security Structure," in _Issues of National Security in the 1970s_ , p. 226.
3. Ibid., p. 229.
4. JCS Reform, pp. 53–54.
5. Bletz, _The Role of the Military Professional in U.S. Foreign Policy_ , p. 149.
6. John P. Burke and Fred I. Greenstein, _How Presidents Test Reality: Decisions on Vietnam, 1954 and 1965_ (New York: Russell Sage Foundation, 1989), pp. 13 and 14.
7. Goodpaster, Burg interview, p. 99.
8. JCS Reform, pp. 12–13.
9. Ibid., pp. 36–37.
10. Paul L. Davies, "A Business Look at the Army," _Harvard Business Review_ , July–August 1954, p. 56, as quoted in Paul Y. Hammond, _Organizing for Defense: The American Military Establishment in the Twentieth Century_ (Princeton, NJ: Princeton University Press, 1961), p. 293.
11. Jordan, _Issues of National Security in the 1970s_ , p. 230.
12. Herspring, _The Pentagon and the Presidency_ , p. 89.
13. Similar, but even more bitter, feelings existed between Secretary of Defense McNamara and the JCS over how to analyze the progress (or lack thereof) in Vietnam and what to do about it. See, for example, Sorley, _Honorable Warrior_.
14. Cited in Sidney Warren, _The President as World Leader_ (New York: J. B. Lippincott, 1964), p. 387.
15. Ibid., p. 388.
16. Barry R. Posen, _The Sources of Military Doctrine: France, Britain, and Germany between the World Wars_ (Ithaca, NY: Cornell University Press, 1984), p. 71.
17. Colin S. Gray, ed., _Strategy and History: Essays on Theory and Practice_ (New York: Routledge, 2006), pp. 76–77.
18. See Maxwell D. Taylor, _The Uncertain Trumpet_ (New York: Harper and Co., 1960). See also Ivo Daalder, _The Nature and Practice of Flexible Response_ (New York: Columbia University Press, 1991). The latter is a detailed discussion of the types of weaponry—including nuclear—and their efficacy as "bargaining tools" that was embraced in the notion of "flexible response." The bibliography is especially thorough.
19. Quoted in John M. Taylor, _An American Soldier: The Wars of General Maxwell Taylor_ (Novato, CA: Presidio Press, 2001), p. 216. The author points out that these views were closer to those of Taylor, Kissinger, and Kennan (p. 215).
20. Andrew P. N. Erdmann, "The Intellectual and Bureaucratic Origins of Flexible Response: The Policy Planning Staff, 1953–1961," unpublished paper for private group, 25 June 1999, p. 5.
21. Christopher A. Preble, _John F. Kennedy and the Missile Gap_ (DeKalb, IL: Northern Illinois University Press, 2004), p. 89.
22. Goodpaster, Burg interview, p. 99.
23. Ibid.
24. Eisenhower, _Waging Peace_ , p. 483.
25. David A. Koplow, "Major Acts of Congress | Arms Control and Disarmament Act (1961) and Amendments," _E-Notes_ , 21 March 2011, <http://www.enotes.com/arms-control-disarmament-act-1961-amendments-reference/arms-control-disarmament-act-1961-amendments>.
26. Ibid. In many respects, the act was a tremendous success. It led to an impressive array of legally binding arms control treaties, with ACDA in the lead role: the 1963 Limited Test Ban Treaty (prohibiting atmospheric nuclear weapons tests), the 1967 Outer Space Treaty (establishing the "rules of the road" for peaceful operations in space), the 1968 Non-Proliferation Treaty (restricting the spread of nuclear weapons capabilities), and the 1972 Biological Weapons Convention (banning the development and production of germ weapons) were early successes. They are still in force. SALT (Strategic Arms Limitation Talks) and START (Strategic Arms Reduction Talks) would not have been possible without ACDA, and all participants acknowledge the agency's leadership role on other such diverse subjects as chemical weapons and conventional forces. A reorganization of the foreign affairs bureaucracy merged ACDA into the State Department on 1 April 1999. The agency was abolished by statute, and its core functions and personnel were absorbed by State.
27. _The Papers of Dwight David Eisenhower_ , ed. Louis Galambos and Daun Van Ee, vol. 21, _The Presidency: Keeping the Peace_ (Baltimore: The Johns Hopkins University Press, 2001), p. 2190. Goodpaster remained with Kennedy until April 1961.
28. Ibid., pp. 2205–2206.
29. John Prados, _Presidents' Secret Wars: CIA and Pentagon Covert Operations from World War II through the Persian Gulf_ , rev. ed. (New York: Ivan R. Dee/Elephant Paperbacks, 1996), p. 197.
30. Memorandum, J. Kenneth McDonald to Robert S. Jordan, n.d.
31. Prados, _Presidents' Secret Wars_ , p. 175.
32. I. M. Destler, "The Presidency and National Security Organization," in _The National Security: Its Theory and Practice, 1945–1960_ , ed. Norman A. Graebner (New York: Oxford University Press, 1986), pp. 238–239.
33. Don Paarlberg to Goodpaster, 26 January 1961.
34. Quoted in Patterson, _The Ring of Power_ , p. 107.
**Chapter 9. Eisenhower's Health Crises**
1. Eisenhower, _Mandate for Change_ , p. 537. Eisenhower termed the coronary occlusion a "coronary difficulty."
2. Memorandum, Eisenhower to Nixon, 1 October 1955, Eisenhower Presidential Library.
3. Chester J. Pach Jr. and Elmo Richardson, _The Presidency of Dwight D. Eisenhower_ , rev. ed. (Lawrence, KS: The University Press of Kansas, 1991), p. 119.
4. Dockrill, _Eisenhower's New-Look National Security Policy, 1953–61_ , p. 145.
5. Stephen E. Ambrose, _Eisenhower, Soldier and President_ (New York: Simon & Schuster, 1990), pp. 396–397.
6. Whitman to Gruenther, n.d., Eisenhower Presidential Library.
7. Memorandum, Goodpaster to Adams, 14 December 1955, Eisenhower Presidential Library.
8. Goodpaster, Mandel and McCall interview, 16 January 2002, p. 16.
9. Kinnard, _President Eisenhower and Strategic Management_ , pp. 40–41.
10. Goodpaster, Mandel and McCall interview, 16 January 2002, pp. 16–17.
11. Eisenhower, _Waging Peace_ , p. 4.
12. John S. D. Eisenhower, _Strictly Personal_ (Garden City, NY: Doubleday, 1974), pp. 185–187.
13. Sherman Adams, _First-Hand Report: The Story of the Eisenhower Administration_ (New York: Harper and Bros., 1961), pp. 193–194.
14. Eisenhower, _Waging Peace_ , pp. 9–10.
15. Geoffrey Perret, _Eisenhower_ (New York: Random House, 1999), p. 388.
16. Ibid., p. 10n4.
17. Press Conference, 12 June 1956, Hagerty File, Eisenhower Presidential Library.
18. H. W. Brands, _Woodrow Wilson_ (New York: Henry Holt, 2003), p. 123. Eisenhower's successor, Kennedy, put the final stamp to any notion that presidential health secrecy was politically or morally acceptable.
19. Memorandum, "Notes on Arrangements Incident to President's Illness," n.d., Eisenhower Presidential Library.
20. Memorandum (handwritten), signed by Goodpaster, 21 October 1955, Eisenhower Presidential Library. It specifically directed that the vice president should not take any specific action "with recognition of the incapacity of the President"(Memorandum, Goodpaster to Adams, 27 September 1955). Eisenhower also did not want the phrase "all indications point to a rapid recovery" used (Memorandum, Goodpaster to Adams, 29 November 1955).
21. John Eisenhower, _Strictly Personal_ , p. 195.
22. Eisenhower, _Waging Peace_ , pp. 227–228.
23. John Eisenhower, _Strictly Personal_ , p. 195.
24. Ibid., pp. 196–197.
25. Eisenhower, _Waging Peace_ , p. 229. Officially, he had "an occlusion of a small branch of a cerebral vessel which has produced a slight difficulty on occasion. There is no evidence of a cerebral hemorrhage or any serious lesion of the cerebral vessels." (Press Release, The White House, 26 November 1956.)
26. Goodpaster to Norstad, 26 November 1957, USNMR SHAPE, Norstad Papers, Eisenhower Presidential Library.
27. Eisenhower, _Waging Peace_ , pp. 601–602.
28. Ibid., p. 407.
29. Ibid., p. 205.
30. David Eisenhower with Julie Nixon Eisenhower, _Going Home to Glory_ , p. 273.
31. Ann Whitman to Goodpaster, undated, George C. Marshall Research Library.
**Chapter 10. The U-2 and Overflights**
1. Goodpaster, Mandel and McCall interview, 16 January 2002, p. 7.
2. Eisenhower, _Waging Peace_ , p. 483. It is dubious that anyone in either the American or the Soviet governments took Open Skies seriously, given the closed society of the Soviet Union. Allen Dulles' successor at the CIA, John McCone, had a thorough memorandum on the history of the U-2 episode prepared for General Eisenhower after he had retired to Gettysburg, which was probably used in Eisenhower's memoirs.
3. Memorandum of Conference with the President, 24 November 1954.
4. Goodpaster, Mandel and McCall interview, 16 January 2002, p. 15. Another version is that the whole thing was a setup by the Americans in order to scuttle the Paris Conference—and hence détente; see James A. Nathan, "A Fragile Détente: The U-2 Incident Re-examined," _Military Affairs_ , October 1975.
5. Memorandum, Rearden to Jordan, n.d. As Steven Rearden remarked: "Throughout his career, Goodpaster was intimately involved in off-the-books operations. Later, as Assistant to the Chairman of the Joint Chiefs, one of his major functions was to represent the JCS in these discussions."
6. Richard Immerman, ed., _John Foster Dulles and the Diplomacy of the Cold War_ (Princeton, NJ: Princeton University Press, 1990), p. 13.
7. Richard H. Immerman, _John Foster Dulles: Piety, Pragmatism, and Power in U.S. Foreign Policy_ (Wilmington, DE: Scholarly Resources, 1999), p. 47.
8. Quoted in David Haight to Robert Jordan, November 2011.
9. Goodpaster, interview by Soapes, p. 80.
10. Goodpaster, interview by Burg, pp. 15–16.
11. Eisenhower, _Waging Peace_ , pp. 544–545.
12. Mosley, _Dulles_ , p. 366.
13. Beschloss, _Mayday_ , pp. 155–156. This is an exhaustive recounting of the U-2 crisis. Within two years after the program got under way, Bissell claimed that 90 percent of all hard intelligence coming into the CIA about the Soviet Union was "funneled through the lens of the U-2's aerial cameras."
14. See Richard Helms, with William Hood, _A Look over My Shoulder: A Life in the Central Intelligence Agency_ (New York: Ballantine Books, 2003). See also Ambrose, _Ike's Spies_.
15. Joseph J. Trento, _The Secret History of the CIA_ (New York: Carroll and Graf, 2001), p. 139.
16. Tim Weiner, _Legacy of Ashes: The History of the CIA_ (New York: Anchor Books, 2008) p. 183.
17. Mosley, _Dulles_ , pp. 367–368.
18. Richard M. Bissell, with Jonathan E. Lewis and Frances E. Pudlo, _Reflections of a Cold Warrior: From Yalta to the Bay of Pigs_ (New Haven, CT: Yale University Press, 1996), p. 115.
19. Ibid., p. 176.
20. Ibid., p. 183.
21. Arthur Krock, _Memoirs: Sixty Years on the Firing Line_ (New York: Funk and Wagnalls, 1968), p. 297.
22. Dino A. Brugioni, _Eyes in the Sky: Eisenhower, the CIA, and Cold War Aerial Espionage_ (Annapolis, MD: Naval Institute Press, 2010), p. 193.
23. Gregory W. Pedlow and Donald E. Welzenbach, _The CIA and the U-2 Program, 1954–1974_ (Washington, DC: History Staff, Center for the Study of Intelligence, Central Intelligence Agency, 1998), p. 187.
24. Ambrose, _Eisenhower, Soldier and President_ , pp. 434–435.
25. Keith Eubank, _The Summit Conferences, 1919–1960_ (Norman, OK: University of Oklahoma Press, 1966), pp. 191–192.
26. Bissell, Lewis, and Pudlo, _Reflections_ , p. 123. This book is an excellent discussion, with historical references. See also Pedlow and Welzenbach, _The CIA and the U-2 Program, 1954–1974_ , for an authoritative account.
27. Mosley, _Dulles_ , p. 456.
28. John S. D. Eisenhower, interview by Carol Hegeman, 26 January 1984, Eisenhower Presidential Library, p. 10.
29. Eisenhower, _Waging Peace_ , p. 550.
30. Ibid., p. 548.
31. Ibid., pp. 552 and 554.
32. Gregory F. Treverton, _Covert Action: The CIA and American Intervention in the Postwar World_ (London: I. B. Tauris, 1987), p. 229.
33. James Bamford, _Body of Secrets: From the Cold War through the Dawn of a New Century_ (New York: Doubleday, 2001), p. 50.
34. Paraphrased in ibid., p. 52.
35. Rebecca Burg, "Powers, U-2 Pilot Captured by Soviets, Awarded Silver Star," _Washington Post_ , 16 June 2010. Powers himself, once captured, behaved according to the rules of war, revealing nothing during the course of his interrogations and public trial. He was posthumously awarded the Silver Star medal in 2010.
36. Bamford, _Body of Secrets_ , pp. 54–55.
37. Goodpaster, Hegeman interview.
38. Quoted in Brugioni, _Eyes in the Sky_ , p. 357.
39. Ibid., p. 358.
40. Memorandum for the President, "Measures to Obtain the Release of the RB-47 Officers, 10–11 November 1960," Eisenhower Presidential Library. On 14 November, Eisenhower wrote: "Approved as to Phase II; approved for planning purposes only as to Phase III."
41. Brugioni, _Eyes in the Sky_ , pp. 358–359.
42. Eubank, _The Summit Conferences_ , p. 205. Eubank commented further: "The feeling that the Cold War was merely the result of misunderstanding and that if Eisenhower could only charm Khrushchev all would be well, was as erroneous as some of Roosevelt's views regarding Stalin."
43. This observation is cited in several places, among which is Perret, _Eisenhower_ , p. 584.
**Chapter 11. Deputy Commander and Commander-Designate in Vietnam**
1. Goodpaster, Johnson interview, p. 205. This interview is an exposition of the argument that if the nation's military had been left to fight the war without civilian interference and with what it considered adequate resources (including reinstituting the draft), the United States could have avoided the humiliating outcome that ensued.
2. Ibid.
3. David Eisenhower and Julie Nixon Eisenhower, _Going Home to Glory_ , p. 167.
4. Ibid., pp. 165–166. President Johnson also telephoned frequently and invited Eisenhower to lunch at the White House periodically to discuss Vietnam and foreign policy.
5. McMaster, _Dereliction of Duty_ , p. 63.
6. C. Richard Nelson and Kenneth Weisbrode, eds., _Reversing Relations with Former Adversaries: U.S. Foreign Policy after the Cold War_ (Gainesville, FL: University Press of Florida, 1998), p. 84. This is a concise exposition of the twists and turns in American policy toward Vietnam prior to eventual formal diplomatic recognition and reconciliation.
7. John J. Mearsheimer, _The Tragedy of Great Power Politics_ (New York: W. W. Norton, 2001), p. 60.
8. Lewis Sorley, _Thunderbolt: General Creighton Abrams and the Army of His Times_ (Bloomington, IN: Indiana University Press, 2008), p. 251.
9. James Chace, _Acheson: The Secretary of State Who Created the American World_ (Cambridge, MA: Harvard University Press, 1998), p. 426.
10. Ibid.
11. Col. Harry G. Summers Jr., _On Strategy: The Vietnam War in Context_ (Carlisle Barracks, PA: Strategic Studies Institute), p. 80.
12. Chace, _Acheson_ , pp. 8–9.
13. Lewis Sorley, _A Better War: The Unexamined Victories and Final Tragedy of America's Last Years in Vietnam_ (New York: Harcourt, Inc., 1999), pp. 90–91.
14. Ibid.
15. Lewis Sorley, _Westmoreland: The General Who Lost Vietnam_ (New York: Houghton Mifflin Harcourt, 2011), pp. 104–105. See also Michael D. Pearlman, _Warmaking and American Democracy: The Struggle over Military Strategy, 1700 to the Present_ (Lawrence, KS: University Press of Kansas, 1999), p. 375.
16. For more on this, see Prados, _Presidents' Secret Wars_ , pp. 268–290. This is a very readable and detailed account of the tortuous negotiations and the accompanying on-the-ground events over this period.
17. Sorley, _A Better War_ , p. 217.
18. Paul Kennedy, _The Rise and Fall of the Great Powers: Economic Change and Military Conflict from 1500 to 2000_ (New York: Vintage Books, 1989), pp. 405–406.
19. Quoted in ibid., p. 216.
20. Sorley, _Westmoreland_ , p. 199.
**Chapter 12. As NATO Supreme Allied Commander**
1. For more on this, see Robert S. Jordan, _Norstad_.
2. Gruenther to Goodpaster, 23 October 1955, NATO Series, Eisenhower Presidential Library.
3. David D. Newsom, "The Allied Quarrel: Consultations Are No Panacea," _Christian Science Monitor_ , 22 September 1982.
4. Ferguson et al., _The 1970s in Perspective_ , p. 58.
5. Quoted in Lewis Sorley, "Goodpaster: Maintaining Deterrence during Détente," in _Generals in International Politics: NATO's Supreme Allied Commander, Europe_ , ed. Robert S. Jordan (Lexington, KY: The University Press of Kentucky, 1987), p. 126.
6. Ibid.
7. Ibid., p. 124.
8. Goodpaster, Mandel and McCall interview, p. 12.
9. "Goodpaster's Warning," _Die Welt_ , 22 October 1970. He was addressing the German Foreign Policy Society.
10. Robert Kennedy, "International Leadership in an Era of Détente," in _National Security and Détente_ (New York: Thomas Y. Crowell Co., 1976, for the U.S. Army War College), p. 304.
11. Ibid., p. 17.
12. Goodpaster, Mandel and McCall interview, p. 20.
13. Earlier, during General Ridgway's short tenure as SACEUR, the fact that he came to NATO directly from Korea (where he had replaced Gen. Douglas MacArthur) and was pictured everywhere wearing his battle-dress, including a grenade attached to his shoulder, did not enhance his prestige in Europe. This obviously did not hurt his standing at home, however, as he went on from NATO to become the Army chief of staff.
14. Remarks given to the Royal United Services Institute (RUSI), 16 December 1970, _RUSI Journal_ , p. 31.
15. "Paying for Defense," reprinted in the _International Herald Tribune_ , 4 November 1969.
16. Gen. Andrew J. Goodpaster, "New Challenges, New Problems, New Dangers," _The Atlantic Community Quarterly_ (Winter 1972–1973): 458.
17. Goodpaster, "Remarks," _RUSI Journal_ , p. 35.
18. Goodpaster, "New Challenges," p. 460.
19. Ibid.
20. Goodpaster, "Interests and Strategies," p. xi.
21. David Callahan, _Dangerous Capabilities: Paul Nitze and the Cold War_ (New York: Harper/Collins, 1990), p. 334.
22. Goodpaster, "Interests and Strategies," pp. x–xi.
23. Ibid., pp. xii–xiii.
24. Goodpaster to Gruenther, 9 April 1974, Gruenther Papers, Eisenhower Presidential Library.
25. Ibid., p. 6.
26. Lawrence J. Korb, _The Joint Chiefs of Staff: The First Twenty-Five Years_ (Bloomington, IN: Indiana University Press, 1976), p. 34.
27. Goodpaster, Mandel and McCall interview, pp. 20–21.
28. Ibid., p. 7.
29. Conversation between author and Lt. Gen. Brent Scowcroft, June 2010.
30. Daalder and Destler, _In the Shadow of the Oval Office_ , p. 67.
31. Linda Charlton, "New West Point Superintendent," _New York Times_ , 5 April 1977.
32. See photo insert, Jordan, _Generals_.
33. SHAPE Public Affairs Office, Press Cutting Distribution Sheet, Subject: Change of Command, Source: AP Night Tapes, dated 16 December 1974.
34. SACEUR Message to Chiefs of Defense, 16 September 1974. The author is grateful to Richard Nelson for supplying this information and the note above.
35. Reported in the _Washington Star-News_ , 6 February 1975.
36. For a confirmation of this point, see Jordan, _Generals_ , passim.
**Chapter 13. Returning to West Point as Superintendent**
1. While at the center, he wrote _For the Common Defense_. He identified himself as being at The Citadel when it was published.
2. Goodpaster, Mandel and McCall interview, 12 February 2004, p. 13.
3. Charlton, "New West Point Superintendent." The adjective "avuncular" was attached to him at this time.
4. Goodpaster to Professor G. A. Lincoln, 17 September 1951.
5. Goodpaster, Mandel and McCall interview, 4 February 2004, p. 3.
6. Lt. Richard P. Hansen, USN, "The Crisis of the West Point Honor Code," _Military Affairs_ (April 1985), p. 57.
7. Goodpaster, Johnson interview, p. 27.
8. Letter from the Department of Social Sciences, "Brothers," 29 August 1951. A copy was sent to Lincoln's brother, which was five single-spaced typed pages in length, reflecting the seriousness of the matter. An official explanatory letter subsequently was sent by the Association of Graduates, USMA, 23 August 1951.
9. Quoted in Sorley, _Westmoreland_ , p. 223. Westmoreland sent a copy to Goodpaster at West Point.
10. Ibid., p. 4.
11. Quoted in Lewis Sorley, _Honor Bright: History and Origins of the West Point Honor Code and System_ (New York: McGraw-Hill Learning Solutions, 2009), p. 18. This small book summarizes the issues surrounding a code of honor that relies more on voluntary adherence than coercion.
12. Goodpaster, Mandel and McCall interview, p. 58.
13. Recounted in Cox, _Grey Eminence_ , p. 13. See also: Russ Stayanoff, "Major General Fox Conner: Soldier, Mentor, Enigma: Operations Chief (G-3) of the AEF," _The Doughboy Center: American Expeditionary Forces, World War One_ , <http://www.worldwar1.com/dbc/foxconner.htm>.
14. Charlton, "New West Point Superintendent."
15. Ibid.
16. Memorandum, Subject: "Concept for Duty Development," Office of the Superintendent, U.S. Military Academy, 1 April 1981.
17. Ibid., attachment.
18. Goodpaster, Johnson interview, p. 15.
19. Goodpaster to Joe Dalton, 21 May 1981.
20. Linda Charlton, "New West Point Superintendent: Andrew Jackson Goodpaster," New York Times, 5 April 1977. Also see "Goodpaster + Two: West Point Today," Army Journal, June 1979.
21. Ibid., p. 27.
22. Quoted in Sorley, _Honor Bright_ , p. 138.
23. Ibid., pp. 138–139.
**Conclusions**
1. Husted, _George C. Marshall: Rubrics of Leadership_ , p. 192.
2. Report to Congress, 12 January 1961, pp. 4 and 5, Office of the Staff Secretary, 1952–1961, Eisenhower Presidential Library.
3. Ironically, the more they disagreed with their commander-in-chief and former chief of staff, the more popular they were with their fellow Army colleagues.
4. Goodpaster's successor, McGeorge Bundy, had been a Harvard dean who did not have any prior experience in top-level national security policy-making. The fact that he was a Republican contributed to Kennedy's decision to bring him "on board."
5. Memorandum, Eisenhower to the Secretary of the Army, 26 May 1959, Goodpaster Papers, George Marshall Foundation Research Library.
6. Pickett, "General Andrew Jackson Goodpaster: Managing National Security," pp. 36–37.
7. McMaster, _Dereliction of Duty_ , p. 215.
8. Paradoxically, the most famous "hawk" in regard to containing Communism, Paul Nitze, did not agree with his Democratic colleagues that Vietnam was a major threat. See Callahan, _Dangerous Capabilities_ , p. 290: "He argued that Vietnam was the wrong place to take a stand against communist expansion. . . . Undesirable as a takeover of the whole of Vietnam surely was, it did not pose an immediate or direct threat to the safety of the United States."
9. Ibid., p. 217.
10. Ibid., pp. 259–260. This report was submitted in July 1965. The sad thing is that "the 1965 record is of a great swirl of policy recommendations and analyses, much of which simply floated past the president."
11. Gen. Andrew J. Goodpaster, Epilogue to _Evolution of the American Military Establishment since World War II_ , ed. Paul R. Schratz (Lexington, VA: George C. Marshall Research Foundation, 1978), pp. 111–113.
12. Geoffrey Blainey, _The Causes of War_ (New York: The Free Press, 1973), pp. 12–13.
13. I am grateful to C. Richard Nelson for suggesting this analysis.
14. Jere Clemens King, _Generals and Politicians_ (Berkeley: University of California Press, 1951), p. 243.
15. Donald Kagan, _On the Origins of War and the Preservation of Peace_ (New York: Doubleday, 1995), pp. 7–8.
16. Robert Conquest, _Reflections on a Ravaged Century_ ((New York: W. W. Norton, 2000), p. 289.
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Index
Abrams, Creighton, , , , , ,
accomplishments when not seeking credit, , 154–55
Acheson, Dean,
Adams, Sherman, 55–56, 95–96, 99–100
adulthood behaviors and definition, 4–5
Advanced Research Projects Agency (ARPA),
Air Force, U.S.: interservice rivalries, 86–87; joint committees of the services, 14–15; lobbying of Congress by, ; reconnaissance flights over Soviet Union, , 112–13
Alaska-Hawaii-Panama strategic triangle,
All Souls College, Oxford University, 164n29
Alliance Defense program,
Allied Command Europe (ACE): activation of, , 165n13; command structure organization, 24–29; deterrence, defense, and détente objectives of, 30–31; formation of,
Allied nations combined chiefs-of-staff committee, 14–15
ambition, politics, and careers,
American Veterans Center, Andrew J. Goodpaster Prize and Lecture, 158n1
Amory, Robert,
Anderson, Dillon,
Anderson, Dorothy. _See_ Goodpaster, Dorothy "Dossy" Anderson
Andrew J. Goodpaster Award, George C. Marshall Foundation, ix, 158n1
Andrew J. Goodpaster Endowed Leadership and Honor Lecture Series,
Andrew J. Goodpaster Prize and Lecture, American Veterans Center, 158n1
arms control and disarmament, 66–68, 88–91
Arms Control and Disarmament Act, 90–91, 178n26
Arms Control and Disarmament Agency (ACDA), 90–91, 178n26
Army, U.S.: budget for, ; commitment to Army career, 6–7, 141–42; Eighth Infantry Division command, ; Eisenhower and interservice deliberations, , 185n3; force strength before World War II, ; future of Army, study by young officers to shape, ; Goodpaster as Chief of Staff, consideration for, , ; interservice rivalries, 86–87; joint committees of the services, 14–15; lobbying of Congress by, ; New Look policy and conventional forces, 43–44; officer corps class size increase to prepare for war, ; war-fighting doctrine, ; Westmoreland as Chief of Staff,
Army Corps of Engineers, U.S.: Camp Claiborne assignment, ; Camp Gruber assignment, , 161n26; Command and General Staff College course, ; commission in, ix, ; construction project specs, ; infantry service as second mission for engineers, ; number of officers and enlisted men pre–World War II, 160n18; Panama and Panama Canal assignment, 7–9
Association of Princeton Graduate Alumni (APGA),
Atlantic Council: meetings between Soviets and, ; nuclear weapons policy, 152–53; role at, xii, ; Soviet and Russian policy, 153–54
behavior, meaning of, ix
Beloff, Max, 164n29
Berry, Sidney,
Beukema, Herman, 162n4
Biological Weapons Convention, 178n26
Bissell, Richard, Jr.: CIA role, ; Cuba and Bay of Pigs plans, ; reconnaissance flights over Soviet Union, , 105–7, , 109–10, 180n13
Bosnia,
Bradlee, Ben,
Bradley, Omar N.,
Brodie, Bernard, 18–19
Brussels Treaty,
Bundy, McGeorge, , , 186n4
Burke, Arleigh, 85–86
Burma Road, 161n26
Cambridge University, 164n30
Camp Claiborne, , 161n26
Camp Gruber, , 161n26
Cardin, Benjamin,
career: advancements in, 3–4; approach to policy problems, x; combat command as measure of capabilities, ; commitment to Army career, 6–7; length of military career, xi; promotion to brigadier general, , 173n40; promotion to four-star rank, ; rank and status of senior government personnel, 31–32; success of, xi–xii, , 141–48; three-star superintendent position, , ; warrior-thinker character, xi
Carroll, Paul T. "Pete," , , ,
Center for Strategic and International Studies, 158n1
Central Intelligence Agency (CIA): CORONA program, 47–48; espionage technologies development, 105–6; propaganda operations of, . _See also_ U-2 aircraft
China: involvement in Korea and surge of Communism, ; Sino-Soviet Communist threat, , ,
Churchill, Winston, , , 172n16
The Citadel, , 158n1, 184n1
Clifford, Clark,
coalition theory, 166–67n30
Cold War: containment policy, 34–36, , , , , ; definition and concept of, ; deterrence versus offense debate, 87–88; Eisenhower legacy, , ; European front, , , ; histories of, ; misunderstanding as cause and charming of Khrushchev to end, 182n42; policy planning role, xi, ; psychological warfare and propaganda, , , ; rollback option, , , ; Solarium initiative and policy development, 36–42, , 75–76, 169n30; Southeast Asia as superpower rivalry center, ; winning of, debate about,
Collins, J. Lawton,
colonialism, decolonization, and American policy, 41–42, 50–51,
Columbia University, ,
Communism: Chinese involvement in Korea and surge of, ; Korea and global communist assault against the West, ; public opinion about response to, ; Sino-Soviet bloc, , , ; threat from in Indochina, ; types and ideological differences within, 49–50; Vietnam and threat from, , 186n8
competition,
"conflicting approaches" strategy, 168–69n28
Connor, Fox,
containment policy, 34–36, , , , ,
CORONA program, 47–48
Corps of Engineers. _See_ Army Corps of Engineers, U.S.
Council on Foreign Relations–sponsored conference and debate,
counter-insurgency methods,
Cuba and Bay of Pigs incident, , 92–93,
Cutler, Robert "Bobby": Eisenhower, relationship with, ; Goodpaster, relationship with, 175n21; national security policy study, 175n15; NSC role of, , , , 176n23; opinion of Goodpaster, 174n63; Solarium initiative, , 38–40
Davis, A. C.,
Deagle, Edwin,
Deakin, William, 164n29
decision-making, timing of, , 166–67n30
decolonization and American policy, 41–42, 50–51,
Defense, Department of: defense budget, , , , 87–88; reorganization of, ; Secretary of Defense, authority of, 77–78
defense chief of staff,
Defense Reorganization Act (1958), 77–78, 86–87
deterrence, defense, and détente: ACE objectives, 30–31; Cold War deterrence versus offense debate, 87–88; concept and definition of, , ; diplomatic challenge of détente, ; European détente policy, 126–27; grand strategy for, 87–88; linkage to détente-related agreements, , 170n29; nuclear weapons stockpiles and, 45–47, 48–52, , 87–88, 169n8; peace and détente policy, 51–52
Dillon, Douglas, ,
dissertation and oral defense, 20–21
Distinguished Unit Citation,
Doolittle, James,
Drummond, Eric, 162n8
Dulles, Allen: meetings with Eisenhower, ; reconnaissance flights over Soviet Union, 105–6, , , ; report dinner meeting and Goodpaster role, ; reports meetings and Goodpaster role, ; Solarium initiative,
Dulles, John Foster: conventional military force missions, ; death and funeral of, , ; Eisenhower, relationship with, ; Eisenhower meetings with, , ; Kennan, relationship with, 169n30; local defenses, adequacy of, ; massive retaliation concept, , ; meetings and duties during illnesses of Eisenhower, 95–96; reconnaissance flights over Soviet Union, ; Solarium initiative, , , 169n30; Suez crisis,
duty, honor, country: development of duty concept, , ; exposure to and grasp of concepts, ; West Point Honor Code and System, , , , 185n11; worthiness of service to country,
Earle, Edward Meade, ,
Eden, Anthony, 63–65
education: Command and General Staff College course, ; disciplines to study for a complete education, ix–x, 5–6, 18–19; doctoral degree, xii; McKendree College education, ; Princeton University graduate education, , 18–22, 164n30. _See also_ West Point
Egypt, , , , 63–65
Eisenhower, David,
Eisenhower, Dwight D.: Army interservice deliberations, , 185n3; Cold War as misunderstanding and charming of Khrushchev to end, 182n42; conventional military force, expansion of, ; death of, ; Dulles meetings with, , ; engagement of and figurehead presidency, 68–69; future of Army, study by young officers to shape, ; Goodpaster, relationship with, xii, , , 61–62, , , 142–43, ; Goodpaster character and qualities, 84–85; Goodpaster opinion of, ; health concerns post-presidency, 101–2; health concerns while in office, 94–101, 178n1, 179n20, 179n25; inner power of, ; intervention by, avoidance of, ; Johnson discussions with, , 182n4; Korea, campaign promise about, ; leadership style, , , 86–87, , ; legacy of, , 90–91, , , ; Lincoln, relationship with, ; Marshall, relationship with, 73–74, 160–61n24, 174–75n9; mentor of, ; mentor role of, xi; NATO command structure organization, 24–29; personal staff of, ; political and economic issues, frustration of dealing with, ; public diplomacy, 57–58, 66–67, ; SACEUR role, , 165n10; Soviet nuclear surprise attack on U.S., concern about, 47–48; Suez crisis, response to, , 63–65, 173n38; Vietnam War, progress of and assurance of winning, 117–18; writing skills and reputation, . _See also_ New Look policy
Eisenhower, John S. D.: administration role of, 80–82, 176n31; Cuba and Bay of Pigs incident, ; Eisenhower's health concerns, , ; reconnaissance flights over Soviet Union, ; SHAPE, role at, 166n18
Eisenhower, Mamie, , ,
Eisenhower administration: arms control and disarmament, 66–68, 88–91; chief of staff and access to the president, 55–56; détente, diplomatic challenge of, ; deterrence and nuclear weapons stockpile, 45–47, 48–52, 169n8; influence of Goodpaster in, 65–71; length of career in, , 80–81; national security policy development, 59–70, 75–79, 83–91; NSC role, , , 75–79, 176n21; Open Skies proposal, 66–67, , 180n2; roles and responsibilities in, xii; Solarium initiative and Cold War policy, 36–42, , 75–76, 169n30; Soviet policy of, 33–36; staff in, 55–56; Staff Secretary and Defense Liaison Officer role, , , 57–70, , 171n8; surprise attack panel, 47–48. _See also_ New Look policy; U-2 aircraft
Elsey, George, 176n24
espionage technologies development, 105–6
Europe: Cold War in, , , ; détente policy in, 126–27; Mansfield Amendment and troops in, ; morale in and interest in military matters, ; U.S. force in,
flexible response, 88–89, 177n18
focus of attention and changing viewpoints,
Ford, Gerald, , ,
Ford Foundation,
foreign policy and national security: arms control and disarmament, 66–68, 88–91; assignments related to, xi; buying into and support for policies, 40–41; colonialism and decolonization, 41–42, 50–51, ; complexity factor, ; concepts of national security, 86–88; early interest in, ; economy as pillar of U.S. strength and security, , ; Eisenhower administration policy development, 59–70, 75–79, 83–91; Goodpaster legacy, 141–46; heads-of-state conferences, 113–14; importance of, 83–84; important security environment areas, 144–45; interests in opinions about, xi; Kennedy administration policy development, , , , 186n4; national security, importance of, ; national security policy, evolution of body to coordinate, 72–74; Nixon administration policy development, 125–29; off-the-books programs, , 180n5; political framework for, 84–86, 142–43, , 186n4; public diplomacy, 57–58; security environment, dynamism of, 144–45; State-War-Navy Coordinating Committee, 13–14, , 163n12; summit meetings and conferences, diplomatic activity at, 113–14; technology and, 20–21, 164n34, 164n38; Truman administration policy development, 175n15; U.S. policy toward Soviets, 33–36
Formosa Strait crisis and Quemoy and Matsu islands, 50–51, ,
Fort Leavenworth,
France: start of World War II, ; Suez crisis, , , , 63–65, 173n38
Fulbright scholarship,
George C. Marshall Foundation, 158n1
George C. Marshall Foundation, Andrew J. Goodpaster Award, ix, 158n1
Germany, , , 183n9
giants, standing on the shoulders of,
Gibbs, Norman, , 164n29
Glendening, Parris,
Goodpaster, Andrew J. "Andy": analytical and problem-solving skills, 29–30; appearance of, , , 156–57; awards and honors, , , 164n32; birth and early life of, ; character and personality of, xi–xii, 3–4, , , 60–62, , 84–85, 134–35, 141–43, 147–48, 174n63, 184n3; conceptual thinking capabilities, ; daughters of, ; diplomat-soldier approach to problems, 67–68; efficiency reports on, , 69–70, , ; Eisenhower, relationship with, xii, , , 61–62, , , 142–43, ; ideas facilitator role, 154–55; Ike's alter ego, ; importance of role of, ; influence of, , 65–71, ; insider role, xi; intellect of, , 174n63; legacy of, 141–48; Lincoln, relationship with, 5–6, 13–14; marriage of, 6–7, ; nickname of, ; notes of appreciation to, ; obituary of, 61–62; opinions about, ix–x, , , 28–29, , , , , 147–48, , 156–58, 166n18, 174n63; parents of, ; reputation of, , 129–30; Soviet threat, opinion about, , 168n13; wounding and recovery of, , ; writing skills and reputation,
Goodpaster, Anne,
Goodpaster, Dorothy "Dossy" Anderson, 6–7,
Goodpaster Hall, St. Mary's College, ix,
Goodpaster Sullivan, Susan, , 160n13
Gorbachev, Mikhail,
Gray, Gordon: Eisenhower, relationship with, ; NSC role of, , , , 176n23; nuclear weapons testing and verification,
Great Britain: cabinet secretariat administration system, 14–15; start of World War II, ; Suez crisis, , , , 63–65, 173n38
Greece,
Gruenther, Alfred M.: Congressional testimony of, ; Goodpaster character and qualities, 84–85; NATO command structure organization, , , 26–27; nuclear weapons use, ; SACEUR role,
Guatemala,
Habib, Philip, ,
Hagerty, Jim, , ,
Hague, Gabriel,
Haig, Alexander M., Jr., 130–33
Hankey, Maurice, , 172n16
Harlow, Bryce,
Harriman, W. Averill, 28–29, ,
Harsch, Joe,
Hawaii,
health concerns, illness, and presidential leadership, 94–101, 179n18, 179n20, 179n25.
Helms, Richard, ,
Herter, Christian "Chris": Cuba and Bay of Pigs incident, 92–93; Eisenhower, relationship with, ; Eisenhower meetings with, 81–82, ; Geneva conference, message about, ; nuclear weapons testing and verification, ; U-2 overflights of USSR, ,
Hoffmann, Martin R.,
honor. _See_ duty, honor, country
Hoover, Herbert, II,
Hopkins, Harry, 60–61
Humphrey, George, ,
Hungary, 40–41, , 168–69n28
Indochina: Communist threat in, ; public opinion about actions in, ; review and development of policy toward, . _See also_ Vietnam and Vietnam War _Infantry in Battle_ (Marshall),
Institute for Defense Analyses, 158n1
intellectuals, role for in politics, 169n30
intelligence: CORONA program, 47–48; panel to development technology for, 47–48; reconnaissance flights over Soviet Union, 103–13, 180n13
International Institute for Strategic Studies (IISS), 156–58
Iran,
Ismay, Lord, 162n8, 172n16
isolationism,
Italian campaign, 9–12, 161n29, 161n33, 161–62n36
Jackson, C. D., ,
Jackson, William J., 176n23
James Madison Medal, , 164n32
Japan, 15–16, 163n12
Johnson administration and Lyndon Johnson: Eisenhower discussions with Johnson, , 182n4; Vietnam War counter-insurgency methods, ; Vietnam War, progress of and assurance of winning, 117–18; Vietnam War strategy, 119–23, 143–44
Joint Advanced Study Committee (JASC), 16–18, 163n16
Joint Chiefs of Staff (JCS): Assistant Chairman position, , ; authority of chairman, 86–87; CINCEUR reporting to, ; consolidation of authority of, ; defense budget and disagreements between, 85–86; defense chief of staff, replacement with, ; Defense Reorganization Act, 77–78, 86–87; director of Joint Staff, 117–18; Joint Advanced Study Committee, 16–18, 163n16; Joint War Plans Committee, 15–16, 163n12; progress in Vietnam, analysis of, 177n13; reconnaissance activity under, ; reorganization of, ; special assistant for policy role, ; Vietnam policy, role in, 143–44
Joint Reconnaissance Center,
Joint War Plans Committee (JWPC), 15–16, 163n12
Joulwan, Stanley,
Kaplan, Lawrence S., 165n3
Kennan, George: Cold War and containment views of, 34–36; conventional military force, expansion of, 177n19; Dulles, relationship with, 169n30; Solarium initiative, , , , 169n30; Soviet collapse, X article about, 167n1; Truman Doctrine of aid to Greece and Turkey,
Kennedy administration and John F. Kennedy: Cuba and Bay of Pigs incident, , 92–93, ; Goodpaster role in, 91–93; length of career in, , 91–92, 178n27; national security policy development, , , , 186n4; NSC role, 79–80; presidential election, ; presidential health secrecy, 179n18; Staff Assistant to the President role, 31–32
Khrushchev, Nikita, , , , , 113–14, 182n42
Killian, James R., 47–48
Kissinger, Henry A., , , , , 177n19
Korea: Chinese involvement in, ; Eisenhower campaign promise about, ; end of conflict in, ; feint as preliminary to full-scale war, ; public opinion about actions in, ; tactical nuclear weapons use in, , ; U.S. policy and the Korean conflict,
Kosovo,
Land, Edwin, 47–48
Laos,
leadership: command procedures and command decision process, ; continuity of management in military, ; disciplines related to, ix; early life opportunities for, ; facilitators, 3–4; famemakers, 3–4; framework to give leadership, ix; illness and presidential leadership, 94–101, 179n18, 179n20, 179n25; Marshall Rules of Leadership, 8–9, 161n25; message to troops, ; morale importance, 11–12; natural skills, ; post-heroic leadership, , 164n23; progressive development at West Point, ; self-advertising and self-image, 3–4; style of Eisenhower, , , 86–87, , ; style of Goodpaster, x, 124–25, 147–48; style of Marshall, 73–74
League of Nations, 162n8
Lemnitzer, Lyman: character and personality of, xi, 124–25, ; Solarium initiative and New Look policy, ,
Liddell-Hart, Basil, 64–65
Limited Test Ban Treaty, 178n26
Lincoln, George "Abe": career of, 13–14, 162n4; curriculum expansion with humanities and social sciences courses, 5–6; education of, ; Eisenhower, relationship with, ; Goodpaster, relationship with, 5–6, 13–14; Goodpaster character and qualities, 84–85; inner power of, ; Marshall, relationship with, ; McCloy, relationship with, ; mentor role of, xi, 5–6, 13–14; Rhodes scholarship, 13–14; Strategic Policy Section, , ; Strategy and Policy Group chief role, 13–14; TCC assignment, , 166n26; West Point position of, 162n4
Lincoln, Lawrence,
Lincoln Brigade,
Live Oak, 166n19
Lockheed U-2 aircraft. _See_ U-2 aircraft
MacArthur, Douglas, 183–84n13
Mansfield, Mike,
Mansfield Amendment,
Marshall, George C.: accomplishments when not seeking credit, 154–55; character and personality of, , 73–74, 141–42; colleagues, treatment of, 160–61n24; Eisenhower, relationship with, 73–74, 160–61n24, 174–75n9; Eisenhower and political and economic issues, ; headquarters staff reorganization, ; _Infantry in Battle_ , ; influence on Goodpaster, ; inner power of, ; joint and combined committees administration system, 14–15, 162n8; leadership style, 73–74; Lincoln, relationship with, ; McCarthyite attacks on, 174–75n9; mentor of, ; national security policy, creation of body to coordinate, ; Nobel Peace Prize award and speech, ; opinions about, xi, , 73–74, 174–75n9; Philippines commitment, disagreement with Stimson about, ; plans and planning, opinion about, , 73–74; Rules of Leadership, 8–9, 161n25
Marshall Plan, , ,
Marshall scholarships, , 164n31
Matsu and Quemoy islands and Formosa Strait crisis, 50–51, ,
McCloy, John,
McCone, John, , 180n2
McCormack, James,
McNamara, Robert: policy initiative for Vietnam, ; progress in Vietnam, analysis of, 177n13; replacement of, ; strategic review to determine assurance of winning in Vietnam,
McNarney, Joseph,
meatpacking plant job,
mentors and mentoring: Connor as, ; Eisenhower as mentor, xi; importance of in the military, , ; Lincoln as mentor, xi, 5–6, 13–14
military services, U.S.: conventional military force, expansion of, 34–36, 44–45, , 86–87, 88–89; defense budget, , , 85–86, 87–88; Defense Reorganization Act, 77–78, 86–87; flexible response, 88–89, 177n18; intellectual honesty in, 163n22; interservice rivalries, 86–87; joint committees, 14–15; lobbying of Congress by, ; mentoring relationships in, , ; mutual and balanced force reductions, 128–29; New Look policy and conventional forces, 43–44
Monnet, Jean,
Muller, Steven,
National Security Council (NSC): advisory role of, ; authority of, 74–78; creation of, 74–75; decision-making role of, ; during Eisenhower administration, , , 75–79, 176n23; Goodpaster role, , , 78–79; during Kennedy administration, 79–80; national security policy coordination before creation of, 72–74; NSC-68 report, 34–36, 44–45, 169n4; NSC-162/2 report, , , ; policy making by, ; policy planning role, , ; during Truman administration, 74–75
National War College: commandant at, ix; political-military emphasis of graduates,
Navy, U.S.: interservice rivalries, 86–87; joint committees of the services, 14–15; lobbying of Congress by,
Nesnow, Sarah, , 160n13
Neutrality Act,
New Look policy: arms control and disarmament and, ; concepts and strategies of, 43–44, ; development of, 37–42; economy as pillar of U.S. strength and security, , ; naming of, ; nuclear weapons use strategy, 45–47, 169n6
Newton, Isaac,
Nitze, Paul, , , 44–45, , 186n8
Nixon, Richard: authority and duties during illnesses of Eisenhower, 94–95, , , 179n20; foreign policy of, 125–29; Goodpaster role in administration of, 130–31; honorable conclusion in Vietnam, 125–26; Mansfield Amendment, ; presidential election, ; resignation of, ; vice president role of,
Nobel Peace Prize award and speech,
Non-Proliferation Treaty, 178n26
Norstad, Lauris, xi, , 124–25, ,
North Atlantic Council, , 165n10
North Atlantic Treaty Organization (NATO): American military contingents assigned to, ; assignment to, 25–31; civilian structure of, 28–29; conventional military forces of member nations, ; formation of, , ; grand strategy for, 128–29; International Staff/Secretariat organization, 162n8; military structure and militarization of, 23–31; mutual and balanced force reductions, 128–29; planning group responsibilities, 26–27, 166n15; political and economic aspects of, ; political and military guidelines for, ; political general from U.S., ; Russian opinion of, ; security policy development, ; U.S. commitment to, , ; writings about, 165n3. _See also_ supreme allied commander, Europe (SACEUR)
nuclear weapons: arms control and disarmament, 66–68, 88–91; decision-making changes because of, 17–18; deterrence and stockpile of, 45–47, 48–52, 169n8; effects on the conduct of military activities, 17–18, , , 86–88, 152–53, 163n20; Eisenhower strategy on use of, 45–47, 169n6; elimination of, , , ; Goodpaster thoughts on, 152–53; grand strategy for, 87–88; JASC study of, ; Korea, tactical nuclear weapons use in, ; Live Oak role, ; massive retaliation, 43–44, 45–46, , , 87–88, ; more weapons and ideal number to have, 152–53, 155n1; New Look policy and reliance on, 43–44; planning for use of, 17–18; proliferation of in volatile regions, ; psychological readiness to use, ; reduction in inventories of, ; roles and limitations of, ; Soviet detonation of, ; Soviet surprise attack on U.S., ; stockpiling of, ; strategic and tactical use of, 17–18, 50–51; testing and verification, ; threat from and preparing to act on threat, 43–44; U.S. inventory of, 45–47
O'Brien, Jane Margaret,
Okinawa,
Open Skies proposal, 66–67, , 180n2
Operations and Plans Division (OPD), War Department: duties at, , ; General Marshall's Command Post, ; Japan invasion planning, 15–16, 163n12; mandate and mission, ; Pacific wartime planning trip, ; plans and strategic direction of military forces, responsibility for, ; principles to guide dealings with overseas commands, ; recruitment to, ; Strategy and Policy Group chief, Lincoln as, 13–14
Osmana, Sergio,
Outer Space Treaty, 178n26
Oxford University, , , , 164nn29–31
Panama and Panama Canal, 7–9
Paris Conference, , 109–12, , 180n4
Partnership for Peace (PfP) program,
Patton, George,
peace: détente policy and, 51–52; maintenance of,
Persons, Wilton "Jerry," ,
Philippines, ,
Plowden, Edwin,
Poland, ,
Political-Military Survey Section,
politics: ambition, politics, and careers, ; foreign policy and national security, political framework for, 84–86, 142–43, , 186n4; intellectuals, role for in, 169n30; political war, dangers of, 168–69n28
Powers, Francis Gary, , , 109–11, , 181n35
Princeton University, , 18–22, 164n30
psychological warfare and propaganda, , ,
public service, 154–55
Quemoy and Matsu islands and Formosa Strait crisis, 50–51, ,
Radford, Arthur W., , , , , ,
RAND Corporation, , 166–67n30
RB-47H aircraft, , 182n40
RB-57D aircraft,
retirement: policy interests after, xii; post-Army activities, 160n13; SACEUR role and request for, 131–33
Rhodes scholarship, , 13–14,
Ridgway, Matthew, xi, , , 183–84n13
Rogers, Bernard, ,
Roosevelt, Franklin D., , 60–61,
Rotary scholarship,
Rowny, Edward L.,
Rubenstein, Terry Meyerhoff,
Rusk, Dean,
Russia. _See_ Soviet Union and Russia
St. Anthony's College, Oxford University, 164n29
St. Mary's City,
St. Mary's College: board member at, x, xii, 149–51; Goodpaster Hall, ix, ; Heritage Project, ; improvements to programs at, x, 149–50; lecture series at,
San Francisco Engineer District,
Schaefer, E. M.,
Schaefer, William Donald,
Schriever, Bernard, 47–48, 170n14
Scowcroft, Brent, , ,
Screening and Costing Staff,
service to country. _See_ duty, honor, country
Silver Star medal, , 181n35
Smith, Walter Bedell, , , ,
Snyder, Howard, ,
Solarium initiative, 36–42, , 75–76, 169n30
Soviet Union and Russia: collapse of, 167n1; deliberate attack by, chance of, ; détente, diplomatic challenge of, ; Goodpaster thoughts on, 153–54; mutual and balanced force reductions, 128–29; nuclear weapons capabilities of, 48–49; nuclear weapons detonation by, ; peace advocate propaganda, ; reconnaissance flights to gather information on, 103–13, 180n13; rights and responsibilities as a Great Power, ; Sino-Soviet Communist threat, , , ; space race, ; threat from and expansion of U.S. military forces, 34–36, 44–45, ; U.S. policy toward, 33–36
space operations: CORONA program, 47–48; Outer Space Treaty, 178n26; space race,
Sprout, Harold H., , 164n29, 164n31
Stalin, Joseph,
State, Department of, 178n26
State-War-Navy Coordinating Committee (SWNCC), 13–14, , 163n12
Stevens, Leslie C.,
Stimson, Henry, ,
Strategic Air Command (SAC), , 112–13
Strategic Arms Limitation Talks (SALT), , 178n26
Strategic Arms Reduction Talks (START), 178n26
strategy: concept of, ; grand strategy,
Suez crisis, , , 63–65, 173n38
Sullivan, Susan Goodpaster, , 160n13
supreme allied commander, Europe (SACEUR): challenges and responsibilities as, 125–29; change-of-command ceremony, ; CINCEUR role, ; Eisenhower as, , 165n10; Goodpaster as, xii, , 124–29; Gruenther as, ; Haig as, 130–33; Live Oak role, ; political and economic issues, time spent on, ; politics and, , 129–33; replacement by Haig, 129–33; retirement request, 131–33; Ridgway as, 183–84n13; Westmoreland as, recommendation for,
Supreme Headquarters Allied Powers Europe (SHAPE), 25–26, , , 165n13, 166n18
Taylor, Maxwell D., , , 88–89, 173n40, 177n19
Technological Capabilities Panel (TCP), 47–48
technology: espionage technologies development, 105–6; good and bad aspects of, ; importance of to national power, 20–21, 164n34, 164n38; interest in, ix; new technology integration, limitations of, ; roles of military services and advances in, 170n14
Temporary Council Committee (TCC), 27–29, 166n22, 166n26
Three Wise Men, 28–29, 166n26
Thucydides,
Truman administration and Harry S Truman: Cold War and containment policy, 34–36, , , , , ; Eisenhower appointment as SACEUR, ; national security policy during, 175n15; NSC role, 74–75, 176n24; Philippines commitment and meeting with Osmana, ; Soviet policy of, 33–36; Truman Doctrine of aid to Greece and Turkey,
trust and trustworthiness, , , , ,
Turkey,
Twining, Nathan,
U-2 aircraft: approval of flights, 106–7, 108–9; budget for and cost of program, , ; CIA responsibility for, ; defense of program, ; development of, ; downing of, handling of, , 180n4; embarrassment and diplomatic disaster of, , , , 109–12, 113–14, 181n35; history of, 180n2; intelligence from, 180n13; meetings about, , 180n5; mission of and justification for program, 103–5; reconnaissance flights over Soviet Union, 103–12, 180n13; shooting down of Powers' flight, , , 109–11, , 181n35
Ukraine,
United States commander-in-chief, European command (USCINCEUR), ,
Vietnam and Vietnam War: acceptable (honorable) victory, ; Communist threat and, , 186n8; conventional military force development, ; counter-insurgency methods, ; deputy commander assignment, , 118–23; Eisenhower and military intervention in, ; Goodpaster assignment, ; Goodpaster opinion about fighting, ; honorable conclusion, promise of, 125–26; military force and resources to win, 117–18, 182n1; mission in, ; negotiating end of, , ; Paris peace talks, ; planning related to, ; Pleiku airfield attack, ; policy decisions and outcome of, , 143–44, 182n6; progress in, analysis of, 177n13; public opinion about actions in, ; resources for winning, ; strategic review to determine assurance of winning, 117–18, , 186n10; strategy for, 119–23, 143–44, 183n16; U.S. policy and, ; U.S. power and outcome of, ; victory, doubt about, ; Vietnamization of, 121–22; will of U.S. to win, 117–18,
War Plans Division (WPD), . _See also_ Operations and Plans Division (OPD), War Department
warfare: adequacy of defenses, 87–88; Army war-fighting doctrine, ; motivation for, ; nuclear weapons and changes to, 17–18, , , 86–88, 152–53, 163n22; planning for, ; political war, dangers of, 168–69n28; postwar debate about changes in, ; psychological warfare and propaganda, , , ; strains imposed on nations by, 145–46; technology and,
Waring, Tom,
weapons of mass destruction,
Weitzel, Harry,
West Point: appointment to and education at, 4–7; cheating scandals at, , 135–36, 139–40; class size increase to prepare for war, ; competition concept, ; curriculum expansion with humanities and social sciences courses, 5–6; Department of Social Sciences, Lincoln's role in, 162n4; discipline at, ; football program at, 139–40; football team and cheating scandal at, , , 185n8; Honor Code and System, , , , , 185n11; objectives and purpose of, 137–40; progressive leadership development at, ; scandals at, xii; superintendent at, ix, xii, 134–40, , 184n3; three-star superintendent position, , ; women at,
Western Union Defense Organization (WUDO),
Westmoreland, William, , , , ,
Weyand, Fred,
Wheeler, Earle, ,
Whitman, Ann, , ,
Wilson, Charles, 59–60, , ,
Wilson, Woodrow, , 97–98
Wood, R. J.,
Woodrow Wilson International Center for Scholars, , 158n1, 184n1
World War II: casualty rates, ; Distinguished Unit Citation, ; Italian campaign, 9–12, 161n29, 161n33, 161–62n36; Pacific campaign, planning for, ; start of, ; wounded troops, visits to in hospitals,
Yale University,
Zeldin, Theodore,
Zhukov, Georgy,
About the Author
**Robert S. Jordan** , who holds doctorates from both Princeton and Oxford Universities, has taught advanced courses in national security and international organization at U.S. war colleges and at private and public universities in the United States, Europe, and Africa. He served as director of research for the United Nations Institute for Training and Research and has participated in research projects at the Battelle Memorial Institute, the Ford Foundation, the Lucius Littauer Foundation, the Rockefeller Foundation, and the Atlantic Council. He was Distinguished Professor and Fleet Professor for the U.S. Naval War College. He also was University Research Professor at the University of New Orleans. He has published widely on Cold War alliance policy, coalition maritime affairs, international administration, and military biography.
**The Naval Institute Press** is the book-publishing arm of the U.S. Naval Institute, a private, nonprofit, membership society for sea service professionals and others who share an interest in naval and maritime affairs. Established in 1873 at the U.S. Naval Academy in Annapolis, Maryland, where its offices remain today, the Naval Institute has members worldwide.
Members of the Naval Institute support the education programs of the society and receive the influential monthly magazine _Proceedings_ or the colorful bimonthly magazine _Naval History_ and discounts on fine nautical prints and on ship and aircraft photos. They also have access to the transcripts of the Institute's Oral History Program and get discounted admission to any of the Institute-sponsored seminars offered around the country.
The Naval Institute's book-publishing program, begun in 1898 with basic guides to naval practices, has broadened its scope to include books of more general interest. Now the Naval Institute Press publishes about seventy titles each year, ranging from how-to books on boating and navigation to battle histories, biographies, ship and aircraft guides, and novels. Institute members receive significant discounts on the Press's more than eight hundred books in print.
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| {
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Luna è una municipalità di quarta classe delle Filippine, situata nella Provincia di La Union, nella Regione di Ilocos.
Luna è formata da 40 baranggay:
Alcala (Pob.)
Ayaoan
Barangobong
Barrientos
Bungro
Buselbusel
Cabalitocan
Cantoria No. 1
Cantoria No. 2
Cantoria No. 3
Cantoria No. 4
Carisquis
Darigayos
Magallanes (Pob.)
Magsiping
Mamay
Nagrebcan
Nalvo Norte
Nalvo Sur
Napaset
Oaqui No. 1
Oaqui No. 2
Oaqui No. 3
Oaqui No. 4
Pila
Pitpitac
Rimos No. 1
Rimos No. 2
Rimos No. 3
Rimos No. 4
Rimos No. 5
Rissing
Salcedo (Pob.)
Santo Domingo Norte
Santo Domingo Sur
Sucoc Norte
Sucoc Sur
Suyo
Tallaoen
Victoria (Pob.)
Note
Altri progetti
Collegamenti esterni
Comuni della provincia di La Union | {
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Q: Parsing errors when loading dataset I was given the code below to customize the variable types and it doesn't know how to interpret "f". any ideas on how to fix this?
library(readr)
data2014 <- read_csv("data2014.csv", col_types = cols(
.default = "f",
Time = col_skip(),
Minutes = col_integer(),
Seconds = col_integer(),
Away = col_character(),
Away_Points_Added = col_integer(),
Score = col_character(),
Home_Points_Added = col_integer(),
Home = col_character()
))
Error: Unknown shortcut: f
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 3,094 |
{"url":"https:\/\/docs.microsoft.com\/en-us\/dotnet\/framework\/app-domains\/shadow-copy-assemblies?redirectedfrom=MSDN","text":"Shadow copying enables assemblies that are used in an application domain to be updated without unloading the application domain. This is particularly useful for applications that must be available continuously, such as ASP.NET sites.\n\nImportant\n\nShadow copying is not supported in Windows 8.x Store apps.\n\nThe common language runtime locks an assembly file when the assembly is loaded, so the file cannot be updated until the assembly is unloaded. The only way to unload an assembly from an application domain is by unloading the application domain, so under normal circumstances, an assembly cannot be updated on disk until all the application domains that are using it have been unloaded.\n\nWhen an application domain is configured to shadow copy files, assemblies from the application path are copied to another location and loaded from that location. The copy is locked, but the original assembly file is unlocked and can be updated.\n\nImportant\n\nThe only assemblies that can be shadow copied are those stored in the application directory or its subdirectories, specified by the ApplicationBase and PrivateBinPath properties when the application domain is configured. Assemblies stored in the global assembly cache are not shadow copied.\n\n\u2022 Enabling and Using Shadow Copying describes the basic use and the options that are available for shadow copying.\n\n\u2022 Startup Performance describes the changes that are made to shadow copying in the .NET Framework 4 to improve startup performance, and how to revert to the behavior of earlier versions.\n\n\u2022 Obsolete Methods describes the changes that were made to the properties and methods that control shadow copying in the .NET Framework 2.0.\n\n## Enabling and Using Shadow Copying\n\nYou can use the properties of the AppDomainSetup class as follows to configure an application domain for shadow copying:\n\n\u2022 Enable shadow copying by setting the ShadowCopyFiles property to the string value \"true\".\n\nBy default, this setting causes all assemblies in the application path to be copied to a download cache before they are loaded. This is the same cache maintained by the common language runtime to store files downloaded from other computers, and the common language runtime automatically deletes the files when they are no longer needed.\n\n\u2022 Optionally set a custom location for shadow copied files by using the CachePath property and the ApplicationName property.\n\nThe base path for the location is formed by concatenating the ApplicationName property to the CachePath property as a subdirectory. Assemblies are shadow copied to subdirectories of this path, not to the base path itself.\n\nNote\n\nIf the ApplicationName property is not set, the CachePath property is ignored and the download cache is used. No exception is thrown.\n\nIf you specify a custom location, you are responsible for cleaning up the directories and copied files when they are no longer needed. They are not deleted automatically.\n\n\u2022 Optionally limit the assemblies that are shadow copied by using the ShadowCopyDirectories property.\n\nWhen you enable shadow copying for an application domain, the default is to copy all assemblies in the application path \u2014 that is, in the directories specified by the ApplicationBase and PrivateBinPath properties. You can limit the copying to selected directories by creating a string that contains only those directories you want to shadow copy, and assigning the string to the ShadowCopyDirectories property. Separate the directories with semicolons. The only assemblies that are shadow copied are the ones in the selected directories.\n\nNote\n\nIf you don\u2019t assign a string to the ShadowCopyDirectories property, or if you set this property to null, all assemblies in the directories specified by the ApplicationBase and PrivateBinPath properties are shadow copied.\n\nImportant\n\nDirectory paths must not contain semicolons, because the semicolon is the delimiter character. There is no escape character for semicolons.\n\n## Startup Performance\n\nWhen an application domain that uses shadow copying starts, there is a delay while assemblies in the application directory are copied to the shadow copy directory, or verified if they are already in that location. Before the .NET Framework 4, all assemblies were copied to a temporary directory. Each assembly was opened to verify the assembly name, and the strong name was validated. Each assembly was checked to see whether it had been updated more recently than the copy in the shadow copy directory. If so, it was copied to the shadow copy directory. Finally, the temporary copies were discarded.\n\nBeginning with the .NET Framework 4, the default startup behavior is to directly compare the file date and time of each assembly in the application directory with the file date and time of the copy in the shadow copy directory. If the assembly has been updated, it is copied by using the same procedure as in earlier versions of the .NET Framework; otherwise, the copy in the shadow copy directory is loaded.\n\nThe resulting performance improvement is largest for applications in which assemblies do not change frequently and changes usually occur in a small subset of assemblies. If a majority of assemblies in an application change frequently, the new default behavior might cause a performance regression. You can restore the startup behavior of previous versions of the .NET Framework by adding the <shadowCopyVerifyByTimestamp> element to the configuration file, with enabled=\"false\".\n\n## Obsolete Methods\n\nThe AppDomain class has several methods, such as SetShadowCopyFiles and ClearShadowCopyPath, that can be used to control shadow copying on an application domain, but these have been marked obsolete in the .NET Framework version 2.0. 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Home Banking
Can Crypto Help Banks Do Banking?
in Banking
I guess I would symbolize this tale as:
The banks are like, "oh man, sure, that sounds remarkable, signal us up.
Banks are the entities in our society that maintain lists of who has how a good a deal of cash. When banks need to replace the one's lists — to mirror that I have sent you money, for instance, so now I actually have much less money, and you've got greater — it's far very tough for them, and it takes them a long term to do it. When two banks are worried — while my money is at one bank and yours is at every other — it's miles clearly not possible, don't even ask; it can be days, weeks even. And if we are in one-of-a-kind international locations, forget about approximately it. International Business Machines Corp., a huge laptop/consulting/enterprise-machines organization, has long passed to the banks to recommend a way of preserving the lists of money on computer systems, so that if I need to send cash to you, our banks should simply make the relevant entries electronically, almost right away, in place of spending days seeking to figure it out.
Like: Fine, yes, that could be an inexpensive story if it changed into a set within the Fifties. Sure! The banks had armies of clerks who saved handwritten ledgers through the smoky light of whale-oil lamps and an easy-cut younger International Business Machines Corp. The salesman confirmed up to mention, "how about an enterprise system," and the banks had been like, "it's so crazy that it just might work, let's do it," and that they were brought out of the darkness into the electronic age. Why not? I am probably a piece off on a number of the details of the historical surroundings, however. Basically, it feels believable.
But this tale was set in 2019! It's set now! Now, these days, when you could order any bodily object on earth from Amazon.Com and get equal-day shipping, IBM salespeople are showing up at banks and being like, "what if we instructed you there has been a way to transfer money without placing gold cash in a sack, loading them on a horse and crossing a mountain variety to reach their destination?" And the banks are like, "what's this witchcraft?"
International Business Machines Corp., an issuer of technology for creating the digital currency, stated at the least two "principal U.S. Banks" are thinking about whether to observe JPMorgan Chase & Co.'s lead in issuing a coin. Jesse Lund, IBM's vice president of the blockchain, said that the organization had held preliminary discussions with the 2 creditors on issuing a so-known as stable coin — a digital token that is pegged 1:1 to established foreign money just like the U.S. Dollar. JPMorgan, the biggest U.S. Financial institution using belongings, announced in February that it'd issue digital foreign money tied to the dollar, known as JPM Coin. …
Digital cash can spot transfers of funds between institutional bills, reduce agreement instances, and make it less complicated to transport money internationally. JPMorgan, which movements extra than $5 trillion in wholesale payments each day, stated its coin would use its personal blockchain to hurry bills amongst company clients. "Stablecoin," in this context, I don't assume, means a lot more than "a manner to maintain a list of bucks on a pc, but faster." I fear that the right conclusion here is probably that tech organizations recognize the
way to be banks and that banks, in no way thoughts not knowing a way to be tech groups, don't understand how to be banks. At this point, Amazon probably could ship me a sack of gold and a horse quicker than my bank ought to do an electronic twine switch. If you positioned the bucks on computer systems, you can lend them out and fee interest! It's a new sales opportunity! How are those banks? If you'd want to get Money Stuff in the available electronic mail form, proper for your inbox, please subscribe at this link. Thanks! | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 8,275 |
Boating for Beginners was an off-shore audio guide. Anyone hiring a boat on the lake in Battersea Park during the summer of 2002 could take a Walkman with them with the specially prepared 15 minutes tape. The recording is very much a spoof on those guides one gets in historic and cultural buildings. The narration read by the Rev Alan Dupuy mixes some fact with much fancy, and treated sound recordings made in and around the park. This was the second of three pieces with a rowing theme. The first was called If O became E which was part of the group show Gym at the Conductors Hallway, the third piece a video entitled Row Row made this year and is a 'workout' of a picture of the Rev Dupuy out on the lake during 2002. | {
"redpajama_set_name": "RedPajamaC4"
} | 713 |
Q: I Need to remove distinct rows from my table As you can see by the picture all i need to do is to remove all the row who are multiple but leave only one
https://imgur.com/4RUajPQ
A: A pretty straightforward but inefficient way would be to cross join the table with itself and remove duplicate entries as given below:
DELETE t1 FROM my_table t1, my_table t2 WHERE t1.id > t2.id AND t1.user_id = t2.user_id AND t1.name = t2.name AND t1.time = t2.time AND t1.temperature = t2.temperature AND t1.activity = t2.activity AND t1.create_time = t2.create_time
Perhaps you could remove the extra equality checks in the where clause of the query if you are sure about the columns whose values can directly be used to identify if two rows are possible duplicates of each other.
A: You can also create a Row_number() over ( Partition by ID, Name, Temperature, activity, Order by ID, Name, Temperature, activity, create date desc ). Once the Rw number is created, you can delete the other rows from DELETE TABLE COMMAND
I'm assuming that you want only want one-row per to create date.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 5,924 |
Get the salsa ready, relocated Roburrito's in West York is finally open
The announcement came six months after the local restaurant chain made it public it would be relocating its West York location.
Get the salsa ready, relocated Roburrito's in West York is finally open The announcement came six months after the local restaurant chain made it public it would be relocating its West York location. Check out this story on ydr.com: https://www.ydr.com/story/news/local/2019/06/28/roburritos-west-york-now-open-york-county-restaurants/1595635001/
Neil Strebig, York Daily Record Published 12:27 p.m. ET June 28, 2019 | Updated 1:14 p.m. ET June 28, 2019
Grab a friend, grab a burrito and rejoice. The wait is finally over.
Roburrito's in West York is finally open.
The announcement came on Friday, June 28 via the restaurant's Facebook page. In November, the local franchise announced it would be closing its former West York location on Market Street and relocating.
More: Bike races to Jeep shows: Here's a look at what's happening around central PA in July
The restaurant is now located in the former site of Silbaugh Memorials at 800 N. Highland Ave. and is one of five Roburrito's locations in central Pennsylvania. Roburrito's West York is open 11 a.m. to 7 p.m., Sunday through Saturday.
Read or Share this story: https://www.ydr.com/story/news/local/2019/06/28/roburritos-west-york-now-open-york-county-restaurants/1595635001/
I-83 Mount Rose Avenue project: A timeline of events
Man standing trial in deadly 2017 shooting in York
Mysterious car found burning; police seek info
Group says opossum was beaten with golf club | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 2,030 |
#import <CoreFoundation/NSDate.h>
// Not exported
@interface __NSTaggedDate : NSDate
{
}
+ (id)allocWithZone:(struct _NSZone *)arg1;
+ (_Bool)automaticallyNotifiesObserversForKey:(id)arg1;
+ (id)__new:(double)arg1;
- (id)initWithTimeIntervalSinceReferenceDate:(double)arg1;
- (void)dealloc;
- (double)timeIntervalSinceReferenceDate;
@end
| {
"redpajama_set_name": "RedPajamaGithub"
} | 47 |
Vadd är ett voluminöst material av fibrer eller fibertussar som endast hålls samman av sin egen vidhäftningsförmåga, d.v.s. utan behandling för att hållas samman.
Vadd består av naturmaterial eller syntetfibrer. Exempel på användningsområden:
fyllnadsmaterial i kuddar, madrasser och dynor av olika slag
skydd vid förpackning av bräckliga föremål
inom sjukvården för uppsugning vid blödningar och liknande (bomullsvadd)
klädesplagg är ibland vadderade på särskilda ställen där det enkla tyget kan förväntas inte skydda kroppen tillräckligt mycket, till exempel kan arbetsbyxor vara vadderade över knäna
Materialet är en biprodukt vid till exempel spinning, eller från produktion av fiberduk, filtvaror eller kviltvaror.
Textilmaterial | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 9,034 |
Q: Understanding why translation seems to be done three times in the Bot Builder Framework sample: MultiLingualBot The official Microsoft sample which provides language translation in middleware in the bot seems to provide language translation which is triggered 3 different times/ways in the middleware.
My question is why aren't the 3 different types/ways overlapping. (How are the triggers mutually exclusive?)
The code in question lives here
The three times it seems to be triggered:
1) if (turnContext.Activity.Type == ActivityTypes.Message) //trigger translation
2) turnContext.OnSendActivities(async (newContext, activities, nextSend) => //trigger translation
3) turnContext.OnUpdateActivity(async (newContext, activity, nextUpdate) => //trigger translation
A separate question that may help add clarity -> The documentation says..."beware short circuiting" your middleware but isn't clear on how one my (purposely or accidentally) short circuit their middleware. Do either of the following two return statements short circuit the middleware?
return await nextSend(); //LINE 83 at time of writing
return await nextUpdate(); //LINE 100 at time of writing
For posterity, the referenced code is:
// Copyright (c) Microsoft Corporation. All rights reserved.
// Licensed under the MIT License.
using System;
using System.Collections.Generic;
using System.Linq;
using System.Threading;
using System.Threading.Tasks;
using Microsoft.Bot.Builder;
using Microsoft.Bot.Schema;
namespace Microsoft.BotBuilderSamples.Translation
{
/// <summary>
/// Middleware for translating text between the user and bot.
/// Uses the Microsoft Translator Text API.
/// </summary>
public class TranslationMiddleware : IMiddleware
{
private readonly MicrosoftTranslator _translator;
private readonly IStatePropertyAccessor<string> _languageStateProperty;
/// <summary>
/// Initializes a new instance of the <see cref="TranslationMiddleware"/> class.
/// </summary>
/// <param name="translator">Translator implementation to be used for text translation.</param>
/// <param name="languageStateProperty">State property for current language.</param>
public TranslationMiddleware(MicrosoftTranslator translator, UserState userState)
{
_translator = translator ?? throw new ArgumentNullException(nameof(translator));
if(userState == null)
{
throw new ArgumentNullException(nameof(userState));
}
_languageStateProperty = userState.CreateProperty<string>("LanguagePreference");
}
/// <summary>
/// Processes an incoming activity.
/// </summary>
/// <param name="turnContext">Context object containing information for a single turn of conversation with a user.</param>
/// <param name="next">The delegate to call to continue the bot middleware pipeline.</param>
/// <param name="cancellationToken">A cancellation token that can be used by other objects or threads to receive notice of cancellation.</param>
/// <returns>A <see cref="Task"/> representing the asynchronous operation.</returns>
public async Task OnTurnAsync(ITurnContext turnContext, NextDelegate next, CancellationToken cancellationToken = default(CancellationToken))
{
if (turnContext == null)
{
throw new ArgumentNullException(nameof(turnContext));
}
var translate = await ShouldTranslateAsync(turnContext, cancellationToken);
if (translate)
{
if (turnContext.Activity.Type == ActivityTypes.Message)
{
turnContext.Activity.Text = await _translator.TranslateAsync(turnContext.Activity.Text, TranslationSettings.DefaultLanguage, cancellationToken);
}
}
turnContext.OnSendActivities(async (newContext, activities, nextSend) =>
{
string userLanguage = await _languageStateProperty.GetAsync(turnContext, () => TranslationSettings.DefaultLanguage) ?? TranslationSettings.DefaultLanguage;
bool shouldTranslate = userLanguage != TranslationSettings.DefaultLanguage;
// Translate messages sent to the user to user language
if (shouldTranslate)
{
List<Task> tasks = new List<Task>();
foreach (Activity currentActivity in activities.Where(a => a.Type == ActivityTypes.Message))
{
tasks.Add(TranslateMessageActivityAsync(currentActivity.AsMessageActivity(), userLanguage));
}
if (tasks.Any())
{
await Task.WhenAll(tasks).ConfigureAwait(false);
}
}
return await nextSend();
});
turnContext.OnUpdateActivity(async (newContext, activity, nextUpdate) =>
{
string userLanguage = await _languageStateProperty.GetAsync(turnContext, () => TranslationSettings.DefaultLanguage) ?? TranslationSettings.DefaultLanguage;
bool shouldTranslate = userLanguage != TranslationSettings.DefaultLanguage;
// Translate messages sent to the user to user language
if (activity.Type == ActivityTypes.Message)
{
if (shouldTranslate)
{
await TranslateMessageActivityAsync(activity.AsMessageActivity(), userLanguage);
}
}
return await nextUpdate();
});
await next(cancellationToken).ConfigureAwait(false);
}
private async Task TranslateMessageActivityAsync(IMessageActivity activity, string targetLocale, CancellationToken cancellationToken = default(CancellationToken))
{
if (activity.Type == ActivityTypes.Message)
{
activity.Text = await _translator.TranslateAsync(activity.Text, targetLocale);
}
}
private async Task<bool> ShouldTranslateAsync(ITurnContext turnContext, CancellationToken cancellationToken = default(CancellationToken))
{
string userLanguage = await _languageStateProperty.GetAsync(turnContext, () => TranslationSettings.DefaultLanguage, cancellationToken) ?? TranslationSettings.DefaultLanguage;
return userLanguage != TranslationSettings.DefaultLanguage;
}
}
}
A: Message translation needs to occur when certain types of activities are received by the bot. Some types of activities do not require a translation. The protocol's activity types can be found here
"message",
"contactRelationUpdate",
"conversationUpdate",
"typing",
"endOfConversation",
"event",
"invoke",
"deleteUserData",
"messageUpdate",
"messageDelete",
"installationUpdate",
"messageReaction",
"suggestion",
"trace",
"handoff"
The MultiLingualBot sample demonstrates translating:
1) incoming message activities into TranslationSettings.DefaultLanguage for processing by the bot
2) outgoing message activities back into the user's preferred language
3) messageUpdate activities
1) if (turnContext.Activity.Type == ActivityTypes.Message) //trigger translation
2) turnContext.OnSendActivities(async (newContext, activities, nextSend) => //trigger translation
3) turnContext.OnUpdateActivity(async (newContext, activity, nextUpdate) => //trigger translation
Short circuiting the middleware would be not calling
await next(cancellationToken).ConfigureAwait(false);
or
return await nextSend();
or
return await nextUpdate();
If these are not called, message processing stops. Other middleware down the stack will not process the incoming message.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 2,510 |
{"url":"http:\/\/mathhelpforum.com\/calculus\/165550-epsilon-delta-definition-limit.html","text":"Thread: Epsilon delta definition of limit\n\n1. Epsilon delta definition of limit\n\nHow to prove that $\\lim_{x\\to2}{x^2}=4$ by using the formal definition of limit?\nI tried to solve it, but the problem was to find delta that depends on epsilon.\n\n2. Consider:\n\n$\\left |{x^2-4}\\right |< \\epsilon \\Leftrightarrow \\left |{x-2}\\right |\\left |{x+2}\\right |< \\epsilon$\n\nFor choosing $\\delta$ take into account that $|x+2|$ is (for example) bounded on $[1,3]$.\n\nRegards.\n\nFernando Revilla\n\n3. I am sorry, but I still couldnot get it.\n\n4. On $(1,3)$ we have $|x+2|<5$,\n\nthen, on $(1,3)$\n\n$|x^2-4|=|x-2||x+2|<5|x-2|<\\epsilon \\Leftrightarrow |x-2|<\\epsilon\/5$\n\nNow, choose\n\n$\\delta=\\min\\{1,\\epsilon\/5\\}$\n\nRegards.\n\nhttp:\/\/www.fernandorevilla.es\/","date":"2017-06-25 08:57:08","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\": 0, \"img_math\": 0, \"codecogs_latex\": 10, \"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\": 0.9879502058029175, \"perplexity\": 851.1102491913417}, \"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-2017-26\/segments\/1498128320476.39\/warc\/CC-MAIN-20170625083108-20170625103108-00643.warc.gz\"}"} | null | null |
\section{Introduction}
In recent years, many heavy mesons with open or hidden charm were
discovered, which contribute to the revival of hadron spectroscopy
(for recent reviews, see \cite{charmreview}). One outstanding example
among them is the $D_{s0}^*(2317)$ discovered by the BABAR
Collaboration in the $D_s\pi$ final state~\cite{Aubert:2003fg}. The
measured mass of the $D_{s0}^*(2317)$ which is
$2317.8\pm0.6$~MeV~\cite{Yao:2006px} is much lower than that predicted
in many quark models. An appealing alternative is that the
$D_{s0}^*(2317)$ is a hadronic molecule, which means that it owes its
existence to meson--meson dynamics~\cite{Barnes:2003dj,eef}. In this
work we exploit further this idea. Note, in Refs.~\cite{mehen} it was
argued that a molecular interpretation of the $D_{s0}^*(2317)$ (and
its vector counter part) is at variance with heavy quark effective
field theory. However, this conclusion is based on the assumption that
the decay of a hadronic molecule is proportional to the molecular wave
function at the origin --- in Ref.~\cite{f0gg} it is shown that this
assumption is not justified for the decay of hadronic molecules.
The mass alone is not a signal for a molecule, as stressed, e.g., in
Ref.~\cite{Guo:2007up}. A consistent treatment of the mass and various
decays is required --- see also Ref.~\cite{evidence}. The difference
from the molecular state will presumably be revealed in the decay
pattern into various channels. However, no branching ratio of the
$D_{s0}^*(2317)$ has been reported accurately. The only experimental
constraints are upper limits for the ratios of some other decay
channels to the $D_{s0}^*(2317)^+\to D_s^+\pi^0$. For
instance~\cite{Yao:2006px},
\begin{equation}
\label{eq:exp} {\Gamma({D_{s0}^*(2317)^+\to D_s^*(2112)^+\gamma})
\over\Gamma ({D_{s0}^*(2317)^+\to D_s^+\pi^0})} < 0.059.
\end{equation}
The $D_{s0}^*(2317)$ can be dynamically generated from Goldstone
boson--$D$-meson scattering as a hadronic molecule using unitarized
amplitudes from chiral pertrubation
theory~\cite{Hchua,lutz04npa,Guo:2006fu,Lutz:2007sk}. The width of the
isospin violating decay $D_{s0}^*(2317)^+\to D_s^+\pi^0$ was estimated
to be about $8.7\,$keV in Ref.~\cite{Guo:2006fu} by considering only
the $\pi^0$--$\eta$ mixing in the final state. However, Faessler {\it
et al}. pointed out that the mass differences between neutral and
charged kaons and $D$--mesons give an important contribution
\cite{Faessler:2007}, which was confirmed later in
Ref.~\cite{Lutz:2007sk}. In Refs.~\cite{lutz04npa,Lutz:2007sk} also
subleading operators were studied. Note that isospin symmetry
violation in hadronic physics has two different sources: one
originates from the mass difference of the light $u$ and $d$ quarks,
and the other one stems from the electromagnetic (e.m.) interaction.
While the $\pi^0$--$\eta$ mixing and part of the meson mass
differences account for the former one, the effect of the latter on
the decay $D_{s0}^*(2317)^+\to D_s^+\pi^0$ will be investigated here
for the first time.
The first step is to construct the interaction Lagrangian to
next--to--leading order in the chiral expansion. Based on this we
can disentangle the e.m. and the strong contribution to the
$D$--meson mass difference. As will be demonstrated, the Lagrangian
also links these mass differences directly to the isospin--violating
Goldstone boson--$D$-meson scattering amplitudes, in full analogy to
the case of $\pi N$ scattering and the proton--neutron mass
difference~\cite{wein,Meissner:1997ii}. We can therefore calculate
the decay width of the $D_{s0}^*(2317)^+\to D_s^+\pi^0$ --- within
the molecular picture utilizing the chiral Lagrangian up to the
next-to-leading order (NLO) ${\mathcal O}(p^2)$, where $p$ denotes a small
parameter --- with a small number of free parameters. Note, in this
paper for the first time both the strong and the e.m. contributions
to the decay are incorporated systematically.
\section{Lagrangians at next-to-leading order}
The scattering between the Goldstone bosons and $D$--mesons is
similar to the case for pion-nucleon scattering (for reviews, see
Refs.~\cite{Bernard:1995dp,Bernard:2007zu}) because the $D$--mesons
have heavy masses which do not vanish in the chiral
limit\footnote{In this work we consider the SU(3) chiral limit,
$m_u, \, m_d,\, m_s\to 0$.}. We count the $D$--meson masses ($\sim
1.9$~GeV) as order ${\mathcal O}(\Lambda_{\chi}) \sim {\mathcal O}(p^0)$ where
$\Lambda_\chi\simeq 1$~GeV. Hence the leading order terms in the
chiral Lagrangian are of ${\mathcal O}(p)$, and the NLO terms are of ${\mathcal O}(p^2)$.
The leading order Lagrangian is just the kinetic energy term of the
heavy mesons~\cite{hclo}
\begin{equation}
{\cal L}^{(1)} = {\cal D}_{\mu}D{\cal D}^{\mu}D^{\dag}-m_D^2
DD^{\dag}
\end{equation}
with $D=(D^0,D^+,D_s^+)$ denoting the $D$--mesons, and the covariant
derivative being
\begin{eqnarray}
{\cal D}_{\mu} &\!\!=&\!\! \partial_{\mu}+\Gamma_{\mu}, \nonumber\\
\Gamma_{\mu} &\!\!=&\!\!
{1\over2}\left(u^{\dag}\partial_{\mu}u+u\partial_{\mu}u^{\dag}\right),
\end{eqnarray}
where
\begin{eqnarray}%
U = \exp \left( {\sqrt{2}i\phi \over F_\pi}\right),\quad u^2=U.
\end{eqnarray}%
The Goldstone boson fields are collected in the matrix
\begin{eqnarray}%
\label{eq:phi}
\phi =
\left(
\begin{array}{c c c}
\frac{1}{\sqrt{2}}\pi^0+\frac{1}{\sqrt{6}} \eta & \pi^+ & K^+ \\
\pi^- & - \frac{1}{\sqrt{2}}\pi^0+\frac{1}{\sqrt{6}} \eta & K^0 \\
K^- & \bar K ^0 & -\frac{2}{\sqrt{6}} \eta \\
\end{array}
\right) .
\end{eqnarray}%
We now consider the NLO chiral Lagrangian describing the interactions of
the pseudoscalar charm mesons with the Goldstone bosons. Considering
the heavy mesons as matter fields, similarly to the
pion-nucleon sector~\cite{Meissner:1997ii}, the strong part is
\begin{eqnarray}%
\label{eq:L2str} {\cal L}^{(2)}_{\rm str.} &\!\!=&\!\! D \left(
-h_0\langle\chi_+\rangle - h_1\tilde{\chi}_+ + h_2\left\langle
u_{\mu}u^{\mu} \right\rangle - h_3u_{\mu}u^{\mu}
\right) {\bar D} \nonumber\\
&\!\!&\!\! + {\cal D}_{\mu}D \left( h_4\langle u^{\mu}u^{\nu}\rangle
- h_5 \{u^{\mu},u^{\nu}\} - h_6 [u^{\mu},u^{\nu}] \right) {\cal
D}_{\nu}{\bar D} .
\end{eqnarray}%
The chiral symmetry breaking terms, i.e. $h_0$ and $h_1$ terms, have
been introduced before~\cite{Cheng:1993kp,lutz04npa}. The $h_2$ and
$h_3$ terms were introduced in Ref.~\cite{lutz04npa}.
We stress that the contributions of the $h_5$ and $h_3$ terms to $s$--wave
amplitudes differ only to order ${\mathcal O}(p/m_D)$. However, we still
keep them in our covariant formalism for in this way we have an additional tool
to estimate the theoretical uncertainty --- see section~\ref{sec:results}.
The
electromagnetic part is
\begin{equation}%
\label{eq:L2em} {\cal L}^{(2)}_{\rm e.m.} = F_{\pi}^2 D \left[ g_0
\left({Q_+^2-Q_-^2}\right) + g_1
\left\langle{Q_+^2-Q_-^2}\right\rangle + g_2{{Q_+}}\left\langle
Q_+\right\rangle + g_3\left\langle Q_+\right\rangle^2 \right] {\bar
D} \ ,
\end{equation}%
where
\begin{eqnarray}
\chi_+ &\!\!=&\!\! u^\dagger \chi u^\dagger + u\chi u ,\nonumber\\
\tilde{\chi}_+ &\!\!=&\!\! \chi_+ -
{1\over3}\left\langle\chi_+\right\rangle,\nonumber\\
u_{\mu} &\!\!=&\!\! iu^{\dag}{\cal D}_{\mu}Uu^{\dag}, \nonumber\\
Q_\pm &\!\!=&\!\! \frac12\left( u^\dagger Q u \pm uQu^\dagger
\right).
\end{eqnarray}%
The quark mass matrix and the $D$--meson charge matrix are
diagonal
\begin{equation}
\chi = 2B\cdot {\rm diag}\left\{m_u,m_d,m_s\right\}, \quad Q =
e\cdot {\rm diag}\left\{0,1,1\right\}~,
\end{equation}
in terms of $B= |\langle 0 |\bar q q |0\rangle|/F_{\pi}^2 $ and the
elementary charge $e$. Further, $F_{\pi}$ is the pion decay constant.
The unknown coefficients $h_i~(i=0,1,...,6)$ and $g_i~(i=0,1,2,3)$ in
Eqs.~(\ref{eq:L2str},\ref{eq:L2em}) are the so-called low energy
constants (LECs). As we will show in the next section, $h_1$ and a
linear combination of $g_0$ and $g_2$, namely $g_0+2g_2$, can be
determined from the mass differences among the $D$--mesons. Since
$\langle Q_+\rangle=2e$, the $g_3$ term in ${\cal L}^{(2)}_{\rm e.m.}$
only gives an overall e.m. mass shift of the $D$--mesons, and hence
can be absorbed in the bare masses. The $g_1$ term contains only
isospin symmetric e.m. interaction and is irrelevant here. Terms with
one more flavor trace in the strong interaction Lagrangian are
suppressed in the large $N_C$ limit of QCD~\cite{Manohar:1998xv}. We
therefore follow Ref.~\cite{Lutz:2007sk} and drop the $h_0$, $h_2$ and
$h_4$. Formally the $h_6$ term is of ${\mathcal O}(p^2)$. However, due
to the commutator structure, it is suppressed by one order, see
Appendix~\ref{app:h6}. We are therefore left with only two free,
active parameters, both isospin conserving, namely $h_3$ and
$h_5$. We will investigate their effect on the isospin violating decay
of the $D_{s0}^*$ below.
One should note that the $\pi^0$ and $\eta$ in Eq.~(\ref{eq:phi})
are not mass eigenstates because of the $\pi^0$--$\eta$ mixing. The mass
eigenstates are defined as
\begin{eqnarray}
\tilde{\pi}^0 &\!\!=&\!\!
\pi^0\cos\epsilon_{\pi^0\eta}+\eta\sin\epsilon_{\pi^0\eta},
\nonumber\\
\tilde{\eta} &\!\!=&\!\! -\pi^0\sin\epsilon_{\pi^0\eta}
+\eta\cos\epsilon_{\pi^0\eta},
\end{eqnarray}
where $\epsilon_{\pi^0\eta}$ is the well-known $\pi^0$--$\eta$
mixing angle, which reads to leading order
\begin{equation}%
\epsilon_{\pi^0\eta}
= \frac{\sqrt{3}}{4}\frac{m_d-m_u}{m_s-\hat m}
\end{equation}%
with $\hat m=(m_u+m_d)/2$ the average mass of the $u$ and $d$
quarks.
\section{$D$--meson mass differences}
The terms which can contribute to the mass differences among the
$D^+,~D^0$ and $D_s^+$ mesons come from the Lagrangian of order
${\mathcal O}(p^2)$, Eqs.~(\ref{eq:L2str},\ref{eq:L2em}). Only three among all
the terms contribute.
We find
\begin{eqnarray}%
m_{D^0}^2-m_{D^+}^2 &=& \bar h \lambda + \bar g, \nonumber\\
m_{D^+}^2-m_{D^+_s}^2 &=& \bar h\left(1-\frac{ \lambda}{2}\right),
\label{parafix}
\end{eqnarray}%
where we define
\begin{equation}%
\bar h = 4Bh_1(m_s-\hat m), \quad \bar g = F_{\pi}^2 e^2(g_0+2g_2).
\label{bardefs}
\end{equation}%
The strength of
isospin violation due to quark mass effects is encoded in the
parameter $\lambda$ that is connected to $\epsilon_{\pi^0\eta}$
through
\begin{equation} \lambda = \frac{m_d-m_u}{m_s-\hat m}
=\frac{4}{\sqrt{3}}\epsilon_{\pi^0\eta}. \end{equation}
A recent analysis of
$\rho$--$\omega$ mixing in chiral perturbation theory gives
$1/\lambda=42\pm4$~\cite{Kucukarslan:2006wk}, correspondingly we have
$\lambda=0.024\pm 0.002$. Using the masses for the
$D$--mesons~\cite{Yao:2006px}, $m_{D^0}=1864.84\pm 0.17$ MeV,
$m_{D^+}=1869.62\pm 0.20$ MeV, and $m_{D_s^+}=1968.49\pm 0.34$ MeV,
we find
\begin{equation}%
\bar h = (384.1\pm 2.5)\times 10^3~{\rm MeV}^2, \quad \bar g =
(4\pm1)\times 10^3~{\rm MeV}^2 ,
\end{equation}%
where the largest uncertainty comes from the masses of the
$D$--mesons. Note that here only the uncertainties from the
experimental inputs are considered. For a discussion of the
theoretical uncertainty, see Section~\ref{sec:results}. Then the
dimensionless LECs $h_1$ and $g_0+2g_2$ can be determined as
\begin{equation}%
\label{eq:lec} h_1 = 0.42\pm0.00 , \quad g_0+2g_2 = 11\pm 3,
\end{equation}%
where we use
$B(m_s-\hat{m})=\left(M_{K^0}^2+M_{K^+}^2\right)/2-M_{\pi^0}^2$. The
basic assumption in setting up an effective field theory is the
naturalness of the low energy constants --- especially the
dimensionless coefficient $h_1$ should be of order one. This is
indeed the case for we find $h_1 = 0.42$. A naturalness estimate for
$g_0$ and $g_2$ comes from requiring that the contribution
of the corresponding operators to the $D$--meson mass shift
should be of the order
of a typical virtual
photon loop~\cite{Fettes:2000vm}, thus
\begin{equation}
e^2F_{\pi}^2g_i\sim \left({e\over 4\pi}\right)^2m_D^2.
\end{equation}
This leads to $g_i\sim 4$ as a natural estimate of the order of
magnitude, compatible with the value determined for $g_0+2g_2$.
The parameter $\bar h$, fixed from the amount of $SU(3)$ violation
encoded in the mass difference between the $D_s^+$ and the $D^+$
(see Eq.~(\ref{parafix})), controlls also the strong part of the $D^0$
and $D^+$ mass difference. Therefore, the electromagnetic
contribution to this mass difference, which is given by the ${\bar
g}$ term, can be extracted from data. This is different to the case of,
e.g., nucleons, where the operator structure is more complicated. We
therefore get
\begin{eqnarray}
\left(m_{D^+}-m_{D^0}\right)_{\rm str.} &\!\!=&\!\!
(2.5\pm0.2)~{\rm MeV}, \\
\left(m_{D^+}-m_{D^0}\right)_{\rm e.m.} &\!\!=&\!\!
(2.3\pm0.6)~{\rm MeV},
\end{eqnarray}
where the first equation refers to the strong contribution to the
mass difference and the second to its e.m. counterpart. Note,
contrary to what is common for nucleons as well as kaons, here the
electromagnetic and the strong effects enter with the same sign.
This is a direct consequence of the different quark content of the
states.
The strong and e.m. mass differences of $m_{D^+}-m_{D^0}$ are
consistent with those determined long time ago by Gasser and
Leutwyler using a simple quark model ansatz~\cite{Gasser:1982ap},
which are $3.3\pm0.9$~MeV and $1.7\pm0.5$~MeV, respectively.
\section{Width of the {\boldmath$D_s^*(2317)$}}
For studying isospin violating decays, it is better to work in the
particle basis. For the scalar charm-strange sector, there are four
channels involving a $D$--meson and a Goldstone boson: $D^0K^+$,
$D^+K^0$, $D_s^+\eta$ and $D_s^+\pi^0$. One can expect that the
isospin violating contributions to the mass of the $D_{s0}^*(2317)$
is negligible, therefore we only consider them for calculating the
isospin violating decay width. The strong contribution to this decay
is given in terms of the known $\pi^0$--$\eta$ mixing angle and the
meson mass differences.
The only non-vanishing e.m. contribution is from
the transition $D^0K^+\to D_s^+\pi^0$
\begin{equation}%
V_{D^0K^+\to D_s^+\pi^0}^{\rm e.m.} = -{\sqrt{2}\over
8}(g_0+2g_2)e^2.
\end{equation}%
Especially, the amplitude for $D_s^+\eta\to D_s^+\pi^0$
vanishes.
The linear combination of LECs $(g_0+2g_2)$
has been determined from the $D$--meson mass differences in the previous section.
Thus, all relevant isospin violating interactions are fixed from data.
\subsection{Unitarization of the scattering amplitudes at next-to-leading order}
A unitarization procedure was proposed in Ref.~\cite{Oller:2000fj}
which can be used for any finite order in the chiral expansion. Similar
to the case for pion-nucleon scattering, in our case, up to NLO
there is no loop contribution. Hence we obtain the following
$T$--matrix equation after matching to the chiral expansion at NLO
\begin{equation}
T(s)=V(s)\left[1-G(s)\cdot V(s)\right]^{-1},
\end{equation}
with $V(s)=V_{\rm LO}(s)+V_{\rm NLO}(s)$ the sum of the $S$--wave
scattering amplitudes of the LO and NLO orders~\cite{Oller:2000fj}.
$G(s)$ is a diagonal matrix with the diagonal element given by the
two-meson loop integral~\cite{Oller:2000fj,Oller:1998zr}
\begin{eqnarray}
\label{eq:G} G(s)_{ii} &\!=&\! i \int{d^4q\over (2\pi)^4} {1\over
\left(q^2-m_1^2+i\epsilon\right)\left[(P-q)^2-m_2^2+i\epsilon\right]}
\nonumber\\
&\!=&\! \frac{1}{16\pi^2}\left\{a(\mu)+\ln{\frac{m_2^2}{\mu^2}} +
\frac{m_1^2-m_2^2+s}{2s}\ln{\frac{m_1^2}{m_2^2}}
+\frac{\sigma}{2s}\left[\ln({s-m_1^2+m_2^2+\sigma})\right.\right.\nonumber\\
&\!&\! \left.\left. -\ln({-s+m_1^2-m_2^2+\sigma}) +
\ln({s+m_1^2-m_2^2+\sigma})-\ln({-s-m_1^2+m_2^2+\sigma}) \right]
\right\},
\end{eqnarray}
where $a(\mu)$ is the subtraction constant, $\mu$ denotes the scale
of the dimensional regularization, and
$\sigma=\left\{[s-(m_1+m_2)^2][s-(m_1-m_2)^2]\right\}^{1/2}$. In our analysis we
use the somewhat lengthy expression given above, for it allows for a
straightforward analytic continuation into the complex plain,
contrary to more compact representations that are
applicable in a particular parameter space only.
The subtraction constant $a(\mu)$ is determined by fitting the mass
of the $D_{s0}^*(2317)$ using the LO Lagrangian. It turns out to be
$a(\mu=1~{\rm GeV})=-1.846$ for reproducing
$m_{D_{s0}^*}=2317.8$~MeV~\cite{Yao:2006px}. Probably by accident,
it coincides exactly with that obtained from matching the value of
the loop function at the threshold of the $D$ and $K$ calculated by
Eq.~(\ref{eq:G}) with that calculated by using a 3-momentum cut-off
$q_{\rm max}=m_{\rho}$~\cite{Guo:2006fu}.
\subsection{Results}
\label{sec:results}
In calculations, we take physical values of all the meson masses and
the pion decay constant, as listed in the
following~\cite{Yao:2006px}:
\begin{eqnarray}
&& F_{\pi}=92.42~{\rm MeV},\quad M_{\pi^0}=134.98~{\rm MeV},\quad
M_{\pi^+}=139.57~{\rm MeV},
\nonumber\\
&& M_{K^0}=497.65\pm0.02~{\rm MeV},\quad
M_{K^+}=493.68\pm0.02~{\rm MeV},\nonumber\\
&& m_{D^0}=1864.84\pm0.17~{\rm MeV},\quad
m_{D^+}=1869.62\pm0.20~{\rm MeV},\nonumber\\
&& m_{D_s^+}=1968.49\pm0.34~{\rm MeV},\quad
M_{\eta}=547.51\pm0.18~{\rm MeV}.
\end{eqnarray}
After unitarization,
the hadronic molecule $D_{s0}^*(2317)$ appears as a pole
in the second
Riemann sheet at $\left(m_{D_{s0}^*}-i\Gamma(D_{s0}^*\to
D_s\pi^0)/2\right)$. Denoting the three-momentum of one particle in
the center-of-mass frame of
channel $i$ by $k_{i}$, the second Riemann sheet is
specified by ${\rm Im}\,k_{D_s^+\pi^0}<0$ and ${\rm Im}\,k_{i}>0$
($i=D^0K^+,~D^+K^0,~D_s^+\eta$). First, let us focus on the results
considering the LO amplitudes only.
There are two different kinds of
contributions to the isospin violating decay width at leading order.
One is from the $\pi^0$--$\eta$ mixing
and the other one is from
the mass differences between charged and neutral kaons and
$D$--mesons, which predominantly enters through
an isospin violating contribution to the loop function
of Eq.~(\ref{eq:G}).
However,
$\epsilon_{\pi^0\eta}=1/\sqrt{3}B(m_d-m_u)/\left(M_{\eta}^2-M_{\pi^0}^2\right)$
is suppressed by $M_\pi^2/M_{\eta}^2$ --- in SU(2) chiral perturbation
theory, where the strange quark is also viewed as heavy, this operator
appears only at NNLO, even an order below those given in
Eqs.~(\ref{eq:L2str}) and (\ref{eq:L2em}). Therefore, one can expect
that the mass differences give a larger contribution. The results
confirm this expectation as shown in the second and third column in
Table~\ref{tab:width}, corresponding to the widths considering only
the $\pi^0$--$\eta$ mixing and meson mass differences, respectively.
Furthermore, similar to Refs.~\cite{Faessler:2007,Lutz:2007sk}, in our
calculation the interference between these two kinds of contributions
are constructive, giving rise to a width of about 150~keV --- see the
first column of Table~\ref{tab:width}. However, when it comes to a
quantitative comparison, the result for the width to leading order of
Ref.~\cite{Lutz:2007sk} is smaller by a factor of two--- a direct
comparison with the more phenomenological work of
Ref.~\cite{Faessler:2007} is not possible. The difference can be
traced to differences in the input parameters and a different method
to fix the subtraction constant $a(\mu)$ of Eq.~(\ref{eq:G}). Those
differences should be of higher order. Thus the spread in the reported
results calls for a calculation to next--to--leading order in the
chiral expansion, c.f. Ref.~\cite{Lutz:2007sk}, together with an
analysis of the uncertainties.
\begin{table}[t]
\begin{center}
\begin{tabular}{|ccc|}\hline\hline
LO & $\pi^0$--$\eta$ mixing & Mass differences \\ \hline%
149.4 & 15.0 & 69.7 \\ \hline\hline%
\end{tabular}
\smallskip
\caption{\label{tab:width}Decay widths of the $D_{s0}^*(2317)\to
D_s\pi^0$ with LO amplitudes. All units of the decay widths are in
keV.}
\end{center}
\end{table}
\begin{figure}[t]
\begin{center}\vspace*{0.0cm}
\includegraphics[width=0.67\textwidth]{h3.eps}%
\vglue -0.65cm\caption{\label{fig:h3} Resulting $h_3$ from fitting
the mass of the $D_{s0}^*(2317)$ to 2317.8~MeV in the isospin
symmetric case for given $h_5'$.}
\end{center}
\end{figure}
We
take $[-1,1]$ as a natural range for the dimensionless parameter
$h_5'\equiv h_5/m_{D^0}^2$ --- note that for $h_5'=\pm1$ the
contribution of the $h_5$ term to the $D^0K^+\to D^0K^+$ scattering
amplitude is of the same order as the leading one. The subtraction
constant is kept fixed to $a(1~{\rm GeV})=-1.846$. The value of
$h_3$ is then determined from fitting the pole position in the
second Riemann sheet to the mass of the scalar charm meson
$m_{D_{s0}^*}=2317.8\pm0.6$~MeV in the isospin symmetric case. For
each value of $h_5'$, there is a corresponding $h_3$, as shown in
Fig.~\ref{fig:h3}.
For each value of $h_5'$
the resulting widths are plotted in
Fig.~\ref{fig:wid_h5}.
\begin{figure}[htb]
\begin{center}\vspace*{0.0cm}
\includegraphics[width=0.67\textwidth]{width_h5_band_exp.eps}%
\vglue -0.5cm\caption{\label{fig:wid_h5}
$\Gamma\left(D_{s0}^*(2317)^+\to D_s^+\pi^0\right)$ as a function of
$h_5'$. The solid curve results from choosing the central value for
$\lambda$, while the grey band is found by varying $\lambda$ within
its allowed bounds and taking into account theoretical uncertainty.
The dashed curve refers to neglecting the e.m. term in the decay
(let $g_0=-2g_2$).}
\end{center}
\end{figure}
In the figure, the solid line is the result for producing the mass
of the $D_{s0}^*(2317)$ at 2317.8 MeV with both the strong and e.m.
isospin violating contributions and using central values for all the
parameters. The dashed curve represents the result without e.m.
contributions. The uncertainties from the experimental inputs
are reflected in the shaded band.
To estimate the theoretical uncertainty observe that, as
stressed above, the effect of the $h_3$ and the $h_5$ term
differ at ${\mathcal O}(p/m_D)$. Therefore, since one of
the two is fixed already from the mass of the $D_{s0}$,
the dependence of the width on $h_5$ is a measure of
(some) NNLO effects. We may read off the figure directly
a spread of about 50 keV around the central value of 180 keV
induced by the variation of $h_5$. To be on the safe side
we take as the theoretical uncertainty of our calculation twice
this spread. Another way to estimate the theoretical uncertainty
is to use $2(M_K/\Lambda_{\chi})^2\simeq50\%$, since we include
contributions to the amplitude up to next--to--leading order in
$(M_K/\Lambda_{\chi})$ in our calculation. The factor of 2 appears
since the width is proportional to the square of the amplitude.
It is reassuring that both methods lead to essentially similar numbers
for the uncertainty. Our final result therefore reads
\begin{equation}
\Gamma\left(D_{s0}^*(2317)^+\to D_s^+\pi^0\right) = \left(
180\pm 40 \pm 100 \right)~{\rm keV},
\end{equation}
where the first error is from experimental inputs and the second
reflects the theoretical uncertainty.
Amongst the former uncertainties,
the largest ones are from the uncertainties of the $D$--meson masses
and the $\pi^0$--$\eta$ mixing parameter $\lambda=0.024\pm0.002$.
Schematically, let us consider the case corresponding to $h_5'=1$.
The central result for the width is 233 keV.
When the central values of all
the meson masses are taken, the width can change from 219~keV for
$\lambda=0.022$ to 248~keV for $\lambda=0.026$. When we take the
central value $\lambda=0.024$ and the central values of the masses
of all the mesons except $D^0$ and $D^+$, the width can change from
233~keV for taking the central values of $m_{D^0}$ and $m_{D^+}$ to
249~keV for taking $m_{D^0}=1864.65$~MeV and $m_{D^+}=1869.82$~MeV.
Among all the others, the uncertainties caused by $g_0+2g_2$, see
Eq.~(\ref{eq:lec}), and the masses of kaons are the largest, and
they amount to an uncertainty of 3~keV and 1~keV at most,
respectively. All other terms give negligible contributions to the
uncertainty.
Within the molecular picture, different calculations gave the width of
the radiative decay $D_{s0}^*(2317)\to D_s^*\gamma$ in the range from
$1-6$~keV~\cite{Gamermann:2007bm,Faessler:2007,Lutz:2007sk}.
Combining with the experimental result in Eq.~(\ref{eq:exp}), the
lower limit for the width of the decay $D_{s0}^*(2317)\to D_s\pi^0$ is
of the order of 100~keV. Our result is compatible with this extracted
lower limit.
\section{Summary and Outlook}
In this paper we investigate the isospin violating decay
$D_{s0}^*(2317)\to D_s\pi$ up to NLO in the chiral expansion, assuming
that the $D_{s0}^*(2317)$ is a hadronic molecule. We take into account
electromagnetic contributions systematically for the first time. Up to
order ${\mathcal O}(p^2)$, we obtain both the strong and e.m. mass
differences of the $D$--mesons. We confirm that the mass differences
between charged and neutral mesons in the same isospin multiplets play
a significant role in the decay width. The decay width of the
$D_{s0}^*(2317)\to D_s\pi$ calculated to next--to--leading order is
found to be $180\pm 110$ keV, where the uncertainties are added in
quadrature. The uncertainty is dominated by the theoretical
one. The resulting width is consistent with the present
experimental constraint.
Our results for the hadronic decay width of the $D_{s0}^*(2317)$
within uncertainty are consistent with previous analyses of the
$D_{s0}^*(2317)$ within a molecular picture considering both the
$\pi^0$--$\eta$ mixing and the meson mass differences:
Ref.~\cite{Faessler:2007} gives $79.3\pm 32.6$ keV, while
Ref.~\cite{Lutz:2007sk} gives $76$ keV ($140$ keV) as the result at
leading (next--to--leading) order.
Assigning the $D_{s0}^*(2317)$ to be a $c{\bar s}$ meson, its
hadronic width was estimated within quark models with typical values
of the order of 10~keV~\cite{godfrey}, although larger values were
reported --- see collection of results in table II of
Ref.~\cite{Faessler:2007}, which is consistent with the analysis
utilizing heavy quark effective field theory~\cite{mehen}. Within
the tetraquark picture a similar width as in the $c{\bar s}$ picture
was found~\cite{tetra}, which is about one order of magnitude
smaller than our predictions in the molecular picture. We therefore
conclude that the decay width of the $D_{s0}^*(2317)\to D_s\pi^0$
can be a good criterion for testing the nature of the
$D_{s0}^*(2317)$. A simultaneous study of radiative decays within
the various scenarios is also necessary, as advocated for the light
scalar mesons in Ref.~\cite{sraddec}. To expose the nature of the
$D_{s0}^*(2317)$, experimental efforts are highly appreciated to
improve the quantitative understanding of the $D_{s0}^*(2317)$
decays.
In this paper, we only considered the pseudoscalar $D$--mesons and
the Goldstone bosons. The effects of all the higher states are
incorporated in the LECs. However, the mass difference between $D^*$
and $D$ is only about 140~MeV, which is approximately equal to
$(m_{\Delta}-m_N)/2$. As it is sometimes important to include the
$\Delta(1232)$ in the chiral effective field theory for baryons (for
a recent review, see Ref.~\cite{Bernard:2007zu}), it would be
interesting to check what would happen if we include the vector
charm mesons explicitly in the effective Lagrangian, as in
Ref.~\cite{Lutz:2007sk}. This extension of the scheme will be
investigated in the future.
\section*{Acknowledgments}
We would like to thank A.~Wirzba, M.F.M.~Lutz, M.~Soyeur, and
T.~Gutsche for useful discussions and helpful comments. The work is
partially supported by the Helmholtz Association through funds
provided to the virtual institute ``Spin and strong QCD''(VH-VI-231)
and by the EU Integrated Infrastructure Initiative Hadron Physics
Project under contract number RII3-CT-2004-506078.
\begin{appendix}
\section{Suppression of the $h_6$ terms}
\label{app:h6}
Due to the commutator structure in Eq.~(\ref{eq:L2str}), all the
$h_6$ terms in amplitudes are proportional to
\begin{equation}
(p_1\cdot p_2)(p_3\cdot p_4) - (p_1\cdot p_4)(p_2\cdot p_3) \ ,
\end{equation}
where $p_1$ ($p_2$) and $p_3$ ($p_4$) are the momenta of the
heavy mesons (Goldstone bosons) in the initial and final state,
respectively. Let $v$ denote the velocity of a heavy meson, we
separate the momenta of the heavy mesons into two parts as
\begin{eqnarray}%
p_1 &\!\!=&\!\! M_1 v+k_1, \nonumber\\
p_3 &\!\!=&\!\! M_3 v+k_3,
\end{eqnarray}%
where $M_1$ and $M_3$ are the masses of the heavy mesons, and $k_1$
and $k_3$ are small residual momenta which are of order ${\mathcal O}(p)$. Let
$p_3=p_1+\Delta p$ with $\Delta p=\left(M_3-M_1\right)v+k_3-k_1$, we
have \begin{equation} (p_1\cdot p_2)(p_3\cdot p_4) - (p_1\cdot p_4)(p_2\cdot p_3) =
\Delta p\cdot\left[\left(p_1\cdot p_2\right)p_4 - \left(p_1\cdot
p_4\right)p_2\right]. \end{equation} Because $|M_3-M_1|\simeq 100$~MeV at
most, $\Delta p$ should be counted as ${\mathcal O}(p)$. Thus the above
equation should be counted as ${\mathcal O}(p^3)$, and hence is suppressed by
one more order.
\end{appendix}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 970 |
\section{Introduction}
Let $\Sigma_{g}$ be a genus $g$ surface and
$\Mod(\Sigma_{g})$ be the mapping class group of $\Sigma_{g}$, that is, the
group of isotopy classes of orientation-preserving homeomorphisms of $\Sigma_{g}$ (see
\cite{IvanovSurvey} for a survey of $\Mod(\Sigma_g)$).
An important theme in the study of $\Mod(\Sigma_g)$ and its subgroups is the close
relationship between algebraic properties of $\Mod(\Sigma_g)$ (e.g.\ cohomology, finiteness
properties, automorphisms, etc.)\ and the structure of $1$-submanifolds of $\Sigma_g$. The combinatorics
of these $1$-submanifolds have been encoded in the structure of a number
of simplicial complexes, such as the curve complex and the pants complex. A key property
of these complexes is that they are often highly connected. In this paper, we
discuss a general trick which yields simple proofs that complexes of this sort
are connected or simply connected; in many cases this is sufficient for the applications.
In the past, these sorts of theorems have been proven using a variety of tools, such as
curve surgery (see, e.g., \cite{FarbIvanov, HatcherEasy, MasurSchleimer, McCarthyVautaw, SchleimerNotes, WajnrybElementary}),
parametrized Morse theory (see, e.g., \cite{HatcherThurston, IvanovCurves}), and
Teichm\"{u}ller theory (see, e.g., \cite{BowditchEpstein, HarerVirtual, PennerTeichmuller}). We
instead exploit the basic combinatorial group theoretic properties of $\Mod(\Sigma_{g})$
and its subgroups, deducing that complexes are connected from the structure of generating sets
and deducing that they are simply connected from relations. Of course, we may be
accused of circular reasoning, as the standard construction of generators and relations
for $\Mod(\Sigma_g)$ involves investigating connected and simply connected complexes upon which it acts!
The point of this paper is that this only needs to be done once -- as soon as generators and relations for
$\Mod(\Sigma_g)$ are found, one can prove that essentially any complex upon which $\Mod(\Sigma_g)$ acts in a reasonable way is connected or simply
connected by a formal, finitely checkable (and in practice quite easy) process.
The first complex we will examine is the complex of curves (introduced by Harvey in \cite{HarveyCurves}), together
with two of its subcomplexes.
\begin{definition}
The {\em complex of curves} $\Curves(\Sigma_g)$ is the simplicial complex whose
simplices are sets $\{c_1,\ldots,c_k\}$ of non-trivial isotopy classes of simple closed
curves on $\Sigma_g$ which can be realized disjointly. The {\em complex of separating curves} $\CSep(\Sigma_g)$ and the
{\em complex of nonseparating curves} $\CNosep(\Sigma_g)$
are the full subcomplexes of $\Curves(\Sigma_g)$ spanned by separating and nonseparating curves, respectively.
\end{definition}
\noindent
We will give a simple, unified proof of the following theorem, which for $\Curves(\Sigma_g)$ and
$\CNosep(\Sigma_g)$ is due to Lickorish \cite{LickorishGenerators} (though he did not use this language) and
for $\CSep(\Sigma_g)$ is due to Farb and Ivanov \cite{FarbIvanov}. Other proofs
of the connectedness of $\CSep(\Sigma_g)$ can be found in \cite{MasurSchleimer} and \cite{McCarthyVautaw}.
\begin{theorem}
\label{theorem:curvesconnected}
$\Curves(\Sigma_g)$ and $\CNosep(\Sigma_g)$ are connected for $g \geq 2$, while $\CSep(\Sigma_g)$
is connected for $g \geq 3$.
\end{theorem}
In fact, our trick allows us to achieve rather precise control over the topology
of the curves which appear in our complexes. For instance, consider the following complex.
\begin{definition}
Let $\CHalf(\Sigma_{2g})$ be the simplicial complex whose simplices are sets $\{c_1,\ldots,c_k\}$ of
isotopy classes of simple closed curves on $\Sigma_{2g}$ which satisfy the following two conditions.
\begin{itemize}
\item Each $c_i$ separates $\Sigma_{2g}$ into two genus $g$ subsurfaces.
\item For $i \neq j$, the geometric intersection number $i_g(c_i,c_j)$ is {\it minimal} among such curves. This minimality
means the following : if $g = 1$, then $i_g(c_i,c_j)=4$, while if $g \geq 2$, then $i_g(c_i,c_j)=2$.
\end{itemize}
\end{definition}
\noindent
We will prove the following theorem, answering a question posed to the author by Schleimer (who
proved the theorem for $g = 1$ \cite{SchleimerNotes}).
\begin{theorem}
\label{theorem:halfconnected}
$\CHalf(\Sigma_{2g})$ is connected for $g \geq 1$.
\end{theorem}
We next investigate the cut system and pants graphs, which were introduced
by Hatcher and Thurston in \cite{HatcherThurston}.
\begin{definition}
A {\em cut system} on $\Sigma_g$ is a set $\{c_1,\ldots,c_g\}$ of isotopy classes of simple closed
curves on $\Sigma_g$ which can be realized disjointly with $\Sigma_g \setminus (c_1 \cup \cdots \cup c_g)$ connected (see
Figure \ref{figure:modconnected}.d). Two cut systems $\{c_1,\ldots,c_g\}$ and $\{c_1',\ldots,c_g'\}$
differ by an {\em elementary move} if
there is some $1 \leq i \leq k$ so that $i_g(c_i,c_i')=1$ and so that $c_j = c_j'$ for $j \neq i$. The
{\em cut system graph} $\CutSystem(\Sigma_g)$ is the graph whose vertices are cut systems on $\Sigma_g$
and whose edges correspond to elementary moves between cut systems.
\end{definition}
\begin{definition}
For $g \geq 2$, a {\em pants decomposition} of $\Sigma_g$ is a maximal simplex $\{c_1,\ldots,c_k\}$ of $\Curves(\Sigma_g)$ (see
Figure \ref{figure:modconnected}.e). Observe that $k = 3g-3$ and that cutting $\Sigma_g$ along the
$c_i$ results in a collection of $3$-holed spheres (the ``pairs of pants'').
Two pants decompositions $\{c_1,\ldots,c_k\}$ and $\{c_1',\ldots,c_k'\}$ differ by an {\em elementary move} if
there is some $1 \leq i \leq k$ so that for $j \neq i$ we have $c_j = c_j'$ and so that $i_g(c_i,c_i')$ is {\it minimal} among such
curves. This minimality means the following (see Figure \ref{figure:modconnected}.g) : if $S$ is the component of $\Sigma_g$ cut along
$c_1 \cup \cdots \cup c_{i-1} \cup c_{i+1} \cup \cdots \cup c_k$ containing $c_i$, then $i_g(c_i,c_i')=2$ if $S$ is a 4-holed sphere and
$i_g(c_i,c_i')=1$ if $S$ is a 1-holed torus. The {\em pants graph} $\Pants(\Sigma_g)$ is the graph whose vertices
are pants decompositions of $\Sigma_g$ and whose edges correspond to elementary moves between pants decompositions.
\end{definition}
\begin{remark}
Hatcher and Thurston in fact considered $\CutSystem(\Sigma_g)$ and $\Pants(\Sigma_g)$ with a number of 2-cells
attached to render them simply connected. We will make no use of these 2-cells.
\end{remark}
\noindent
We will give a new proof of the following theorem of Hatcher and Thurston, which for $\CutSystem(\Sigma_g)$ is
Theorem 1.1 of \cite{HatcherThurston} and for $\Pants(\Sigma_g)$ is contained in the appendix of \cite{HatcherThurston}.
\begin{theorem}
\label{theorem:cutpantsconnected}
$\CutSystem(\Sigma_g)$ is connected for $g \geq 1$, while $\Pants(\Sigma_g)$ is connected for $g \geq 2$.
\end{theorem}
Next, we will use the action of the Torelli subgroup of the mapping class group (defined below)
to prove the following theorem, which elucidates the nature of the homology relation
on a surface. It says that this relation is generated by ``embedded homologies'' (in the statement
of this theorem and throughout this paper, when we say that two simple closed unoriented curves
are homologous, we mean that they can be oriented in such a way that they are rendered homologous).
\begin{theorem}
\label{theorem:homologyconnected}
Fix $g \geq 3$, and let $\gamma$ and $\gamma'$ be homologous non-trivial simple closed curves on
$\Sigma_g$. Then there exists a sequence
$$\gamma = \gamma_1, \gamma_2, \ldots, \gamma_k = \gamma'$$
of non-trivial simple closed curves on $\Sigma_g$ so that for $1 \leq i < k$ the curves $\gamma_i$
and $\gamma_{i+1}$ are disjoint and there exists an embedded subsurface $S_i \hookrightarrow \Sigma_g$
with $\partial S_i = \gamma_i \sqcup \gamma_{i+1}$ (in particular, $\gamma_i$ and $\gamma_{i+1}$ are homologous).
\end{theorem}
\begin{remark}
This theorem is false for $g=2$, as there exist no subsurfaces $S$ of $\Sigma_2$ so that $\partial S$ consists
of two simple closed curves which are nonseparating and nonisotopic on $\Sigma_2$.
\end{remark}
Finally, we will show that our methods can be extended to prove that various complexes are simply connected. As
an example, we prove the following.
\begin{theorem}
\label{theorem:csepsimplyconnected}
For $g \geq 4$, the complex $\CSep(\Sigma_g)$ is simply connected.
\end{theorem}
\begin{remark}
Hatcher and Vogtmann \cite{HatcherVogtmann} have proven a much stronger theorem which says
that $\CSep(\Sigma_g)$ is $\lfloor \frac{g-3}{2} \rfloor$-connected. Their
result, however, does not imply Theorem \ref{theorem:csepsimplyconnected} for $g=4$.
\end{remark}
\begin{notation}
Let $P_1,P_2\ldots,P_k$ be a sequence of paths in a simplicial complex $X$ each of which begins and ends
in the $0$-skeleton $X^{(0)}$ (we allow degenerate paths $P_i$ consisting of single vertices). For all
$1 \leq i < k$, let $q_i$ be the terminal point of $P_i$ and $p_{i+1}$ be the initial point of $P_{i+1}$, and assume
that $\{q_i,p_{i+1}\} \in X^{(1)}$. Thus either $q_i = p_{i+1}$ or $\{q_i,p_{i+1}\}$ is a 1-simplex. We then denote
the path which first traverses $P_1$, then $P_2$, etc.\ by
$$P_1 - P_2 - \ldots - P_k.$$
\end{notation}
\section{Connectivity}
Our trick for proving that complexes are connected is contained in the following easy lemma.
\begin{lemma}
\label{lemma:main}
Consider a group $G$ acting upon a simplicial complex $X$. Fix
a basepoint $v \in X^{(0)}$ and a set $S$ of generators
for $G$. Assume the following hold.
\begin{enumerate}
\item For all $v' \in X^{(0)}$, the orbit
$G \cdot v$ intersects the connected component of $X$ containing $v'$.
\item For all $s \in S^{\pm 1}$, there is some path
$P_s$ in $X$ from $v$ to $s \cdot v$.
\end{enumerate}
Then $X$ is connected.
\end{lemma}
\begin{proof}
Consider $v' \in X^{(0)}$. By Condition 1, there is some $g \in G$
together with a path $P$ from $g \cdot v$ to $v'$. Write
$g$ as a word $s_1 \cdots s_k$ in $S^{\pm 1}$. Then
$$P_{s_1} - s_1 P_{s_2} - \ldots - s_1 s_2 \cdots s_{k-1} P_{s_k} - P$$
is a path from $v$ to $v'$. \qed
\end{proof}
\InsertFigure{figure:modconnected}{ModConnected.eps}{The various figures needed for the proof of Theorems \ref{theorem:curvesconnected},
\ref{theorem:halfconnected}, and \ref{theorem:cutpantsconnected} (see that proof for more details)}
\noindent
We now prove Theorems \ref{theorem:curvesconnected}, \ref{theorem:halfconnected}, and \ref{theorem:cutpantsconnected}.
\begin{likeproof}[Proof of Theorems \ref{theorem:curvesconnected}, \ref{theorem:halfconnected}, and \ref{theorem:cutpantsconnected}]
Let
$$S=\{T_{\alpha_1},T_{\delta_1},\ldots,T_{\alpha_g},T_{\delta_g},T_{\beta_1},\ldots,T_{\beta_{g-1}}\}$$
be the Dehn twists about the curves in Figure \ref{figure:modconnected}.a; Lickorish proved that $S$ generates
$\Mod(\Sigma_g)$ (see \cite[\S 4]{IvanovSurvey} for the definition of a Dehn twist and a discussion of Lickorish's
theorem). For each complex in question, we will pick a basepoint $v$ and verify that the two conditions of Lemma
\ref{lemma:main} are satisfied for the action of the mapping class group upon the complex. We emphasize
that in each proof the basepoint $v$ and all other ancillary curves are chosen to intersect the (already fixed)
generators in simple ways. In particular, they depend on the choice of generators.
\Heading{$\boldsymbol{\Curves(\Sigma_g)}$, $\boldsymbol{\CNosep(\Sigma_g)}$, and $\boldsymbol{\CSep(\Sigma_g)}$}
The proofs for these three complexes are similar; we will discuss $\CSep(\Sigma_g)$ and leave the other two to
the reader. Our basepoint $v \in \CSepk{0}(\Sigma_g)$ will be the curve indicated in Figure \ref{figure:modconnected}.b.
The orbit $\Mod(\Sigma_g) \cdot v$ consists of all separating curves which cut off 1-holed
tori. Indeed, let $w$ be another separating curve which cuts off a 1-holed torus. The classification of surfaces
implies that we get homeomorphic non-connected surfaces when we cut $\Sigma_g$ along either $v$ or $w$. Gluing
together homeomorphisms between the cut surfaces yields the desired homeomorphism of
$\Sigma_g$ taking $v$ to $w$ (this trick will be used repeatedly; we will call
it the {\em classification of surfaces trick}).
Since every separating curve is adjacent (in $\CSep(\Sigma_g)$) to a curve which cuts off a 1-holed torus, condition 1
follows. To check condition 2, we will need the curve $v'$ indicated in Figure \ref{figure:modconnected}.b.
Consider $s \in S^{\pm 1}$. If $s = T_{\beta_{g-1}}^{\pm 1}$, then $v - v' - s \cdot v$ is the desired path.
Otherwise, we have $s \in S^{\pm 1}$ but $s \neq T_{\beta_{g-1}}^{\pm 1}$, so $s \cdot v = v$. Condition 2 follows.
\Heading{$\boldsymbol{\CHalf(\Sigma_{2g})}$}
Here $S$ is the corresponding generating set for $\Mod(\Sigma_{2g})$.
Our basepoint $v \in \CHalfk{0}(\Sigma_{2g})$ will be the curve indicated in Figure \ref{figure:modconnected}.c.
If $g \geq 2$, we will also
need the ancillary curve $v'$ from the same figure. Now, by the classification of surfaces trick,
$\Mod(\Sigma_{2g})$ acts transitively on $\CHalfk{0}(\Sigma_{2g})$,
so condition 1 is trivial. To check condition 2, consider $s \in S^{\pm 1}$. If $s = T_{\beta_g}^{\pm 1}$, then for $g=1$ the vertices
$v$ and $s \cdot v$ are adjacent, while for $g \geq 2$, the desired path is $v - v' - s \cdot v$.
If instead $s \neq T_{\beta_g}^{\pm 1}$, then $s \cdot v = v$. Condition 2 follows.
\Heading{$\boldsymbol{\CutSystem(\Sigma_g)}$}
Our basepoint $v \in \CutSystemk{0}(\Sigma_g)$ will be the cut system indicated in Figure \ref{figure:modconnected}.d. By
the classification of surfaces trick, $\Mod(\Sigma_g)$ acts transitively on $\CutSystemk{0}(\Sigma_g)$, so condition 1 holds.
Also, for $s \in S^{\pm 1}$, either $s \cdot v = v$ or $s \cdot v$ is adjacent to $v$, so condition 2 holds.
\Heading{$\boldsymbol{\Pants(\Sigma_g)}$}
Our basepoint $v \in \Pantsk{0}(\Sigma_g)$ will be the pants decomposition indicated in Figure \ref{figure:modconnected}.e. We start by
verifying condition 2. Consider $s \in S^{\pm 1}$. If $s = T_{\delta_i}^{\pm 1}$, then $s \cdot v = v$. If
$s = T_{\beta_i}$, then Figure \ref{figure:modconnected}.h contains the desired path (we only draw the portion
of the pants decomposition which changes). A similar path works if $s = T_{\beta_i}^{-1}$.
If $s = T_{\alpha_1}^{\pm 1}$ or $s = T_{\alpha_g}^{\pm 1}$, then
$s \cdot v$ is adjacent to $v$. If $s = T_{\alpha_i}$ but $i \neq 1$ and $i \neq g$, then Figure \ref{figure:modconnected}.i contains
the desired path. A similar path works if $s = T_{\alpha_i}^{-1}$ with $i \neq 1$ and $i \neq g$. Condition 2 follows.
We now verify condition 1. It is enough to show that $\Pants(\Sigma_g) / \Mod(\Sigma_g)$ is connected. For each
pants decomposition $p=\{c_1,\ldots,c_k\}$ of $\Sigma_g$, define a graph $\phi(p)$ as follows (see
Figure \ref{figure:modconnected}.f). The vertices of $\phi(p)$ are the connected components of $\Sigma_g$ cut along
the $c_i$ (the ``pairs of pants''). The edges are in bijection with the curves $c_i$; the edge corresponding
to $c_i$ connects the vertices corresponding to the components on either side of $c_i$. Thus $\phi(p)$ is
a trivalent graph with $2g-2$ vertices (a loop at a vertex counts as $2$ edges abutting that vertex). It
is clear that each such graph comes from a pants decomposition. Moreover, it is not hard to see that
for pants decompositions $p$ and $p'$ we have $\phi(p)$ isomorphic to $\phi(p')$ if and only if there is some $f \in \Mod(\Sigma_g)$
so that $p = f \cdot p'$.
Now consider an elementary move from $p=\{c_1,\ldots,c_k\}$ to $p'=\{c_1',\ldots,c_k'\}$.
Let $c_i$ be the curve which changes in this move. If $i_g(c_i,c_i')=1$ (so $c_i$ corresponds to a loop
in $\phi(p)$; see the left hand part of Figure \ref{figure:modconnected}.g), then $\phi(p)=\phi(p')$. If $i_g(c_i,c_i')=2$ (see
the central part of Figure \ref{figure:modconnected}.g), then $\phi(p)$ is transformed into $\phi(p')$ in the following
way (see the right part of Figure \ref{figure:modconnected}.g) : we first collapse the edge in $\phi(p)$
corresponding to $c_i$, yielding a vertex of valence 4, which we then ``expand'' to two vertices of valence 3, each
of which abuts 2 of the edges which once abutted the vertex of valence 4. We will call this an {\em elementary shift} of the graph.
It is not hard to see that any elementary shift of $\phi(p)$ is induced by an elementary move of $p$.
It is enough, therefore, to prove that if $G$ and $G'$ are trivalent graphs with the same (necessarily even)
number of vertices, then $G$ may be transformed into $G'$ by a sequence of elementary shifts.
The proof will be by induction on the number $k$ of vertices. The base case $k=2$ being trivial, we
assume that $k > 2$. Since neither $G$ nor $G'$ can be a tree, each must contain
a simple closed edge-path. Transform $G$ and $G'$ by elementary shifts so that these closed edge paths
are as short as possible. Observe that these minimal-length closed edge paths must be loops --
if they were not loops, then we could shorten them by performing elementary shifts which collapse edges in them.
Let $\overline{G}$ and $\overline{G}'$ be the result of removing these loops, deleting the resulting
valence 1 vertices, and then finally deleting the resulting valence 2 vertices while combining the 2 edges abutting
them into a single edge (see Figure \ref{figure:modconnected}.j). By induction we can convert $\overline{G}$ into $\overline{G}'$ by a sequence of elementary
shifts. It is easy to see that we can then ``lift'' this sequence of elementary shifts to $G$, thus proving the
theorem. \qed
\end{likeproof}
Next, we prove Theorem \ref{theorem:homologyconnected}.
\begin{likeproof}[Proof of Theorem \ref{theorem:homologyconnected}]
This theorem is clearly equivalent to the connectedness of the following complex for $g \geq 3$.
\begin{definition}
Let $\Curves^{\gamma}(\Sigma_g)$ denote the full subcomplex of $\Curves(\Sigma_g)$ spanned
by curves homologous to $\gamma$.
\end{definition}
If $\gamma$ is separating, then $\Curves^{\gamma}(\Sigma_g) = \CSep(\Sigma_g)$, which is connected by
Theorem \ref{theorem:curvesconnected}. Assume, therefore, that
$\gamma$ is nonseparating, and let $\Torelli(\Sigma_g) \subset \Mod(\Sigma_g)$ (the {\em Torelli group}) be
the kernel of the action of $\Mod(\Sigma_g)$ on $\HHHH_1(\Sigma_g;\Z)$. We will apply Lemma \ref{lemma:main} to the
action of $\Torelli(\Sigma_g)$ on $\Curves^{\gamma}(\Sigma_g)$.
To apply Lemma \ref{lemma:main}, we need a base point and a generating set. Since $\gamma$ is nonseparating, the classification
of surfaces trick implies that there is a homeomorphism taking $\gamma$ to the curve $v$ depicted in Figure
\ref{figure:boundingtwist}.a. We can therefore assume without loss of generality that $\gamma$ in fact equals
the curve $v$; this will be our base point. It is well known (see, e.g., \cite[Lemma 6.2]{PutmanCutPaste})
that $\Torelli(\Sigma_g)$ acts transitively on the $0$-skeleton of $\Curves^{\gamma}(\Sigma_g)$, so condition 1 is trivial.
For the generating set, recall that Johnson \cite{JohnsonFinite} proved
that $\Torelli(\Sigma_g)$ is finitely generated. Our generating set $S$ will be the generating set for $\Torelli(\Sigma_g)$
constructed in \cite{JohnsonFinite}. We will need two facts
about $S$. First, $S$ consists of {\em bounding pair maps}, that is, mapping classes $T_{\gamma_1} T_{\gamma_2}^{-1}$ where the $\gamma_i$ are
disjoint nonseparating curves so that $\gamma_1 \cup \gamma_2$ separates $\Sigma_g$. Second, for
$T_{\gamma_1} T_{\gamma_2}^{-1} \in S$, either $\gamma_1 \cap v = \gamma_2 \cap v = \emptyset$ or a regular neighborhood
of $\gamma_1 \cup \gamma_2 \cup v$ is homeomorphic to the curves pictured on the left hand side of Figure \ref{figure:boundingtwist}.b. These
facts imply that for $s \in S^{\pm 1}$, either $s \cdot v = v$ or (as demonstrated by Figure \ref{figure:boundingtwist}.b) $s \cdot v$ is
disjoint from $v$. Condition 2 follows. \qed
\end{likeproof}
\InsertFigure{figure:boundingtwist}{BoundingTwist.eps}{a. Our base vertex in $\Curves^{\gamma}(\Sigma_g)$ \CaptionSpace b. $T_{\gamma_1} T_{\gamma_2}^{-1}(v)$ is disjoint from $v$}
\section{Simple connectivity}
We conclude this paper by proving Theorem \ref{theorem:csepsimplyconnected}.
\begin{likeproof}[Proof of Theorem \ref{theorem:csepsimplyconnected}]
Let
$$S=\{T_{\alpha_1},T_{\delta_1},\ldots,T_{\alpha_g},T_{\delta_g},T_{\beta_1},\ldots,T_{\beta_{g-1}},h\}$$
be the collection of twists
about the curves in Figure \ref{figure:modconnected}.a together with the hyperelliptic involution $h$ (see \cite[page 52]{IvanovSurvey} for
the definition of $h$; the need for $h$ will become clear shortly). Also, let $v$ and
$v'$ be the curves in Figure \ref{figure:modconnected}.b. There is a natural map $\Mod(\Sigma_g) \rightarrow \CSep(\Sigma_g)$ taking $g$ to
$g(v)$. Closely examining the proofs of Lemma \ref{lemma:main} and Theorem \ref{theorem:curvesconnected}, we see that they say that this map
extends to a $\Mod(\Sigma_g)$-equivariant map
$$\phi : \Cayley(\Mod(\Sigma_g),S) \longrightarrow \CSep(\Sigma_g).$$
Here $\Cayley(\Mod(\Sigma_g),S)$ is the {\em Cayley graph} of $\Mod(\Sigma_g)$, that is, the graph whose vertices are elements of
$\Mod(\Sigma_g)$ and where $g_2$ is connected by an edge to $g_1$ if $g_2 = g_1 s$ for some $s \in S$. We will prove that
the induced map $\phi_{\ast} : \pi_1(\Cayley(\Mod(\Sigma_g),S),1) \rightarrow \pi_1(\CSep(\Sigma_g),v)$ is the zero map by examining
the images of the loops associated to a set of relations for $\Mod(\Sigma_g)$. We will then show that $\phi_{\ast}$ is surjective; this will allow
us to conclude that $\pi_1(\CSep(\Sigma_g),v)=0$, as desired.
\begin{liketheo}[Claim 1]
$\phi_{\ast} : \pi_1(\Cayley(\Mod(\Sigma_g),S),1) \rightarrow \pi_1(\CSep(\Sigma_g),v)$ is the zero map.
\end{liketheo}
\begin{likeproof}[Proof of claim]
It is well known that we can construct a simply connected complex $X$ from $\Cayley(\Mod(\Sigma_g),S)$ by attaching discs to the $\Mod(\Sigma_g)$-orbits
of the loops associated to any complete set of relations for $\Mod(\Sigma_g)$. We will show that
the images in $\CSep(\Sigma_g)$ of the loops associated to these relations are contractible. This will imply that we can
extend $\phi$ to $X$. Since $X$ is simply connected, we will be able to conclude that $\phi_{\ast}$ is the zero map, as desired.
Now, the loop in $\Cayley(\Mod(\Sigma_g),S)$
associated to a relation $s_1 \cdots s_k = 1$ with $s_i \in S^{\pm 1}$ is
$1 - s_1 - s_1 s_2 - \ldots - s_1 s_2 \cdots s_k$. Since the only elements of $S^{\pm 1}$ which act
non-trivially on $v$ are $T_{\beta_{g-1}}^{\pm 1}$, the function
$\phi$ maps the edge $s_1 \cdots s_{i-1} - s_1 \cdots s_i$ to a fixed vertex unless $s_i = T_{\beta_{g-1}}^{\pm 1}$,
in which case it maps it to the path $s_1 \cdots s_{i-1} (v) - s_1 \cdots s_{i-1} (v') - s_1 \cdots s_i(v)$. Observe that
the only elements of $S^{\pm 1}$ which act non-trivially on $v'$ are $T_{\beta_1}^{\pm 1}$. If
none of the $s_i$ equal $T_{\beta_1}^{\pm 1}$, then for all $i$ we would have $s_1 \cdots s_{i-1} (v')=v'$, so $\phi$ would
take the loop associated to the relation $s_1 \cdots s_k=1$ to a loop of the form $v_1 - v_2 - \ldots - v_{2l+1}$ with $v_{2i} = v'$ for $1 \leq i \leq l$.
This loop can be contracted to $v'$.
We therefore only need to worry about relations which involve both $T_{\beta_1}^{\pm 1}$ and $T_{\beta_{g-1}}^{\pm 1}$. By
Theorem \ref{theorem:modpresentation} from the appendix, we can find a presentation for $\Mod(\Sigma_g)$ whose
generators are $S$ and whose only relations involving both $T_{\beta_1}^{\pm 1}$ and $T_{\beta_{g-1}}^{\pm 1}$ are
\begin{equation}
T_{\beta_1}^{-1} T_{\beta_{g-1}}^{-1} T_{\beta_1} T_{\beta_{g-1}} = 1 \label{commute}
\end{equation}
and
\begin{equation}
T_{\alpha_g} T_{\beta_{g-1}} T_{\alpha_{g-1}} \cdots T_{\beta_1} T_{\alpha_1} T_{\delta_1}^2 T_{\alpha_1} T_{\beta_1} \cdots T_{\beta_{g-1}} T_{\alpha_g} h^{-1} = 1. \label{hyper}
\end{equation}
We conclude that we must only check that the $\phi$-image of the loops associated to these two relations are contractible. For
the relation given in (\ref{commute}), it is clear that we can find a separating curve disjoint from every vertex of the associated
$\CSep(\Sigma_g)$-loop (for instance, $v''$ in Figure \ref{figure:modconnected}.b is such a curve), so this loop is contractible. For
the relation given in (\ref{hyper}), the associated loop is the following, where we suppress the (trivial) edges $w(v) - w s (v)$ associated
to generators $s \in S^{\pm 1}$ not equal to $T_{\beta_{g-1}}^{\pm 1}$:
\begin{align*}
&v - T_{\alpha_g}(v') - T_{\alpha_g} T_{\beta_{g-1}}(v) \\
&\ \ \ \ \ \ - T_{\alpha_g} T_{\beta_{g-1}} T_{\alpha_{g-1}} \cdots T_{\beta_1} T_{\alpha_1} T_{\delta_1}^2 T_{\alpha_1} T_{\beta_1} \cdots T_{\alpha_{g-1}}(v') - v \\
= &v - v' - T_{\alpha_g} T_{\beta_{g-1}}(v) - v' - v.
\end{align*}
This is clearly contractible, so the claim follows. \qed
\end{likeproof}
\begin{liketheo}[Claim 2]
$\phi_{\ast} : \pi_1(\Cayley(\Mod(\Sigma_g),S),1) \rightarrow \pi_1(\CSep(\Sigma_g),v)$ is surjective.
\end{liketheo}
\begin{likeproof}[Proof of claim]
We first find a sufficient condition for a loop to lie in the image of $\phi_{\ast}$. Consider any
loop $\ell = v_1 - v_2 - \ldots - v_{2n+1}$ in $\CSep(\Sigma_g)$ with $v_1 = v_{2n+1}=v$. Assume that
each $v_i$ is a separating curve which cuts off a 1-holed torus and that for $0 \leq i <n$ there
exists a simple closed nonseparating curve $\epsilon_i$ and some $e_i = \pm 1$ so that
$v_{2i+3} = T_{\epsilon_i}^{e_i} (v_{2i+1})$, so that $i_g(\epsilon_i, v_{2i+1}) = 2$, and
so that $i_g(\epsilon_i, v_{2i+2}) = 0$ (for instance, we could have $v_{2i+1}=v$, $v_{2i+2}=v'$, and $\epsilon_i = \beta_{g-1}$).
We claim that $\ell$ is in the image of $\phi_{\ast}$.
To begin with, it is enough to find some word $w$ in $S^{\pm 1}$ (not necessarily a
relation) so that $\ell$ is the image under $\phi_{\ast}$ of the path in $\Cayley(\Mod(\Sigma_{g}),S)$ associated to $w$. Indeed,
we then would have $w(v) = v$. Since $S \setminus \{T_{\beta_{g-1}}\}$ generates the stabilizer in $\Mod(\Sigma_g)$
of $v$, we can find some word $w'$ in $(S \setminus \{T_{\beta_{g-1}}\})^{\pm 1}$ so that $w w' =1$; this is the desired
relation.
We will prove the existence of $w$ by induction on $n$ (in this part of the proof, we do not assume that $\ell$ is a loop).
The case $n=0$ being trivial, we assume that $n>0$. Using the induction
hypothesis, we can find a word $w_{n-1}$ so that $\phi_{\ast}$ takes the path associated to $w_{n-1}$ to $v_1 - \ldots - v_{2n-1}$. Observe
that
\begin{align*}
&i_g(w_{n-1}^{-1}(v_{2n}),w_{n-1}^{-1}(\epsilon_n)) = i_g(v_{2n},\epsilon_n) = 0, \\
&i_g(w_{n-1}^{-1}(v_{2n}), v) = i_g(v_{2n},w_{n-1}(v)) = i_g(v_{2n},v_{2n-1}) = 0, \\
&i_g(w_{n-1}^{-1}(\epsilon_n), v) = i_g(\epsilon_n,w_{n-1}(v)) = i_g(\epsilon_n, v_{2n-1}) = 2.
\end{align*}
This implies that there must exist some $f \in \Mod(\Sigma_g)$ so that $f(v') = w_{n-1}^{-1}(v_{2n})$,
so that $f(\beta_{g-1}) = w_{n-1}^{-1}(\epsilon_n)$, and so that $f(v) = v$. Since the stabilizer in $\Mod(\Sigma_g)$
of $v$ is generated by $S \setminus \{T_{\beta_{g-1}}\}$, we can find some word $w''$ in $(S \setminus \{T_{\beta_{g-1}}\})^{\pm 1}$
so that $w'' = f$. We claim that $w=w_{n-1} w'' T_{\beta_{g-1}}^{e_n}$ works. Indeed, since $w_{n-1} f(v') = v_{2n}$,
the path associated to $w$ consists of $v_1 - \ldots - v_{2n-1}$ followed by the path
\begin{align*}
w_{n-1} f (v') - w_{n-1} f T_{\beta_{g-1}}^{e_n} (v) &= v_{2n} - w_{n-1} (f T_{\beta_{g-1}}^{e_n} f^{-1}) (v) \\
&= v_{2n} - w_{n-1} T_{f (\beta_{g-1})}^{e_n} (v) \\
&= v_{2n} - w_{n-1} T_{w_{n-1}^{-1} (\epsilon_n)}^{e_n} (v) \\
&= v_{2n} - w_{n-1} w_{n-1}^{-1} T_{\epsilon_n}^{e_n} w_{n-1} (v) \\
&= v_{2n} - T_{\epsilon_n}^{e_n} (v_{2n-1}).
\end{align*}
Since $T_{\epsilon_n}^{e_n} (v_{2n-1}) = v_{2n+1}$, this is the desired path.
Now consider an arbitrary $\ell' \in \pi_1(\CSep(\Sigma_g),v)$. We claim that we can homotope $\ell'$ so that it satisfies the
above condition. In fact, we will prove more generally that if $\ell'$ is any (not necessarily closed) path starting at $v$ whose
final endpoint corresponds to a curve cutting off a 1-holed torus, then we
can homotope it (fixing the endpoints) so that it satisfies all of the above conditions except for the closedness of
the path.
We can assume without loss of generality that $\ell'$ is a simplicial path in the 1-skeleton. It is an
easy exercise to see that we can homotope $\ell'$ so that all of its vertices cut off 1-holed tori, and
in addition we can arrange for $\ell'$ to contain an odd number of vertices and for no two adjacent vertices of $\ell'$ to be
identical. Enumerate the vertices of
of $\ell'$ as $v_1 - \ldots - v_{2m+1}$. By induction on $m$, we can assume that $v_1 - \ldots - v_{2m-1}$ satisfies
the desired condition. Now, using standard properties of $\Mod(\Sigma_g)$ we can find a sequence of
simple closed curves $\eta_1,\ldots,\eta_k$ and numbers $f_1,\ldots,f_k=\pm 1$ so that
$T_{\eta_1}^{f_1} \cdots T_{\eta_k}^{f_k} (v_{2m-1}) = v_{2m+1}$ and so that for $1 \leq i \leq k$ we have
$i_g(\eta_i,v_{2m-1})=2$ and $i_g(\eta_i,v_{2m})=0$. We can then homotope $\ell'$ (adding ``whiskers'') so that
the path $v_{2m-1} - v_{2m} - v_{2m+1}$ is replaced by
\begin{align*}
v_{2m-1} &- v_{2m} - T_{\eta_1}^{f_1} (v_{2m-1}) - v_{2m} - T_{\eta_1}^{f_1} T_{\eta_2}^{f_2} (v_{2m-1}) \\
&- v_{2m} - \ldots - T_{\eta_1}^{f_1} \cdots T_{\eta_k}^{f_k} (v_{2m-1}) = v_{2m+1},
\end{align*}
thus proving the claim. \qed
\end{likeproof}
\noindent
This completes the proof of Theorem \ref{theorem:csepsimplyconnected}. \qed
\end{likeproof}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 5,884 |
The transition from high school to college is complex enough and recently I've been wondering if technology has made it easier or harder. I don't have much analysis on the matter because it is more a problem I have been dealing with and have felt more acutely since being home. College has long been regarded as a time where you can start over and find out who you are but, how easy is it in this very connected world? In this transitional time where society is becoming more and more dependent on the technologies that make us connected is my generations college experience (or our lives for that matter) setting a new precedent?
For instance, cellphones keep you connected at all times and even screening calls is a little more difficult because people know you can see their missed calls. People even get upset if you are the type of person that keeps your cellphone off regularly (I used to be this type of person) because not being able to contact someone at every moment is just horrible, right? I'm not trying to put down connectivity because I have been enjoying the benefits of applications like Twitter ever since the Faculty Academy but, I'm wondering how do we go about disconnecting from certain things? Isn't there a time when we need to move on or readjust our connections?
Perhaps I feel my worlds (yes worlds) are colliding (or will soon be) and I don't know if I should put up boundaries or just let it be. Most of my family knows I blog but, I am still reluctant to give those who ask the URL. I can think of some family members I wouldn't mind sharing it with but, others I rather not see it. The same thing goes for friends from high school and friends from college. My blog is out there though, isn't it? I don't make posts private and I really don't talk about embarrassing personal stories that I wouldn't want my mom to know but, I can't help feel that there needs to be a separation. In an attempt to try to sort out who I am my thoughts often end up being showcased on my blog. A simple solution would be not to blog about it or limit it but, I don't think I could really consider that option. Maybe I feel like I am under a microscope of sorts and because my generation spends countless hours on Facebook following people I fear if I shared my blog with peers I would be subject to that same watchful eye, especially since there aren't many student bloggers. Maybe it is my fear of being known or maybe I just care too much about what others might think?
Today I googled my name and on the first page there was multiple links connecting people to me. It is becoming easier to find me and things I have said.
One of my friends recently left a post on my wall on Facebook and told me while doing a google search she found my blog.
Am I really afraid to fail and "fail gloriously"? Yes. Years of being subtly told failure is to be avoided and making a mistake is a sign of sloppiness, stupidity, or apathy. I'm struggling because I'm not sure I am really ok with making a mistake. When people are more likely to ask me what my GPA is than what I learned I cannot help but feeling failure needs to be avoided. People will try to put learning from mistakes in a shiny light but, more often it feels like it would have been better to have avoided making the mistake in the first place.
Here I am though, sharing this with the whole world. Although while I am writing this I am thinking about the people who read my blog and comment, more than I am imagining everyone on the web. A wise friend recently said to me it is "…interesting how the audience can call something out of us. We know that at least a few trusted readers will read it. Later we learn that many other folks will also love it–but it's the trusted circle that calls it forth". I think that is one of the reasons I continue to share and put this out there, it is these people who I can trust to respond with something meaningful to say. If I fail in front of these people I need not fear being ridiculed, these people embrace "making a mess".
My life is the editing stages, preparing for a major mashup of my past and present lives. As my online life becomes more transparent and as I plan to purposely do this starting this fall (atleast that is what I am telling myself) I have come back to idea of connections. It is clear that not all connections are equal, some are more valued than others. So as I deal with feelings of anxiety and worry about how well things will come together I have to remember to take a deep breath. I am starting to realize I am not enslaved by these connections, in fact I may very well be in charge of these connections. This may just be a matter of asserting myself and taking risks but, that is an issue for another blog post.
Just a brief update from the Emerald Isle.
I haven't missed the internet too much but, I miss having instant access to connection. I know there is so much going on and I don't enjoy missing the action but, I needed a break from it.
We are staying in a cottage in Doneraile in County Cork and it is really out in the country. It takes us about 20 minutes to get to Mallow which is not even that big of a city. There are cows in the backyard and the roads are very narrow. I think I have determined that Europeans aren't more environmentally conscious than Americans but, in actuality it would be a physical impossibility to drive a large car on the narrow roads.
I've gone through several batteries so there will be plenty of pictures to upload when I return. We plan on going to the Dingle Peninsula soon guess I need to buy more batteries, I've got to remember not to take a picture of every green hill, it is hard not to though.
Being disconnected from the internet (for the most part) has given me time to just write without checking out what everyone was doing every five minutes. When I'm not writing I'm reading some books I picked up in the Atlanta airport. More reflections to come when I get home, when I don't have to pay for internet access.
The craic has been mighty.
Will my laptop finally be fixed?
Back in September my Toshiba laptop mysteriously decided it no longer thought its shift keys were useful and they promptly stopped working. I recorded my misadventures here and here and finally after all these months I've decided it needs to be fixed. Carrying around an external keyboard is not my definition of cool.
My original plan was to go back to the store where I purchased my laptop. I arrived at the store only to find that they were going out of business! I walked in and they recommended I call 1-800-CompUSA, well I wasn't about to be bothered with that so I called up India, I mean the Toshiba Helpline, to see if they could give me the closest authorized dealer to fix my problem. Apparently the closest place is in Brooklyn and even though I certainly love my laptop, I am not about to drive to Brooklyn to get it repaired. So being the globalization savvy consumer I remembered that Toshiba has a program where you can go to a UPS store and drop off your laptop and they will take care of the rest. I asked the tech person about this and he transferred me to another department. On a side note, before I had called Toshiba I remembered the option of taking it to a UPS store, but I couldn't remember if I had to call Toshiba first or just walk into the store so I did a google search and what do you know my own blog posts popped up (and yes I did have to call beforehand). I was given a service order and an address for the closest UPS store.
So with my service order number in hand I drove dutifully to the local UPS store, located right in my town. Apparently they don't get a lot of Toshibas going out so it took them a few minutes to figure out the proper procedure, but we all took it in stride and we had it set to be shipped. It should take about 7 business days to get it repaired, but knowing my luck I'll probably get a call saying that my laptop was swept away in a spontaneous flood, but they'll send me two new shift keys free of charge!
For now I am stuck using the slower than molasses family computer. Thank goodness for online tracking of shipments, that way I can know when my baby laptop is coming home. I think I am already showing signs of withdrawal. | {
"redpajama_set_name": "RedPajamaC4"
} | 6,481 |
The Sigma APO 120-400mm F4.5-5.6 DG OS HSM lens is a super-telephoto lens produced by Sigma Corporation. It contains three SLD (Special Low Dispersion) glass elements to provide correction for chromatic aberration. It is aimed toward advanced consumers.
See also
List of Nikon compatible lenses with integrated autofocus-motor
References
External links
120-400 | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 4,934 |
Q: Pattern to many parameters I'm creating an application that has a single Entrypoint, the application user has 10 parameters to fill, only 3 are optional. These parameters are filled in an object called ContextConfig. When the application starts there 10 parameters are delivered for 3 objects and different objects takes repetitive parameters, are there any pattern to this?
class DeltaContext:
def __init__(self, delta_context: DeltaContextConfig):
self.delta_context = delta_context
self.hive_operations = HiveOperations(
hive_config=HiveConfig(
spark_df=self.delta_context.spark_df,
table_name=self.delta_context.table_name,
database_name=self.delta_context.database_name,
partition_column=self.delta_context.partition_column,
destination_path=self.delta_context.destination_path,
spark_context=self.delta_context.spark_context,
)
)
self.delta_writer = DeltaWriter(
delta_write_config=DeltaWriteConfig(
spark_df=self.delta_context.spark_df,
column_to_order=self.delta_context.column_to_order,
destination_path=self.delta_context.destination_path,
partition_column=self.delta_context.partition_column,
primary_key=self.delta_context.primary_key,
files_count_first_batch=self.delta_context.files_count_first_batch,
spark_context=delta_context.spark_context,
operation_type=delta_context.operation_type,
update_condition=delta_context.update_condition,
set_expression=delta_context.set_expression
)
)
self.auto_compaction = AutoCompaction(
auto_compaction_config=AutoCompactionConfig(
spark_context=self.delta_context.spark_context,
destination_path=self.delta_context.destination_path,
partition_column=self.delta_context.partition_column,
ideal_file_size=self.delta_context.ideal_file_size,
compaction_interval_time=self.delta_context.compaction_interval_time,
)
)
How can I make it better?
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 4,822 |
Cluster Series
==============
Requirements:
* python > 3.4
* numpy > 1.10
* matplotlib > 1.5
* scipy - Install using pip<code>pip install scipy</code>
If scipy is not able to be installed using pip (e.g. with Python 3.6), download
* numpy inkl. MKL (Intel® Math Kernel Library) from http://www.lfd.uci.edu/~gohlke/pythonlibs/#numpy and install it using pip
* scipy from http://www.lfd.uci.edu/~gohlke/pythonlibs/#scipy and install it using pip
| {
"redpajama_set_name": "RedPajamaGithub"
} | 2,771 |
Q: Magento: Rebuilding Index after self-written product import/update throws exception we have a module to import products into magento. The module was written by a Magento programmer. It uses the Magento API and is written in PHP. It reads a CSV-like file (the actual delimiter used is '#'), translates a line into a product, then writes back the product to Magento. So far, so good.
I've duplicated and changed the module a few times. The last change was to update products, not import whole products. The module worked for about 950 of these products, then threw an exception:
magento:/srv/www/vhosts/www.mysite.com/shell # php import_colors.php ../var/import/colors.csv.out.csv
PHP Fatal error: Uncaught exception 'Zend_Db_Statement_Exception' with message 'SQLSTATE[23000]: Integrity constraint violation: 1062 Duplicate entry '12804-176-1-563' for key 'PRIMARY'' in /srv/www/vhosts/www.mysite.com/lib/Zend/Db/Statement/Pdo.php:234
Stack trace:
#0 /srv/www/vhosts/www.mysite.com/lib/Zend/Db/Statement.php(300): Zend_Db_Statement_Pdo->_execute(Array)
#1 /srv/www/vhosts/www.mysite.com/lib/Zend/Db/Adapter/Abstract.php(468): Zend_Db_Statement->execute(Array)
#2 /srv/www/vhosts/www.mysite.com/lib/Zend/Db/Adapter/Pdo/Abstract.php(238): Zend_Db_Adapter_Abstract->query('INSERT INTO `ca...', Array)
#3 /srv/www/vhosts/www.mysite.com/lib/Varien/Db/Adapter/Pdo/Mysql.php(333): Zend_Db_Adapter_Pdo_Abstract->query('INSERT INTO `ca...', Array)
#4 /srv/www/vhosts/www.mysite.com/lib/Varien/Db/Adapter/Pdo/Mysql.php(1537): Varien_Db_Adapter_Pdo_Mysql->query('INSERT INTO `ca...', Array)
#5 /srv/www/vhosts/www.mysite.com/app/code/core/Mage/Catalog/Model/Resource/Eav/Mysql4/Product/Indexer/Eav in /srv/www/vhosts/www.mysite.com/lib/Zend/Db/Statement/Pdo.php on line 234
Fatal error: Uncaught exception 'Zend_Db_Statement_Exception' with message 'SQLSTATE[23000]: Integrity constraint violation: 1062 Duplicate entry '12804-176-1-563' for key 'PRIMARY'' in /srv/www/vhosts/www.mysite.com/lib/Zend/Db/Statement/Pdo.php:234
Stack trace:
#0 /srv/www/vhosts/www.mysite.com/lib/Zend/Db/Statement.php(300): Zend_Db_Statement_Pdo->_execute(Array)
#1 /srv/www/vhosts/www.mysite.com/lib/Zend/Db/Adapter/Abstract.php(468): Zend_Db_Statement->execute(Array)
#2 /srv/www/vhosts/www.mysite.com/lib/Zend/Db/Adapter/Pdo/Abstract.php(238): Zend_Db_Adapter_Abstract->query('INSERT INTO `ca...', Array)
#3 /srv/www/vhosts/www.mysite.com/lib/Varien/Db/Adapter/Pdo/Mysql.php(333): Zend_Db_Adapter_Pdo_Abstract->query('INSERT INTO `ca...', Array)
#4 /srv/www/vhosts/www.mysite.com/lib/Varien/Db/Adapter/Pdo/Mysql.php(1537): Varien_Db_Adapter_Pdo_Mysql->query('INSERT INTO `ca...', Array)
#5 /srv/www/vhosts/www.mysite.com/app/code/core/Mage/Catalog/Model/Resource/Eav/Mysql4/Product/Indexer/Eav in /srv/www/vhosts/www.mysite.com/lib/Zend/Db/Statement/Pdo.php on line 234
I thought nothing of it. The customer was happily changing the last 50 or so products on his own, and the error message was forgotten.
However, today the customer called that his product attribute index would not build, the index in the backoffice remained on orange "Processing". So I've investigated and found out that the index can be built by using shell/indexer.php. So I've tried and, and lo and behold, the exact same error message I almost forgot.
I've dumped the database and tried to find out which table actually contained the data listed in the error message (12804-176-1-563), but I had no luck. It seems that these 4 dates are nowhere to be found in this order.
Now, there are two options on how to proceed. One would be to find out which table actually contains the problem, so that it might be fixed using Magento itself. The other way might be to clear the corresponding index table and rebuild the index from scratch. I'm not certain digging around in a database schema I do not fully understand is a good idea.
Can anybody help me identify the problem?
A: Please check that this is not something simple such as some duplicated products in the database that have been 'aborted' to leave a product entry with no SKU value.
A: I have the same issue with a self written PHP import script. I am still not sure how to fix this, but I found that in 12804-176-1-563, 12804 refers to the id of the product in the DB. So if you delete/recreate or disable that product, then the indexer will work fine will work fine.
If you have any tip on why there are some integrity constrain violations please share! :-)
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 7,912 |
Amy Wong Fund
Amy Wong
In memory of Amy Wong (5/14/1951–10/2/2000)
The Amy Wong Client Fund helps people who are facing problems that they can't afford to fix and who do not qualify for public funding.
This charitable fund provides services such as in-home care, emergency services and other health related items for adults with disabilities who wish to remain living independently in their own homes.
All contributions are tax deductible.
The Amy Wong Client Fund provides help to adults with disabilities who wish to live independently. Sometimes all a person needs is a wheelchair-accessible ramp added to their home or a pair of orthopedic shoes. Something so simple can mean the difference between staying at home or moving to a nursing facility.
Currently, there are far more people who need help than the Fund can assist. Your gift will be used for those with the greatest needs. All contributions are tax deductible.
You can contribute by sending a check payable to Amy Wong Client Fund to:
Amy Wong Client Fund
c/o Aging and Disability Services
City of Seattle employees can contribute through the City's annual charitable giving campaign.
At this time, we are unable to process credit card donations.
History of the Amy Wong Client Fund
Amy Yuet-Lan Wong was a devoted wife and mother, an active volunteer in the community, and a dedicated case manager at Aging and Disability Services.
After a battle with cancer, Amy died at age 49. Right to the end, she continued to help her clients. Amy's spirit of providing assistance reflects the intent of the Fund, and her family graciously allowed it to be renamed after her.
Originally titled the Client Specific Fund, the Amy Wong Client Fund has helped thousands of clients since its inception in 1996—enabling adults with functional disabilities to fulfill their wish to remain independent in their own homes.
All of us know people who do everything possible to stay independent. The Amy Wong Client Fund was established to help those who face problems they can't afford to fix and who do not qualify for public funding.
The Fund provides help for small items or services that can make a big difference. Some examples:
Several clients with memory problems received bill paying assistance.
One client with diabetes needed her refrigerator repaired to keep her insulin chilled.
A client needed a pair of orthopedic shoes.
Read stories below to understand how the Amy Wong Client Fund has enabled more adults to live independently.
A female client had complex medical issues that resulted in a loss of appetite, chronic fatigue, depression, and anxiety. She could not prepare complicated meals and her health was deteriorating. The purchase of a microwave oven and a juicer helped to improve her nutritional status and allowed her to continue to remain in her home. Total cost: $119.44
A male client lived alone and had multiple diagnoses including arthritis. The client had trouble grasping and lifting items. The purchase of a microwave oven improved his ability to continue to cook for himself for a total cost of $97.73
A 36-year-old bed-bound, terminally-ill client had a brain tumor with resulting seizures. Her case manager authorized massage therapy as a comfort measure for the last months of her life. Total cost: $200.
An 83-year-old woman worked part-time to help make ends meet, but was let go from her job in December. Her Social Security income was only $50 more than her rent. With no way to earn additional money, her only option was to move to subsidized housing. The waiting period for her to receive a placement was five months. At the same time, she had problems with her knees and found it difficult to get to her medical appointments and to perform household chores such as cooking. The Amy Wong Client Fund provided partial rent assistance for the period of time required to get the housing, have knee surgery, apply for energy assistance, Meals on Wheels, transportation assistance, and help paying her Medicare premiums. She now lives near her granddaughter in a subsidized apartment.
The Amy Wong Client Fund provides assistance to purchase goods and services that will enable adults with disabilities to remain in their own homes. Because of the limited amount of funds, these services are provided on a short-term basis.
Funds are available only to clients who are currently enrolled in the Case Management Program administered by Aging and Disability Services—the Area Agency on Aging for Seattle-King County. The Case Management Program provides comprehensive care for frail elderly and adults with disabilities who have significant social and health needs.
To find out whether you are or a family member qualifies for the Case Management Program, call Community Living Connections at 206-962-8467 (toll-free 1-844-348-KING (5464)) or e-mail info@communitylivingconnections.org.
The Amy Wong Client Fund is for Case Management clients of Aging & Disability Services. Please see Eligibility (above) or call Community Living Connections at 206-962-8467 (toll-free 1-844-348-KING (5464)) or e-mail info@communitylivingconnections.org.
For questions about donating or for general questions the Amy Wong Client Fund, contact Andrea Yip, Aging and Disability Services, at 206-386-0035 or andrea.yip@seattle.gov.
The Amy Wong Client Fund is administered by Aging & Disability Services (ADS). ADS is a division of the City of Seattle's Human Services Department and is designated as the Area Agency on Aging for King County, Washington. ADS is co-sponsored by the City of Seattle and King County. | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 5,070 |
Eric Ortiz est un boxeur mexicain né le à Mexico.
Carrière
Passé professionnel en 1996, il remporte le titre vacant de champion du monde des poids mi-mouches WBC le après sa victoire par arrêt de l'arbitre au round contre Jose Antonio Aguirre. Ortiz est en revanche battu dès le combat suivant par Brian Viloria le et met un terme à sa carrière de boxeur en 2012 sur un bilan de , et .
Référence
Lien externe
Boxeur mexicain
Champion du monde de boxe WBC
Naissance en mai 1977
Naissance à Mexico | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 3,595 |
var moment = require("moment");
module.exports.getDayOfWeekLocalisedText = function(language, dayOfWeek) {
var m = moment.localeData(language || "en");
var languageObject = m._weekdaysShort;
return languageObject[dayOfWeek];
};
| {
"redpajama_set_name": "RedPajamaGithub"
} | 7,150 |
The TV station transmitters are located in two different directions from your location. To receive all available channels my recommendation is for the EZ HD Bi-directional antenna kit #2. This kit comes with two EZ HD antennas, one antenna coupler, one AP 8780 preamplifier and three connection coax cables. Install one antenna aiming North and the other East. This system will provide reception on all available channels without the need to adjust or rotate the antenna. | {
"redpajama_set_name": "RedPajamaC4"
} | 6,537 |
Szabadkígyós is a village in Békés County, in the Southern Great Plain region of south-east Hungary.
Geography
It covers an area of 45.56 km² and has a population of 2434 people (2015).
Gallery
References
Populated places in Békés County
Palaces in Hungary | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 1,156 |
A Costureirinha da Sé é uma longa-metragem portuguesa, realizado por Manuel Guimarães, no ano de 1958.
Elenco
Maria de Fátima Bravo... Aurora
Jacinto Ramos... Sebastião
Alina Vaz... Leonor
Baptista Fernandes... Armando
Carlos José Teixeira... Filipe
Costinha... Vicente
Luísa Durão... Glória
Emílio Correia... Bernardino
Alma Flora... a professora
Maria Olguim... Augusta
Alda Rodrigues... Beatriz
"A Costureirinha da Sé" é aquilo a que alguns autores chamam de crónica bairrista do Porto. O filme é uma adaptação de opereta popular de Armando Leite e Heitor Campos Monteiro. A protagonista é a cantora popular Maria de Fátima Bravo, então no auge da sua carreira. A trama conta a história de Aurora, uma jovem das origens humildes do bairro da Sé. Aurora trabalha num atelier de costura e está caida de amores por Armando, motorista de táxi. Mas, o romance causa inveja vizinhança. Há quem queira o rapaz para si. O argumento retrata um Portugal dos anos 50 onde a vida não tem a dimensão/complexidade de hoje, onde cada bairro reclama para si o estuto de mais importante. Para exemplificar bem isso, nada melhor que um concurso, "o concurso do vestido de chita" que todos querem vencer.
O filme revela aspectos de uma vida pacata, sentida e em que as pessoas estão muito próximas umas das outras.
Ligações externas
A Costureirinha da Sé
Filmes de Portugal de 1958
Filmes realizados por Manuel Guimarães
Filmes em língua portuguesa
Filmes ambientados no Porto | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 4,617 |
Q: Regular Expression to find the exact match of the string Hi I have records like
MicroAlgae 7.5
AlgaeSerum 6.5
Algae 1.5
Here i need to extract the value of algae that is 1.5 and it should not extract the values of microalgae and algaeserum. I have used the regex as
/(?!Micro)/Algae,
Algae\s*/^(!Serum)/,
\\bAlgae\\b
Kindly let me know how can I write the regex according to that
A: If you have some large text where you need to pull the number from, you may use a simple regex with a capturing group around the part you need to extract:
import re
s = """MicroAlgae 7.5
AlgaeSerum 6.5
Algae 1.5"""
m = re.search(r'\bAlgae\s+([0-9.]+)', s)
if m:
print(m.group(1))
See the Python demo
The [0-9.]+ may be replaced with a more precise [0-9]+(?:\.[0-9]+)?.
Details:
*
*\b - the leading word boundary
*Algae - the literal char sequence Algae
*\s+ - one or more whitespaces
*([0-9.]+) - Group 1: one or more digits or dots or
*[0-9]+(?:\.[0-9]+)? - 1+ digits ([0-9]+), followed with an optional sequence of a . (\.) and 1+ digits ([0-9]+).
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 3,288 |
{"url":"http:\/\/www.sciencemadness.org\/talk\/viewthread.php?tid=78296","text":"Not logged in [Login - Register]\n Sciencemadness Discussion Board \u00bb Non-chemistry \u00bb Detritus \u00bb Offtopic from Advice for a 15 year old interested in amateur chemistry? Select A Forum Fundamentals \u00a0 \u00bb Chemistry in General \u00a0 \u00bb Organic Chemistry \u00a0 \u00bb Reagents and Apparatus Acquisition \u00a0 \u00bb Beginnings \u00a0 \u00bb Miscellaneous \u00a0 \u00bb The Wiki Special topics \u00a0 \u00bb Technochemistry \u00a0 \u00bb Energetic Materials \u00a0 \u00bb Biochemistry \u00a0 \u00bb Radiochemistry \u00a0 \u00bb Computational Models and Techniques \u00a0 \u00bb Prepublication \u00a0 \u00bb References Non-chemistry \u00a0 \u00bb Forum Matters \u00a0 \u00bb Legal and Societal Issues \u00a0 \u00bb Whimsy \u00a0 \u00bb Detritus \u00a0 \u00bb The Moderators' Lounge\n\nAuthor: Subject: Offtopic from Advice for a 15 year old interested in amateur chemistry?\nDraconicAcid\nInternational Hazard\n\nPosts: 2221\nRegistered: 1-2-2013\nLocation: The tiniest college campus ever....\nMember Is Offline\n\nMood: Semi-victorious.\n\nOfftopic from Advice for a 15 year old interested in amateur chemistry?\n\n Quote: Originally posted by Quaff Metals chemistry is really cool, you can ...make homeopathic vitamins...\n\n?? If you want to make homeopathic *anything*, just pour yourself a glass of tapwater, succuss it against a leather-bound book, and call it a day. But why bother?\n\nPlease remember: \"Filtrate\" is not a verb.\nWrite up your lab reports the way your instructor wants them, not the way your ex-instructor wants them.\nQuaff\nBanned\n\nPosts: 24\nRegistered: 31-10-2017\nMember Is Offline\n\nQuote: Originally posted by DraconicAcid\n Quote: Originally posted by Quaff Metals chemistry is really cool, you can ...make homeopathic vitamins...\n\n?? If you want to make homeopathic *anything*, just pour yourself a glass of tapwater, succuss it against a leather-bound book, and call it a day. But why bother?\n\nEven though known for over 65 years, I still find it fascinating that Echinochrome A is biologically active at a concentration of just one part per two billions in water (Kuhn and Wallenfels in Fieser, 1944 edition, pp 753).\n\nAnd that only a single molecule of crocin is required to determine sex activity in C. augamentos F. simplex and Chlarnydomonas genus of algae. Wow.\n\nProfessor Gilbert Smith in 1947 reported the production of motility in certain plant sex cells by use of only one part crocin to 250,000,000,000 parts of water !!\n\nAnd that heparin is activein suspending blood coagulation in amounts so minute that there is no method to detect its presence !!\n\nAnd that acetyl choline renews suspended contractions in the intestinal muscle in guinea pigs in a diluiton of one part per billion in water !! (Karrer p. 239 1947 ed)\n\nAnd that three micrograms of vitamin B-12 is an effective therapeutic dose, 0.01 millimicrograms giving a definite groth response to bacteria.\n\nCool stuff, that strongly suggests initiation of a cascade of peroxidation chain reactions, given these materials are all quinones having relatively high OR potentials.\n\nI used to think homeopathy was bunk, that was before !!\nDiachrynic\nHarmless\n\nPosts: 20\nRegistered: 23-9-2017\nLocation: Germany\nMember Is Offline\n\nMood: existent\n\nBut, you know that Avogadros' Limit is D23?\n\nThen you know, beyond that you don't even have a chance of actually having a single molecule. (It's worse than lottery.)\n\nBesides, most of the stuff that gets diluted (or succussed >.> is ordinary stuff - like table salt (Natrium chloratum), phosphorous (Phosphorus) or lead (Plumbum metallicum).\n\nThis is ridiculous.\n\nIt gets worse though. Look at the things which supposedly make the sympthoms worse (NaCl):\n\n\"sun, heat, having sex, hate against society, overexertion of eyes, mind, voice etc., full moon, music\"\n\nIt is hard to imagine something more random. I'm not making this up. http:\/\/www.naturheilkunde-essen.de\/homoeopathie_natrium_muri... (It is a german page)\n\nHomoepathy is just taking advantage of people that want to believe in something. (The profit 2013 was 2 billion dollars worldwide!)\n\nAnd I know it doesn't work because I took it for a long time (had to) and it didn't work at all!\n\nStudies show the same. In fact, there are so many of them there are meta-analyses everywhere.\n\nhttp:\/\/edzardernst.com\/2017\/04\/new-meta-analysis-confirms-th...\nhttps:\/\/www.ncbi.nlm.nih.gov\/books\/NBK68085\/\nhttps:\/\/scilogs.spektrum.de\/detritus\/gesamtschau-der-studien...\n\nI'm sorry, I'm ranting, but if I dislike something it is homeopathy.\n\nSignature currently under construction. We apologize for the inconvenience.\nCalling all. This is our last cry before our eternal silence.\nQuaff\nBanned\n\nPosts: 24\nRegistered: 31-10-2017\nMember Is Offline\n\nI agree, like the 12 tissue remedies of Schuessler, basically simple inorganic salts.\n\nBut, given what we know about free radical chemistry and how cascades of oxidations can be initiated to perpetuate themselves, I'm joined in with believing that tiny amounts of certain organic molecules of high redox potential can literally make wonderful things happen.\n\nBack in the day I studied and worked some with a renowned fellow named Boris D. Kahan at Case Western's center for electrochemical sciences. All the water we used was triple-distilled, the apparati being all pyrex. The last little pipe that delivered the triple distilled water to its storage reservoir... had to be replaced every other month because it corroded at its elbow, every time. I'm not bs'ing. There is quite a bit about water most folk take for granted. Given this discussion is for a 15 year old, lets not stray too far and to keep on topic I just suggest to the 15 year old to maybe look into the magical and amazing properties of something most chemists take for granted - the properties of.. Water !!\n\nspeaking of geniuses, I invite those interested to read the publications of William F Koch, PhD, MD, who himself studied under the father of free radical chemistry himself, Dr. Moses Gomberg. I suggest to all good chemists to investigate and read every publication you can that is available at www.williamfkoch.com because there is a mountain of gold there.\n\nI used to also dismiss \"homeopathy\" as bunk, but let us note that the medical system in Europe recognizes it, and will even pay public funds for a patient to be treated homeopathically !! Are they st*pid ? I don't know, but witness the Heel company in Deutschland selling \"carbonylgruppen\" ampuoles for injection with much success, yet the same benzoquinone diluted to one part per million is illegal in the USA for a licensed physician to administer. Why ?? Many cases of metabolic diseases have been historically documented to go away, even in advanced stages. You can find the patient histories at the above website maintained by Dr. Koch's family. This is, literally, life-saving information for some.\n\nThere is much we still don't know. If anyone wants to ever discuss the Koch material, I've read it all. Maybe on another thread, but for the young 15 year old, I suggest to develop your analytical skills to think differently than what is taught in the schools. Look at Baltimore and other school systems where the graduates can't even do simple math. Imagine if they just did away with education..... in that scenario, somethign like 10% of the students would be inquisitive enough by themselves to learn more than the record \/ statistics of the current system shows. What I'm saying is, the current education systems are actually more detrimental than if they did not exist at all, for some of the population. So, to the 15 year old, I suggest to not let yourself be blinded by what others try to ram into your head. Eat a good diet, avoid dietary toxins, and follow your common sense.\n\nmit freundlichen Gruessen,\nHerr Quaff\n\n[Edited on 16-11-2017 by Quaff]\nQuaff\nBanned\n\nPosts: 24\nRegistered: 31-10-2017\nMember Is Offline\n\nLet me also refer you to Wagner, Kreher, and Jurcic in their paper in Arzneimittel-Forschung 38(1):273-275 (1988)entitled \"In vitro stimulation of human granulocytes and lymphocytes by pico-and femtogram quantities of cytostatic agents\"\n\nThe gist of it, is that there is a range that is between the pico and femto dilution range at which cytostatic activity is observed using some molecules of high redox potentil, but at less dilution, i.e., stronger solutions, the activity is nil. Stated another way, benzoquinone can actually cause cancers at gram per liter levels, whereas when diluted to part per billion, can in a high percentage of cases cause remissions of many ailments, including what some call \"cancer\" Given that 1:3 men and 1:2 women are projected to experience such a metabolic disease at some point in their lives, this information is Darwinian, those who learn and apply it will survive, and those who don't, wont. The contemporaries of Gomberg dismissed him but later he is accepted. Its that same old Schopenauer cycle of rejection, ridicule and finally acceptance. This is a fascinating subject, much to digest for those initially starting out on it, it seems overwhelming. Once you're through the material a few times, you get the \"aha\" moment. After that, life is peachy because the fear of the unknown is gone. Hab guten abend\nDraconicAcid\nInternational Hazard\n\nPosts: 2221\nRegistered: 1-2-2013\nLocation: The tiniest college campus ever....\nMember Is Offline\n\nMood: Semi-victorious.\n\n Quote: Originally posted by Quaff Its that same old Schopenauer cycle of rejection, ridicule and finally acceptance.\n\nYeah, they laughed at Einstein, they laughed at the Wright brothers. But they also laughed at Bozo the Clown.\n\nHomeopathy is trash, and the fact that people spend billions on it is not a testament to homeopathy, but a testament to human gullibility.\n\nPlease remember: \"Filtrate\" is not a verb.\nWrite up your lab reports the way your instructor wants them, not the way your ex-instructor wants them.\nDiachrynic\nHarmless\n\nPosts: 20\nRegistered: 23-9-2017\nLocation: Germany\nMember Is Offline\n\nMood: existent\n\n Quote: Originally posted by Quaff Back in the day I studied and worked some with a renowned fellow named Boris D. Kahan at Case Western's center for electrochemical sciences.\n\nEither I can't use Google or this guy isn't as renowned as said.\n\nAlso, it isn't looking good for William F. Koch either...\n\n Quote: In the 1940s he marketed\u00a0glyoxylide, a drug which he claimed would cure\u00a0cancer. The claims were never scientifically proved, and he was considered a\u00a0charlatan\u00a0by the\u00a0United States Food and Drug Administration\u00a0(FDA). [...] In the early 1940s, Koch announced his discovery of glyoxylide, a miracle drug that would cure a long list of diseases, even when administered at one part per trillion dilution. He sold the drug through an entity called the\u00a0Christian Medical Research League. He never revealed his process for the manufacture of glyoxylide, and there never was any evidence that glyoxylide in any amount had any therapeutic effect. Analysis showed it to be distilled water. Over 3,000 health practitioners in the U.S. paid $25 per ampoule for Koch's treatment and charged patients as much as$300 for a single injection.\n\nhttps:\/\/en.m.wikipedia.org\/wiki\/William_Frederick_Koch\n\n Quote: Koch's treatment was one of the greatest medical hoaxes of all time. Analysis showed it to be distilled water of extraordinary purity. but Koch claimed his medicine contained I part of a chemical called glyoxylide per 1 trillion parts of water. [...] There was no evidence that glyoxylide in any amount had any therapeutic effect.\n\nhttps:\/\/www.cancertreatmentwatch.org\/q\/janssen.shtml\n\n...so I'm not going to read the dozens upon dozens of papers on that website.\n\n@DraconicAcid\n\nWell put.\n\nI think the biggest danger of homeopathy lies in the fact that some people choose it over an actual treatment and get serious health issues. This includes children that can't decide for themselves.\n\nSignature currently under construction. We apologize for the inconvenience.\nCalling all. This is our last cry before our eternal silence.\nQuaff\nBanned\n\nPosts: 24\nRegistered: 31-10-2017\nMember Is Offline\n\nMy stage IV metastic friend was given 4-8 months to live, 3 years ago. An anecdotal case perhaps, but to me it matters not what anyone calls it, because she remains breathing and walking Before calling homeopathy \"trash\" you have the opportunity to digest the teachings of Dr. Koch, or you also have the opportunity to ignore it. I laugh at the medical system in the US, and the clowns who buy into the (barnyard explicative). You all chemistry people have the ability to pick up and understand it, it is based on fact - free radical chemistry, plain and simple. Never let your schooling interfere with your education.\nQuaff\nBanned\n\nPosts: 24\nRegistered: 31-10-2017\nMember Is Offline\n\nQuote: Originally posted by Diachrynic\n Quote: Originally posted by Quaff Back in the day I studied and worked some with a renowned fellow named Boris D. Kahan at Case Western's center for electrochemical sciences.\n\nEither I can't use Google or this guy isn't as renowned as said.\n\nAlso, it isn't looking good for William F. Koch either...\n\n Quote: In the 1940s he marketed\u00a0glyoxylide, a drug which he claimed would cure\u00a0cancer. The claims were never scientifically proved, and he was considered a\u00a0charlatan\u00a0by the\u00a0United States Food and Drug Administration\u00a0(FDA). [...] In the early 1940s, Koch announced his discovery of glyoxylide, a miracle drug that would cure a long list of diseases, even when administered at one part per trillion dilution. He sold the drug through an entity called the\u00a0Christian Medical Research League. He never revealed his process for the manufacture of glyoxylide, and there never was any evidence that glyoxylide in any amount had any therapeutic effect. Analysis showed it to be distilled water. Over 3,000 health practitioners in the U.S. paid $25 per ampoule for Koch's treatment and charged patients as much as$300 for a single injection.\n\nhttps:\/\/en.m.wikipedia.org\/wiki\/William_Frederick_Koch\n\n Quote: Koch's treatment was one of the greatest medical hoaxes of all time. Analysis showed it to be distilled water of extraordinary purity. but Koch claimed his medicine contained I part of a chemical called glyoxylide per 1 trillion parts of water. [...] There was no evidence that glyoxylide in any amount had any therapeutic effect.\n\nhttps:\/\/www.cancertreatmentwatch.org\/q\/janssen.shtml\n\n...so I'm not going to read the dozens upon dozens of papers on that website.\n\n@DraconicAcid\n\nWell put.\n\nI think the biggest danger of homeopathy lies in the fact that some people choose it over an actual treatment and get serious health issues. This includes children that can't decide for themselves.\n\nYou're quick on the scene on this topic, and quick to cut it down.\nKoch was sued 3 times in Federal Court, AMA, FDA, FTC and each time, his naysayers lost the case because it was proven, he cured cancer. They tried so hard to hide it. The hundreds of thousands who were cured of cancers and other ailments, dn't care about folk who pipe for the bullsht USA medical industry, that murders people. You all are so transparent. Koch cures cancer, everybody with a brain who can read knows it. Morris Fishbein, who went after him and Hoxsey and Royal Raymond Rife and others, was forced to resign from being head of the bogus AMA. That's the fact Jack !!\n\n[Edited on 16-11-2017 by Quaff]\nQuaff\nBanned\n\nPosts: 24\nRegistered: 31-10-2017\nMember Is Offline\n\nIts all public record, Koch cures cancer about 80% of the time, and its free-radical chemistry, in super-diluted amounts. Two cc's of a solution containing one microgram per cc of benzoquinone injected subcutaneously or intramuscularly causes a febrile reaction, calcification and shrinkage of tumors, and restoration of natural bodily immunity. Only an enemy of humanity would be quick to cut this down. Its not \"homeopathy\" , its rather, simple free radical chemistry, administered in the tiny amounts shown in the paper by Wagner. The evil ones just hate America and want to hide this stuff. Its awesome chemistry. Before this gets deleted, I suggest at least one of you all download all of Koch's materials, if you have a loved one suffering un-necesarily because you were deprived the knowledge, because of the greed and desire of others to control you and your families. I'm not a doctor, make your own judgements, I only cited Koch for purposes of discussion, under Article 19 of the UN Charter and the first amendment of the Constitution for the United States which my ancestors shed blood to establish\n\n[Edited on 16-11-2017 by Quaff]\ngdflp\nSuper Moderator\n16-11-2017 at 13:37\nQuaff\nBanned\n\nPosts: 24\nRegistered: 31-10-2017\nMember Is Offline\n\nQuaff Junk\n\nBut, we can also use glyoxal and methyl glyoxal at the same dilutions, for the same purpose. I can refer you to this link, for you to obtain a pdf of any issued patent:\nhttp:\/\/www.pat2pdf.org\/\n\nThere, you can enter the numbers of Dr. Koch's patents for his process of producing the agents that cured cancer, diabetes, syphillis, hoof and mouth disease in cattle, and more. You see, all these ailments have a common cause !!\n\nTwo of Dr. Koch's patents are numbered 2,257,748 and 2,382,425. I suggest to download them. The dude studied under Gomberg, and was not only an MD, but also a PhD in chem.\n\nI injected myself with a 1 ppb solution of triple distilled water containing benzoquinone, methylglyoxal, and glyoxal. The weird bumps on my skin I had for 30 years disappeared 3 weeks later. Read the entirety of the williamfkoch.com website !! Download all of it !! The cancer industry hates this knowledge, because you could \"treat\" 300 million people , using only 35 bucks of material !! there's a lesson for the 15 year old, that there's a bunch of greedy bsrtds out there who want control so badly, they'll have no qualms about letting you grandma die, for their greedy ends, when cures for these things have been long known. Also look up Harry Hoxsey and how he had a network of cancer clinics around the USA in the 50's that Fishbein hated so much the AMA had him arrested like 300+ times, but he never once lost in any Court of Law. These people HATE it if you have knowledge. Also look up Rene Caisse, Virginia Livingston Wheeler, then you realize\n\n[Edited on 16-11-2017 by Quaff]\ngdflp\nSuper Moderator\n16-11-2017 at 13:58\nQuaff\nBanned\n\nPosts: 24\nRegistered: 31-10-2017\nMember Is Offline\n\nQuaff\n\n Quote: Originally posted by gdflp Let's keep this thread on topic everyone. Quaff, don't continue to post off-topic nonsense after I've already pruned the thread.\n\nf-you, most of your poeple in organic chem are posting shit about drug making. We have enough drugs in this county, maybe you're DEA running this, whatever. I posted powerful legitimate chemistry materials. You all in the US are totally fkd, so go jerk yourself off some more, you stupid cunt\ngdflp\nSuper Moderator","date":"2017-11-22 07:35:11","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\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.325390487909317, \"perplexity\": 5741.28330884437}, \"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-2017-47\/segments\/1510934806509.31\/warc\/CC-MAIN-20171122065449-20171122085449-00207.warc.gz\"}"} | null | null |
Q: Convert vector back to a grid in Matlab In Matlab I a have 5-D grid X. I can use
Xsind=find(X>a)
to obtain the index values of X above scalar a. However, this gives the indices in vector form. Is there a quick way to convert this back to a grid indices giving the position in each dimension? I can do the conversion using the floor function 4 times but there must be an easier and faster way.
A: Ok I found the solution:
[i,j,k,l,m]=ind2sub([n1,n2,n3,n4,n5],Xsind)
where n1,n2,n3,n4,n5 are the lengths of the 5 dimensions.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 7,818 |
6clipsal9 Nice and friendly person to deal with. Will deal again soon.
rai.asyura Friendly buyer. Had smooth transaction eventhough there is some error printing deliver, buyer insisted to gave extra prints. Thank you soo much..
Thanks a lot for the kind compliment! Really appreciate it.
bynurulbaker_pteltd perfect frames for my children! will definitely have her to do more for my family! thanks so much sis! | {
"redpajama_set_name": "RedPajamaC4"
} | 6,475 |
/*Entire page styles*/
body {
font-family: Verdana, Geneva, Tahoma, sans-serif;
background-color: darkkhaki;
}
/*All link styles*/
a {
color: steelblue;
text-decoration: none;
}
/*All paragraph styles*/
p {
color: darkslategray;
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"redpajama_set_name": "RedPajamaGithub"
} | 9,866 |
require 'gosu'
require_relative 'states/game_state'
require_relative 'states/menu_state'
require_relative 'states/play_state'
require_relative 'game_window'
module Game
def self.media_path(file)
File.join(File.dirname(File.dirname(
__FILE__)), 'media', file)
end
end
$window = GameWindow.new
GameState.switch(MenuState.instance)
$window.show
| {
"redpajama_set_name": "RedPajamaGithub"
} | 2,903 |
{"url":"https:\/\/math.libretexts.org\/Courses\/Mount_Royal_University\/MATH_3200%3A_Mathematical_Methods\/3%3A_Series_Solutions_of_Linear_Second_order_Equations\/3.2%3A_Series_Solutions_Near_an_Ordinary_Point_I","text":"\n# 3.2: Series Solutions Near an Ordinary Point I\n\n\n## Series Solutions Near an Ordinary Point\n\nMany physical applications give rise to second order homogeneous linear differential equations of the form\n\n\\label{eq:3.2.1}\nP_0(x)y''+P_1(x)y'+P_2(x)y=0,\n\nwhere $$P_0$$, $$P_1$$, and $$P_2$$ are polynomials. Usually the solutions of these equations can't be expressed in terms of familiar elementary functions. Therefore we'll consider the problem of representing solutions of \\eqref{eq:3.2.1} with series.\n\nWe assume throughout that $$P_0$$, $$P_1$$ and $$P_2$$ have no common factors. Then we say that $$x_0$$ is an $$\\textcolor{blue}{\\mbox{ordinary point}}$$ of \\eqref{eq:3.2.1} if $$P_0(x_0)\\ne0$$, or a $$\\textcolor{blue}{\\mbox{singular point}}$$ if $$P_0(x_0)=0$$. For Legendre's equation,\n\n\\label{eq:3.2.2}\n(1-x^2)y''-2xy'+\\alpha(\\alpha+1)y=0,\n\n$$x_0=1$$ and $$x_0=-1$$ are singular points and all other points are ordinary points. For Bessel's equation,\n\n\\begin{eqnarray*}\nx^2y''+xy'+(x^2-\\nu^2)y=0,\n\\end{eqnarray*}\n\n$$x_0=0$$ is a singular point and all other points are ordinary points. If $$P_0$$ is a nonzero constant as in Airy's equation,\n\n\\label{eq:3.2.3}\ny''-xy=0,\n\nthen every point is an ordinary point.\n\nSince polynomials are continuous everywhere, $$P_1\/P_0$$ and $$P_2\/P_0$$ are continuous at any point $$x_0$$ that isn't a zero of $$P_0$$. Therefore, if $$x_0$$ is an ordinary point of \\eqref{eq:3.2.1} and $$a_0$$ and $$a_1$$ are arbitrary real numbers, then the initial value problem\n\n\\label{eq:3.2.4}\n\nhas a unique solution on the largest open interval that contains $$x_0$$ and does not contain any zeros of $$P_0$$. To see this, we rewrite the differential equation in \\eqref{eq:3.2.4} as\n\n\\begin{eqnarray*}\ny''+{P_1(x)\\over P_0(x)}y'+{P_2(x)\\over P_0(x)}y=0\n\\end{eqnarray*}\n\nand apply Theorem $$(2.1.1)$$ with $$p=P_1\/P_0$$ and $$q=P_2\/P_0$$. In this section and the next we consider the problem of representing solutions of \\eqref{eq:3.2.1} by power series that converge for values of $$x$$ near an ordinary point $$x_0$$.\n\nWe state the next theorem without proof.\n\n### Theorem $$\\PageIndex{1}$$\n\nSuppose $$P_0$$, $$P_1$$, and $$P_2$$ are polynomials with no common factor and $$P_0$$ isn't identically zero. Let $$x_0$$ be a point such that $$P_0(x_0)\\ne0,$$ and let $$\\rho$$ be the distance from $$x_0$$ to the nearest zero of $$P_0$$ in the complex plane. (If $$P_0$$ is constant, then $$\\rho=\\infty$$.) Then every solution of\n\n\\label{eq:3.2.5}\nP_0(x)y''+P_1(x)y'+P_2(x)y=0\n\ncan be represented by a power series\n\n\\label{eq:3.2.6}\ny=\\sum_{n=0}^\\infty a_n(x-x_0)^n\n\nthat converges at least on the open interval $$(x_0-\\rho,x_0+\\rho)$$. (If $$P_0$$ is nonconstant, so that $$\\rho$$ is necessarily finite, then the open interval of convergence of \\eqref{eq:3.2.6} may be larger than $$(x_0-\\rho,x_0+\\rho).$$ If $$P_0$$ is constant then $$\\rho=\\infty$$ and $$(x_0-\\rho,x_0+\\rho)=(-\\infty,\\infty)$$.)\n\nProof\n\nAdd proof here and it will automatically be hidden if you have a \"AutoNum\" template active on the page.\n\nWe call \\eqref{eq:3.2.6} a $$\\textcolor{blue}{\\mbox{power series solution in \\(x-x_0$$}} \\) of \\eqref{eq:3.2.5}. We'll now develop a method for finding power series solutions of \\eqref{eq:3.2.5}. For this purpose we write \\eqref{eq:3.2.5} as $$Ly=0$$, where\n\n\\label{eq:3.2.7}\nLy=P_0y''+P_1y'+P_2y.\n\nTheorem $$(3.2.1)$$ implies that every solution of $$Ly=0$$ on $$(x_0-\\rho,x_0+\\rho)$$ can be written as\n\n\\begin{eqnarray*}\ny=\\sum_{n=0}^\\infty a_n(x-x_0)^n.\n\\end{eqnarray*}\n\nSetting $$x=x_0$$ in this series and in the series\n\n\\begin{eqnarray*}\ny'=\\sum_{n=1}^\\infty na_n(x-x_0)^{n-1}\n\\end{eqnarray*}\n\nshows that $$y(x_0)=a_0$$ and $$y'(x_0)=a_1$$. Since every initial value problem \\eqref{eq:3.2.4} has a unique solution, this means that $$a_0$$ and $$a_1$$ can be chosen arbitrarily, and $$a_2$$, $$a_3$$, $$\\dots$$ are uniquely determined by them.\n\nTo find $$a_2$$, $$a_3$$, $$\\dots$$, we write $$P_0$$, $$P_1$$, and $$P_2$$ in powers of $$x-x_0$$, substitute\n\n\\begin{eqnarray*}\ny=\\sum^\\infty_{n=0}a_n(x-x_0)^n,\n\\end{eqnarray*}\n\n\\begin{eqnarray*}\ny'=\\sum^\\infty_{n=1}na_n(x-x_0)^{n-1},\n\\end{eqnarray*}\n\n\\begin{eqnarray*}\ny''=\\sum^\\infty_{n=2}n(n-1)a_n(x-x_0)^{n-2}\n\\end{eqnarray*}\n\ninto \\eqref{eq:3.2.7}, and collect the coefficients of like powers of $$x-x_0$$. This yields\n\n\\label{eq:3.2.8}\nLy=\\sum^\\infty_{n=0}b_n(x-x_0)^n,\n\nwhere $$\\{b_0, b_1, \\dots, b_n, \\dots\\}$$ are expressed in terms of $$\\{a_0, a_1, \\dots,a_n, \\dots\\}$$ and the coefficients of $$P_0$$, $$P_1$$, and $$P_2$$, written in powers of $$x-x_0$$. Since \\eqref{eq:3.2.8} and part (a) of Theorem $$(3.1.6)$$ imply that $$Ly=0$$ if and only if $$b_n=0$$ for $$n\\ge0$$, all power series solutions in $$x-x_0$$ of $$Ly=0$$ can be obtained by choosing $$a_0$$ and $$a_1$$ arbitrarily and computing $$a_2$$, $$a_3$$, $$\\dots$$, successively so that $$b_n=0$$ for $$n\\ge0$$. For simplicity, we call the power series obtained this way $$\\textcolor{blue}{\\mbox{the power series in \\(x-x_0$$ for the general solution}} \\) of $$Ly=0$$, without explicitly identifying the open interval of convergence of the series.\n\n### Example $$\\PageIndex{1}$$\n\nLet $$x_0$$ be an arbitrary real number. Find the power series in $$x-x_0$$ for the general solution of\n\n\\label{eq:3.2.9}\ny''+ y=0.\n\nHere\n\n\\begin{eqnarray*}\nLy=y''+y.\n\\end{eqnarray*}\n\nIf\n\n\\begin{eqnarray*}\ny=\\sum_{n=0}^\\infty a_n(x-x_0)^n,\n\\end{eqnarray*}\n\nthen\n\n\\begin{eqnarray*}\ny''=\\sum_{n=2}^\\infty n(n-1)a_n(x-x_0)^{n-2},\n\\end{eqnarray*}\n\nso\n\n\\begin{eqnarray*}\nLy=\\sum_{n=2}^\\infty n(n-1)a_n(x-x_0)^{n-2}+\\sum_{n=0}^\\infty a_n(x-x_0)^n.\n\\end{eqnarray*}\n\nTo collect coefficients of like powers of $$x-x_0$$, we shift the summation index in the first sum. This yields\n\n\\begin{eqnarray*}\nLy=\\sum^\\infty_{n=0}(n+2)(n+1)a_{n+2}(x-x_0)^n + \\sum^\\infty_{n=0}a_n(x-x_0)^n =\\sum^\\infty_{n=0}b_n(x-x_0)^n,\n\\end{eqnarray*}\n\nwith\n\n\\begin{eqnarray*}\nb_n=(n+2)(n+1)a_{n+2}+a_n.\n\\end{eqnarray*}\n\nTherefore $$Ly=0$$ if and only if\n\n\\label{eq:3.2.10}\n\nwhere $$a_0$$ and $$a_1$$ are arbitrary. Since the indices on the left and right sides of \\eqref{eq:3.2.10} differ by two, we write \\eqref{eq:3.2.10} separately for $$n$$ even $$(n=2m)$$ and $$n$$ odd $$(n=2m+1)$$. This yields\n\n\\begin{eqnarray}\na_{2m+2}&=&{-a_{2m}\\over(2m+2)(2m+1)},\\quad m\\ge0, \\label{eq:3.2.11} \\\\%dummy \\eqref{eq:3.2.14}\n\\end{eqnarray}\n\nComputing the coefficients of the even powers of $$x-x_0$$ from \\eqref{eq:3.2.11} yields\n\n\\begin{eqnarray*}\na_2&=&-{a_0\\over2\\cdot1}\\\\\na_4&=&-{a_2\\over4\\cdot3}=-{1\\over4\\cdot3} \\left(-{a_0\\over2\\cdot1}\\right)= {a_0\\over4\\cdot3\\cdot2\\cdot1}, \\\\\na_6&=&-{a_4\\over6\\cdot5}=-{1\\over6\\cdot5} \\left({a_0\\over4\\cdot3\\cdot2\\cdot1}\\right)=-{a_0\\over6\\cdot5\\cdot4\\cdot3\\cdot 2\\cdot1},\n\\end{eqnarray*}\n\nand, in general,\n\n\\label{eq:3.2.13}\na_{2m}=(-1)^m {a_0\\over(2m)!}\\; ,\\quad m\\ge0.\n\nComputing the coefficients of the odd powers of $$x-x_0$$ from \\eqref{eq:3.2.12} yields\n\n\\begin{eqnarray*}\na_3&=&-{a_1\\over3\\cdot2}\\\\\na_5&=&-{a_3\\over5\\cdot4}=-{1\\over5\\cdot4} \\left(-{a_1\\over3\\cdot2}\\right)= {a_1\\over5\\cdot4\\cdot3\\cdot2}, \\\\\na_7&=&-{a_5\\over7\\cdot6}=-{1\\over7\\cdot6} \\left({a_1\\over5\\cdot4\\cdot3\\cdot2}\\right)=-{a_1\\over7\\cdot6\\cdot5\\cdot4\\cdot 3\\cdot2},\n\\end{eqnarray*}\n\nand, in general,\n\n\\label{eq:3.2.14}\n\nThus, the general solution of \\eqref{eq:3.2.9} can be written as\n\n\\begin{eqnarray*}\ny=\\sum_{m=0}^\\infty a_{2m}(x-x_0)^{2m}+\\sum_{m=0}^\\infty a_{2m+1}(x-x_0)^{2m+1},\n\\end{eqnarray*}\n\nor, from \\eqref{eq:3.2.13} and \\eqref{eq:3.2.14}, as\n\n\\label{eq:3.2.15}\ny=a_0\\sum_{m=0}^\\infty(-1)^m{(x-x_0)^{2m}\\over(2m)!} +a_1\\sum_{m=0}^\\infty(-1)^m{(x-x_0)^{2m+1}\\over(2m+1)!}.\n\nIf we recall from calculus that\n\n\\begin{eqnarray*}\n\\end{eqnarray*}\n\nthen \\eqref{eq:3.2.15} becomes\n\n\\begin{eqnarray*}\ny=a_0\\cos(x-x_0)+a_1\\sin(x-x_0),\n\\end{eqnarray*}\n\nwhich should look familiar.\n\nEquations like \\eqref{eq:3.2.10}, \\eqref{eq:3.2.11}, and \\eqref{eq:3.2.12}, which define a given coefficient in the sequence $$\\{a_n\\}$$ in terms of one or more coefficients with lesser indices are called $$\\textcolor{blue}{\\mbox{recurrence relations}}$$. When we use a recurrence relation to compute terms of a sequence we're computing $$\\textcolor{blue}{\\mbox{recursively}}$$.\n\nIn the remainder of this section we consider the problem of finding power series solutions in $$x-x_0$$ for equations of the form\n\n\\label{eq:3.2.16}\n\\left(1+\\alpha(x-x_0)^2\\right)y''+\\beta(x-x_0) y'+\\gamma y=0.\n\nMany important equations that arise in applications are of this form with $$x_0=0$$, including Legendre's equation \\eqref{eq:3.2.2}, Airy's equation \\eqref{eq:3.2.3}, Chebyshev's equation,\n\n\\begin{eqnarray*}\n(1-x^2)y''-xy'+\\alpha^2 y=0,\n\\end{eqnarray*}\n\n\\begin{eqnarray*}\ny''-2xy'+2\\alpha y=0.\n\\end{eqnarray*}\n\nSince\n\n\\begin{eqnarray*}\nP_0(x)=1+\\alpha(x-x_0)^2\n\\end{eqnarray*}\n\nin \\eqref{eq:3.2.16}, the point $$x_0$$ is an ordinary point of \\eqref{eq:3.2.16}, and Theorem $$(3.2.1)$$ implies that the solutions of \\eqref{eq:3.2.16} can be written as power series in $$x-x_0$$ that converge on the interval $$(x_0-1\/\\sqrt|\\alpha|,x_0+1\/\\sqrt|\\alpha|)$$ if $$\\alpha\\ne0$$, or on $$(-\\infty,\\infty)$$ if $$\\alpha=0$$. We'll see that the coefficients in these power series can be obtained by methods similar to the one used in Example $$(3.2.1)$$.\n\nTo simplify finding the coefficients, we introduce some notation for products:\n\n\\begin{eqnarray*}\n\\end{eqnarray*}\n\nThus,\n\n\\begin{eqnarray*}\n\\prod^7_{j=2}b_j=b_2b_3b_4b_5b_6b_7,\n\\end{eqnarray*}\n\n\\begin{eqnarray*}\n\\prod^4_{j=0}(2j+1)=(1)(3)(5)(7)(9)=945,\n\\end{eqnarray*}\n\nand\n\n\\begin{eqnarray*}\n\\prod^2_{j=2}j^2=2^2=4.\n\\end{eqnarray*}\n\nWe define\n\n\\begin{eqnarray*}\n\\end{eqnarray*}\n\nno matter what the form of $$b_j$$.\n\n### Example $$\\PageIndex{2}$$\n\nFind the power series in $$x$$ for the general solution of\n\n\\label{eq:3.2.17}\n(1+2x^2)y''+6xy'+2y=0.\n\nHere\n\n\\begin{eqnarray*}\nLy=(1+2x^2)y''+6xy'+2y.\n\\end{eqnarray*}\n\nIf\n\n\\begin{eqnarray*}\ny=\\sum_{n=0}^\\infty a_nx^n\n\\end{eqnarray*}\n\nthen\n\n\\begin{eqnarray*}\n\\end{eqnarray*}\n\nso\n\n\\begin{eqnarray*}\nLy&=&(1+2x^2) \\sum^\\infty_{n=2}n(n-1)a_nx^{n-2}+ 6x \\sum^\\infty_{n=1}na_nx^{n-1} +2 \\sum^\\infty_{n=0}a_nx^n\\\\\n&=&\\sum_{n=2}^\\infty n(n-1)a_nx^{n-2}+\\sum_{n=0}^\\infty \\left[2n(n-1)+6n+2\\right]a_nx^n\\\\\n&=&\\sum_{n=2}^\\infty n(n-1)a_nx^{n-2}+2\\sum_{n=0}^\\infty(n+1)^2a_nx^n.\n\\end{eqnarray*}\n\nTo collect coefficients of $$x^n$$, we shift the summation index in the first sum. This yields\n\n\\begin{eqnarray*}\nLy=\\sum_{n=0}^\\infty(n+2)(n+1)a_{n+2}x^n+2\\sum_{n=0}^\\infty(n+1)^2a_nx^n =\\sum_{n=0}^\\infty b_nx^n,\n\\end{eqnarray*}\n\nwith\n\n\\begin{eqnarray*}\n\\end{eqnarray*}\n\nTo obtain solutions of \\eqref{eq:3.2.17}, we set $$b_n=0$$ for $$n\\ge0$$. This is equivalent to the recurrence relation\n\n\\label{eq:3.2.18}\n\nSince the indices on the left and right differ by two, we write \\eqref{eq:3.2.18} separately for $$n=2m$$ and $$n=2m+1$$, as in Example $$(3.2.1)$$. This yields\n\n\\begin{eqnarray}\na_{2m+2}&=&-2 {2m+1\\over2m+2}a_{2m}=-{2m+1\\over m+1}a_{2m},\\quad m \\ge0,\\label{eq:3.2.19}\\\\\n\\end{eqnarray}\n\nComputing the coefficients of even powers of $$x$$ from \\eqref{eq:3.2.19} yields\n\n\\begin{eqnarray*}\na_2&=&-{1\\over1}a_0,\\\\\na_4&=&-{3\\over2}a_2=\\left(-{3\\over2}\\right)\\left(-{1\\over1}\\right)a_0 ={1\\cdot3\\over1\\cdot2}a_0,\\\\\na_6&=&-{5\\over3}a_4= -{5\\over3}\\left(1\\cdot3\\over1\\cdot2\\right)a_0 =-{1\\cdot3\\cdot5\\over1\\cdot2\\cdot3}a_0, \\\\\na_8&=&-{7\\over4}a_6=-{7\\over4} \\left(-{1\\cdot3\\cdot5\\over1\\cdot2\\cdot3}\\right)a_0= {1\\cdot3\\cdot5\\cdot7\\over1\\cdot2\\cdot3\\cdot4}a_0.\\\\\n\\end{eqnarray*}\n\nIn general,\n\n\\label{eq:3.2.21}\n\n(Note that \\eqref{eq:3.2.21} is correct for $$m=0$$ because we defined $$\\prod_{j=1}^0b_j=1$$ for any $$b_j$$.)\n\nComputing the coefficients of odd powers of $$x$$ from \\eqref{eq:3.2.20} yields\n\n\\begin{eqnarray*}\na_3&=&-4\\,{1\\over3}a_1, \\\\\na_5&=&-4\\,{2\\over5}a_3=-4\\,{2\\over5}\\left(-4{1\\over3}\\right)a_1 =4^2{1\\cdot2\\over3\\cdot5}a_1, \\\\\na_7&=&-4\\,{3\\over7}a_5=-4\\,{3\\over7}\\left(4^2{1\\cdot2\\over3\\cdot5}\\right)a_1=-4^3{1\\cdot2\\cdot3\\over3\\cdot5\\cdot7}a_1,\\\\\na_9&=&-4\\, {4\\over9}a_7=-4\\, {4\\over9}\\left(4^3{1\\cdot2\\cdot3\\over3\\cdot5\\cdot7}\\right)a_1=4^4{1\\cdot2\\cdot3\\cdot4\\over3\\cdot5\\cdot7\\cdot9}a_1.\n\\end{eqnarray*}\n\nIn general,\n\n\\label{eq:3.2.22}\n\nFrom \\eqref{eq:3.2.21} and \\eqref{eq:3.2.22},\n\n\\begin{eqnarray*}\ny=a_0 \\sum^\\infty_{m=0}(-1)^m {\\prod_{j=1}^m(2j-1)\\over m!}x^{2m}\n+a_1 \\sum^\\infty_{m=0}(-1)^m {4^mm!\\over\\prod_{j=1}^m(2j+1)} x^{2m+1}.\n\\end{eqnarray*}\n\nis the power series in $$x$$ for the general solution of \\eqref{eq:3.2.17}. Since $$P_0(x)=1+2x^2$$ has no real zeros, Theorem $$(2.1.1)$$ implies that every solution of \\eqref{eq:3.2.17} is defined on $$(-\\infty,\\infty)$$. However, since $$P_0(\\pm i\/\\sqrt2)=0$$, Theorem $$(3.2.1)$$ implies only that the power series converges in $$(-1\/\\sqrt2,1\/\\sqrt2)$$ for any choice of $$a_0$$ and $$a_1$$.\n\nThe results in Examples $$(3.2.1)$$ and $$(3.2.2)$$ are consequences of the following general theorem.\n\n### Theorem $$\\PageIndex{2}$$\n\nThe coefficients $$\\{a_n\\}$$ in any solution $$y=\\sum_{n=0}^\\infty a_n(x-x_0)^n$$ of\n\n\\label{eq:3.2.23}\n\\left(1+\\alpha(x-x_0)^2\\right)y''+\\beta(x-x_0) y'+\\gamma y=0\n\nsatisfy the recurrence relation\n\n\\label{eq:3.2.24}\n\nwhere\n\n\\label{eq:3.2.25}\np(n)=\\alpha n(n-1) +\\beta n+\\gamma.\n\nMoreover, the coefficients of the even and odd powers of $$x-x_0$$ can be computed separately as\n\n\\begin{eqnarray}\n\\end{eqnarray}\n\nwhere $$a_0$$ and $$a_1$$ are arbitrary.\n\nProof\n\nHere\n\n\\begin{eqnarray*}\nLy=\\left(1+\\alpha(x-x_0\\right)^2)y''+\\beta(x-x_0) y'+\\gamma y.\n\\end{eqnarray*}\n\nIf\n\n\\begin{eqnarray*}\ny=\\sum_{n=0}^\\infty a_n(x-x_0)^n,\n\\end{eqnarray*}\n\nthen\n\n\\begin{eqnarray*}\ny'=\\sum_{n=1}^\\infty na_n(x-x_0)^{n-1} \\quad\\mbox{ and }\\quad y''=\\sum_{n=2}^\\infty n(n-1)a_n(x-x_0)^{n-2}.\n\\end{eqnarray*}\n\nHence,\n\n\\begin{eqnarray*}\n\\begin{array}{ccl}\nLy&=&\\displaystyle{\\sum_{n=2}^\\infty n(n-1)a_n(x-x_0)^{n-2}+\n\\sum_{n=0}^\\infty \\left[\\alpha\nn(n-1)\n+\\beta n+\\gamma\\right]a_n(x-x_0)^n}\\\\\n&=&\\displaystyle{\\sum_{n=2}^\\infty n(n-1)a_n(x-x_0)^{n-2}+\\sum_{n=0}^\\infty\np(n)a_n(x-x_0)^n},\n\\end{array}\n\\end{eqnarray*}\n\nfrom \\eqref{eq:3.2.25}. To collect coefficients of powers of $$x-x_0$$, we shift the summation index in the first sum. This yields\n\n\\begin{eqnarray*}\nLy=\\sum_{n=0}^\\infty \\left[(n+2)(n+1)a_{n+2}+p(n)a_n\\right](x-x_0)^n.\n\\end{eqnarray*}\n\nThus, $$Ly=0$$ if and only if\n\n\\begin{eqnarray*}\n\\end{eqnarray*}\n\nwhich is equivalent to \\eqref{eq:3.2.24}. Writing \\eqref{eq:3.2.24} separately for the cases where $$n=2m$$ and $$n=2m+1$$ yields \\eqref{eq:3.2.26} and \\eqref{eq:3.2.27}.\n\n### Example $$\\PageIndex{3}$$\n\nFind the power series in $$x-1$$ for the general solution of\n\n\\label{eq:3.2.28}\n(2+4x-2x^2)y''-12(x-1)y'-12y=0.\n\nWe must first write the coefficient $$P_0(x)=2+4x-x^2$$ in powers of $$x-1$$. To do this, we write $$x=(x-1)+1$$ in $$P_0(x)$$ and then expand the terms, collecting powers of $$x-1$$; thus,\n\n\\begin{eqnarray*}\n2+4x-2x^2&=&2+4[(x-1)+1]-2[(x-1)+1]^2\\\\\n&=&4-2(x-1)^2.\n\\end{eqnarray*}\n\nTherefore we can rewrite \\eqref{eq:3.2.28} as\n\n\\begin{eqnarray*}\n\\left(4-2(x-1)^2\\right)y''-12(x-1)y'-12y=0,\n\\end{eqnarray*}\n\nor, equivalently,\n\n\\begin{eqnarray*}\n\\left(1-{1\\over2}(x-1)^2\\right)y''-3(x-1)y'-3y=0.\n\\end{eqnarray*}\n\nThis is of the form \\eqref{eq:3.2.23} with $$\\alpha=-1\/2$$, $$\\beta=-3$$, and $$\\gamma=-3$$. Therefore, from \\eqref{eq:3.2.25}\n\n\\begin{eqnarray*}\np(n)=-{n(n-1)\\over2}-3n-3=-{(n+2)(n+3)\\over2}.\n\\end{eqnarray*}\n\nHence, Theorem $$(3.2.2)$$ implies that\n\n\\begin{eqnarray*}\na_{2m+2}&=&-{p(2m)\\over(2m+2)(2m+1)}a_{2m}\\\\\na_{2m+3}&=&-{p(2m+1)\\over(2m+3)(2m+2)}a_{2m+1}\\\\\n\\end{eqnarray*}\n\nWe leave it to you to show that\n\n\\begin{eqnarray*}\n\\end{eqnarray*}\n\nwhich implies that the power series in $$x-1$$ for the general solution of \\eqref{eq:3.2.28} is\n\n\\begin{eqnarray*}\ny=a_0\\sum_{m=0}^\\infty{2m+1\\over2^m}(x-1)^{2m}+a_1\\sum_{m=0}^\\infty {m+1\\over2^m}(x-1)^{2m+1}.\n\\end{eqnarray*}\n\nIn the examples considered so far we were able to obtain closed formulas for coefficients in the power series solutions. In some cases this is impossible, and we must settle for computing a finite number of terms in the series. The next example illustrates this with an initial value problem.\n\n### Example $$\\PageIndex{4}$$\n\nCompute $$a_0$$, $$a_1$$, $$\\dots$$, $$a_7$$ in the series solution $$y=\\sum_{n=0}^\\infty a_nx^n$$ of the initial value problem\n\n\\label{eq:3.2.29}\n\nSince $$\\alpha=2$$, $$\\beta=10$$, and $$\\gamma=8$$ in \\eqref{eq:3.2.29},\n\n\\begin{eqnarray*}\np(n)=2n(n-1)+10n+8=2(n+2)^2.\n\\end{eqnarray*}\n\nTherefore\n\n\\begin{eqnarray*}\n\\end{eqnarray*}\n\nWriting this equation separately for $$n=2m$$ and $$n=2m+1$$ yields\n\n\\begin{eqnarray}\na_{2m+3}&=&-2{2m+3\\over2m+2}a_{2m+1}=-{2m+3\\over m+1}a_{2m+1},\\quad m\\ge0. \\label{eq:3.2.31}\n\\end{eqnarray}\n\nStarting with $$a_0=y(0)=2$$, we compute $$a_2, a_4$$, and $$a_6$$ from \\eqref{eq:3.2.30}:\n\n\\begin{eqnarray*}\na_2&=&-4\\,{1\\over1}2=-8,\\\\\na_4&=&-4\\,{2\\over3}(-8)={64\\over3},\\\\\na_6&=&-4\\,{3\\over5}\\left(64\\over3\\right)=-{256\\over5}.\n\\end{eqnarray*}\n\nStarting with $$a_1=y'(0)=-3$$, we compute $$a_3,a_5$$ and $$a_7$$ from \\eqref{eq:3.2.31}:\n\n\\begin{eqnarray*}\na_3&=&-{3\\over1}(-3)=9,\\\\\na_5&=&-{5\\over2}9=-{45\\over2},\\\\\na_7&=&-{7\\over3}\\left(-{45\\over2}\\right)={105\\over2}.\n\\end{eqnarray*}\n\nTherefore the solution of \\eqref{eq:3.2.29} is\n\n\\begin{eqnarray*}\ny=2-3x-8x^2+9x^3+{64\\over3}x^4-{45\\over2}x^5-{256\\over5}x^6+{105\\over2}x^7+\\cdots\\; .\n\\end{eqnarray*}\n\nComputing coefficients recursively as in Example $$(3.2.4)$$ is tedious. We recommend that you do this kind of computation by writing a short program to implement the appropriate recurrence relation on a calculator or computer. You may wish to do this in\nverifying examples and doing exercises (identified by the symbol \\Cex) in this chapter that call for numerical computation of the coefficients in series solutions. We obtained the answers to these exercises by using software that can produce answers in the form of rational numbers. However, it's perfectly acceptable - and more practical - to get your answers in decimal form. You can always check them by converting our fractions to decimals.\n\nIf you're interested in actually using series to compute numerical approximations to solutions of a differential equation, then whether or not there's a simple closed form for the coefficients is essentially irrelevant. For computational purposes it's usually more efficient to start with the given coefficients $$a_0=y(x_0)$$ and $$a_1=y'(x_0)$$, compute $$a_2$$, $$\\dots$$, $$a_N$$ recursively, and then compute approximate values of the solution from the Taylor polynomial\n\n\\begin{eqnarray*}\nT_N(x)=\\sum_{n=0}^Na_n(x-x_0)^n.\n\\end{eqnarray*}\n\nThe trick is to decide how to choose $$N$$ so the approximation $$y(x)\\approx T_N(x)$$ is sufficiently accurate on the subinterval of the interval of convergence that you're interested in. In the computational exercises in this and the next two sections, you will often be asked to obtain the solution of a given problem by numerical integration with software of your choice (see Section $$3.1)$$ for a brief discussion of one such method), and to compare the solution obtained in this way with the approximations obtained with $$T_N$$ for various values of $$N$$. This is a typical textbook kind of exercise, designed to give you insight into how the accuracy of the approximation $$y(x)\\approx T_N(x)$$ behaves as a function of $$N$$ and the interval that you're working on. In real life, you would choose one or the other of the two methods (numerical integration or series solution). If you choose the method of series solution, then a practical procedure for determining a suitable value of $$N$$ is to continue increasing $$N$$ until the maximum of $$|T_N-T_{N-1}|$$ on the interval of interest is within the margin of error that you're willing to accept.\n\nIn doing computational problems that call for numerical solution of differential equations you should choose the most accurate numerical integration procedure your software supports, and experiment with the step size until you're confident that the numerical results are sufficiently accurate for the problem at hand.","date":"2020-07-08 21:44:24","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\": 0.9413198828697205, \"perplexity\": 336.2362032769308}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.3, \"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-2020-29\/segments\/1593655897707.23\/warc\/CC-MAIN-20200708211828-20200709001828-00069.warc.gz\"}"} | null | null |
Seirei Kairo Drive társasjáték - Magyarország társasjáték keresője! A társasjáték érték!
A Seirei Kairo Drive egy nagyszerű társasjáték, 2 - 4 játékos részére, az átlagos játékidő rövidebb, csak 40 perc. A társast, 10 éves kortól ajánljuk kipróbálni. Kooperatív jellegű, a játékmenet erősen épít a váltakozó képességek és a pakli tervezés mechanizmusokra.
In this cooperative game, players begin by selecting hero cards from among four different colors (representing the elements earth, wind, fire, and water) to form a party. Each player then receives a hand of cards drawn from a central deck, which also represents the players' hit points. The players face a series of monster cards drawn from an enemy deck.
The heroes begin at level one, but they earn tokens during the game that may be spent to level up their attack abilities. Each hero may only attack when the player has played a card matching its color. The card that is played must match either the color or the number of the card that was previously played, though multiple cards may be played under special circumstances.
Monster attacks force players to discard from the central deck, decreasing the available hit points. Leveling up the heroes helps players to reclaim these discarded hit points, essentially "healing" the group.
After facing a series of monsters, the players confront a powerful boss monster in a final battle. The players all win or lose together. | {
"redpajama_set_name": "RedPajamaC4"
} | 2,913 |
Greece asks for exemption from systematic border checks
Greece has submitted a request, the second in the last four months, to be exempt from the obligation of enforcing systematic checks on its borders, Kathimerini understands.
In a document sent last week to the European Commission, the European border agency Frontex and EU member states, the Greek Police (ELAS) is asking for an 18-month suspension of the obligation to implement new and stricter border checks – in line with amendments in March to the Schengen Border Codes, which came into effect in April.
Greek authorities are citing infrastructure shortcomings and increased traffic at 12 airports across the country, including Athens International Airport.
ELAS is also also asking for a suspension of the new Schengen rules at the country's land borders at the checkpoints of Evzones, on the border with the Former Yugoslav Republic of Macedonia, as well as Promachonas and Nymphaia bordering Bulgaria.
According to ELAS, these checkpoints deal with large numbers of travelers and the implementation of the new rules could have serious consequences on traffic, especially during the summer months.
Police say they will continue "targeted" checks of individuals suspected of people trafficking or terrorism, adding that other countries have also requested similar suspensions to the new rules.
The amendment obliges member states to conduct systematic checks against relevant databases on all persons, including those enjoying the right of free movement under EU law (ie EU citizens and members of their families who are not EU citizens) when they cross the external borders).
Greece started to implement the new rules on April 7, but just two days later, asked and received a six-month suspension due to serious bottlenecks, mainly at Athens International Airport.
Diplomacy EU Migration
EU wants China's help to stop boats being used by migrants
EU migration commissioner meets with Greek PM on refugee crisis, Ukraine visit
Tsipras, Merkel discuss Cyprus, Turkey, refugee agreement over the phone
Turkey's EU minister says migrant deal may end without visa liberalization
Avramopoulos plays down concerns over EU-Turkey migrant deal
Erdogan to EU on migrant deal: Where is the money? | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 14 |
WebRPGs
=======
This (will) be a basic website with RPGs like The Kingdom of Loathing.
What I need help with:
======================
ANY help with pictures and design would be great! But, any help would be useful.
How to Run:
===========
Host a local server with PHP and MySQL, run the SQL in the "run me.sql" file, copy all the files ending with .php and the .htaccess file into the DocumentRoot, and everything should work! Note: you might need to change the href property of the <a> tags.
Notes:
======
When you contribute, you may add your name to the contributors.txt file.
All content must be clean! If you are not sure, make sure it would be school appropiate!
Donate
======
Donations can be sent to the following Bitcoin address: 1DtTFj1NBUr3LWsH5QZWEAje8Z8aej4SQD
Thanks!
News
====
9-7-14 I decided not to use pictures, at least for now.
| {
"redpajama_set_name": "RedPajamaGithub"
} | 9,344 |
\section{Introduction}
Statistical machine learning methods produce models that are not comprehensible for
humans because they are algebraic solutions to optimization problems such as
risk minimization or data likelihood maximization. These methods do not produce
any intuitive description of the learned model. Lack of intuitive descriptions
makes it hard for users to understand and verify the underlying rules that
govern the model. Also, these methods cannot produce a justification for
a prediction they compute for a new data sample. Additionally, if prior
knowledge (background knowledge) is extended in these methods, then the
entire model needs to be re-learned. Finally, no distinction is made between
exceptions and noisy data in these methods.
Inductive Logic Programming \cite{Muggleton91}, however, is one technique where
the learned model is in the form of logic programming rules (Horn clauses) that
are comprehensible to humans. It allows the background knowledge to be incrementally
extended without requiring the entire model to be relearned. Meanwhile, the
comprehensibility of symbolic rules makes it easier for users to understand and
verify induced models and even edit them.
ILP learns theories in the form of Horn clause logic programs. Extending
Horn clauses with negation as failure (NAF) results in more powerful applications
becoming possible as inferences can be made even in absence of information. This
extension of Horn clauses with NAF where the meaning is computed using the stable
model semantics \cite{GelfondL88}---called Answer Set Programming\footnote{We use the
term answer set programming in a generic sense to refer to normal logic programs,
i.e., logic programs extended with NAF, whose semantics is given in terms of
stable models \cite{baral}.}---has many powerful applications.
Generalizing ILP to learning answer set programs
also makes ILP more powerful.
For a complete discussion on the necessity of NAF in ILP, we refer the reader
to \cite{sakama05}.
Once NAF semantics is allowed into ILP systems, they
should be able to deal with multiple stable models which arise due
to presence of mutually recursive rules involving negation (called
{\it even cycles}) \cite{baral} such as:
{\tt
p :- not q.
q :- not p.
}
Inducing answer set programs in presence of even cycles in the background knowledge has
first been explored in \cite{stableilp}, where the author describes the added
expressiveness that results once background knowledge is allowed to have multiple stable
models. Work by Otero \cite{otero} on induction of stable models formalizes induction
of answer set programs with stable model semantics \cite{GelfondL88} such that in situations
where $B \cup H$ ($B$ represents the background knowledge and $H$ the hypothesis)
has multiple stable models, it is just necessary to guarantee that
each positive example is true in at least one stable model of $B \cup H$. It also
attempts to characterize inducing answer set programs from partial answer sets of
$B \cup H$ (the author calls them non-complete set of examples). These partial answer sets
are treated as examples in the ILP problem. Otero also suggests that researchers should
focus on learning answer set programs that model combinatorial and planning problems, but
does not present any solution. Addressing the problem of learning such programs
is the goal of our research presented in this paper.
In \cite{sakama05}, Sakama introduces algorithms to induce
a {\it categorical} logic program\footnote{A categorical logic program is an
answer set program with at most one stable model.} given the answer set of
the background knowledge and {\it either} positive {\it or} negative examples. Essentially,
given a single answer set, Sakama tries to induce a program that
has that answer set as a stable model.
In \cite{brave}, Sakama extends his work to learn from
multiple answer sets. He introduces {\it brave} induction, where the learned
hypothesis $H$ is such that {\it some} of the answer sets of
$B \cup H$ cover the positive examples. The limitation of this work is that it accepts only
one positive example as a conjunction of atoms. It does not take into account negative examples at all.
Cautious induction, the counterpart of brave induction, is also
too restricted as it can only induce atoms in the intersection
of all stable models. Thus, neither brave induction nor cautious induction are able
to express situations where something should hold in all
or none of the stable models. An example of this limitation arises in the graph
coloring problem where the following should hold in all answer sets: no two neighboring
nodes in a graph should be painted the same color.
ASPAL \cite{DBLP:conf/ilp/CorapiRL12} is the first ILP system to learn answer
set programs by encoding ILP problems as ASP programs and having an ASP solver
find the hypothesis. Its successor ILASP \cite{ILASP}, is an ILP system capable of
inducing hypotheses expressed as answer set programs too. ILASP defines a framework that subsumes
brave/cautious induction and allows much broader class of problems relating to learning answer
set programs to be handled by ILP. However, the algorithm exhaustively searches the space of
possible clauses to find one that is consistent with all examples and
background knowledge. To make this search feasible, it prohibits predicate
invention, i.e., learning predicates other than the target predicate(s). Resorting to
exhaustive search and not allowing predicate invention are
weaknesses of ILASP that limit its applicability to many useful situations. Our
research presented in this paper does not suffer from these problems.
XHAIL \cite{XHAIL} is another ILP system capable of learning non-monotonic
logic programs. It heavily incorporates abductive logic programming to search
for hypotheses. It uses a similar language-bias as ILASP does, and thus suffers
from the limitations similar to ILASP. It also does not support the notion of inducing
answer set programs from partial answer sets.
All the systems discussed above, resort to an exhaustive search for the hypothesis.
In contrast, traditional ILP systems (that only learn Horn clauses),
use heuristics to guide their search. Use of heuristics allows these system to avoid
an exhaustive search. These system usually start with the most general clauses and then
specialize them. They are better suited for large-scale data-sets with noise,
since the search can be easily guided by heuristics.
FOIL \cite{Quinlan90} is a representative of such algorithms. However, handling negation in FOIL is somewhat
problematic as we will soon show. Also, FOIL can not handle background knowledge
with multiple stable models, nor it can induce answer set programs.
Recently we developed an algorithm called FOLD \cite{fold} to automate
inductive learning of default theories represented as stratified answer
set programs. FOLD (First Order Learner of Default rules) extends the
FOIL algorithm and is able to learn answer set programs that represent the underlying knowledge
very succinctly.
However, FOLD is only limited to dealing with stratified answer set programs, i.e.,
mutually recursive rules through negation are not allowed in the background knowledge
or the hypothesis. Thus, FOLD is incapable of handling cases where the
background knowledge or the hypotheses admits multiple stable models. In this paper,
we extend the FOLD algorithm to allow both the background
knowledge and the hypothesis to have multiple stable models.
The extended FOLD algorithm---called the XFOLD algorithm---is much more general than previously
proposed methods.
This paper makes the following novel contributions: it presents the XFOLD algorithm,
an extension of our previous FOLD algorithm, that can
handle background knowledge with multiple stable models as well as allow
inducing of hypotheses that have multiple stable models. To the best of our knowledge, XFOLD is the first
heuristic based algorithm to induce such hypotheses. The XFOLD algorithm
can learn ASP programs to solve combinatorial problems such as graph-coloring and N-queens.
Because the XFOLD algorithm is based on heuristic search, it is also scalable. Lack of
scalability is a major problem in previous approaches.
The rest of this paper is organized as follows: In section
\ref{sec:background}, we present the motivation of the FOLD algorithm by
recalling some of the problems in FOIL algorithm. In section \ref{sec:fold}, we
introduce the FOLD algorithm. In section \ref{sec:foldasp}, we present our
extension to the FOLD algorithm, called XFOLD, to induce answer set programs with multiple
stable models. In section \ref{sec:application}, we show how XFOLD algorithm can
induce programs for solving combinatorial problems. In section \ref{sec:related}, we
present related work while in
section \ref{sec:conclusion}, we present our conclusions and future work.
We assume that the reader is familiar with answer set programming and stable
model semantics. Books by Baral \cite{baral} and Gelfond and Kahl \cite{gelfondbook}
are good sources of background material.
\section{Background}
\label{sec:background}
In this section we describe our work on learning stratified answer set programs, i.e.,
learning hypothesis without cyclical rules using background knowledge that also does not
have cyclical rules. The learning algorithm, called FOLD (First Order Learning of Default
rules) \cite{fold}, is itself an extension of the well known FOIL algorithm.
FOIL is a top-down ILP algorithm which follows a
\textit{sequential covering} approach to induce a hypothesis. The FOIL
algorithm is summarized in Algorithm \ref{algo:foil}. This algorithm repeatedly
searches for clauses that score best with respect to a subset of
positive and negative examples, a current hypothesis and a heuristic called
\textit{information gain} (IG). The FOIL algorithm learns a target predicate
that has to be specified. Essentially, the target predicate appears as the head of
the learned goal clause that FOIL aims to learn.
\begin{algorithm}
\caption{Overview of the FOIL algorithm}
\label{algo:foil}
\begin{algorithmic}[1]
\Input $goal,B,E^+,E^-$
\Output Hypothesis H \\
Initialize $H \gets \emptyset $
\While{\textbf{not}($stopping \ criterion$)}
\State $c \gets$ \texttt{\{goal :- true.\}}
\While{\textbf{not}($stopping \ criterion$)}
\For{all $ \ c' \in \rho (c)$}
\State $compute \ score(E^+,E^-,H \cup \{c'\},B)$
\EndFor
\State let $\hat{c}$ be the $c' \in \rho(c)$ with the best score
\State $c \gets \hat{c}$
\EndWhile
\State add $\hat{c}$ to $H$
\State $E^+ \gets E^+ \setminus covers(\hat{c},E^+,B)$
\EndWhile
\end{algorithmic}
\end{algorithm}
The inner loop searches for a clause with the highest information gain using a
general-to-specific hill-climbing search. To specialize a given clause $c$, a
refinement operator $\rho$ under $\theta$-subsumption \cite{plotkin70} is
employed. The most general clause is \texttt{\{p($X_1,...,X_n$) :- true.\}},
where the predicate \texttt{p/n} is the target and each $X_i$ is a variable.
The refinement operator specializes the current clause \texttt{\{h :-
$b_1$,...,$b_n$.\}}. This is realized by adding a new literal \texttt{l} to the
clause, which yields the following: \texttt{\{h :- $b_1$,...,$b_n$,l\}}. The
heuristic based search uses \textit{information gain}. In FOIL, information
gain for a given clause is calculated as follows
\cite{Mitchell97}:
\begin{equation}
IG(L,R) = t\left(log_2 \frac{p_1}{p_1 + n_1} - log_2 \frac{p_0}{p_0+ n_0}
\right)
\end{equation}
where $L$ is the candidate literal to add to rule $R$, $p_0$ is the number of
positive bindings of $R$, $n_0$ is the number of negative bindings of $R$,
$p_1$ is the number of positive bindings of $R+L$, $n_1$ is the number of
negative bindings of $R+L$, $t$ is the number of positive bindings of $R$ also
covered by $R+L$.
FOIL handles negated literals in a naive way by adding the literal $not \ L$ to
the set of specialization candidate literals for any existing candidate $L$.
This approach leads to learning predicates that do not capture the concept
accurately as shown in the following example:
\begin{exmp}
\label{ex:pinguin}
$ B, E^+$ are background knowledge and positive examples
respectively under \textit{Closed World Assumption}, and the target predicate
is \texttt{fly}.
\end{exmp}
\begin{center}
\begin{tabular}{rll}
$B:$ & \texttt{bird(X) :- penguin(X).} & \\
& \texttt{bird(tweety).} & \texttt{bird(et).} \\
& \texttt{cat(kitty).} & \texttt{penguin(polly).} \\
$E^+:$& \texttt{fly(tweety).} & \texttt{fly(et).} \\
\end{tabular}
\end{center}
The FOIL algorithm would learn the following rule:
\begin{center}
\begin{tabular}{l}
\texttt{fly(X) :- not cat(X), not penguin(X).}
\end{tabular}
\end{center}
which does not yield a constructive definition, even though it covers all the
positives (tweety is not a penguin and et is not a cat) and no negatives
(neither cats nor penguins fly). In fact, the correct theory in this
example is as follows: "{\it Only birds fly but, among them there are
exceptional ones who do not fly}". It translates to the following logic programming rule:
\begin{center}
\begin{tabular}{l}
\texttt{fly(X):- bird(X), not penguin(X).}
\end{tabular}
\end{center}
which FOIL fails to discover.
\section{FOLD Algorithm}
\label{sec:fold}
The intuition behind FOLD algorithm is to learn a concept in terms of a default
and possibly multiple exceptions (and exceptions to exceptions, and so on).
Thus, in the bird example given above, we would
like to learn the rule that {\tt X} flies if it is a bird and not a penguin, rather
than that all non-cats and non-birds can fly. FOLD tries first to learn the
default by specializing a general rule of the form
\texttt{\{goal($V_1,...,V_n$) :- true.\}} with positive literals.
As in FOIL, each specialization must rule out some already covered negative
examples without decreasing the number of positive examples covered
significantly. Unlike FOIL, no negative literal is used at this stage. Once
the IG becomes zero, this process stops. At this point, if any negative
example is still covered, they must be either noisy data or
exceptions to the current hypothesis. Exceptions are separated from noise via
distinguishable patterns in negative examples \cite{Srinivasan96}. In other
words, exceptions could be learned by calling the same algorithm recursively.
This swapping of positive and negative examples, then recursively calling the
algorithm can continue, so that we can learn exceptions to exceptions, and so on.
Each time a rule is discovered for
exceptions, a new predicate \texttt{ab($V_1,...,V_n$)} is introduced. To avoid
name collisions, FOLD appends a unique number at the end of the string "ab" to
guarantee the uniqueness of invented predicates. It turns out that the outlier
data samples are covered neither as default nor as exceptions. If outliers are
present, FOLD identifies and enumerates them to make sure that the algorithm converges.
Algorithm \ref{algo:fold} shows a high level implementation of the FOLD
algorithm. At lines
1-8, function FOLD, serves like the FOIL outer loop. At line 3, FOLD starts
with
the most general clause (e.g. \texttt{fly(X) :- true}). At line 4, this clause
is refined by calling the function $SPECIALIZE$. At lines 5-6, set of positive
examples and set of discovered clauses are updated to reflect the newly
discovered clause.
At lines 9-29, the function $SPECIALIZE$ is shown. It serves
like the FOIL inner loop. At line 12, by calling the function
ADD\_BEST\_LITERAL
the ``best'' positive literal is chosen and the best IG as well as the
corresponding clause is returned. At lines 13-24, depending on the IG value,
either the positive literal is accepted or the EXCEPTION function is called.
If, at the very first iteration, IG becomes zero, then a clause that just
enumerates the positive examples is produced. A flag called $first\_iteration$
is used to differentiate the first iteration. At lines 26-27, the sets of
positive and negative
examples are updated to reflect the changes of the current clause. At line 19,
the EXCEPTION function is called while swapping $E^+$ and $E^-$.
At line 31, the ``best'' positive literal that covers more positive
examples and fewer negative examples is selected. Again, note the current
positive examples
are really the negative examples and in the EXCEPTION function, we try to find
the
rule(s) governing the exception. At line 33, FOLD is recursively called to
extract this rule(s). At line 34, a new \texttt{ab} predicate is introduced and
at
lines 35-36 it is associated with the body of the rule(s) found by the
recurring FOLD function call at line 33. Finally, at line 38, default and
exception are combined together to form a single clause.
The FOLD algorithm, once applied to Example \ref{ex:pinguin}, yields the
following clauses:
\begin{center}
\begin{tabular}{l}
\texttt{fly(X):- bird(X), not ab0(X).}\\
\texttt{ab0(X):- penguin(X).}
\end{tabular}
\end{center}
\begin{algorithm}
\caption{FOLD Algorithm}
\label{algo:fold}
\begin{algorithmic}[1]
\Input $goal, B,E^+,E^-$
\Output \Statex $D = \{c_1,...,c_n\}$ \Comment{defaults' clauses}
\Statex $AB = \{ab_1,...,ab_m\}$ \Comment{exceptions/abnormal
clauses}
\Function{FOLD}{$E^+,E^-$}
\While{($size(E^+) > 0 $)}
\State $c \gets (goal$ :- $ \ true.)$
\State $\hat{c} \gets \Call{specialize}{{c},{E^+},{{E^-}}}$
\State $E^+ \gets E^+ \setminus
covers(\hat{c},E^+,B)$
\State $D \gets D \cup \{ \hat{c} \}$
\EndWhile
\EndFunction
\Function{SPECIALIZE}{${c},{E^+},{E^-}$}
\State $first\_iteration \gets true$
\While{($size(E^-) > 0 $)}
\State $(c_{def}, \hat{IG}) \gets
\Call{add\_best\_literal}{{c},{E^+},{{E^-}}}$
\If{$\hat{IG} > 0$}
\State $\hat{c} \gets c_{def} $
\Else
\If{$first\_iteration$}
\State $\hat{c} \gets enumerate(c,E^+)$
\Else
\State $\hat{c} \gets
\Call{exception}{{c},{E^-},{{E^+}}}$
\If {$\hat{c} = null$}
\State $\hat{c} \gets
enumerate(c,E^+)$
\EndIf
\EndIf
\EndIf
\State $first\_iteration \gets false$
\State $E^+ \gets E^+ \setminus
covers(\hat{c},E^+,B)$
\State $E^- \gets E^- \setminus
covers(\hat{c},E^-,B)$
\EndWhile
\EndFunction
\Function{EXCEPTION}{${c_{def}},{E^+},{E^-}$}
\State $\hat{IG} \gets
\Call{add\_best\_literal}{{c},{E^+},{{E^-}}}$
\If{$\hat{IG} > 0$}
\State $ c\_set \gets \Call{FOLD}{E^+,E^-} $
\State $ c\_ab \gets generate\_next\_ab\_predicate()$
\ForEach {$c \in c\_set $}
\State $AB \gets AB \cup \{ c\_ab $:-$ \ bodyof(c) \}$
\EndFor
\State $\hat{c} \gets (headof(c_{def}) $:-$ \ bodyof(c),
\textbf{not}(c\_ab))$
\Else
\State $\hat{c} \gets null$
\EndIf
\EndFunction
\end{algorithmic}
\end{algorithm}
Now, we illustrate how FOLD discovers the above set of clauses given
$E^+ = \{tweety,et\}$ and $E^- = \{polly,kitty\}$ and the
goal \texttt{fly(X)}. By calling FOLD, at line 2 while loop, the clause
\texttt{\{fly(X) :- true.\}} is specialized. Inside the $SPECIALIZE$ function,
at line 12, the
literal \texttt{bird(X)} is selected to add to the current clause, to get the
clause
$\hat{c}$ = \texttt{fly(X) :- bird(X)}, which happens to have the greatest IG
among \texttt{\{bird,penguin,cat\}}. Then, at lines 26-27 the following updates
are
performed: $E^+=\{\}$,\ $E^-=\{polly\}$. A negative example
$polly$, a penguin is still covered. In the next iteration, $SPECIALIZE$ fails
to introduce a positive literal to rule it out since the best IG in this case
is zero. Therefore, the EXCEPTION function is called by swapping the
$E^+$, $E^-$. Now, FOLD is recursively called to learn a
rule for $E^+ = \{polly\}$, $E^-=\{\}$. The recursive call
(line 33), returns \texttt{\{fly(X) :- penguin(X)\}} as the exception. At line
34,
a new predicate \texttt{ab0} is introduced and at lines 35-37 the clause
\texttt{\{ab0(X) :- penguin(X)\}} is created and added to the set of invented
abnormalities namely, AB. At line 38, the negated exception (i.e \texttt{not
ab0(X)}) and the default rule's body (i.e \texttt{bird(X)}) are compiled
together to
form the clause \texttt{\{fly(X) :- bird(X),not ab0(X)\}}.
Note, in two different cases $enumerate$ function is called: i) At very first
iteration of specialization if IG is zero for all the positive literals.
ii) When the $Exception$ routine fails to find a rule governing negative
examples. Whichever is the case, corresponding samples are considered as noise.
The following example shows a learned logic program in presence of noise. In
particular, it shows how $enumerate$ function works: It generates clauses in
which the variables of the goal predicate can be unified with each member of a
list of the examples for which no pattern exists.
\begin{exmp}
Similar to Example \ref{ex:pinguin}, plus we have an extra positive example
fly(jet) without any further information:
\end{exmp}
\begin{center}
\begin{tabular}{cll}
$B:$ & \texttt{bird(X) :- penguin(X).} & \\
& \texttt{bird(tweety).} & \texttt{bird(et).} \\
& \texttt{cat(kitty).} & \texttt{penguin(polly).}\\
$E^+:$ & \texttt{fly(tweety). fly(jet).} & \texttt{fly(et).} \\
\end{tabular}
\end{center}
FOLD algorithm on the Example 4.1 yields the following clauses:
\begin{center}
\begin{tabular}{l}
\texttt{fly(X) :- bird(X), not ab0(X).}\\
\texttt{fly(X) :- member(X,[jet]).}\\
\texttt{ab0(X) :- penguin(X).}
\end{tabular}
\end{center}
FOLD recognizes $jet$ as a noisy data. $member/2$ is a built-in logic programming predicate in
that tests the membership of an atom in a list.
Sometimes, there are nested levels of exceptions. The following example shows
how FOLD manages to learn the correct theory in presence of nested exceptions.
\begin{exmp}
Birds and planes normally fly, except penguins and damaged planes that can't.
There are super penguins who can, exceptionally, fly.
\end{exmp}
\begin{center}
\begin{tabular}{cl}
$B:$ & \texttt{bird(X) :- penguin(X).} \\
& \texttt{penguin(X) :- superpenguin(X).} \\
& \texttt{bird(a). bird(b). penguin(c). penguin(d). }
\\
& \texttt{superpenguin(e). superpenguin(f).} \\
& \texttt{plane(g). plane(h). plane(k).} \\
& \texttt{damaged(k). damaged(m).} \\
$E^+:$ & \texttt{fly(a). \ \ \ fly(b). \ \ \ fly(e).}\\
& \texttt{fly(f). \ \ \ fly(g). \ \ \ fly(h).}
\end{tabular}
\end{center}
FOLD algorithm learns the following theory:
\begin{center}
\begin{tabular}{l}
\texttt{fly(X) :- plane(X), not ab0(X).}\\
\texttt{fly(X) :- bird(X), not ab1(X).}\\
\texttt{fly(X) :- superpenguin(X).}\\
\texttt{ab0(X) :- damaged(X).} \\
\texttt{ab1(X) :- penguin(X).}
\end{tabular}
\end{center}
\noindent
Table \ref{table:accuracy}, presents our experiments with UCI benchmark datasets \cite{Lichman:2013}. In this experiment, we ran FOLD on each dataset and measured the accuracy using a 10-fold cross-validation and the results are compared against that of Aleph \cite{aleph}. Aleph is a popular ILP system that has been widely used in prior work. To induce a clause, Aleph starts by building the most specific clause, which is called the ``bottom clause", that entails a seed example. Then, it uses a branch-and-bound algorithm to perform a general-to-specific heuristic search for a subset of literals from the bottom clause to form a more general rule. In most cases, our FOLD algorithm outperforms Aleph in terms of accuracy and succinctness of induced rules.
FOLD handling of negation and numeric constraints, yields intuitive and precise results. For instance, in UCI Labor-negotiations, which is a dataset of final settlements in labor negotiations in Canadian industry, the following hypothesis is induced by FOLD:
\begin{center}
\begin{tabular}{l}
\texttt{good\_contract(X) :- wage\_inc\_first\_year(X,A), A > 2, not ab0(X).}\\
\texttt{good\_contract(X) :- holidays(X,A), A > 11.}\\
\texttt{good\_contract(X) :- health\_plan\_half\_contribution(X), pension(X).}\\
\texttt{ab0(X) :- no\_longterm\_disability\_help(X).} \\
\texttt{ab0(X) :- no\_pension(X).} \\
\end{tabular}
\end{center}
This hypothesis captures the highest priorities of employees in a good contract. Without having abnormality predicates,
the hypothesis would have contained more clauses depending on the diversity of options on long term disability support and pension,
whereas in default theory approach, as shown in this example, instead of covering examples with multiple clauses,
a single clause is introduced as a default rule, and irrelevant predicates are excluded by abnormality predicates.
\begin{table}
\begin{tabular}{lcccc}
\hline
dataset & size & ALEPH accuracy(\%) & FOLD accuracy(\%) & FOLD execution time(s) \\ [0.5ex]
\hline\hline
Credit-au & 690 & 82 & 83 & 67\\
Credit-j & 125 & 53 & 81 & 20\\
Credit-g & 1000 & 70.9 & 78 & 87\\
Iris & 150 & 85.9 & 95 & 1.3\\
Ecoli & 336 & 91 & 90 & 6.1\\
Bridges & 108 & 89 & 90 & 0.8\\
Labor & 57 & 89 & 94 & 0.4\\
Acute(1) & 34 & 100 & 100 & 0.3\\
Acute(2) & 34 & 100 & 100 & 0.3\\
Mushroom & 7724 & 100 & 100 & 11.4 \\
\hline
\end{tabular}
\caption{FOLD evaluation on UCI benchmarks }
\label{table:accuracy}
\end{table}
\section{Induction of Answer Set Programs with Multiple Stable Models}
\label{sec:foldasp}
In the previous section we assumed that the background knowledge $B$ is a
normal logic program with one stable model and all examples belong to
the only stable model of $ B \cup H $. This would require the language bias not
to allow even cycles which are responsible for generating multiple
stable models.
In this section we extend our FOLD algorithm to learn normal logic programs
that potentially have multiple stable models. The significance of Answer Set
Programming paradigm is that it provides a declarative semantics under which
each stable model is associated with one (alternative) solution to the problem
described by the program. Typical problems of this kind are combinatorial
problems, e.g., graph coloring and N-queens. In graph coloring, one should find
different ways of coloring nodes of a graph without coloring two nodes connected by
an edge with the same color. N-queen is the problem of placing N queens in a chessboard of size
$N\times N$ so that no two queens attack each other.
In order to inductively learn such programs, the ILP problem definition needs to
be revisited. In the new scenario, positive examples $e \in E^+$, may not
hold in every model. Therefore, the ILP problem described in the background
section would only allow learning of predicates that hold in all answer sets. This
is too restrictive. Brave induction \cite{brave}, in contrast, allows examples to
hold only in some stable models of $B \cup H$. However, as stated in
\cite{ILASP} and we will show using examples, this is not enough when it comes
to learning global constraints (i.e, rules with empty head)\footnote{Recall that in
answer set programming, a constraint is expressed as a headless rule of the
form
{\tt :- B.}
which states that {\tt B} must be false. A headless rule is
really a short-form of rules of the form (called odd loops over negation \cite{baral}):
{\tt p :- B, not p.}
}. Learning global
constraints is essential because certain combinations may have to be excluded
from {\it all} answer sets.
When $B \cup H$ has multiple stable models, there will be some instances of target
predicate that would hold in all, none, or some of the stable models. Brave
induction is not able to express situations in which a predicate should hold
in all or none of the stable models. An example is a
graph in which node 1 is colored red. In such a case, none of node 1's
neighbors should be colored red. If node 1 happens to have node 2 as a neighbor, brave induction is not
able to express the fact that if the predicate \texttt{red(1)} appears in any
stable model of $ B \cup H $, \texttt{red(2)} should not. In \cite{ILASP}, the
authors propose a new paradigm called \text{learning from partial answer sets}
that overcomes these limitations. We also adopt this paradigm in our work presented here.
Next, we present our XFOLD algorithm.
\begin{definition}
A partial interpretation E is a pair $E = \langle E^{inc},E^{exc} \rangle$ of
sets of ground atoms called inclusions and exclusions, respectively. Let $A
= AS(B \cup H)$ denote a stable model of $B \cup H$. $A$ {\it extends} $\langle
E^{inc},E^{exc} \rangle$ if and only if $(E^{inc} \subseteq \ A) \wedge
(E^{exc} \cap \ A = \emptyset) $.
\end{definition}
\begin{exmp}
\label{exmp1}
Consider the following background knowledge about a group of friends some of
whom are in conflict with others. The individuals in conflict will not attend a
party together. Also, they cannot attend a party if they work at the time the
party is held. We want our ILP algorithm to discover the rule(s) that will
determine who will go to the party based on the set of partial interpretations provided.
\end{exmp}
\begin{center}
\begin{tabular}{ll}
$B:$ & \texttt{conflict(X,Y) :- person(X), person(Y),
conflict(Y,X).} \\
& \texttt{works(X) :- person(X), not off(X).} \\
& \texttt{off(X) :- person(X), not works(X).} \\
& \texttt{person(p1). person(p2).}
\texttt{conflict(p1,p4).} \\
& \texttt{person(p3). person(p4).} \texttt{conflict(p2,p3).}
\end{tabular}
\end{center}
Some of the partial interpretations are as follows.
The predicates g,w,o abbreviate goesToParty,works,off respectively:\\
\noindent
$E_1 = \{ \langle g(p1),g(p2),o(p1),o(p2),w(p3),o(p4),w(p5) \rangle, \langle
g(p3),g(p4),g(p5) \rangle \}$\\
$E_2 = \{ \langle g(p3),g(p4),g(p5),o(p1),o(p2),o(p3),o(p4),o(p5) \rangle,
\langle g(p1),g(p2) \rangle \}$\\
$E_3 = \{ \langle g(p1),g(p3),g(p5),o(p1),o(p2),o(p3),w(p4),o(p5) \rangle,
\langle g(p2),g(p4) \rangle \}$\\
$E_4 = \{ \langle g(p2),g(p5),g(p5),w(p1),o(p2),w(p3),w(p4),o(p5) \rangle,
\langle g(p1),g(p3),g(p4) \rangle \}$\\
In the above example, each $E_i$ for i = 1,2,3,4 is a partial interpretation
and should be extended by at least one stable model of $ B \cup H $ for a
learned hypothesis $ H $. For instance, let's consider the hypothesis $H_1=$
\texttt{\{goesToParty(X) :- off(X)\}} for learning the target predicate
\texttt{goesToParty(X)}. By plugging the background knowledge, the non-target
predicates in $E_1$, and the hypothesis $H_1$ into an ASP solver (CLASP
\cite{gekasc12c} in our case), the stable
model returned by the solver would contain
\texttt{\{goesToParty(p1),goesToParty(p2),goesToParty(p4)\}}. It does not extend $E_1$. Although,
$E^{inc}_1 \subseteq AS(B \cup H_1)$ but $ AS(B \cup H_1) \cap E^{exc}_1 \neq
\emptyset$. It should be noted that non-target predicates are treated as
background knowledge upon calling ASP solver to compute the stable model of
$B \cup H$.
\begin{definition}
An XFOLD problem is defined as a tuple $P = \langle B,L,E^+,E^-,T
\rangle$. $B$ is a answer set program with potentially
multiple stable models called the background knowledge. $L$ is the language-bias
such that $L = \langle M_h,M_b \rangle$, where $M_h$ (resp. $M_b$) are called the
\textit{head} (resp. \textit{body}) \textit{mode declarations} \cite{Muggleton1995}.
Each mode declaration $m_h \in M_h$ (resp. $m_b \in M_b$) is a literal whose
abstracted arguments are either variable $v$ or constant $c$. Type of a variable
is a predicate defined in B. The domain of each constant should be defined
separately. The clause \texttt{h :- $b_1$,...,$b_n$, not $c_1$,...,not $c_m$} is in the
search space if and only if: i) $h$ is empty; ii) $h$ is an atom compatible
with a mode declaration in $M_h$. Hypothesis $h$ is said to be compatible with a mode
declaration $m$ if each instance of variable in $m$ is replaced by a variable,
and every constant takes a value from the associated domain. The set of
candidate predicates in the greedy search algorithm are selected from $M_b \cup M_h$.
The requirement of mode declarations in the XFOLD algorithm
is due to a technicality: ASP solvers, need
to ground the program, and for that matter, programmer should ensure that every
variable is safe. A variable in \textit{head} is \textit{safe} if it occurs in
a positive literal of \text{body}. XFOLD adds predicates required to ensure
safety, but to keep our examples simple, we omit safety predicates in the
paper. $E^+$ and $E^-$ are sets of partial interpretations called positive and
negative examples, respectively. $T \in M_h$ is the target predicate's name.
Each XFOLD run learns a single target predicate. A hypothesis $h \in L$ is an
inductive solution of $T$ if and only if:
\begin{enumerate}
\item $\forall e^+ \in E^+ \exists A \in AS(B \cup H)$ such that $A$
extends $e^+$
\item $\forall e^- \in E^- \not \exists A \in AS(B \cup H)$ such that $A$
extends $e^-$
\end{enumerate}
\end{definition}
The above definition adopted from \cite{ILASP} subsumes brave and cautious
induction semantics \cite{brave}. Positive examples should be extended by at
least one stable model of $B \cup H$ (brave induction). In contrast, no stable
model of $B \cup H$ extends negative examples (cautious induction). The
\textit{generate and test} problems such as N-queen and graph coloring could be
induced using our XFOLD algorithm. It suffices to use positive examples
for learning the \textit{generate} part and negative examples for
learning the \textit{test} part.
Figure \ref{tab:graph-coloring} represents the input to the XFOLD algorithm
for learning an answer set program for graph coloring. Every positive
example states if a node is colored red, then that node cannot be painted blue
or green. Likewise for blue and green. However, this is not enough to learn the constraint that two nodes
connected by an edge cannot have the
same color. To learn this constraint, negative examples are needed. For instance,
$E^-_1$, states that if any stable model of $B \cup H$ contains
\texttt{\{red(1)\}}, in order not to extend $E^-_1$, it should contain
\texttt{\{not red(2)\}} or equivalently, it should not contain
\texttt{\{red(2)\}}.
\begin{figure}[]
\begin{tabular}{lp{0.4\textwidth}}
\begin{tikzpicture}[baseline=0,->,>=stealth',shorten >=1pt,auto,node
distance=3cm,
thick,main
node/.style={circle,draw,font=\sffamily\Large\bfseries}]
\node[main node] (1) {1};
\node[main node] (2) [right of=1] {2};
\node[main node] (3) [below of=2] {3};
\node[main node] (4) [below of=1] {4};
\path[every node/.style={font=\sffamily\small}]
(1) edge node [] {} (4)
edge node {} (3)
(2) edge node [] {} (1)
(3) edge node [] {} (2)
(4) edge node [] {} (3);
\end{tikzpicture} &
\begin{itemize}
\item Positive examples:
\begin{gather*}
E^+_1=\{ \langle r(1),b(2),g(3),b(4) \rangle,\langle not\
b(1),not\ g(1),not\ r(2),\\
~~~~~~~~~~~~~ not\ g(2),not\ r(3),not\ b(3),not\ r(4),not\ g(4) \rangle
\} \\
E^+_2=\{ \langle b(1),r(2),g(3),r(4) \rangle,\langle not\
r(1),not\ g(1),not\ b(2),\\
~~~~~~~~~~~~~ not\ g(2),not\ r(3),not\ b(3),not\ b(4),not\ g(4) \rangle
\}
\end{gather*}
\item Negative examples:
\begin{gather*}
E^-_1=\{ \langle r(1) \rangle,\langle not\ r(2)\rangle \} \\
E^-_2=\{ \langle r(1) \rangle,\langle not\ r(3)\rangle \}
\end{gather*}
\end{itemize}
\end{tabular}
\captionsetup{justification=centering}
\caption{Partial interpretations as examples in graph coloring problem}
\label{tab:graph-coloring}
\end{figure}
The intuition behind the XFOLD algorithm is as follows: every positive example $e$ that
is a partial interpretation is considered as a separate learning problem. A partial
score is computed for $e$. Once all the positive examples are tested against a
candidate clause, the overall score, i.e, the summation of all partial scores is
stored as the score of current clause. Among all hypotheses, the one with
highest overall score is chosen just like the single stable model case. For
testing any given hypothesis $h$, the background knowledge $B$, all non-target
predicates in $E^{inc}$ and the hypothesis $h$ are passed to the ASP solver as
the input. The returned answer set is compared with the target predicates in
$E^{inc}$ and $E^{exc}$. Next, the partial \texttt{information gain} score is
computed. XFOLD chooses a clause with highest positive score (if one exists).
Next, every partial interpretation is updated by removing the covered target
predicates from $E^{inc}$ and $E^{exc}$. Once no target predicate in $E^{exc}$
is covered, the internal loop finishes and the discovered rule(s) are added to
the learned theory. Just like FOLD, if no literal with positive score exists,
swapping occurs on each remaining partial interpretation and the XFOLD algorithm
is recursively called. In this case, instead of introducing abnormality
predicates, the negation symbol, "-", is prefixed to the current target predicate to
indicate that the algorithm is now trying to learn the negation of concept being
learned. It should also be noted that swapping examples is performed slightly
differently due to the existence of partial interpretations. The summary of
required changes in swapping of examples is as follows:
\begin{enumerate}
\item $\forall e \in E_{inc}$, where $e$ is and old target atom, $e$ is
restored
\item $\forall e \in E_{inc}$, where $e$ is and old target atom, $-e$ is
added to $E_{exc}$
\item $\forall e \in E_{exc}$, where $e$ is and old target atom, $-e$ is
added to $E_{inc}$
\item $ T \leftarrow -T$. (Target predicate T now becomes its negation, -T)
\end{enumerate}
\begin{figure}[]
\centering
\begin{tabular}{l}
After iteration \#1: \texttt\{goesToParty(X) :- off(X)\}
\\ \hline
$E_1 = \{ \langle o(p1),o(p2),w(p3),o(p4),w(p5) \rangle, \langle g(p4)\rangle
\}$ \\
$E_2 = \{ \langle o(p1),o(p2),o(p3),o(p4),o(p5) \rangle, \langle
g(p1),g(p2)\rangle \}$ \\
$E_3 = \{ \langle o(p1),o(p2),o(p3),w(p4),o(p5) \rangle, \langle g(p2)\rangle
\}$ \\
\st{$E_4 = \{ \langle w(p1),o(p2),w(p3),w(p4),o(p5) \rangle, \langle \rangle
\}$} \\
After swapping $E_{inc}$,$E_{exc}$
\\ \hline
$E_1 = \{\langle -g(p4),g(p1),g(p2),o(p1),o(p2),w(p3),o(p4),w(p5) \rangle,
\langle -g(p1),-g(p2) \rangle \}$ \\
$E_2 = \{ \langle
-g(p1),-g(p2),g(p3),g(p4),g(p5),o(p1),o(p2),o(p3),o(p4),o(p5) \rangle,
\langle -g(p3),-g(p4),-g(p5)\rangle \}$ \\
$E_3 = \{ \langle -g(2),g(p1),g(p3),g(p5),o(p1),o(p2),o(p3),w(p4),o(p5)
\rangle, \langle -g(p1),-g(p3),-g(5)\rangle \}$ \\
After iteration \#1: -goesToParty(X) :- conflict(X,Y)
\\ \hline
$E_1 = \{\langle g(p1),g(p2),o(p1),o(p2),w(p3),o(p4),w(p5) \rangle, \langle
-g(p1),-g(p2) \rangle \}$ \\
$E_2 = \{ \langle g(p3),g(p4),g(p5),o(p1),o(p2),o(p3),o(p4),o(p5) \rangle,
\langle -g(p3),-g(p4)\rangle \}$ \\
$E_3 = \{ \langle g(p1),g(p3),g(p5),o(p1),o(p2),o(p3),w(p4),o(p5) \rangle,
\langle -g(p1),-g(p3)\rangle \}$ \\
iteration \#2: -goesToParty(X) :- conflict(X,Y),goesToParty(Y)
\\ \hline
\st{$E_1 = \{\langle g(p1),g(p2),o(p1),o(p2),w(p3),o(p4),w(p5) \rangle, \langle
\rangle \}$} \\
\st{$E_2 = \{ \langle g(p3),g(p4),g(p5),o(p1),o(p2),o(p3),o(p4),o(p5) \rangle,
\langle \rangle \}$} \\
\st{$E_3 = \{ \langle g(p1),g(p3),g(p5),o(p1),o(p2),o(p3),w(p4),o(p5) \rangle,
\langle \rangle \}$} \\ \hline
Hypothesis = \{ \texttt\{goesToParty(X) :- off(X), not -goesToParty(X).\},
\texttt\{-goesToParty(X) :- conflict(X,Y), goesToParty(Y).\}\}
\end{tabular}
\caption{Trace of XFOLD internal loop and recursive call on party example}
\label{tab:party-trace}
\end{figure}
Figure \ref{tab:party-trace} demonstrates execution of XFOLD for Example \ref{exmp1}.
At the end of first iteration, the predicate \texttt{off(X)} gets the highest
score. $E_4$ will be removed as it is already covered by the current hypothesis.
In the second iteration, all candidate literals fail to get a positive score.
Therefore, swapping occurs and algorithm tries to learn the predicate
\texttt{-goesToParty(X)} as if it was an exception to the default case
\texttt{\{goesToParty(X) :- off(X)\}}. Since the new target predicate is
\texttt{-goesToParty(X)}, all ground atoms of \texttt{goesToParty} in $E_{inc}$ are restored
back. The old target atoms in $E_{exc}$ are transformed to negated version
and become members of $E_{inc}$.
In Figure \ref{tab:party-trace}, after one iteration, $E_4$ is removed because
all target atoms in $E_{inc}$ are already covered and targets atoms in
$E_{exc}$ are already excluded. After swapping, XFOLD is recursively called to
learn \texttt{-goesToParty}. After two iterations, since all examples are covered,
the algorithm terminates.
In Example \ref{exmp1}, we haven't introduced any explicit negative example.
Nevertheless, the algorithm was able to successfully find the cases in which
the original target predicate does not hold (via learning \texttt{-goesToParty(X)}
predicate). In general, it is not always feasible for the algorithm to figure
out prohibited patterns without getting to see a very large number of positive examples.
\iffalse
It is also worth noting that \texttt{-goesToParty(X)}, in essence,
represents classical negation. XFOLD learns the negation of
target predicate from negative examples, but then it shifts the negated head to the body
of the rule to produce a constraint.
Thus, given the following rule that is learned,
\begin{center}
\begin{tabular}{c}
\texttt{-goesToParty(X) :- conflict(X,Y),goesToParty(Y).}
\end{tabular}
\end{center}
XFOLD subsequently shifts \texttt{-goesToParty(X)} from the head to the body, to turn it
into a constraint:
\begin{center}
\begin{tabular}{c}
\texttt{:- goesToParty(X),conflict(X,Y),goesToParty(Y).}
\end{tabular}
\end{center}
We will show detailed examples in the applications section.
\fi
\section{Application: Combinatorial Problems}
\label{sec:application}
A well-known methodology for declarative problem solving is the
\textit{generate and test} methodology, whereby possible solutions to a problem
are generated first, and then non-solutions are eliminated by testing. In
Answer Set Programming, the \textit{generate} part is encoded by enumerating
the possibilities by introducing even cycles. The
\textit{test} part is realized by having constraints that would eliminate
answer sets that violate the test conditions.
ASP syntax allows rules of the form $l\{h_1,...,h_k\}u$ such that $0 \leq l
\leq u \leq k$ and $\forall i \in [1,k]$, $h_i \in L$, where L is the language
bias. This is a syntactic sugar for combination of even cycles and constraints,
which is called {\it choice rule} in the literature \cite{baral,gelfondbook}.
ILASP \cite{ILASP} directly
searches for choice rules by including them in the search space. XFOLD, on the
other hand, performs the search based on $\theta$-subsumption \cite{plotkin70}
and hence disallows search for choice rule hypotheses. Instead, it directly
learns even cycles as well as constraints. This is advantageous as it allows
for more sophisticated and flexible language bias.
It turns out that inducing the \textit{generate} part in a combinatorial
problem such as graph-coloring requires an extra step compared to the FOLD algorithm.
For instance, \texttt{red(X)} predicate has
the following clause:
\begin{center}
\begin{tabular}{c}
\texttt{red(X):- not blue(X), not green(X).}
\end{tabular}
\end{center}
To enable XFOLD to induce such a rule, we adopted the ``Mathews Correlation
Coefficient" (MCC) \cite{quickfoil} measure to perform the task of feature selection. MCC is
calculated as follows:
\begin{center}
\begin{tabular}{c}
$ MCC = \frac{TP \times TN - FP \times
FN}{\sqrt{(TP+FP)(TP+FN)(TN+FP)(TN+FN)}}$
\end{tabular}
\end{center}
This measure takes into account all the four terms TP (true positive), TN (true
negative), FP (false positive) and FN (false negative) in the
confusion matrix and is able to fairly assess the quality of classification
even when the ratio of positive tuples to the negative tuples is not close to
1. The MCC values range from -1 to +1. A coefficient of +1 represents a perfect
classification, 0 represents a classification that is no better than a random classifier, and -1
indicates total disagreement between the predicted and the actual labels. MCC
cannot replace XFOLD heuristic score, i.e, \textit{information gain}, because
the latter tries to maximize the coverage of positive examples, while the
former only maximally discriminates between the positives and negatives. Nevertheless,
for the purpose of feature extraction among the negated literals which are
disallowed in XFOLD algorithm, MCC can be applied quite effectively. For that matter,
before running XFOLD algorithm, the MCC score of all candidate literals are
computed. If a predicate scores ``close" to +1, the predicate itself is added
to the language bias. If it scores ``close" to -1, its negation is
added to the language bias. For
example, in case of learning \texttt{red(X)}, after running the feature
extraction on the graph given in Figure \ref{tab:graph-coloring}, XFOLD computes
the scores -0.7, -0.5 for \texttt{green(X)} and \texttt{blue(X)}, respectively.
Therefore, \texttt{\{not green(X),not blue(X)\}} are appended to the list of
candidate predicates. Now, after running the XFOLD algorithm, after two
iterations of the inner loop, it would produce the following rule:
\begin{center}
\begin{tabular}{c}
\texttt{red(X) :- not green(X), not blue(X).}
\end{tabular}
\end{center}
Corresponding rules for \texttt{green(X)} and \texttt{blue(X)} are learned in a
similar manner. This essentially takes care of the \textit{generate} part of
the combinatorial algorithm. In order
to learn the \textit{test} part for graph coloring, we need the negative
examples shown in Figure \ref{tab:graph-coloring}. It should be noted that in
order to learn a constraint, we first learn a new target predicate which is the
negation of the original one. Then we shift the negated predicate from the head to the body
inverting its sign in the process. That is, we first learn a clause of the form
{\tt -T :- b$_1$, b$_2$ $\dots$ b$_n$.}
which is then transformed into the constraint:
{\tt :- b$_1$, b$_2$ $\dots$ b$_n$, T.}
Thus, the following steps should be taken to learn constraints from negative examples:
\begin{enumerate}
\item Add rule(s) induced for \textit{generate} part to B.
\item $\forall e^+ \in E^+, e^- \in E^-$, if $e^-_{inc} \subseteq
e^+_{inc}$:
\begin{itemize}
\item \textbf{if} $e^-_{exc}$ is of the form (\texttt{not
$p(V_1,...V_m)$}) \textbf{then} $e^+_{inc} \leftarrow e^+_{inc} \cup \{
-p(V_1,...V_m)\}$
\item \textbf{else} $e^+_{exc } \leftarrow e^+_{exc} \cup \{
-p(V_1,...V_m)\}$
\end{itemize}
\item compute the contrapositive form of the rule(s) learned in
\textit{generate} part and remove the body predicates from the list of
candidate predicates
\item run FOLD to learn \texttt{\-p}
\item shift \texttt{-p} from the head to the body for each rule returned
by FOLD
\end{enumerate}
The contrapositive of a statement has its antecedent and consequent inverted
and flipped. For instance, the contrapositive of the clause \texttt{\{red(X) :-
not green(X), not blue(X)\}} is shown in Figure \ref{tab:contrapositive}.
\begin{algorithm}
\caption{Overview of the XFOLD algorithm}
\label{algo:xfold}
\begin{algorithmic}[1]
\Input $ L = \langle M_h, M_b \rangle,B,E^+,E^-$
\Output Hypothesis H \\
\% - \textbf{Induction of ``generate" part} - \%
\State Initialize $H \gets \emptyset $
\State \textbf{let} f be new features discovered by running each $ l \in L$ and measuring MCC
\State $L \leftarrow L \cup f$
\ForEach{$t \in M_h$}
\State $h_t \leftarrow $ FOLD $ \langle B,L,E^+_{inc},E^+_{exc},t\rangle $
\State $H \leftarrow H \cup h_t$
\EndFor
\State $B \leftarrow B \cup H$\\
\% - \textbf{Induction of ``test" part} - \%
\ForEach{$t \in M_h$}
\ForEach{ $e^+ \in E^+,e^- \in E^-$}
\If{$e^-_{inc} \subseteq e^+_{inc}$}
\If{$e^-_{exc}$ is of the form \texttt{not t($V_1,...,V_m$)}}
\State $e^+_{inc} \leftarrow e^+_{inc} \cup $ \{\texttt{-t($V_1,...,V_m$)}\}
\Else
\State $e^+_{exc } \leftarrow e^+_{exc} \cup$ \{\texttt{-t($V_1,...,V_m$)}\}
\EndIf
\EndIf
\EndFor
\EndFor
\State compute the contrapositive form for each $h \in H$ in \textit{generate} part and remove the body predicates from the list of candidate predicates $L$
\ForEach{$t \in M_h$}
\State $h_t \leftarrow $ FOLD $\langle B,L,E^+_{inc},E^+_{exc},-t\rangle $
\State shift -t from the head to the body to get a constraint $\hat{h_t}$
\State $ H \leftarrow H \cup \{ \hat{h_t} \}$
\EndFor
\end{algorithmic}
\end{algorithm}
\begin{figure}[]
\centering
\begin{tabular}{l}
\texttt{-red(X) :- green(X).}\\
\texttt{-red(X) :- blue(X).}
\end{tabular}
\caption{Contrapositive for ``generate" rule in graph-coloring}
\label{tab:contrapositive}
\end{figure}
The reason why step 3 is necessary is the following: running FOLD without eliminating
the literals in contrapositive rule results in learning trivial clauses shown
in Figure \ref{tab:contrapositive}. However, as soon as those trivial choices
are removed from search space, FOLD algorithm comes up with the next best
hypothesis which is as follows:
\begin{center}
\begin{tabular}{l}
\texttt{-red(X) :- edge(X,Y), red(Y).}
\end{tabular}
\end{center}
Shifting the predicate \texttt{-red(X)} to the body yields the following
constraint:
\begin{center}
\begin{tabular}{l}
\texttt{:- red(X), edge(X,Y), red(Y).}
\end{tabular}
\end{center}
In graph coloring problem, $M_h$ = \texttt{\{red(X), green(X), blue(X)\}}. Once
similar examples for \texttt{green(X)} and \texttt{blue(X)} are provided, XFOLD
is able to learn the complete solution as shown in Figure
\ref{tab:full-graph-coloring-theory}. Algorithm \ref{algo:xfold}, presents a high level view of XFOLD to induce a \textit{generate and test} hypothesis.
\begin{figure}[]
\centering
\begin{tabular}{l}
\texttt{ red(X) :- not green(X), not blue(X).}\\
\texttt{ green(X) :- not blue(X), not red(X).}\\
\texttt{ blue(X) :- not green(X), not red(X).}\\
\texttt{:- red(X), edge(X,Y), red(Y).} \\
\texttt{:- blue(X), edge(X,Y), blue(Y).} \\
\texttt{:- green(X), edge(X,Y), green(Y).}
\end{tabular}
\caption{Full graph-coloring ASP theory learned by FOLD algorithm}
\label{tab:full-graph-coloring-theory}
\end{figure}
\begin{exmp}
\label{ex:chess}
Next we discuss learning the answer set program for the
4-queen problem: the following items are assumed: Background knowledge $B$
including predicates describing a $4 \times 4$ board, rules describing
different ways through which two queens attack each other and examples of the
following form:
\begin{center}
\begin{tabular}{ll}
B: &
\texttt{attack\_r($R_1$,$C_1$,$R_2$,$C_2$):-q($R_1$,$C_1$),q($R_2$,$C_2$),$C_1
!= C_2$, $R_1 = R_2$.} \\
&
\texttt{attack\_c($R_1$,$C_1$,$R_2$,$C_2$):-q($R_1$,$C_1$),q($R_2$,$C_2$),$R_1
!= R_2$, $C_1 = C_2$.} \\
&
\texttt{attack\_d($R_1$,$C_1$,$R_2$,$C_2$):-q($R_1$,$C_1$),q($R_2$,$C_2$),$R_1!=
R_2$,$R_1-C_1=R_2-C_2$.}\\
&
\texttt{attack\_d($R_1$,$C_1$,$R_2$,$C_2$):-q($R_1$,$C_1$),q($R_2$,$C_2$),$R_1!=
R_2$,$R_1+C_1=R_2+C_2$.}\\
\hline
E: & $E^+_1 = \{\langle q(2,1),q(4,2),q(1,3),q(3,4)\rangle , \langle
q(1,1),q(1,2),...,q(4,4)\rangle \}$\\
& ... \\
& $E^-_1 = \{\langle q(2,1) \rangle , \langle not\ q(2,2)\rangle \}$ \\
& $E^-_2 = \{\langle q(2,1) \rangle , \langle not\ q(2,3)\rangle \}$ \\
& $E^-_3 = \{\langle q(4,2) \rangle , \langle not\ q(1,2)\rangle \}$ \\
& $E^-_4 = \{\langle q(4,2) \rangle , \langle not\ q(2,3)\rangle \}$
\end{tabular}
\end{center}
\end{exmp}
As far as the \textit{generate} part concerns, XFOLD algorithm would learn the
following program:
\begin{center}
\begin{tabular}{l}
\texttt{q(X,Y) :- not -q(X,Y).}\\
\texttt{-q(X,Y) :- not q(X,Y).}
\end{tabular}
\end{center}
The predicate \text{-q(X,Y)} is introduced by XFOLD algorithm as a result of
swapping the examples and calling itself recursively. After computing the contrapositive
form, \texttt{q(X,Y), -q(X,Y)} are removed from the list of candidate
predicates. Then based on the examples provided in Example \ref{ex:chess}, XFOLD
would learn the following rules:
\begin{center}
\begin{tabular}{l}
\texttt{-q($V_1$,$V_2$) :- attack\_r($V_1$,$V_2$,$V_3$,$V_4$).}\\
\texttt{-q($V_1$,$V_2$) :- attack\_c($V_1$,$V_2$,$V_3$,$V_4$).}\\
\texttt{-q($V_1$,$V_2$) :- attack\_d($V_1$,$V_2$,$V_3$,$V_4$).}
\end{tabular}
\end{center}
After shifting the predicate \texttt{-q($V_1$,$V_2$)} to the body, we get the
following constraint:
\begin{center}
\begin{tabular}{l}
\texttt{:- q($V_1$,$V_2$), attack\_r($V_1$,$V_2$,$V_3$,$V_4$).}\\
\texttt{:- q($V_1$,$V_2$), attack\_c($V_1$,$V_2$,$V_3$,$V_4$).}\\
\texttt{:- q($V_1$,$V_2$), attack\_d($V_1$,$V_2$,$V_3$,$V_4$).}
\end{tabular}
\end{center}
It should be noted that, since XFOLD is a sequential covering algorithm like
FOIL, it takes three iterations before it can cover all examples which in turn
becomes three constraints as shown above.
\section{Related Work}
\label{sec:related}
Many researchers have tried to extend Horn ILP into richer non-monotonic logic formalisms.
``Stable ILP" \cite{stableilp} was the first effort to explore the expressiveness of
background knowledge with multiple stable models. A survey of extending Horn clause based ILP to
non-monotonic logics can be found in \cite{sakama05}. In this paper Sakama also introduces algorithms to learn from the answer
set of a categorical logic program. The algorithms learn from positive and negative
examples separately and the approach also leads to redundant literals in the body of the
induced clause as shown by Example \ref{sakama-issues}.
\begin{exmp}
Consider the following background knowledge and positive example:
\label{sakama-issues}
\end{exmp}
\begin{center}
\begin{tabular}{rll}
$B:$ & \texttt{bird(X) :- penguin(X).} & \\
& \texttt{bird(tweety).} & \texttt{bird(et).} \\
& \texttt{bear(teddy).} & \texttt{penguin(polly).} \\
& \texttt{cat(kitty).} & \\
$E^+:$& \texttt{fly(tweety).} &
\end{tabular}
\end{center}
Sakama's algorithm would induce the following clause:
\begin{center}
\begin{tabular}{l}
\texttt{fly(X) :- bird(X), not cat(X), not penguin(X), not bear(X).}
\end{tabular}
\end{center}
The literals \texttt{not cat(X), not bear(X)} are redundant.
The \textit{brave} induction framework \cite{brave}, although capable of learning ASP
programs, only admits one positive example in the form of conjunction of literals.
As we discussed, many problems, including programs for solving combinatorial problems,
cannot be expressed without having a notion of a negative example. ILASP \cite{ILASP},
introduces a framework that would allow to
induce a hypothesis from multiple positive examples {\it bravely} (i.e., it uses brave induction),
while it would exclude negative examples cautiously (i.e., it uses cautious induction).
However, due to performing an exhaustive search on its predetermined language
bias, ILASP is unable to scale up to large datasets or noisy datasets. It is not able to induce
default theories with nested, or composite abnormality predicates to capture exceptions
as shown in Example \ref{ilasp-issues}.
\begin{exmp}
\label{ilasp-issues}
A default theory with abnormality predicate represented as conjunction of two other predicates, namely \texttt{s(X) and r(X)}.
\end{exmp}
\begin{center}
\begin{tabular}{l}
\texttt{p(X) :- q(X), not ab(X).}\\
\texttt{ab(X) :- s(X), r(X).}
\end{tabular}
\end{center}
XHAIL \cite{XHAIL} is an ILP system capable of learning non-monotonic
logic programs. It relies heavily on abductive reasoning incorporated
in a three-stage algorithm. It does not support inducing from multiple partial answer sets.
\section{Conclusion and Future Work}
\label{sec:conclusion}
In this paper we presented the first heuristic-based algorithm to inductively
learn normal logic programs with multiple stable models. The advantage of this
work over similar ILP systems such as ILASP \cite{ILASP} is that unlike these systems,
XFOLD does not perform an exhaustive search to discover the ``best" hypothesis.
XFOLD adopts a greedy approach,
guided by heuristics, that is scalable and noise resilient. Also, learning knowledge
patterns in terms of defaults and exceptions produces more natural and intuitive results
that correspond to common sense reasoning employed by humans.
We also showed how our algorithm could be
applied to induce declarative logic programs that follow the \textit{generate and
test} paradigm for finding solutions to combinatorial problems such as graph-coloring and N-queens.
Our XFOLD algorithm has a number of novel features absent in other prior works:
(i) it performs a heuristic search for learning hypothesis rather than an exhaustive search
and thus is considerably more scalable; (ii) it admits predicate invention allowing us
to learn a broader class of answer set programs that cannot be learned by other systems such
as ASPAL, ILASP, and XHAIL; (iii) because of swapping of positive and negative examples,
XFOLD is able to distinguish between exceptions and noise, producing more succinct hypotheses.
There are two main avenues for future work: (i) handling large datasets
using methods similar to QuickFoil \cite{quickfoil}. In QuickFoil, all the operations of
FOIL are performed in a database engine. Such an implementation, along with pruning techniques and query
optimization tricks can make the XFOLD training much faster; (ii) XFOLD learns function-free answer set programs.
We plan to investigate extending the language bias towards accommodating functions.
\begin{acknowledgements}
Authors are partially supported by NSF Grant IIS 1718945.
\end{acknowledgements}
\bibliographystyle{spbasic}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 3,485 |
Reviews / Publisher / HarperCollins
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"redpajama_set_name": "RedPajamaCommonCrawl"
} | 971 |
- fix done async callback
- remove folder clean, use grunt-contrib-clean instead
## v0.1.0
- Not tested
- woff and woff2 format only
- Ouput folder is not setted via Gruntfile
- Output folder is completely deleted (./build/fonts, ./build/styles)
- @TODO Downloaded fonts must be in a font-family sub folder
| {
"redpajama_set_name": "RedPajamaGithub"
} | 4,794 |
Essa é uma lista de futebolistas da Associação Chapecoense de Futebol.
Elencos por ano
Temporada de 2016
Elenco
Última atualização: 3 de junho de 2016.
Transferências 2016
: Jogadores que chegaram ou saíram por empréstimo
: Jogadores que chegaram ou saíram após serem emprestados
: Jogadores que chegaram ou saíram sem custos
Jogadores que subiram das categorias de base
: Jogadores que chegaram ou saíram após compra de direitos/multa rescisória
: Jogadores que saíram após o fim do contrato
: Jogadores que saíram após terem seus contratos rescindidos
|}
|}
Elenco
Última atualização: 7 de dezembro de 2017.
<noinclude>
Transferências 2017
: Jogadores que chegaram ou saíram por empréstimo
: Jogadores que chegaram ou saíram após serem emprestados
: Jogadores que chegaram ou saíram sem custos
Jogadores que subiram das categorias de base
: Jogadores que chegaram ou saíram após compra de direitos/multa rescisória
: Jogadores que saíram após o fim do contrato
: Jogadores que saíram após terem seus contratos rescindidos
|}
|}
Temporada de 2018
Elenco
Última atualização: 3 de dezembro de 2018.
Transferências 2018
: Jogadores que chegaram ou saíram por empréstimo
: Jogadores que chegaram ou saíram após serem emprestados
: Jogadores que chegaram ou saíram sem custos
Jogadores que subiram das categorias de base
: Jogadores que chegaram ou saíram após compra de direitos/multa rescisória
: Jogadores que saíram após o fim do contrato
: Jogadores que saíram após terem seus contratos rescindidos
|}
Temporada de 2019
Elenco
Última atualização: 8 de março de 2019.
<noinclude>
Transferências 2019
: Jogadores emprestados a Chapecoense
: Jogadores emprestados pela Chapecoense
: Jogadores que retornam de empréstimo
: Jogadores que chegaram ou saíram após compra de direitos
: Jogadores que chegaram ou saíram sem custos
: Jogadores que chegaram ou saíram após terem seus contratos rescindidos
|}
{|
|width=1% valign=top |
|width=1% valign=top |
Estatísticas
Artilheiros
Estes são os maiores artilheiros da história da Chapecoense:
Partidas
Estes são os jogadores que mais vezes defenderam as cores da Chapecoense:
Estrangeiros
Abaixo estão listados os jogadores de origem estrangeira que já atuaram pela Chapecoense:
Chapecoense
Associação Chapecoense de Futebol | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 1,175 |
Add a lovely glow to your wedding decorations with this Copper Wire LED Mini Light Strand. Wind it among greenery and flowers in a centerpiece, use it to edge a table or arrange it in the shape of a heart behind where the newlyweds will sit at the wedding reception. Get a bunch and really make your love glow throughout the reception venue! Includes on/off switch. Plastic. 33 ft. Requires 6 "AA" batteries, not included. | {
"redpajama_set_name": "RedPajamaC4"
} | 6,073 |
module Casein
module ConfigHelper
# Name of website or client — used throughout Casein.
def casein_config_website_name
'OD4D Network'
end
# Filename of logo image. Ideally, it should be a transparent PNG around 140x30px
def casein_config_logo
'logo-od4d2.png'
end
# The server hostname where Casein will run
def casein_config_hostname
if Rails.env.production?
'http://platform.od4d.org'
else
'http://0.0.0.0:3000'
end
end
# The sender address used for email notifications
def casein_config_email_from_address
'donotreply@od4d.org'
end
# The initial page the user is shown after they sign in or click the logo. Probably this should be set to the first tab.
# Do not point this at casein/index!
def casein_config_dashboard_url
url_for :controller => :posts, :action => :index
end
# A list of stylesheets to include. Do not remove the core casein/casein, but you can change the load order, if required.
def casein_config_stylesheet_includes
%w[casein/casein casein/custom]
end
# A list of JavaScript files to include. Do not remove the core casein/casein, but you can change the load order, if required.
def casein_config_javascript_includes
%w[casein/casein casein/custom]
end
end
end
| {
"redpajama_set_name": "RedPajamaGithub"
} | 8,215 |
<?php
namespace Rentlio\Api\Request;
/**
* Class ListAllUnitTypesRequest
* @package Rentlio\Api\Request
*
* GET Request for listing all unit types (rooms types) for specific property (hotel)
* https://docs.rentl.io/#unit-types-list-all-unit-types
*/
class ListAllUnitTypesRequest extends AbstractRequest
{
public function __construct($id)
{
parent::__construct("GET", "/properties/" . $id . "/unit-types");
}
/**
* @return array
*/
public function getQueryParams()
{
return [];
}
} | {
"redpajama_set_name": "RedPajamaGithub"
} | 3,204 |
New York and Port Alegre are poles apart – but they both played host to important conferences on the future of globalisation over the summer.
Tolkien's epic tale provides a timely reminder that that there are forces of good and evil in the world – and that they are not necessarily where we expect to find them, writes Michael Gadiel.
Mad Monk Sides With Angels … Briefly
By Terry Bell *
President Thabo Mbeki
A tale of two cities, heavy with irony and laden with symbolism, was played out over the summer. One of its more interesting features was the attendance of two prominent South Africans.
Their presence at the respective venues summarises quite well the main ideological and policy debates in the globalising world of today. President Thabo Mbeki attended the World Economic Forum (WEF) in New York; while Cosatu president, Willie Madisha, was at the World Social Forum (WSF) in Porto Alegre, Brazil.
New York is, of course, the brash capital of rampant capitalism; Porto Alegre the centre of the rapidly growing movement against "corporate-driven globalisation".
The WEF was founded privately in Davos, Switzerland as a discussion and lobbying forum for the world's top industrialists and financiers. On an annual basis, they wine, dine and woo the leaders of governments around the world.
The WSF was set up two years ago in direct response to the WEF. It draws together a much larger, more diverse and often fractious group of delegates than the WEF and is committed to the idea of an "alternative" to the present world economic order. Although made up of a variety of ideological strains, the WSF tends to be united in condemning the WEF as an "elitist, rich old boys' club". This "Davos club" is seen as arrogant and authoritarian, even dangerous to the future security of the bulk of the world's population.
But for all the often fiery rhetoric, this thrust from Brazil is not so much revolutionary as reformist; a case of Maynard Keynes versus Milton Friedman; of interventionism versus the anarchy of the market.
At Porto Alegre, the names and ideas of Mao, Trotsky, Lenin and Marx may hover on the fringes, but the centre stage will be held by the likes of Noam Chomsky, an incisive analyst and radical reformer. His opposite number in New York will be seen in the likes of the currency speculating billionaire philanthropist, George Soros.
The two highest profile South African representatives to stride these two stages were Mbeki and Madisha. Mbeki was in New York talking investment and the extolling the virtues of South Africa's liberal macro-economic regime. Madisha was in Porto Alegre, extolling the possibility of "another world" and building links with the large and historically militant trade union federation, CUT.
This was particularly easy to do in Porto Alegre, capital of the province of Rio Grande do Sul, since both are governed by the CUT-supported Workers' Party (PT). But there was some apparent common ground between the two gatherings.
Both tended to agree that increasing poverty and the social and political ramifications of this, amount to the biggest problem facing the world today. Both also tended to agree that the world has a surplus of almost every basic necessity. The parting of the ways comes with the ideas for how to deal with this situation.
This is our own macro-economic battle on an international plane; GEAR (growth employment and redistribution) versus the social equity orientation supported by the trade unions.
The arguments about the need for still greater growth and higher productivity in order to encourage a greater trickle down of wealth should once again emanate from the corridors of the WEF. From the WSF should come freshly packaged versions of the need to redistribute existing wealth in order to encourage equitable growth.
At a fundamental level, these points of departure are impossible to reconcile. So for all the recent murmurings of toenadering between government and Cosatu nothing much appears to have changed. Despite the unions being under the whip of recession and economic restructuring, their battle continues, only becoming more clearly international.
Even the South-South "trade butterfly" touted by the department of trade and industry is now in the process of having a mirror trade union structure created. This "butterfly" concept advanced the notion of increased trade and investment between South Africa ‹ the "body" extending northwards into Africa ‹Asia and South America. Brazil would be key to the "wing" in the west, India and South Korea to the east.
Madisha's talks with CUT were part of a process begun recently, which should see Cosatu working much more closely with the Brazilian unions and with the presently embattled and highly militant unions of South Korea. A "solidarity butterfly" seems in the making. Perhaps it will be another metaphorical butterfly that stings like a bee.
Terry Bell is a Cape Town-based freelance writer, columnist and editor, banned and in exile from South Africa for 27 years. A trade unionist, socialist and former political detainee, has written the syndicated "Inside Labour" column since 1996.
An early editor of Anti-Apartheid News in Britain, keynote speaker at the inaugural conference of the NZ Anti-Apartheid Movement, NZ Peace Squadron activist, founder-principal of the primary division of the Somafco school for SA exiles in Tanzania, and co-ordinator of the international "Friends of Moses Mayekiso" campaign.
Author of the recently published "Unfinished Business - South Africa, apartheid & truth" written in collaboration with leading SA human rights lawyer and former Truth and Reconciliation Commission investigations unit head, Dumisa Ntsebeza.
John Pilger has said of this book: "...a brilliant, important book that should be read by everybody interested in the truth behind the 'truth and reconciliation' hype of the new South Africa...reveals the cover-ups and charades that allowed the shock troops of apartheid to get away with a crime against humanity."
Unfinished Business may be ordered through this e-mail address - [email protected] wn.apc.org - by fax (below) or from P. O. Box 373, Muizenberg 7950, South Africa.
Payment may be via transmission to: T. Bell, Nedbank, Salt River, Cape Town; account number 2021 325385 (please fax/e-mail details of such payments) or by crossed cheque to T. Bell.
PS: we are using any income from the book to finance Understanding Our Past, an attempt to uncover as much hidden apartheid history as we can.
-Tel: +27 +21 +788 9699
Fax: +27 +21 +788 9711-
More South African news
URL: http://workers.labor.net.au/124/c_historicalfeature_wef.html | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 8,013 |
ACCLAIM FOR _SOUL'S GATE_
"Truly a story about freedom from things that we hold on to, this tale will captivate readers and encourage a more active, dynamic spiritual life."
— _RT B OOK REVIEWS_, TOP PICK
"[A] spiritual-warfare thriller that brilliantly takes four perfectly normal people . . . on a journey that begins with skepticism and ends up in places they could never have imagined or predicted."
— _CBA R ETAILERS \+ RESOURCES_
"Readers with high blood pressure or heart conditions be warned: this is a seriously heart-thumping and satisfying read that goes to the edge, jumps off, and 'builds wings on the way down.' "
— _P UBLISHERS WEEKLY_
"Powerful storytelling. Rubart writes with a depth of understanding about a realm most of us never investigate, let alone delve into. A deep and mystical journey that will leave you thinking long after you finish the book."
—TED DEKKER, _N EW YORK TIMES_ BEST-SELLING AUTHOR OF THE CIRCLE SERIES AND _F ORBIDDEN_ (WITH TOSCA LEE)
"Tight, boiled-down writing and an intriguing premise that will make you reconsider what you think you know about the spiritual realm."
—STEVEN JAMES, NATIONAL BEST-SELLING AUTHOR OF _P LACEBO_ AND _O PENING MOVES_
_"Soul's Gate_ takes readers on a wild flight of fantasy into the spiritual realm, where we find the battle for our souls is even wilder than we imagined—and very, very real. With vividly drawn characters, startling imagery, and the power of a spiritual air-raid siren, the story is at once entertaining and breathtakingly enlightening. James L. Rubart has crafted a stunning piece of work, a call to arms for everyone who yearns for the freedom of the abundant life Christ promises us—and is willing to fight for it. Rubart knocks it out of the park with this one."
—ROBERT LIPARULO, AUTHOR OF _T HE 13TH TRIBE_ AND _C OMES A HORSEMAN_
"Don't read this unless you're ready to see with new eyes. Through evocative prose and masterful storytelling, Rubart transports you to the spiritual realm—a realm of vision, mystery, healing and power. A deep and thoughtful—and jet-propelled—spiritual journey of a book."
—TOSCA LEE, _N EW YORK TIMES_ BEST-SELLING AUTHOR OF THE BOOKS OF MORTALS SERIES WITH TED DEKKER AND _D EMON: A MEMOIR_
"This book is provocative . . . It forces the reader to consider components of God's nature not normally focused on."
— _C HURCH LIBRARIES_
ALSO BY JAMES L. RUBART
The Well Spring Series
_Soul's Gate_
_Memory's Door_
_Rooms_
_Book of Days_
_The Chair_
© 2014 by James L. Rubart
All rights reserved. No portion of this book may be reproduced, stored in a retrieval system, or transmitted in any form or by any means—electronic, mechanical, photocopy, recording, scanning, or other—except for brief quotations in critical reviews or articles, without the prior written permission of the publisher.
Published in Nashville, Tennessee, by Thomas Nelson. Thomas Nelson is a registered trademark of HarperCollins Christian Publishing, Inc.
The author is represented by the literary agency of Alive Communications, Inc., 7680 Goddard Street, Suite 200, Colorado Springs, CO 80920. www.alivecommunications.com.
Thomas Nelson, Inc., titles may be purchased in bulk for educational, business, fund-raising, or sales promotional use. For information, please e-mail SpecialMarkets@ThomasNelson.com.
Publisher's Note: This novel is a work of fiction. Names, characters, places, and incidents are either products of the author's imagination or used fictitiously. All characters are fictional, and any similarity to people living or dead is purely coincidental.
THE NEW KING JAMES VERSION. © 1982 by Thomas Nelson, Inc. Used by permission. All rights reserved.
Scriptures from THE HOLY BIBLE, NEW INTERNATIONAL VERSION®, NIV® Copyright © 1973, 1978, 1984, 2011 by Biblica, Inc.® Used by permission. All rights reserved worldwide. NEW AMERICAN STANDARD BIBLE®, © The Lockman Foundation 1960, 1962, 1963, 1968, 1971, 1972, 1973, 1975, 1977, 1995. Used by permission. Holman Christian Standard Bible®, Copyright © 1999, 2000, 2002, 2003, 2009 by Holman Bible Publishers. Used by permission. Holy Bible, New Living Translation. © 1996, 2004, 2007 by Tyndale House Foundation. Used by permission of Tyndale House Publishers, Inc., Carol Stream, Illinois 60188. All rights reserved.
ISBN 978-1-4016-8610-9 (eBook)
**Library of Congress Cataloging-in-Publication Data**
Rubart, James L.
Spirit bridge / James L. Rubart.
pages cm. -- (A Well Spring novel ; 3)
ISBN 978-1-4016-8609-3 (pbk.)
1. Paranormal fiction. 2. Magic--Fiction. I. Title.
PS3618.U2326S65 2014
813'.6--dc23
2013047137
_Printed in the United States of America_
14 15 16 17 18 19 RRD 6 5 4 3 2 1
FOR MOM, WHO TAUGHT ME TO DREAM AND SHOWED ME WHO I AM.
CONTENTS
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
FIFTY
FIFTY-ONE
FIFTY-TWO
FIFTY-THREE
FIFTY-FOUR
FIFTY-FIVE
FIFTY-SIX
FIFTY-SEVEN
FIFTY-EIGHT
FIFTY-NINE
SIXTY
SIXTY-ONE
AUTHOR'S NOTE
READING GROUP GUIDE
ACKNOWLEDGMENTS
ABOUT THE AUTHOR
_"Your real, new self . . . will not come as long as you are looking for it. It will come when you are looking for Him. Give up yourself, and you will find your real self. Lose your life and you will save it. Submit to death, death of your ambitions and favorite wishes every day and death of your whole body in the end: submit with every fiber of your being, and you will find eternal life."_
C.S. LEWIS, _M ERE CHRISTIANITY_
ONE
THE WELL-MANICURED FINGERS CURLED INTO A FIST AND slammed onto the stone table hard enough to rattle the glasses filled with a pale-blond liquid. It also served to focus the attention of the sixteen who sat around the table.
"You let him slip through your fingers like dust." Caustin uncurled his fingers and then clenched them together again as if kneading the hilt of the sword that hung on his hip. "If it were my choice, you would already be flayed and hanging above the pit."
Caustin pulled rapid breaths in and out as his gaze lasered in on Zennon.
"Calm." Caustin's master, who sat to the right, stretched out his fingers on the cool stone, but that was his only movement. "We will hear a response from the accused before you speak again."
"He is incorrect, my lord." Zennon gave a slight bow of his head, looked up again, shifted his gaze to Caustin, and refused to drop his stare even though the eyes of his superior held death in them. _Give in to intimidation? Never._
"I'm wrong?" Caustin leaned forward and his body quivered as if he was about to lunge across the round table and attack. "You have failed to destroy the Warriors Riding. Am I incorrect about that fact?"
"Yes. You are badly mistaken." Zennon bowed and kept his head down longer this time. _Play the game. Give the false respect this imbecile requires. Bide the time because it won't last forever._
In truth, the time to strike was almost here. If one more member of the council would turn, the moment would be seized and Caustin's head would be separated from his body for eternity. Then Zennon would stand next to the Master in his place. "He is a fool, my lord."
Caustin flicked his finger to the right and then the left. Instantly Zennon was yanked from his chair and his arms were pulled tight across his back. The soldiers in Zennon's command who sat to his right and left didn't move to help. He didn't expect them to.
Caustin pulled back slightly but still rested most of his weight on his knuckles, pressed hard on the stone table. "Normally I would slice your throat open for your expression of insubordination, but since the Master is willing to hear an explanation for your failure, I will allow you to speak."
They released Zennon and he returned to his chair. For that insult alone he would kill Caustin. Zennon seethed with rage, but he couldn't allow it to be seen. Not in front of the other warlords. Control was power. The slaying would come later. In private. Where he could savor Caustin's cries for mercy and watch him die slowly and in excruciating pain.
The Master still didn't move. "Review his actions." As the three words leached from his dark maw, they seemed to soak up the light in the room.
Caustin pointed at Zennon with a thin finger. "He was given dominion over Reece Roth, Dana Raine, Brandon Scott, and Marcus Amber. His assignment was simple. Take them out. Destroy their mission. Instead, they have thrived and continue to grow in influence around the globe. Yes, he destroyed Reece's eyes, but he now sees again, with a sight far more powerful than what he had before. Yes, he took out Brandon Scott's singing voice, but it is a minor victory."
Caustin pulled back from the table and paced behind the Master and the four warlords to his right and left. "Under his watch, the angel Tristan Barrow formed an alliance with the Warriors. Zennon knew Barrow before the leaving—he knew Barrow's power and what he was capable of—and yet Zennon was not able to take the precautions to stop it."
Zennon ground his teeth and forced restraint on himself.
"He infiltrated the life of Marcus Amber as a high school student but was discovered before any real damage was done. Then he tried to lure Marcus into an alternate reality and again was unsuccessful."
Caustin's voice rose. "Then a legion of underlings was obliterated when he tried to destroy Reece, Dana, and Brandon. The Wolf was destroyed instead. The talk-show host Carson Tanner has turned back to the narrow path and now is broadcasting a new message across the American continent. Poison seeping into ears of millions of followers of the Nazarene."
Caustin once again pointed at Zennon. "Finally, he allowed the magician to escape, which could decimate a crushing amount of what we have accomplished over the past hundred years if he remembers who he truly is."
The Master turned his malevolent gaze to Zennon. He blinked but refused to drop his eyes. "That Simon the magician no longer resides in the alternate realities is true, Master," Zennon said.
Caustin strode back to the table and slammed his fist down again. "I call for destruction of the accused."
Zennon shifted back in his chair, pulled his gold coin out of his pocket, and spun it on the table. The light from the candles seemed to soak into its surface, making it thicker, and the sound of the coin rang off the table with greater volume. "You see only inches into the lake, Caustin, while I see with great depth. This war is far from over."
Spittle formed in the corners of Caustin's mouth as he leaned forward. "Far from over? Again and again you have—"
"Enough, Caustin." Their Master's voice rumbled through the small council room. "You have spoken." He turned to Zennon and nodded.
"Fellow warriors." Zennon met the gaze of every council member at the table, then pointed to Caustin. "You've heard the words of this fool. You've feasted on his accusations—I see it in your eyes. You salivate for my demise. But it will not come. I have not lost. These minor setbacks will only serve to pave the road of my ultimate victory."
For the first time, a shard of doubt passed over Caustin's face and hesitation wavered in his voice. "What do you feel you've—?"
"Feel! This is not about feelings, is it? It's about facts." Zennon raised his fist and slammed it onto the table in the exact manner Caustin had at the start of the council. Again the glasses rattled, but this time the one in front of Caustin tipped over and spilled its yellow liquid over the edge of the table.
"See?" Zennon smiled. "I can be as childish as you."
The demon didn't move as the liquid spilled onto his lap. "I will kill you."
Zennon's show of defiance riveted every eye in the room on him. Now to finish strong. "The Warriors Riding have attained certain victories, but when is an enemy most vulnerable? When they are tipping back the elixir of conquest and are drunk on the wine of their inflated belief in the loss their opponent has suffered. While they have been focusing on the chess piece right in front of them, I have been planning my moves far into the future."
Zennon turned and spoke to the Master. "I caused Simon the magician to leave the alternate reality. And now, because of what he did for Marcus Amber and the other Warriors, they will fully inculcate him into their inner circle. They will trust him. Embrace him." Zennon flipped the coin into the air, let it land on his palm, and slid it back into his front pocket. "I foresee him being invited to Well Spring where he will change everything in my favor."
"Explain." The Master's voice grew louder, and Zennon knew he must not waste words.
"As I just said, the magician did not escape. I let him go. And while the first phase of my plan with him and the Warriors was thwarted and certain casualties occurred, the second phase is now in place, which will bring about a triumphant conclusion to this war."
Zennon stood and leaned forward on the table, his palms spread wide. "If we are to achieve a resounding victory, it is not enough to destroy Reece and the other members of his band. Their message has spread too far. Killing him would only serve to make him a martyr and rally the millions around the world who look to him for sustenance. They follow Reece. He is their guide. They listen to him. Hundreds of thousands now drink from his stream."
"Continue," the Master said.
"We must change Reece Roth at his core. Blind him spiritually. Help him forget his identity as I did to the magician. Cause what resides inside Simon to spread to all of the Warriors and beyond them."
"Simon has been infiltrated." The faintest hint of a smile appeared in the Master's eyes.
"Yes. He carries the warfare inside. But he has no idea. No one does." Zennon bowed, smiled, and once more forced himself to hold his Master's gaze. "But Reece and his fellow Warriors are about to feel its effects when it is unleashed on them."
The Master ground his knuckles into the table. "And that will happen?"
"Very soon."
TWO
"WHEN WERE YOU GIVEN THIS?" REECE SAT IN HIS upstairs den on Thursday and gripped the armrest of the chair he sat in. So much for any kind of reprieve for the Warriors after the battle against the religious spirit seven days back. He took another drink of his late-morning tea. It was lukewarm but he didn't care.
"I received it yesterday afternoon," Doug Lundeen said.
"Interesting that it was sent to you just days before our first gathering after getting back from Well Spring."
"I agree. It is the Spirit's leading."
"If the words are true."
Doug didn't respond.
Reece shifted in his leather chair and breathed the mid-July air coming in through the open window that overlooked his lush Pacific Northwest backyard. "What if they're not ready to hear this?"
"I don't believe we have a choice."
"They've just been through an emotional Ironman triathlon." Reece rubbed the scar tissue where his eyes used to be with his thumb and forefinger.
"You've been through an emotional one as well, and my deep wish is that there was time to refresh and rest, but apparently there isn't."
"Read it again." Reece needed to hear it once more. Let the words soak in. Try to figure out what exactly each part of this new prophecy meant and how it would impact the Warriors Riding.
The rustle of paper filled Reece's ears and Doug cleared his throat.
WHEN IT IS TIME, YOU WILL JOIN THEM,
THE FOUR; THE TEMPLE, THE LEADER, THE TEACHER, AND THE SONG,
THEY WILL NEED YOUR STRENGTH FOR THEIR LAST BATTLE TOGETHER,
FOR THEIR GREAT ENEMY IS MOUNTING A FINAL STRIKE AGAINST THEM AND WILL HOLD NOTHING BACK,
AND YOU WILL STEP BOLDLY BEFORE THE TEMPLE AND HE WILL RECEIVE YOU,
AND YOU MUST TAKE THE LEADER INTO THE GATEWAY OF DEATH,
AND IN THE GATEWAY ONE WILL REMAIN, WHICH WILL BRING SORROW BUT SET IN MOTION THAT WHICH MUST BE,
AND YOU WILL EMBRACE THE TEACHER FOR HE IS THE FRIEND OF THE RESTORER,
AND ONE YOU WILL TRAIN WHEN THEY ASK IT OF YOU—AND ONLY THAT ONE WILL YOU TRAIN,
YOU ARE A WARRIOR OF WARRIORS, LIVE IN THE TRUTH OF WHO YOU ARE,
AND RIDE WITH THE WIND.
It made little more sense than the first two times Doug had read this new prophecy. Someone else join the Warriors? Why? When? For what purpose? "Who is the one the prophecy was given to?"
Doug sighed. "I already told you, they requested I not say."
"This is me, old friend."
A second later Doug patted Reece on the back. "Yes, yes, and you know I would tell you if I could. But this person was told by the one who gave the prophecy not to reveal any identities. It wasn't an option."
"You trust this person, the one the prophecy was spoken over?"
"As much as I trust you, Reece."
A small list of names raced through Reece's mind. Doug's closest allies. The ones he'd told Reece about and the ones Reece had met. But none of those men made sense to his mind or his heart. But since when did God's thinking mesh completely with man's?
"And you believe the prophecy is true," Reece said.
"Reportedly this person has sought wisdom and revelation from the Spirit as to the truth of these words for the past year, and they told me they are true. And I believe them."
Reece blew out a slow breath. "It doesn't take a genius to figure out the prophecy is talking about Zennon attacking us."
"Of course."
"The Leader in the gateway." Reece gripped the arm of his chair harder. "I will not allow Dana to die."
"No. We will not."
"And who is this 'restorer'? Brandon?"
"That is not clear, is it?" Doug sighed. "What do you see as our next steps?"
"We send out an e-mail to the Warriors about tomorrow night. Tell them we have an announcement, to be praying about it, and leave it at that."
"Agreed."
Reece let his head ease down till it rested on the back of the chair. They weren't ready to hear about another battle, let alone engage in one where Zennon came after them with everything left in his arsenal. What they were ready for—what they'd most certainly earned—was rest. Refreshment from each other's company. But it seemed a dead-end sign had been placed at the end of that road, and the one the Spirit was taking them down instead was peppered with land mines.
THREE
"ANY GUESS AS TO WHAT THE ANNOUNCEMENT IS REECE and Doug have in store for us?" Dana brushed back her light-brown hair and looked at Marcus as she took a sip of her iced tea. They sat in overstuffed chairs in the great room of Reece's log cabin-style home on the outskirts of Seattle. She loved his home almost as much as she loved Reece's private ranch in Colorado: Well Spring.
Marcus sat straighter and pushed up his glasses. "My fervent hope is he announces that our battles together for the kingdom have reached their conclusion. That it's time to retire Warriors Riding, he has commenced construction on a private luxury compound on the north side of Fiji with all the money he acquired selling his photography business, and he's sending Kat and Abbie and Jayla and me there to live in paradise for the rest of our lives."
Dana crossed her legs and smiled at the professor's humor. "I think there's a greater chance that a wormhole will open up in Reece's kitchen over there and we'll all take a trip to the far side of the universe."
"All things are possible with a Creator such as ours, and there is a substantial amount of evidence that wormholes could be around every corner." Doug ambled into the living room from the kitchen. He carried a glass of ice water in one hand and a notepad in the other.
"You have to know what he's going to tell us, Doug," Dana said.
"Yes, I do." Doug settled into the leather couch across from Marcus and her.
Marcus pointed at Doug's notepad. "Would you like to give us a preview before Reece comes down and Brandon arrives?"
"Yes, I would." Doug smiled. "But I'm not going to. You all need to hear this at the same time."
"Okay." Dana clapped her hands together. "Then at least answer a question I've been dying to know the answer to ever since Reece first trained us."
Doug cocked his head.
"Reece trained the Warriors. You trained Reece. Who trained you?"
"Did you know Reece has asked me the same question a number of times?" Doug rubbed his knuckles. "I'm afraid I can't tell you, just as I have never told Reece. Not yet anyway. But things have transpired recently that make me think I will soon be able to. That a long missing piece of the puzzle will finally be restored to its rightful place. And when it is, I will be released to tell the story of the man who discipled me in ways he cannot imagine."
Dana studied Marcus's face. He looked tired, older than last time she'd seen him, and why wouldn't he? He was probably thinking the same thing about her. Their recent battle against the religious spirit had been triumphant, but also exhausting. Probably one reason Reece hadn't gathered the five of them together till now. She appreciated the break. It gave her the chance to get caught up on her work down at the radio station as well as take a few evenings around Puget Sound to exercise her love of photography.
At the same time, she'd missed being with the other Warriors the past eight days. And she wanted to see Brandon. She was worried about him. He'd gone hermit on them since they got back from Well Spring. No contributions to the group e-mail they were all part of. No every-other-day witty text messages to the group either.
Now they were together again as planned, but an ominous tone had been cast over the gathering because of Reece's cryptic e-mail: _When we meet, Doug and I must speak to you about what is coming next for us. It won't be easy to hear, but the Lord is our shield, always._
"In some ways it seems like years since we were at Well Spring together. In others it feels like we were there yesterday," Dana said.
"Time tends to accelerate as we grow older." Marcus drew a small circle in the air with his silver mechanical pencil.
"Do you mean time accelerates literally or figuratively?" Doug patted his slightly oversized stomach and gazed at Marcus.
"My reference was to the physiological sensation of time increasing its velocity as we accumulate more years."
"I love you, Marcus." Dana laughed. "Since Brandon isn't here to translate, allow me the honor. Do you mean we feel like time goes faster as we age?"
Marcus brushed back his thinning brown hair and smiled. "Certainly that would be one alternative way to my thought."
"I can relate, Dana." Doug sipped his ice water. "Since I'm pushing seventy-three now, days seem to fly by like months instead. By the time I reach 173 years of age, the days will seem like seconds."
"You're going to live that long?" Dana smiled at his sense of humor.
"Why not? People used to live far longer. Or maybe I won't die and will simply be carried to heaven as Enoch was."
"There is always the possibility you are Enoch." Marcus pushed up his glasses again.
"Yes, I suppose that is possible. But in this case not true." Doug leaned to the side and tapped Marcus on his kneecap. "Sometime we should chat about the literal acceleration of time. And its literal deceleration." Doug winked. "It's almost time for that lesson, I believe. So many more lessons to teach all of you before my time on earth is finished. Even many lessons for Reece."
Marcus stood and meandered over to the river-rock fireplace that dominated Reece's great room. He placed his hands behind his back and tapped his foot on the hardwood floor. "I'm quite familiar with the physics behind theoretical time travel, time compression, and acceleration."
"Oh, I know you are, Professor. But as you might have surmised, I'm not talking about theory."
Marcus smiled, stopped tapping his foot, and leaned forward. "Your next statement will likely be that we have the ability to do time manipulation ourselves."
"No, not us. But through the one who holds the universe in his palm, the one who is far beyond the reaches of time because he created it, to that I speak a resounding yes."
A voice sounded from above them. "There are things I don't know, old friend? Lessons I still need to learn?"
Reece stood at the top of the stairs looking down on them, as much as it was possible for a man to look whose eyes had been destroyed—not seeing as most did, but still seeing. The prophecy fulfilled. " _And for one, their vision will grow clear."_ A vision that allowed Reece to see into the spiritual realm, an ability to see outlines and shapes in the physical world.
"I trust you've all made yourselves comfortable?" Reece shifted on his six-foot-five-inch frame.
"Will Brandon be engaged with us this evening?" Marcus glanced at his watch.
Reece clomped down the stairs. "He said he would be."
Dana looked up. "Really? You spoke to him?"
"Only via e-mail." Reece eased toward Dana. "Come here, friend."
She rose and a smile broke out as Reece opened his arms. She loped over to him and buried herself in his massive arms. "Hi, Reece."
"It's good to see you, dear one. I know I said this back at Well Spring, but I have to say it again. You stood strong against Zennon and the spirit of religion when we were inside the spiritual realm. You were a light for Brandon and me as darkness closed in. You are truly the Leader. No father could be more proud of his daughter than I am of you."
Dana closed her eyes and pressed her head against Reece's chest. "Does that mean I can adopt you as my dad?"
"What? I thought the paperwork already went through." Reece released her and smiled. She squeezed his hands and sat back in her chair.
"When will my hug be bestowed?" Marcus asked.
"The moment I start thinking about you like a daughter." Reece grinned and then cleared his throat. "Now, has anyone else heard from the Song?"
"I have not," Marcus said with a grim look. "I left him three messages over the past eight days that have not been answered. And I stopped by his house but he wasn't home."
"I left him five." Dana sighed. "No response."
"I fear our friend is not doing well." Doug shook his head. "Reece and I tried to drop in on him too, and either he wasn't there or wasn't answering the door."
"Why do you say he's not doing well?" Dana asked.
"I've sensed it. I've heard the Spirit tell me that." Doug glanced at Marcus and her. "Haven't you?"
She nodded. He hadn't responded to her messages, but she attributed it to the inevitable struggle Brandon must be feeling after losing his voice during the battle with the demons and needing to work through it alone. But alone was rarely good.
Reece strolled into the kitchen, then returned a few minutes later with a tray of cheeses and crackers. For the next ten minutes the four of them caught up on how Marcus's physics classes were going at the University of Washington, Dana's latest highs and lows at the radio station, Reece's increased ability to see into the spiritual realm, and how Doug had put his home in Colorado Springs on the market.
"You're moving out here full-time?"
"For what's coming, I will need to be more accessible to all of you, I believe. I'm looking at houses in Woodinville, Bothell, and north Redmond. I'll be back and forth between here and the Springs every four or five days till I find a house, but yes, the Pacific Northwest will soon be my new home."
"Speaking of what's headed our direction, do we want to call Brandon—see if he's on his way?" Dana said.
Reece lifted the glass lid of his watch and touched the face. "Twenty minutes late. Usually it's only ten. Unlike you, Dana, who has probably never been late for anything in your life." Reece closed the lid of his watch and tapped it. "I'm going to assume he's not coming. So let's get started."
As his words faded, a light rap on the front door filled the great room. It had to be Brandon, even though Reece had told all of them many times that knocking was never required. That whenever they came over they should come right in. A second later the door opened and Brandon stepped through, then wiped his feet on the tan mat just inside the foyer. His face was dark. He wore jeans more torn than usual, and the T-shirt under his Windbreaker looked like its wrinkles had wrinkles.
He took off his coat and tossed it onto the coatrack next to the stairs. He ran his hands through his long dirty-blond hair and sighed.
If Marcus looked like he'd aged a year in the past month, Brandon seemed like he'd aged ten. His thick hair was matted and circles had grown under his eyes. Looked like he hadn't showered in at least three days. Even if he had, no razor had touched his face in at least six—the last time he shaved might have been at Well Spring. Dana didn't need spiritual discernment to know Brandon was tanking.
"Did I miss the party?" Brandon opened his hands and bobbed his head from side to side.
"No." Reece's face was hard. "We were just about to get out the hats."
"Fab. Let's get down tonight. Do a little dance and all that. My thirty-seventh birthday is gonna be here before you know it, so maybe we can wrap that into tonight's celebration as well."
"Are you sure you want to be here?" Reece's voice was low and devoid of emotion.
"Are you asking me to leave?" Brandon rasped out. His voice had improved, but not a great deal. It still sounded like he'd gargled gravel to start the day. "Why would I not want to be here?"
"You don't look so well."
"Really." Brandon narrowed his eyes. "And tell me, how would you know that, blind man?"
All sound was sucked out of the room. But if Brandon had hoped Reece would take the bait, he was disappointed.
"Because in the way I still can see, there is an evident sadness around you. And resignation. Among other things, such as your giving footholds to spirits that are not of the Light."
"Then you need glasses, Reece-O. I'm doing great. Faannnntastic. Couldn't be better. In fact, just knowing I'm a member of the illustrious Warriors Riding makes it a wonderful day. I mean, wow, if it weren't for you, I wouldn't be where I'm at right now."
Again Reece didn't respond to Brandon's jab.
"Why don't you take a seat, friend, and we'll get started."
Brandon stared at Reece, and Dana guessed what Reece saw in the spiritual realm was a spirit of bitterness swirling all around the singer. When she glanced at Marcus, he offered a raised eyebrow but nothing more. Doug held his palms up as if to say, "Peace."
Reece waited till Brandon settled into the overstuffed chair to the right of the fireplace. Then he stood, his legs slightly wider than shoulder width, and prayed for their time together. When he finished he spoke just above a whisper.
"Thank you all for coming on such short notice. My hope is that the past eight days have been a time of refreshment for you." He turned toward Brandon for a moment. "If they haven't been, then I pray tonight will be. We need each other, and I'm afraid in the coming days and weeks, we will need each other more than we ever have. We will need to rise up like we've never done before."
Brandon tapped his feet and clenched and unclenched his hands. He sucked in and puffed out shallow breaths. His gaze darted around the room as if looking for some type of rescue, but none was in sight. If Dana didn't know him as well as she did, she'd say he was having a panic attack.
"Yesterday Doug was sent a prophecy he read to me, and we have been praying over it ever since then. At this point, we both believe it is real. We've been listening to the Spirit, trying to understand precisely what is coming our direction. We must prepare—"
"I've had enough come at me for three lifetimes." Brandon snorted. "I'm done with having things come at me. It's time for a long sabbatical. I need some easy."
"I understand that feeling. I suspect we are all feeling that way to some degree. But in this war there is no neutral zone. No quarter. No time-outs, and this is not a game where we can leave the field. And this prophecy speaks of—"
"Oh my." Brandon wagged his head back and forth. "That's so poetic, Reece. I think I'll put it in a song and sing it for you out at the fire pit on a sunny Seattle evening. It's simply beautiful." Brandon mock slapped his forehead. "Oh, wait. Silly me. I won't be able to do that ever again."
Dana glared at Brandon. It had been a long time since she'd seen him like this. Unless someone at least appeared to take his side, the meeting would head over a cliff in seconds.
She fixed her gaze on him as she spoke. "I understand where Brandon is coming from. Even soldiers in war get to rest. They get furlough. They get to sleep and regroup. We've been through enough for this century and the next. We need a chance to get our strength back."
"I agree." Reece paced in front of the wicker chair in back of him. "We do need that. As I already said, it's what I hoped this past eight days would be for us. But I can see it has only served to exacerbate our fretfulness and give the enemy a chance to offer us lies we might be tempted to agree with that would undermine the ministry."
Reece was astute enough not to single out Brandon as the one displaying the greatest example of that stress.
"Can we get to the specifics of what precisely this prophecy says?" Marcus opened his journal and smoothed the page. "Because I believe the Spirit has told me some things about the coming days as well."
Reece and Doug turned to each other, and Dana had little doubt Reece was using his spiritual eyes to see some kind of answer from Doug. The big man turned after a few seconds and rubbed his hands together before speaking. "That we will face Zennon once more. That we will have to sacrifice—"
"That's it!" Brandon sprang to his feet and shot his fist into the air. "You're a winner because you've just said the secret magic word, Reece Roth! _Sacrifice_!" He spun toward Marcus. "Nicely done. Professor, I'm guessing you've heard the same thing as Reece and Snugly Dougly so you're also going to take home fabulous prizes that will make your life complete. Well, _sacrifice_ is the word that makes Brandon Scott say buh-bye, so glad I could be on the program, thanks for all the wonderful parting gifts, looking forward to the reunion show in about a trillion years."
Brandon strode to Reece's front door and yanked it open. "I'll send you a postcard and a jar of sand from the beach I'm headed to, along with my Warriors Riding membership card. In other words, I'm not coming on your trip to Well Spring in a couple of weeks, so you can give my space to someone else. I'm sure hundreds are pounding on the door in order to take my place and get their lives shoved into a shredder. And, Reece? Thanks for inviting me to this group in the first place and destroying me." He gave a salute and stepped through the door. "Have a great life, all of you. I'll be in touch in twenty years."
The front door slammed hard enough to shake the walls at the front of Reece's house, and after the sound faded, silence fell on the room like they were in a morgue.
After a minute, Doug turned to Reece. "Did you see that coming?"
"No. You?"
"It isn't a complete shock."
The big man turned to Marcus and Dana. "Were either of you surprised?"
Marcus shook his head. "As I indicated earlier, he has been unresponsive to my e-mails and phone calls, which caused a certain amount of trepidation inside me, but no, I didn't expect this."
"Dana? Any idea what's going on with him?"
"Isn't it obvious? Didn't you listen to what he said?" She stared at them and stopped herself just short of letting out an exasperated sigh. Men. Sometimes the thick matter between their temples resembled brains only in the most literal sense. "You don't understand the artist mentality, do you?"
She stared at Doug and Reece, and then focused her gaze on Marcus. "At least _you_ have to know poets and authors and musicians and painters and the like have a seventy percent greater chance of struggling with depression, right?"
She drew a breath through her teeth. "The highs are sky high and the lows are the deepest valleys for many, many artists. For them to be able to tap into the emotional depth you see in their novels, songs, and paintings, they have to be able to experience great sorrow along with great triumphs."
If her words had any impact on them, it wasn't evident from the blank looks on each of their faces. "Is this making any sense?"
"Go on," Reece said, and the others nodded.
"Here is Brandon Scott, one of the most successful Christian artists ever, who has sold millions and millions of albums and played in front of hundreds of thousands of people all over the world. Then _boom_ , his record label basically drops him and his manager and ex–best friend effectively slides into his spot in the world of music. But there's more. He's been told he's the Song, one of four members of a thirty-year-old prophecy, but then he sacrifices himself for me and his throat is almost destroyed, and odds are he'll never sing again.
"It would be wonderful if we were all able to get our entire worth and identity from being a child of the King, but it doesn't always work that way.
"Yes, Brandon was healed of a great deal of his feelings of worthlessness when he was given the name Maximus by the Spirit. But do you see the problem with that? He's been forced to throw down his sword entirely. What is he doing of worth in his mind right now? Last month during the battle, his singing was instrumental—no pun intended—in our victories over Zennon."
She turned to Marcus. "You're the one who broke the hold of the spirit of religion in the physical realm, which broke the hold in the spiritual. I'm the one who held out against the deception and led us away from the lie and into the truth that the Jesus-rider was really Zennon.
"You acted as the Teacher, Marcus, and will continue to. I acted as the Leader, and I pray I can serve well in that role. Reece, you can't help but be the Temple. The health and well-being of the Warriors rests greatly on you as we go on. But how will Brandon be the Song going forward?"
"Maybe he can sing in the spiritual realm in a way he can't in the physical," Marcus said.
"Maybe? What if he goes in and tries and it doesn't happen? What then? If he can't, it would be extremely easy for him to take on the mantle and name of Worthless once again."
Her words seemed to sober the men, and they stayed silent for a long time. When that silence was broken, it was Reece who did it.
"He must be the Song going forward. Do you remember me saying before the battle with Zennon and the religious spirit and their army of demons that the Spirit told me without Marcus we would be lost?" Reece paused. "That's why it was crucial we find him?"
"Yes," Dana said.
"The Spirit told me the same thing about the coming war, but this time the critical member of the team is Brandon. He must be the Song in ways none of us have imagined." Reece tapped a foot against his dark hardwood floor.
"That might be somewhat difficult with him in his current frame of mind," Marcus said.
"Clearly." Doug nodded.
"The difference is, I had no doubt Marcus would respond to the call once we rescued him from the cliff where Zennon tried to bury him in the alternate realities. With Brandon, I'm not so sure what he'll do. He obviously doesn't want to be rescued, let alone respond."
"So what do we do?" Dana said.
"He needs a one-on-one conversation." Reece stopped tapping his foot and tilted his head toward her. "With the one who has had Brandon inside their soul. The one who trusted Brandon more fully than any of us is the one he will most likely let inside, whatever is going on. The one he is still in love with."
Dana sighed and slumped back on the couch. Of course it needed to be her. Who else? "I'll call him in the morning. But don't say he's in love with me. And don't say, 'But it's true.' "
She wasn't ready to deal with that. Yes, Well Spring had stirred her heart again toward him. Yes, major sections of the wall between them had come down, but there were still so many bricks and rubble at the base of the wall that might never be cleared away. And most days she had little desire to crawl over them. But other days she did. Why did her emotions have to be so schizophrenic? Because something about Brandon still felt . . . off. And until it didn't, she would guard her heart like it was the gold inside Fort Knox. But it didn't mean she couldn't try to offer him hope.
"What do you want me to do?" Dana leaned forward and clapped her hands on her knees. "Are you thinking soul travel?"
Reece shook his head. "Not anything that extreme yet. I was thinking a cup of coffee—just the two of you—might be a good start."
She jerked her head up. "Did you know I promised him that?"
Reece nodded. "We all know. Brandon was pretty pumped about it back at Well Spring. You know guys never can stop talking to each other about stuff like this." He smiled.
"That's funny."
"That he would even speak of it to us should tell you how much he's wanted to do it. And it might be the thing to snap him out of whatever grizzly bear trap he's caught himself in."
"Great." Dana sighed. "The problem with that is, sometimes the hunter shows up when you're springing someone from the trap."
FOUR
SIMON PACED ACROSS HIS POSTAGE STAMP–SIZED APARTMENT late Friday night, blinking and clenching and unclenching his fists like he was squeezing two stress balls.
He had to find a way to stop the low humming sound that had filled most of his waking moments for the past nine weeks. Had to. Couldn't, shouldn't, wouldn't be able to take it much longer. But how would he make that happen? When he'd come back or broke out or escaped or whatever you want to call it from the . . . uh . . . other side, or alternate world, or parallel life, or other universe, or whatever it was Zennon trapped him in, his mind had been quiet. But ever since he'd talked to Marcus about his choices, the humming had pounded away at Simon with only infrequent breaks.
Not knowing where the sound came from was a serious detriment to his finding what was producing the humming and stopping it. But he did know where the sound came from. Sort of. The sound didn't come from a clock or watch or time bomb or a metronome telling him how to keep plunking the keys on a piano with the right timing. No, it came from inside his head or his bed, and it was red, full of dread—
_Stop it!_
He pinched his thick salt-and-pepper goatee and clacked his teeth together as if he could distract himself with the noise and tactile sensation. Hardly. _Something else, find something else._
Simon snatched a deck of Bicycle playing cards off his kitchen counter and pulled out fifty-two of his best friends. All of his other friends were gone now. Long ago. Except for the professor. They were friends, weren't they?
But magic was his only true friend. The one who had never let him down. His escape from everything from the time he was seven. It always took him away from the pain when it started to rain and there was no ground to gain.
He brushed back his graying dark hair, stumbled into his living room, and slumped onto his dark-blue couch. Simon lifted a card off the top of the deck, placed a corner of the pasteboard in between the tips of his first and second finger, and flicked his wrist just like _Genii_ magazine had taught him all those decades back.
The card sliced through the air for thirty feet, then slowed and fluttered a few feet higher, and settled back down into a cardboard box he'd set up in front of the fireplace. The penalty for missing was an incinerated card. The penalty for leaving the alternate reality Zennon had locked him in for so many, many years was . . . Simon didn't know.
He didn't believe the demon would let him go this easily, even with his mind as muddled and muddy and oh so ruddy. He couldn't be pleased with what Simon had told the professor. No, Zennon wouldn't like that at all. Simon tried to focus on the cards, but he couldn't with the swirling thoughts of gloom pushing him toward his doom and filling every room.
"Stop it, please!" He pressed his hands to the sides of his head as if that could keep him from rhyming.
He should go find Marcus Amber and see how that whole thing turned out. Get the details. Had he made it? Did Marcus stop himself from slipping down the rabbit hole inside the rabbit hole inside the rabbit hole like a mole without a soul? Yes, yes, of course the professor had made it. Simon had snuck into Marcus's class on the U-Dub campus and watched him teach one of his summer classes just a few days ago.
He tossed another card. Another landed in the box. He threw one more, one more, one more, don't make me snore. Five for five. The touch was still there. Back in the day, he'd been one of the best card throwers in the country. Almost as good as Ricky Jay was in these times, who could embed an ordinary playing card into the side of a watermelon and ended up starring in a James Bond movie. Non sequitur. He smacked the side of his head but the humming continued.
Simon squeezed his temples again till they hurt. He shouldn't be thinking like this; this rambling, jabbering kaleidoscope of thoughts that always made his brain feel like mush. Shouldn't? Sure, right, easy to say. _Think straight. Come on now, brown cow, who is always calm with never a row. Rau? Row?_
Simon moaned. Some days he controlled the humming. Or didn't let it get to him. But there were bad days like today when the noise seeped through his brain and seemed to scatter like head lice when he tried to stop the sound. He fumbled for his music player, snatched it up, and stuffed his earbuds into his ears. _Come on, Bing, bring it, bing it, let's all sing it._ Mr. Crosby would drown out the humming and drumming that was always thrumming in his mind.
"Sunday, Monday, or Always" filled his senses and Simon sighed. It would be okay, they would, they should, and it would be so good, like alabaster wood. Simon smiled. Alabaster wood. That would be a sight.
He thought again of Professor Amber and his big friend Royce, or was it Rice? What did the professor call him? Reece? Yes. Simon was sure of it. Reece would be listening to sixties and seventies rock and roll. And he should. It was the music he'd grown up on. Which was why Simon was listening to Bing. That was his era. But no one knew that. They thought his age to be in his midfifties. Yes, his body was that age. Or at least it was in the condition of most fifty-year-olds. But not his mind. Not his spirit. Not his soul. No, the big three had lived much longer than his body. They'd lived so long. So many years. Too many years.
He scratched himself but the itch was inside as if some sickness had taken root inside him and was trying to get out. He should call the professor. Marcus Amber, a good man. And Simon had helped that good man with a critical choice. A choice of a lifetime. And the professor must have chosen well. Simon sighed again and pulled out his silver coin. If only, if only, if only he had chosen as well as Marcus.
But Simon's chance was gone. The chance to do the right thing for the kingdom that lasts forever, the chance to do something in this life that would echo into eternity and never fade from notice. But he'd made choices that kept him on the other side for too long. Break on through to the other side.
Simon _had_ broken through to hundreds of other sides with help from his pal Zennon, and Simon wished he could warn people that there was nothing worth seeing. Because Zennon was not a pal. Not a friend, no, he was one who tried to bend and then to end. End what? His life, so full of strife, and now the memories cut like knives.
But now, he'd wound up back in this reality, the real reality, and the One had set him free, and he would never go back. Never. But he wasn't free. Wouldn't ever be free. Not here in this life.
Simon set down the rest of the cards and padded over to the three-pegged coat stand next to his door. He snatched a worn leather coat, pulled open his front door, and walked out. Lock the door? Nah. There wasn't a thing inside his apartment worth stealing.
Simon strode east toward campus. He needed to see Marcus. Tell him why he needed to be careful. What to look out for. And why Simon believed Zennon would be coming for the professor and the rest of his friends in a way far worse than anything Marcus could imagine.
FIVE
ON SATURDAY MORNING, BRANDON SHIFTED ON HIS couch and peered at the door that led into his home studio. It was open a crack. Hadn't he closed it? If he hadn't, he should have. Should have welded it shut. Should have poured gasoline all over the room, lit a match, and torched the place. But he loved music. How could he kill the desire inside?
He turned back to his big-screen TV and stared at some old movie from the eighties. But he couldn't focus on the film. All he saw was himself standing onstage with thousands of people with their arms raised singing along with him and the band, and then everyone vanishing, leaving him alone onstage with nothing surrounding him but silence.
Brandon grabbed the bag of sunflower seeds next to him, ripped it open, and popped half a handful into his mouth. They'd never let him down. Wow. How pathetic when the most reliable friend in his life was a bag of seeds.
He snatched the remote off the couch, turned off the TV, and tossed the remote onto the floor. Maybe Zennon was right when he'd said Brandon was all about Brandon. The demon's words sliced across his mind: _Your singing career has been about you. Always about you trying to fill the hole left vacant from your childhood._
Brandon glanced at the oversized book on his coffee table: _Treehouses of the World_. How many years had he dreamed of building a tree house? Since he was twelve, at least. But back then his stepmom had squashed the idea moments after it slipped from his mouth. Now he had the land and time to burn.
He flipped through the book and stared at tree houses with two stories and decks and lights and winding staircases. Yeah, right. As if he had any idea how to start a project like that. And at the moment he wasn't in the mood and doubted if he'd be in the mood to do much of anything ever again.
He turned the TV back on and surfed through the channels till he found a different movie full of explosions and gunfights. But it didn't make the hole in his mind or heart or spirit or soul grow any smaller. After five minutes he gave up trying to bury the flickering desire deep inside, stood, and strode toward the door of his studio.
Brandon stepped into the room that held his guitars and a small recording setup. His Taylor guitar sat in the corner exactly as he'd left it three weeks ago. Part of him longed to pick it up and feel the weight of it on his right leg, feel the steel strings under his fingers, feel the body of the guitar against him. Hear the sound of his favorite chords filling his soul.
But to what end? All that would accomplish would be to remind him of what had been ripped from his hands when he saved Dana. What had been stolen. The thief came to kill, steal, destroy. Goal accomplished. But what about the rest of the verse? Jesus came to give life abundant, right? Really? Where? When would he get that life? He shuffled to his right and slumped against the wall. He had nothing left.
Now that everything was stripped away, the hole was gaping—which proved Zennon's words to be true. Easy to say you'd give it all up before you had to. A lot easier to lay down your life for a friend when you didn't realize what the aftermath would be.
Had he thrown himself between Dana and the demon who was about to kill her because he'd get some reward for doing so? No. He did it because he loved her. But he wouldn't be honest if he didn't admit he expected some kind of positive result to come out of it. Like Dana and him finally back together again. Wasn't that the way it was supposed to work?
Dana woke on Saturday morning knowing what she needed to do, with a bigger part of her wanting to do it than the part that dreaded the idea. It surprised her. She'd expected to wake up seriously queasy about the task of calling Brandon, but now that she'd had three cups of strong black coffee and spent an hour soaking in a waterfall of her favorite movie sound track, the idea felt okay.
She eased into her den and picked up her cell phone, ambled through her living room, through her front door, and sat on the wicker chair on her front porch. A pair of midmorning joggers ran past and waved. A man and woman. Smiles on their faces—probably nothing to worry about except keeping their heart rate at 155 beats per minute. Would that ever be her? Thirty-seven years on earth. She couldn't be that old, could she? Were kids even possible at this point? She pushed the thought to the side and dialed Brandon's number.
_"I might be sorry I missed you. I don't know. Only one way to find out. Leave whatever you want to say and see if I call you back. Brandon out."_
She shook her head. He'd changed the message. She'd always seen hints of his cynical side. But this, combined with his meltdown last night, meant something was seriously wrong in Brandon land. Dana didn't leave a message.
Brandon's cell phone buzzed. He pulled it from his pocket and glanced at the screen. Dana. Forget it. He wasn't taking that call. Probably calling to talk to him about last night and talk him into . . . whatever. It didn't matter because he wouldn't even listen to her voice mail if she bothered to leave a message. He didn't need saving. Reece must have put her up to it.
He looked around his studio before he backed out and shut the door hard behind him. Music and he were over. He was the Song. Was. Past tense.
Should she try Brandon's landline? Why not? Dana stared at her cell phone and smiled to herself. It had been almost four years since she'd called Brandon at home. The last time she'd done it they'd been engaged. Before he'd broken her heart into a trillion pieces.
But things had changed when he'd gone into her soul and brought healing. Things changed again last month when he risked his life and destroyed his voice in order to save her. She'd forgiven him and even opened her heart to the idea of friendship. And in the quiet moments at night before sleep took her, the faint, barely visible light of love. That was only the flicker of a thought, but for the first time since they'd returned from Well Spring, she admitted there was a faint light burning on that hillside a million light-years away.
She started to dial and two thoughts struck her. First, she didn't remember his home phone number, and second, somehow her fingers did remember. Muscle memory? Her fingers crisscrossed across her phone's keypad, then she held the phone up to her ear. Why was her heart beating a little faster? Ridiculous. It never felt weird dialing his cell phone. Of course that hadn't been exactly commonplace for the past four years either.
As Brandon's home phone rang for the fifth time, Dana prepared herself to leave a message. She didn't want to. She wanted to talk to him. Get a clue why he'd stormed out of the Warriors Riding meeting. Get a clue as to whether she should press the issue or just let it go. It wasn't like him. He was having more than an off couple of days.
"Hey."
His voice startled her.
"Hi, um, wow . . . I didn't think you were going to answer."
"Sorry to disappoint you. I can hang up."
"No, I'm glad you picked up. I was trying to figure out what kind of message I was going to leave." The tone of his voice sounded better than it had last night. Maybe a good sign.
"What kind? There are different kinds? Like different flavors of ice cream? Just leave a stupid message."
She'd wanted to get a sense of where he was—if last night was an anomaly or his new standard behavior—and now she had it. The message was back off. But that didn't work for her. It was time to point out the elephant in the center of the room and make Brandon admit it was bright pink.
"What's going on with you? Why are you acting like a moron?"
"You're saying I shouldn't have left last night? Or that I shouldn't have done my impression of Game Show Bob? I practice that one all the time. I think it's really good."
"You didn't just leave. You jumped into the china shop with your bull costume on and didn't leave one plate standing."
Brandon didn't answer, and for a moment she had the sense the next sound she'd hear would be a dial tone. "Are you there?"
"Yeah."
"So are you going to tell me?"
"You want to know the truth?"
"Yes."
The phone went silent for more than twenty seconds. "I lost it in a big way last night, didn't I?"
Dana didn't answer. There was more to come and she didn't want to dam up the flow.
"I took a firecracker and somehow turned it into a colossal stick of dynamite that none of you deserved to watch explode."
"I think there's more to tell."
"Okay." Brandon paused again. "I've built an impressive cave of self-pity and I'm spending the majority of my time hanging out in there. You should see the wallpaper. It's extensive. It has a collection of all my faces that are ticked off at life, ticked off at Reece, and ticked off at God."
"Do you want to tell me why?"
"You've always been a bright woman, Dana. Just think about it for a moment. I'm sure you'll figure it out."
"I can guess, but I'd rather you tell me."
Again Brandon didn't respond.
"I called because I care about you, and I'm worried about you."
"That's touching."
A quote from a speaker Dana heard when she was in her late teens popped into her head. _People treat you the way they feel about themselves._ Time for a different tact. "Remember our talk just before we came back from Well Spring?"
"Why would I have forgotten it? Hello? My voice is gone, not my brain."
Dana bit her tongue. Brandon was rarely if ever this acerbic. But it didn't mean she was going to back down. "Humor me. What was the last thing you said to me as we sat above the river and that I agreed to do with you?"
The answer didn't come right away. "Coffee. Just you and me."
"Yes." Dana pressed her lips together for a second. "Don't you think it's time we did that?"
For the third time Brandon went silent, but this time it lasted far shorter and his tone of voice did a 180. "Yeah, maybe it is." He paused and it seemed as if his breathing calmed. "I'd like that."
Dana shifted the phone to her other ear. "What are you doing tomorrow afternoon?"
"Having my nails done."
This was good. His sense of humor was returning without the acid coating. "Do you think you might have some time after the pink polish dries?"
"Would I have to come out of my cave?"
"Yes, you would."
"What about taking a shower?"
"Not necessary, but I would greatly appreciate it."
"Done. Maybe I'll even wash my hair."
"I don't want you to push it just because it's me."
Dana hung up the phone and sighed. She wasn't ready to be his doctor on this one, but there was little doubt this surgery needed the touch of a woman.
SIX
COFFEE TIME. BRANDON SMILED. THIS WAS GOOD. HE'D tried to push down the idea of Dana and him together again ever since they'd joined Reece's team fourteen months ago, but he'd never succeeded. Now he knew why. Yes, his voice had been stolen, but it seemed highly likely he was about to be given something even better in return. He grinned and shook his head. Amazing how one little change in circumstances could instantly take his attitude to the side of the street the sun shined on.
Brandon stepped into the flower store on Sunday afternoon, and the fragrance of the place took him back to the last time he'd bought flowers for Dana. Over four years ago. But time hadn't erased his memory of her favorite kind. Bluebells. Simple. Delicate. The same flower he'd brought her every month on the day of their first date. Her smile flashed through his memory. He was about to see it once again.
Ten minutes later he walked out of the flower store with a spectacular arrangement of bluebells, but not cut like he'd always brought them to her before. This time they were growing in soil almost black in its richness. Too obvious symbolically of where he wanted their relationship to go? No way. He wanted Dana to get a very clear message of his heart for her and his dreams for them.
He glanced at the card he had made her that sat on his car's passenger seat. If you could call it a card. He'd found a fallen tree branch in his backyard yesterday evening and spent last night and most of the morning sanding it till it was smooth as satin. Then he'd written: " _A branch of forgiveness and new beginnings"_ on the limb and finished the project by shellacking it multiple times.
As he pulled up to the curb in front of her house, his pulse spiked. Stupid. It felt like a first date. But it was just coffee. No, it was much more. He felt it. She had to be feeling it too. This was the start, a new chance for them, and it was going to be powerful. A rebirth, a restoration of what was lost.
He spoke a quick prayer and stepped out of his car. Maybe one thing in his life wasn't going down in flames. And this was the one that meant the most to him. He rang the bell, and a few seconds later the faint sound of Dana clopping across the hardwood floor of her entryway seeped through her front door.
She opened it, her green eyes bright, a smile on her lips. A shy smile? A smile of anticipation? Maybe it was only his imagination.
"Hi, Brandon."
"Hey." His return smile wasn't shy; it was an ear-to-ear grin.
He pulled the flower arrangement out from behind his back, and her gaze fell to the bowl of flowers in his hand. "What's that?" When she looked back up, her smile had weakened.
"Flowers. For you. And this too." He held out the flowers and the branch. She hesitated before taking them. When she did, her smile couldn't even be classified as weak. It was comatose.
"Um, okay." She continued to stare at the flowers and the branch. "Thanks."
"Don't tell me you've turned your back on bluebells." Brandon smiled again in defiance of the sliver of angst growing in his stomach.
"No, never. It's great. They're great. The stick is great. Really. Thank you for . . . bringing them." Her voice went flat. She glanced furtively back and forth between the arrangement and him. "Come in, I'll set them down and we can go."
Brandon stepped through her door and the witticisms that always so naturally popped down into his brain vanished. Dana strode over to the counter, plopped down the flowers and his branch, and wiped her hands. The flowers slid to the edge of the counter and the bowl came to rest with an inch hanging over the edge, but if Dana noticed she didn't say anything.
"Careful."
"Okay." She gave a muted smile. "Sorry."
"The guy at the store said it's been watered and you don't have to worry about watering again for a couple of days. And that you can either let it grow in here, or plant it outside if you want. But it'll need to be in a shady spot."
"Ready to go?" Dana grabbed her coat off the back of a kitchen chair and glanced at him.
Why was bringing her something a crime? Did her last boyfriend, Porky or Pearly or Perry, whatever his name was, bring her the same exact thing and it surfaced a bad memory? This wasn't exactly how he saw her reacting.
"You have a thing against flowers and well-sanded sticks these days?"
"I told you they're great. They are, really. Thanks again." She stood with her hand on her front door knob, her gaze out toward his car. "Can we go?"
"Sure."
Wow. He made a mental note. Flowers bad. Sanded stick bad. No idea why and probably not the moment to ask. When they arrived at his car, he reached out to open the passenger door for her but she skipped ahead of him and opened it for herself. "Thanks, but I've got it." She got in and yanked the car door shut before he could close it for her.
Flowers and sticks _very_ bad. They pulled away and he glanced at Dana. She gazed straight ahead. A few minutes later she reached toward his CD player. "Mind if I get some music going?"
"Yes." He gripped his steering wheel hard. He didn't want to fill the silence with music. He wanted to figure out what was going on inside her head. "Things okay at the station?"
"Fine."
Strike one. "How's Marcus doing?"
"Good. He and Kat and their girls took a long weekend and went to Lake Chelan together. Sounds like they had fun."
Not a base hit, but a walk at least. He might as well try one more swing. "I've been looking forward to this."
"This what?"
"Time together."
Dana turned and looked out the passenger window, then pulled her arms across her chest.
He didn't follow up with another question. Whatever he'd done had thrown liquid nitrogen all over their date, and at this point pressing for more conversation wouldn't help. He waited for Dana to break the silence and when she did, it didn't thaw the ice cloud in the air between them.
"Have you been playing at all?"
Great. The most off-limit subject possible. Let's dig into the wound and see how high the pain meter is pegging. "Playing?"
"You know what I mean."
"No. I haven't been." He massaged the steering wheel.
"Not at all?"
"Didn't I just say no?" He gripped the wheel harder. "I can't touch that yet."
"Can't touch your guitar or can't touch the subject?"
"Both." He glared at her. "Did Reece put you up to this? Getting together with me? Or did you want to all on your own?"
This time the silence lasted longer.
"Do you want to talk about the other night?" Dana said.
"Not really."
"You should." She rubbed her forehead.
"I think we should start this whole conversation over." Brandon took a right-hand turn and pulled up to the curb half a block later, directly in front of the coffee shop. "How are you? I'm fine."
"Me too." The hint of a smile played on Dana's face.
They sat in the back of the shop and for ten minutes talked about nothing of consequence, but their meandering conversation seemed to thaw the ice curtain Dana had thrown up the second she saw the flowers. By the time Brandon was halfway done with his caramel macchiato, the usual warmth had started to come back into her eyes and Dana seemed back to being Dana.
The small talk continued but that was okay. Being with her, just the two of them—not because they were at Well Spring or with the other Warriors—was enough. Five minutes later, Dana's laughter and now-relaxed shoulders gave him the courage to toss out an idea he'd thought about daily since their talk back at Well Spring.
"I'm thinking it might be fun to take a little day trip together."
"Where?" She frowned.
"Up to Larrabee State Park." He reached across the table and gave her hand a quick squeeze. "You know, where we—"
"I know what we did there." She pulled both hands off the table and set them in her lap. "Why do you want to go back?"
"Why wouldn't we? It would be the perfect place to rekindle—"
"Brandon." Dana pushed her chair back a few inches. "I'm sorry if I gave you the wrong impression, but we need to back up a bit."
"Back what up?" He gripped the edge of the table with both hands.
"What are you trying to do?"
"What do you mean? I—"
"I said I'd have coffee with you." She crossed her legs. "That's all."
"So is this where you explain the ice-queen routine?"
She tilted her head back, then turned it to stare out the window at the cold Seattle rain.
"Did I miss something back at Well Spring? Wasn't that you sitting with me and we talked about us and you said there was, 'one person you've thought of from time to time lately'?" Brandon opened his arms wide. "That wasn't me?"
"Yes, you did miss something or . . . okay, you didn't miss it, but you've added to whatever went on there or what you thought went on there. I have thought of us from time to time—what the future might be—but . . ." She sighed. "If you think I was saying we should start dating again, you misread me.
"I do want a friendship with you." Dana pulled her light-brown hair back behind her ears. "Maybe . . . maybe even a close friendship. But I don't have any idea what that looks like."
She clasped her hands tight. "Brandon, with what it seems like we're about to go through with Warriors Riding and what you're going through and what I'm still working through, I'm not ready for anything more than that. And neither are you, okay?"
Brandon's body felt like he'd taken a bath in Novocain. This was not the Dana he'd talked to back at the ranch after the battle where he laid down his life for her. The one who seemed—not seemed— _was_ open and tender and thinking about them in a way far more than friendship. "What's going on with you? What do you have to work through?"
"Don't start in on me."
"Start in on you how?"
"Just don't."
Brandon crumpled his coffee cup and tossed it into a garbage can five feet to his right. "I didn't make up our conversation at Well Spring. I don't care how deep down they are, I know you still have very real feelings for me. For us."
"You didn't imagine it." Dana rubbed her face and sighed. "But since getting back I've given it a lot of thought. We were both caught up in an emotional moment. And yes, I have had flickering feelings for you. But I think they're remnants of something we once had. The emotions you might have if you bumped into a girlfriend from high school or college and spent time together. I've wanted to tell you this, but you haven't exactly been accessible. Plus, I didn't want to hurt you because I thought you were feeling exactly how you _are_ feeling. I'm sorry, Brandon. You and I aren't going any further than friends."
"No chance?"
"I'm sorry." She shook her head.
He stared at her as his gut filled with a slew of cannonballs. Just being friends wasn't good enough. Even close friends. She didn't have feelings for him? He didn't believe her. For some reason she was pushing down whatever she truly felt inside. But it didn't matter. She believed it. Her wall had gone back up, and he had no idea how to bring it down.
SEVEN
A KNOCK ON BRANDON'S FRONT DOOR MONDAY AFTERNOON yanked his mind away from an absolutely riveting match of online, beginner-level chess. He logged out and pushed away from his computer with a bored sigh. No wonder he'd never bothered to learn the game.
Whoever was at the door knocked again. He wasn't expecting anyone. And who dropped by unannounced these days? Brandon blew out another sigh. Might as well. He shuffled to the door and opened it to find Doug standing on his porch. "Might I come in?"
"How are you, Brandon?" Doug asked after they had settled onto the couch and love seat in the family room and gone through a smattering of small talk.
Brandon gazed at Doug with respect. _How are you?_ Such a simple phrase, uttered millions of times across the country every day with an appalling lack of sincerity. But not from Doug. The way he said it, leaning forward slightly, his brows furrowed, his tone with its soft intensity, Brandon knew the older man meant it with everything inside. And not only meant it, but expected a reaction equally sincere. "I'm fine" wouldn't cut it.
But Brandon wasn't going to deliver the honest response. Not because he disliked Doug. On the contrary, he thought the universe of the man. But Doug was too tied into Reece—Doug was the fifth Beatle of Warriors Riding, for crying out extremely loud—that made him guilty by association. Brandon didn't want whatever he said to be repeated and analyzed by anyone. No more Warriors. No more Dana. No more music. So now he was going to indulge that dream he'd had since he was a kid and build a tree house. That was his new mission.
"I'm fantastic."
Doug nodded, his piercing gray eyes boring into Brandon's till he had to turn away.
"Really, I'm doing okay." Brandon took a drink of his Gatorade. "I know the meltdown on Friday night says otherwise, but I just needed to get that off my chest, and it helped, and now I'm working through it and I'm going to be fine."
Doug didn't answer till Brandon looked into his eyes, which said Doug didn't even start to believe him.
"Someone very close to me gave me the prophecy Reece and I spoke of the other night, and as you know, it indicates Zennon will—"
"Oh boy, how exciting. I want to learn more. Do I lose my arms this time?"
"It indicates Zennon is mounting a charge against us that will be far greater than what we've experienced so far."
"Is that supposed to inspire me?"
"Reece and I have prayed extensively over the prophecy." Doug bowed his head and clasped his hands. "I believe we've heard from the Spirit that without you, the casualties will be substantial. That without you, much will be lost. You are the key, and just as Marcus made a choice, you will have a choice to make that will shift forces in heaven and on earth."
"I don't suppose you want to let me in on what that choice will be."
"The answer to that has not been given to me."
"Nothing like a little pressure of having to make the right choice to save the world to jump-start my day." Brandon shook his head and slumped back on his love seat. "Sorry, Doug. I'm done with the Warriors. Maybe not forever, but for right now, it's over. I want to feel normal again. At least try."
"You are more than needed, Brandon. You will be at the forefront of this war and are the one who can release God's power in ways beyond our comprehension."
"Sorry, wish I could help, but I did my hero bit during our last little skirmish against the Wolf." Brandon pointed to his throat. "So I'm all tapped out on the battle front. And I did my part of the prophecy, you know? Death before the appointed time and all that? So I figure the Warriors can now ride without me."
"It's not something you can stop. You will take your place whether you want to or not. It is your destiny. Give in to hope. Restoration is coming. Life will come out of death for death cannot hold life in its clutches."
"Tell that to my voice."
"He has not forsaken you, Brandon. You will sing again."
"Oh really? With this voice?"
"No. With a voice you can't imagine."
"When? Is this where you tell me I'll sing like I used to when we all rendezvous on the new earth?"
Doug smiled. "It will be far sooner than that, I believe."
"Uh-huh."
"You can't stop his relentless pursuit of you. Love is patient. Kind. Endures all things. Believes all things. It protects and perseveres. Love never fails. Love cannot be stopped. And he is Love."
EIGHT
ON WEDNESDAY AFTER THE SUN BROKE THROUGH THE late-morning fog, Brandon headed for the Edmonds waterfront on Puget Sound just to get a change of scenery. He was the key to whatever this battle was? Sorry, there weren't going to be any locks in his future. God and Reece and the others could find someone else.
He sat for an hour and watched the ferryboats chug in and out of the Edmonds slip. Straight in front of him was the Edmonds Underwater Park where scuba divers descended to explore old boats, a sunken dry dock, tires full of sea anemones, and search for crabs that skittered across the ocean floor. Little buoys with red dive flags and diagonal white stripes across the flags signaled divers below.
Slightly to his left, in between the dive park and the ferry, families and couples and elderly men sauntered along the small stretch of beach, poking at rocks and strolling out on the short jetty that jutted into the blue-green waters of Puget Sound. The briny smell of the ocean tickled his senses and for a few seconds he forgot about everything except this moment.
A car stopped in back of him and its tires scraping against the curb yanked him from his moment of peace. A young couple pulled out a blanket and a picnic basket. After they settled in, they poured two glasses of what appeared to be white wine and spread out crackers and what looked like brie cheese.
They toasted each other, but the woman's eyes seemed dead. Somehow Brandon knew whatever the toast was—it sounded like an anniversary from the snatches of conversation he overheard—she was only going through the motions.
As he turned back to watch the divers slog in and out of the water, a melody filled the air—so crisp and clean Brandon knew immediately it was sung live. No words, just notes from a . . . He laughed at himself. He couldn't tell what instrument played the song. Some musician he was.
As the song grew, Brandon almost gasped. It soared through his mind into his heart and made him want to shout with joy and a moment later took him to a place of profound sadness. A song hadn't affected him this deeply in years. Maybe ever. But where was this one coming from? The music seemed to come from all around him.
He spun slowly in a full circle—pushing himself around on the grass with his heels—looking for the source but saw no one. He glanced at the couple to his left and then at a teenager with a skateboard and a German shepherd ten yards to his right. Neither seemed to have the least interest in the song. How could they not have some sort of reaction? Then the words started. It was a song about longing and regret and trying to hope when hope refused to come.
When it was over, Brandon sat with his arms around his knees, and a chill raced over his body. Stunning. He glanced around once more, but it seemed he was the only one along the strip of grass who had been moved by the piece or even heard it.
A few seconds later, he began to sing the song, but too soft for anyone to hear. His voice sounded rough, of course, but he didn't care—couldn't care. The song refused to let him think about anything but itself, and he couldn't hold back. He let his raspy voice grow louder.
When he finished, the sound of muffled crying floated over to him from his left. It was the woman who had sat down earlier. After a few minutes of tears, she dug her fingers into the man's coat, pulled him toward her, whispered in his ear, and pointed in Brandon's direction. Within seconds the man began to sob as well.
Brandon turned away but couldn't stop from watching with his peripheral vision. They held each other for a few minutes, then pulled away and talked with animated gestures and held each other again. Laughter. More crying. Then a silence that seemed louder than their passionate whispers to each other. Finally they gathered up their blanket and food and drink and walked to their car.
After their trunk slammed shut, she held up a finger. "Wait," she said and shuffled over to Brandon. Her eyes were still wet from tears. She squatted next to him and closed her eyes a moment before opening them and staring into his with a quiet intensity. "How did you know?"
"I don't—"
"How could you know about what I've been going through? Where did you learn that song? How did you know those words"—she blinked back tears—"were exactly what I needed to hear? It's like you wrote that song for me. For us."
The woman wanted to know where the song came from? So did he. "I didn't write it. I heard it for the first time while we were sitting here."
"Heard it where?"
"It was all around us. You guys had to have heard it too."
The woman furrowed her brow. "There wasn't any song till you started singing."
"You didn't hear anything before I—?" Brandon stopped himself. Why ask her again? He didn't think she was lying. But if she couldn't hear it, how could he?
"Thank you with everything inside me. And that's from both of us. I don't know who you are or how you did that, but for the first time in three years, I have hope." She glanced at her man. "We both do. For the first time in five years I know I'm going to make it."
She covered her face with her hand as fresh tears came and she wiped them away. "Thank you, thank you, thank you. I wish I had better words, but just thank you, okay?" She reached out and squeezed Brandon's hand, then scampered back to the man who stood holding the passenger-side door open.
She leaned into him and pressed her head against his chest. The man looked over her shoulder at Brandon, nodded, and then mouthed the words _thank you_.
Brandon stared at the car as it pulled away. What just happened? How did they even understand the words with his burnt-out, raspy voice singing?
A few seconds later the teen with the skateboard shuffled over to him. "Amazing song, brohan. Is it yours?"
Brandon shook his head and smiled at the kid's shirt that had a picture of a diamond on it and said "Don't judge me yet, I'm still in the rough" underneath it.
"No."
"Whose is it?"
Brandon didn't think before answering. "God's."
"Cool. God could totally chart out with that one if he recorded it."
"Chart out?" Brandon knew what he meant, but his mind was only half engaged in the conversation. He was still trying to figure out what the Spirit had just done.
"Number one in the sun, man."
"God in the Top 40." Brandon laughed. "That would be interesting."
"He should let you record it. Rockin' song, even more rockin' voice. You should be a singer."
"My voice?" Brandon cocked his head. "Yeah, right. Maybe I could sing once upon a long ago and far away."
"Sorry." The kid frowned. "Not on your track, jack."
"What?"
The kid smiled. "What I mean is, I'm not tracking with you. You don't like your voice?" He shook his head. "Crazy."
"Not cool making fun of someone older than you." Brandon stood and pulled his car keys out of his pocket.
"Dude, your voice is unlike anything I've ever heard. Straight up." The kid held up both palms. "I'd pay serious coin for one of your albums, so keep rockin' it."
Doug's words floated back to him. _Restoration. It's on its way._
Was it possible? Brandon massaged his throat as he thanked the kid and turned to go. Was it healed or was the kid delusional? His voice had sounded raspy when he'd sung the song, and it was highly likely the teen's definition of "rockin' voice" might be far different from Brandon's.
He turned to the kid. "You like gritty voices?"
"Nah, not really. I don't look it, but Bublé is more my style. Josh Groban too, you know?" The teen smiled. "And your voice crushes on both of 'em."
Brandon jogged back to his car, jumped inside, and fired it up. He took a few minutes to let what had happened soak in, but as soon as he reached I-5, he dialed Doug's number.
"You're not going to believe this," Brandon said.
"You've had a revelation."
"I think I might have been healed." Brandon swerved around a minivan going sixty as he headed toward home.
"Tell me why you think that."
"I don't think it, I know it. My voice has been restored."
"When?"
"Just now. Ten minutes ago down in Edmonds." Brandon told Doug what had happened and the older man listened without comment. "I'm back, Doug. I almost don't believe it myself, but I'm back. I'm the Song again. You were so right."
Doug didn't respond.
"Are you there?"
"Yes, Brandon. I am. Be careful, son."
"What does that mean?"
"I'm not sure, but this isn't what I sensed the Spirit saying when he told me you'd be restored."
"What else could it be? Are you saying the couple and the kid weren't hearing straight?"
"Again, I don't know, but I do have a strong sense you should be careful."
"Careful of what?"
"Of letting your soul be deceived as to what really happened down on the Sound."
"Our wavelengths are missing each other. Not with you at all here."
"I'm sorry. I wish there was more I could say and that I was clearer in my own mind about what is going on here."
"Me too." Brandon jammed on the gas. "I gotta go."
What was wrong with Doug? He comes over and spouts all that verbiage about being restored, and then when it happens he wants to toss ice water on it? It didn't matter. The instant he got home, Brandon was going to prove the restoration was real.
NINE
BRANDON BOLTED THROUGH HIS FRONT DOOR AND TOSSED his keys onto his kitchen counter. They slid across the surface and smacked into his stainless-steel toaster as he jogged toward his studio. What was wrong with Doug? Brandon didn't need doubters; he needed someone to celebrate with him. _Fine, Doug. Be a downer._ _Doesn't matter_.
Unbelievable. _Boom!_ Just like that his voice was restored. _So cool, Lord._ The doctors had said maybe—a less than ten percent chance maybe—his voice would get close to what it was before. But they hadn't factored God into the equation. Close to what it was? Way beyond close if the kid was right.
Brandon had always had a good voice, maybe great, but not in the same league as Bublé or Groban. If the couple and the kid down in Edmonds were right about how his voice sounded, God had restored his voice in a way only he could do it—even better than it was before.
"Freedom!" he shouted as he fired up his computer and set up his mics. He'd record the song he just sang down in Edmonds. Yes, it was God's song as he'd told the kid, but that didn't mean he couldn't get it down on tape as a tribute to what God had done in the couple, and in him.
He closed his eyes and waited for the words of the song and the melody to fill his mind as it had an hour earlier. But nothing came. It was like a dream where the images were staggeringly vivid but faded within moments of waking.
Despair sloshed through Brandon's mind, but then he laughed. Of course. It was her song. Their song. For them alone. For them to carry in their memories and no one else. Brandon was the instrument, but that was all and why the song was gone. Exactly how it should be.
So he would lay down a different song. Which one? He snapped his fingers. The choice was obvious. One of the first songs he'd ever written: "Chain Break." Perfect because of what God had just broken loose in him.
Brandon hit Record, opened his mouth, and sang the first line with his old confidence. But what fed back through his headphones sounded hideous. Why were his headphones distorting the sound of his voice? Brandon tried it again. Same result.
His legs shuddered and he slumped to his knees. It couldn't be. He tried it a third time and sang till the chorus, then played it back. Atrocious. His voice was as trashed as ever, back to where it had been weeks ago, maybe worse.
His guitar slipped out of his hand, crashed to the floor, and sent out a discordant sound. Brandon turned and walked out of his studio and slammed the door behind him. He snatched his cell phone from his pocket and called Doug again.
"You knew, didn't you?"
Doug didn't answer for a moment. "No. Not entirely. But I suspected something like this might happen."
"What is going on?"
"Come to Well Spring with us next week."
"What is going on, Doug?"
"Can you believe God is in this?"
"I don't know."
"Come to Well Spring."
"Sorry, Doug, it ain't gonna happen."
TEN
THE UNSETTLING SENSATION WASHED OVER MARCUS FOR the third time—the feeling of someone staring at him. There was no scientific evidence to back up the impression, but there was no scientific evidence for teleportation or invisibility or the power of prayer or traveling inside someone else's soul either. Yet those things certainly were not only possible but had become facts—and almost normal—in his life and the lives of the other Warriors.
He turned back to his book, _Separating Soul and Spirit: A Quantum Understanding_.
The warm summer sun was almost too hot for Marcus as he sat on a bench in the University of Washington's Red Square. He'd come hoping to see Simon, but so far there had been no sign of the magician.
His cell phone rang. It was Kat. "Hello, wife of my youth."
"Sorry, you just missed her. This is the wife of your middle age."
"Forty-four is not middle-aged."
"I'm glad to hear you're going to live past your eighty-eighth birthday. I want you around." Kat paused. "I was praying just now and have a feeling you need to find Simon. He's going to play a significant role in what the Warriors will be facing soon."
"That's excellent confirmation of what I've been feeling as well. Which is why I'm sitting in Red Square right now hoping he'll appear. I want to speak with him. I need to speak with him."
"He'll show. Maybe not today, but he will."
After their standard "I love yous," Marcus ended the call and turned back to his book. The moment he picked it up, his cell phone buzzed again. He didn't recognize the number, but the area code indicated the call was generated from somewhere in the Los Angeles area.
"Marcus Amber here."
"You saved my life, Professor." A low, animated voice poured out of Marcus's phone.
"Carson Tanner?"
"In body, soul, and spirit. How are you, Marcus?"
He smiled. It was good to hear the radio talk-show host's voice. "All systems are firing with adequate strength at the moment, and you? Nice to hear from you."
"I meant to call you before now, but I've been working sixteen hours a day since you paid me that in-studio visit."
"I see."
"So do I. Now. And you're the one who handed me the glasses that allowed me to get my vision back to where it should be. Wow, what a ride I've been on. All good. All freedom. Big changes, you know?"
A deep sense of relief settled on Marcus. He'd feared the radical change in Carson during his encounter with the radio-show host had been more out of the emotion of the moment than a true revolution. Every day since his showdown in Carson's studio almost two weeks ago, Marcus had interceded for the man.
"Have any quantifiable results come out of your long hours?"
"Without question. Radical shift on the level of a 9.7 quake." Marcus heard a smile in Carson's voice. "You haven't been listening to my show? C'mon, Professor."
Marcus mentally flicked himself on the forehead. Of course. Why hadn't he tuned in to the show to see if Carson had made any programming alterations that would reflect the shift in his heart?
"I have to confess I haven't. That likely would have answered a considerable amount of my questions."
"Like if my rebirth was real." Carson chuckled.
"Since you raise the question, yes, precisely."
"It's real, baby. We've revamped the entire show. I've sat down in person with six of our seven major sponsors and did a video call with the seventh. I met with each of my staff one-on-one and asked for their forgiveness. I've started a gathering once a week for any of my team who wants to come, and we've been pushing into freedom."
"It's exhilarating to hear that."
"And the e-mails from listeners are mind-blowing. We're changing lives, Marcus. The themes we talk about now are spreading like gas-soaked wildfire."
"How are your ratings?"
Carson laughed. "That's pretty funny. Just this morning someone asked me that and I had to answer, 'I have no clue.' I had to ask Sooz what they were. Up until our encounter, I could quote enough statistics to impress even you, Professor. But since our meeting I've lost all interest."
"Why is that?"
"I've learned a simple lesson that you and the other Warriors probably already know. Ratings aren't success. The world cares about them, but God doesn't. Based on 'ratings' and followers who stuck around, Jesus was one of the biggest failures in history."
"Agreed. But you still have sponsors and advertisers who will want to know if their money is well spent."
"Sooz told me the show is trending twelve percent higher than we've ever been."
"Congratulations."
Carson laughed. "Hey, you know I could do your ministry a lot of good. Get you a lot of exposure. Since I slammed the Warriors so hard in the past, I'd like to make up by running some free ads and promotions. Pump you up big-time. I've talked a little about what you've done for me, but I'd like to make it official. Whaddya think?"
Marcus smiled at the kindness but shook his head. "I'm thinking not."
"Really?" Carson's voice was incredulous.
"You said you're not about the numbers. Reece isn't either. None of us are. We've had offers from major players to do a reality TV show based on what's going on with our ministry. We've had men and women with deep pockets want to help us build a huge staff with satellite offices in other parts of the world, as well as a dozen other similar offers, but we've clearly heard the Spirit say over and over again, 'Stay small.' "
"You're not small. You're worldwide. How many people are on your e-mail subscriber list?"
"Two hundred and eighty thousand and growing."
Carson whistled. "Those're serious numbers for such a short time you guys have been around. And without pushing the ministry at all."
"I suppose it is. But the power isn't our number of followers. The true power of Warriors Riding will always be the people who have taken the message back to their cities and countries. We'll always be a nuclear-filled iceberg."
"That's an interesting image. Care to elaborate?"
"Warriors Riding has a great deal of influence, but most of it is below the surface where no one can see."
"So you fuel the people who fuel the people who fuel the people."
"Precisely." Marcus leaned back on the bench. "As Reece says, we're not out to form a mega ministry because the day we start getting big is the day we die."
"Okay. I respect that. But just know if you ever change your mind, I'm here for you." Carson blew out a quick breath. "Listen, gotta run. Can we touch base again in a few weeks?"
"I'd like that."
As soon as Marcus hung up, the sensation hit him again, a feeling of certainty he was being watched. He looked up and turned his gaze to U-Dub's Odegaard Library and made a slow sweep from left to right. No one stared in his direction. He started to turn back to his book but spun back a second later. Movement near the base of the library snagged his attention. A head peering around the corner, then pulling back.
Marcus waited and the head came around the edge of the building again and stayed there. Was it him? Marcus smiled as Simon rose from behind the brick wall and strolled toward him.
Finally. He'd been anxious to speak with the magician ever since the Warriors had returned from Well Spring nearly two weeks ago. But if Simon didn't want to be found, he wouldn't be. Marcus could have gone to Simon's apartment, but the magician had forbade him from doing that for reasons he wouldn't explain. And leaving messages on his cell phone held less than a twenty percent chance of being answered. Probably because most of the time Simon didn't know if he had a cell phone or not. But now, finally, he would have the opportunity to speak to the man who had saved him, saved all of the Warriors.
The magician, taking time to notice every blade of grass and smell every flower laid out before him, ambled toward Marcus like he was in the middle of the University of Washington arboretum. While he was still twenty yards away, Simon opened his arms and wiggled his fingers as if to beckon Marcus to come his way.
Marcus stood and strolled toward Simon. His friend looked well overall. The magician's goatee was flecked with a spot more gray than the last time he'd seen him, and his clothes hung a mite looser. But other than that he looked the same.
"Simon, my remarkable friend."
"In the end, I was indeed a true friend, and by the sound of your voice, I'm guessing you made the right choice." The magician wiggled his slightly oversized ears.
"Yes, I did. If I hadn't, I don't think I'd be here."
"True, _mon frère_." Simon nodded and folded his arms as a smile played on his face.
"That is something I've been longing to talk to you about." Marcus motioned back toward the bench on which his book and briefcase sat. "Care to join me in accumulating a splash of vitamin D from the star above us?"
Simon squinted into the sun. "We Seattleites can't overdose on it, can we?"
"Not likely."
As they walked and then sat down, neither man spoke. Marcus wasn't sure where to begin but finally said, "You were aware of the choices I was going to face on the cliff and in front of the door of my memories, weren't you?"
"I did indeed know, like falling summer snow, which comes when unexpected, but can form a kind of nexus."
"That isn't a perfect rhyme, friend." Marcus grinned.
"No. 'Tis not. It's a slant rhyme or oblique rhyme, but I don't think I need to explain such mundane definitions to a man of your cranial prowess."
"It's good to see you, Simon." It wasn't in Marcus's nature to hug the man, but seeing the magician again almost made him do it. Instead, he squeezed his friend's shoulder.
"You as well, Professor." Simon leaned forward on the bench in a mock bow. "I'd like very much to hear how you escaped from Zennon's hell."
"I almost didn't. I came very close to making a choice that would have left me there. Without you, I'm afraid, I would have chosen poorly. Words aren't adequate to thank you for what you showed me down by the fountain back in June."
"It was my great pleasure."
"And you did it through a card trick."
Simon pulled out a deck of cards and opened the case. "Visual and tactile lessons tend to sink into the brain with much greater intensity than simply saying the words, don't you think?"
"Yes."
"Then why don't you apply them more often in your classes?"
"I probably should." Marcus smiled and pointed at the cards. "Perhaps you should teach me a few tricks."
"Are you quite serious or a touch delirious?"
"Maybe both."
"Lessons are of course free for you."
"I might take you up on that."
"Anytime." Simon bowed again.
Marcus studied the magician. The man fidgeted as he always did, shifting his weight back and forth from hip to hip, his eyes always moving. Most people would describe Simon as being slightly off. Marcus would describe him as being slightly tormented. More than slightly. Simon needed relief and restoration, but Marcus had no idea where to begin. "I want you to meet the others."
"Others?"
"The other members of the Warriors Riding."
Simon shook his head. "I'm good at a distance. Good with a crowd. Not so good close up and personal."
"You're good with me."
"I make it with you most of the time, yes. But it's not always easy, makes my head feel breezy. And I came to you because I saw myself all over you. I sensed it. I saw what Zennon was doing to you. I couldn't let what happened to me happen to someone else."
"What happened to you, Simon?"
"No, no, no, that would be a blow." He waved his hand as if to push away a memory. "Not back there, only here, elude the fear."
Marcus leaned in. "Come meet my friends. They want to thank you. It was not just my life you saved. Freeing me from my past allowed me to go to battle in a way that brought great victory to my closest allies. That's why I want you to meet them. Why they want to meet you. But also, I believe they can bring you healing."
"I can't. Not now brown cow." Simon shuffled the deck, then sprang them into a card fountain. "You and they are involved in strange things on the fringe of God. I need to stay as far away from them as possible."
"You mean soul travel. Sending our spirits into the souls of others to fight for their freedom and healing. Traveling into other spiritual realms. Fighting spirits not of God."
Simon stuck his fingers in his ears and shouted, "La, la, la, la, la. I can't hear you." A thin sheen of sweat appeared on his forehead.
"Because you spent such a great deal of time in another reality."
"Never again, if you are my friend, speak of that path." Simon stood, spun in a full circle, jerked two steps away, spun again, and staggered back. "Never. I'm done traveling anywhere spiritual or delving into spiritual matters that dance on the razor's edge, till I shed this body for good."
"My apologies."
"It's okay." Simon winked. "But let's let the subject drop."
"But I have to speak of one more item." Marcus leaned in. "There's a third reason I want you to meet the other Warriors. I believe we need you."
"Why?"
"Because a war is coming far bigger than any we've faced before. And we believe Zennon is behind it."
"And since I know him—"
"Yes." Marcus spread his hands. "We need to know everything he's capable of."
"It's more than you can imagine."
"We need to know his tactics."
"Layer upon layer of deception. You cannot defeat his mind. He's far smarter than any of you could dream of being. Even you, Professor."
"What else?"
"Don't underestimate him. He's cunning. Vicious. You might think you know his plans, but you don't. He's nine steps ahead of you and then the lies will start to spew. Plus, he has the angel of light dance down to perfection. He'll fool you just like he did when he pretended to be your daughter's boyfriend."
"Come and teach us about him."
"I don't know." Simon held up his silver coin. "So you liked my trick that showed you the path to make the right choice?"
_Ask him again._
The voice of the Spirit was so clear, Marcus didn't hesitate. "What happened to you when you didn't make the right choice, Simon?"
Simon's slate gray eyes went cold. "I told you, even in my mind I can't go back. Vicious attack." He stared at his cards and cut them with one hand, but his other hand shook. "Because I still can't tell if it's more than in my mind, which isn't kind . . . brings emotions of serious decline."
"My impression is you need to speak of it. With someone who has faced the same choices and can walk through it with you. Healing can come for you as it did for me."
"No. Too late, he's shut the gate." Simon turned to the left and continued to execute various one-handed cuts.
"If you ever have desire to speak of it, I would like to hear your story."
"Maybe. A very large maybe." Simon shook his head and the brightness in his eyes faltered. Then the magician's face went pale and his eyes locked shut. "Don't make me go back there, Professor, please."
But if the look on his face was any indication, Simon was already gone.
ELEVEN
AS THE WORDS ESCAPED SIMON'S MOUTH, A MEMORY BURIED under decades of time bubbled to the surface. He sat in the bedroom he grew up in, his hands over his ears, but it didn't help much.
The screaming above continued and seeped down through the ceiling, settled on Simon's ten-year-old shoulders as he sat in the center of his room, and soaked into his soul. He blinked back tears and opened his book, _Tarbell's Course of Magic Volume 1_ , a gift from his uncle the previous Christmas. He crawled over to the door of his closet, pulled it open, and snuggled up against the back wall where he'd laid out a blanket for his frequent visits. There he buried himself in the pages that would teach him how to instantly switch places with a volunteer from the audience, and make a ring crawl up a rubber band, defying the laws of gravity, and how to amaze anyone with a pack of playing cards.
He took the four aces out of his Bicycle deck and whispered the things he was supposed to say as he made them change into the four kings and then the four queens and then the four jacks with faster and faster flicks of his wrist. He smiled as the yelling from his parents faded and the imaginings of standing on a stage in Chicago or Los Angeles or the big one—New York—filled his mind.
Plus, the party was almost here! The one where he would perform for those little kids and show them a world of astonishment and wonder. A world where people would love him and cheer for him and made him feel like he mattered. He would put on a show they would always remember.
The scene in his bedroom vanished, and Simon breathed a sigh as he stole a glance at Marcus. But then another memory sliced into his mind—one much worse—the day all the gears of his life's final destruction started turning.
He stood in front of a small audience of men—seven or eight if he remembered right. Simon's father sat in the back row with his arms folded, a smirk on his face. It wasn't easy getting this audience to come. But in the end Simon, convinced his dad to invite some of his buddies to come over and see the show. This would be the one that would make his dad proud.
His father hadn't ever shown interest in Simon's magic, but it didn't matter. Today he would prove to his dad that his magic was mesmerizing and worthy of his dad's praise. And maybe, just maybe, they could start to learn magic tricks together. Study books and go to shows and even perform together someday. That would be true magic!
He performed all of his most powerful tricks for the men: making small billiard balls multiply and disappear, tearing up a chosen card, then making it vanish and reappear fully restored inside an orange, and pulling a rope right through one of the men's arms. But he saved his best trick for the finale.
Twelve-year-old Simon pulled out four silks—one blue, one green, one yellow, and one red—and waved them through the air. "As you can see, each of these silks is a different color and they are completely separate from each other."
Again he showed the men each silk one at a time. Then he rolled the four silks into a tight ball. "Now watch closely because in the blink of an eye, you're going to see a miracle!"
Simon tossed the silks in the air, and a moment later a flash of fire exploded above him. When the smoke cleared, the silks fluttered down into his waiting hands. But now the silks were melded together in a swirling pattern of colors.
The men gave him polite applause, except for Simon's father, who turned to the man next to him and laughed. "Can you believe it? Silks? Playing with silks. Can I get him interested in football? No. Baseball? No. Basketball? Doesn't interest the kid. Can't even get him to fire a BB gun. But magic grabs his little pea brain, and it hasn't turned him into a rabbit; it's turned him into a sissy boy."
His dad laughed along with most of the other men, and in that instant, Simon was the assistant and his dad had just sawed him in half.
The next day after school, Simon sat alone in a park near his home practicing a coin roll across his fingers and pretending he could run away from home. He had no brother. No sister. No friends he could talk to. And his mom . . . she wouldn't stand up to his dad anyway, so what was the point in trying to tell her about what had happened?
"Hey."
Simon looked up from his picnic table to find a guy who looked like he was in college standing nine or ten yards away, hands shoved in the front of his slacks. A gray velvet bag hung from his wrist and his dark hair flopped down on his forehead.
"Who are you?"
The young man took out a pack of cards and made a perfect fan with one hand. "My name is Aaron. And yours is Simon, right?"
"How do you know my name?"
"My dad is a friend of your dad's. He came to your show yesterday and told me about it. That you're a magician just like me." Aaron grinned but his smile quickly faded. "And he told me what your dad said. Sorry about that. That wasn't right. I bet he doesn't really feel that way. Just trying to be funny, you know?"
"It's okay."
"Mind if I sit?" Aaron pointed at the table.
"Sure. I mean, no."
For the next two hours, Aaron showed Simon amazing moves with cards and coins and sponge balls and matches and pencils and rings till Simon's mind spun with the excitement of it all.
"You're amazing!" Simon grinned.
"Ah, thanks, but I've just been practicing a lot longer than you." Aaron shoved his cards and coins and his other props into a small bag and stood. "Listen, I have to go now, but if you like, you can start coming to a magic club I'm part of. We get together once a month and show each other tricks and stuff."
"That'd be great."
"Okay. So if it's all right with your dad, I'll pick you up next Monday night around seven." Aaron scribbled on a small sheet of paper. "That's my phone number. Ring me if you can't come. If I don't hear from you, we'll learn some more cool stuff together."
"My dad won't care if I go." Simon scratched his fingernail along the wood of the picnic table.
"Hey." Aaron's gaze seemed to pierce Simon. "It's going to be all right. Most dads are like that. You'll make it, okay?"
Simon squeezed his lips together and nodded.
Aaron took a step away, then turned back. "You have a big brother?"
"Nah, it's just me."
"Well, you do now." Aaron grinned and loped off and Simon smiled.
For the next ten years, Simon didn't miss a night at the magic club. Neither did Aaron. By the time Simon moved away from Seattle after graduating from college, the hook was set so deep inside his soul it was part of him.
"Simon?" Marcus said for the third time. From the look on the magician's face, wherever he'd slipped off to was a place of darkness. "Are you okay?"
Simon blinked as if waking from drug-induced sleep and peered at Marcus. "He won't let you rest. Never. He's out to destroy you. All of you."
"Zennon."
"Yes, Zennon, of course. To bring devastation across many nations." Simon stood and started to walk away.
"Simon, stop."
The magician turned.
"I can't help but say this again. I believe you're part of defeating him more than you can conceive."
"If I am, I don't want to know about it. I've done enough and enough has been done to me." Simon shook his head, sighed, and called out over his shoulder as he trudged away, "Don't contact me anymore, Professor. Our time together has come to an end."
TWELVE
BRANDON SAT ON HIS DECK TWENTY MILES EAST OF Seattle on Saturday afternoon and watched a stiff breeze buffet the Douglas fir trees in his backyard. The sun cast thick, black shadows across his well-manicured lawn and his wind chimes chattered at him. The only other sound was the clink of ice against his glass of Mike's Black Cherry Lemonade as he downed the last of the beverage.
In the old days he would have had music blasting from the outdoor speakers, but those days were over. Music was the last thing he needed. Then again, maybe it was the first. He didn't care. He didn't want to hear it. He shifted in his Adirondack chair, trying to think of nothing, but not having a great deal of success.
The thought of playing again—singing again—was like a boomerang he tossed away, but it kept returning no matter how far away he flung the idea. Something miraculous had happened down in Edmonds and he couldn't ingnore that fact. Doug said God was in it. Sure he was.
Intellectually he knew his soul was starving without music, but he couldn't convince his heart of that truth. Too painful to be reminded his dream was dead forever. He was the Song? Right. What role did he have in Warriors Riding now? He felt like one of those old-school actors who wasn't relevant anymore but was still invited to the award ceremonies for sentimental reasons. His cell phone vibrated and he looked at the caller ID. Reece. Great. Doug's tag-team partner.
"Yeah?"
"You need to hear the truth. And accept it." Reece's voice was monotone.
"What is this? First Doug and now you? Can't you just leave me alone?"
"No." Reece paused. "You're not on this journey alone, Song."
"Don't call me that. I'm not the Song. Not anymore." Brandon kicked at a green leaf on his deck. "That died. I will never be that person again."
Reece didn't respond.
"It's over for me. Forever. Done. Finished. Gone. Sign the papers and turn over the deed."
"If you're so convinced of that, then why do you still seek it?" Reece said.
"I'm not."
"Hmm."
"I just want to have some kind of purpose again."
"So this is all about Brandon Scott?"
He didn't answer.
"I've learned a few things during my sixty-four years. One of them is this life is not about you. Not even a little about you or me. We no longer live a life in the flesh, but a life in the Spirit. A life where we have given up what we want. And we pursue what he wants. And you're being the Song is part of what I believe the Spirit wants."
"For some strange reason I don't want anything to do with music anymore. Any insight as to why I might feel that way?"
"As I just said, you are still the Song. You can't run from that."
"Sure I can, Reece. I just bought a pair of stellar track shoes and I'm sprinting faster than the Flash." Brandon scowled. "You got your sight back, at least in a way. I have nothing. I had this wild, insane idea that Dana and I might have something, at least the hope of a future together, but even that has crashed and burned like a kamikaze fighter."
"You have everything."
"Really? I must have misplaced my everything because I can't seem to find it." Brandon patted his front and back pockets and then his chest. "Dad gum it all to tarrrrrrnation, where da heck did my everything go now, y'all?"
"That's quite humorous."
"It doesn't sound like you're smiling."
"Blind people rarely smile."
"Is _that_ supposed to be funny?"
"Mildly," Reece said. "You have the Spirit inside you. That is everything."
"Is that how you felt when you first lost your eyes? Completely content? We both know it isn't."
"True."
"And now you've got this superpowered spiritual laser-beam eyesight where you can see into the spiritual realms all around us." Brandon stood and paced on his deck. "And somehow see shapes and outlines of people and whatever else as well. Funny how your attitude has improved since that happened."
"It improved long before I got a new kind of sight."
"That's because you had hope. You believed the prophecy would come true and you would see again."
"What do you believe, Brandon?"
"Nothing left in that candy store, Willy. The kids have cleaned out the chocolate bars and the Wing Dings, and there aren't going to be any candy canes this Christmas."
"At least you still have your sarcasm." Reece gave a soft chuckle. "Don't give up on hope, son."
"I don't even get why you and Doug are pushing for something more. The Warriors are done, aren't they? The prophecy is fulfilled, Reece. I don't see why we can't disband this thing."
Brandon shuffled through a stack of papers on his end table and pulled out a copy of the prophecy. "Listen to your prophecy carefully, Reece:
WHEN THE TIME COMES, THE SPIRIT WILL REVEAL EACH OF THEM TO YOU. YOU WILL TEACH THEM THE WONDERS OF MY POWER THEY CAN'T YET IMAGINE. AND INSTRUCT THESE WARRIORS HOW TO GO FAR INSIDE THE SOUL AND MARROW.
THEY WILL RISE UP AND FIGHT FOR THE HEARTS OF OTHERS. THEY WILL DEMOLISH STRONGHOLDS IN THE HEAVENS AND GRIND THEIR ENEMIES TO DUST. THEIR VICTORIES WILL SPREAD ACROSS THE NATIONS. YOU WILL POUR OUT YOUR LIFE FOR THEM AND LEAD THEM TO FREEDOM, AND THEY WILL TURN AND BRING HEALING TO THE BROKEN AND SET THE HEARTS OF OTHERS FREE.
AND WHEN THE WOLF RISES, THE FOUR MUST WAR AGAINST HIM AND BRING ABOUT HIS DESTRUCTION,
ONLY THEY HAVE HOPE OF VICTORY.
AND FOR ONE, THEIR VISION WILL GROW CLEAR,
AND FOR ONE, THE DARKNESS OF CHOICE WILL RAIN ON THEM,
AND FOR ONE, THE OTHER WORLD WILL BECOME MORE REAL THAN THIS ONE,
AND FOR ONE, DEATH WILL COME BEFORE THE APPOINTED TIME.
"See? It's over. You taught us your skills. We took out the Wolf. Marcus did the choice thing. Our message is certainly spreading across the nations, one little gathering of believers at a time. Have you been reading about the number of groups—?" Of course he hadn't. "Sorry."
"You don't have to be."
"Warriors Riding groups are forming in the UK, Australia, South Africa, Wales, Korea, I kid you not."
"Yes, I know."
"So why can't we let it continue to spread on its own at this point? They don't need us anymore." Brandon stepped off his deck onto the grass. "The death of my career certainly came before the appointed time, so that part of the prophecy is done. Your turbocharged vision is certainly the answer to the clear-vision part, and with that, the spiritual world is much more real to you than this one. Finished."
"But there is another prophecy now."
"Yeah, Doug told me about that. I'm supposed to believe it's real, right?"
"Yes."
"And when were you going to tell me about it?"
"It's what we wanted to tell you at the gathering on Friday night where you—"
"Came off the rails and slammed into the other trains on the neighboring tracks. I know. Bad behavior. Sorry."
"Come to Well Spring with us, Brandon."
"My answer hasn't changed since talking to Doug." Brandon stepped back onto his deck and slumped back into his chair. "I gotta go."
"Pray about it, Brandon. Not a rub-a-dub-dub, thanks-for-the-grub, yay-God prayer. A real one. Which means listening more than speaking."
"I'll think about it." Brandon tossed his cell phone onto the small, round wooden table to his left. He sat up and tried to believe Reece's words and tried to listen for the Spirit's voice but gave up after a few minutes. He was about to go inside when he saw something move from the corner of his eye.
He turned to his right and stared at the thick row of fir trees along his property line. There. High up, maybe eighteen or twenty feet above the ground, something was moving. He rose from his chair, walked the fifteen feet to the end of his deck, and eased down the stairs leading onto his thick jade grass. What _was_ that?
A blurred picture of a woman the size of a small movie screen shimmered against the trees. The tone of her skin and her dark hair made her appear to be African-American, but Brandon couldn't tell for sure. The image was transparent, but he could make out her walking through a building made of glass. Business people moved past her from in front and behind. Was she wearing a dark sweat suit? It seemed out of place. She smiled and shook hands with someone who had his back to Brandon.
As he stared at her, she became more solid but still too blurry to completely make out her features. Then her surroundings changed. He could make out a field with trees forming a half circle around it. As more of the vision came into focus, Brandon saw a swing set and merry-go-round with a few children playing on it.
The woman pulled a granola bar out of her pocket, turned it over, and stuffed it back into her sweat suit. She stared at the children, looked up at the sky, then down at her upturned hands in her lap, and began to cry.
That's when the music started. A song of such joy it created an instant discord between the woman's racking sobs and the tune that swirled around Brandon's head. Even before the words started, he knew the song was about her deepest fear. This time the lyrics leaped out at him immediately.
_Push your body, push your talent, take it to extremes,_
_Will they love you, when it's shaken, no longer their great dream?_
_Can you leave it, lay it down, when the race comes to an end,_
_When the cheers have vanished, and the spikes are tarnished, will they still call you friend?_
The rest of the lyrics flowed into his mind like a river, but the words weren't what set Brandon's heart pounding. It was the music. A melody that pierced him like a rapier where one edge of the blade was cast from the fires of joy and one from the fires of pain.
Brandon fell back into his chair and the vision faded along with the song. For a few seconds he begged for it to come back, then turned and staggered across his deck and into his house till he reached his studio. He picked up his guitar. He had to get this down on tape. The guitar felt strange in his hands, but he threw off the feeling and punched Record. He wouldn't lose this song like he'd done last time.
Maybe this was the way he would be the Song again. No, he couldn't sing like he used to, but he could write the songs, record them, produce them, reach the world through the voices of others. Maybe Doug and Reece were right. Maybe God was in this.
A giddiness washed over him that he hadn't felt since he recorded his first album. This was it, the key to his return. The Spirit had given him a song of such power, there was no question in his mind it would be a major hit. He'd done some producing—three albums and a couple of singles. He'd always said he'd get more into that side of the business someday. Someday was here.
He laid down the melody on tape—he didn't care that his voice sounded like metal on concrete—scribbled down the lyrics, and then tried a variety of chord progressions, searching for ones that would fit the melody. Once he found them, he toyed with making the song up-tempo or keeping it slow as he'd heard it out back. In the end he decided on keeping it slower. In twenty minutes he was ready. He hit Record and began to sing.
_Stop._
The voice of the Spirit was not still and it was not small. It thundered inside him and Brandon blinked. "Lord?"
_This is not your song; it is not for you. It is her song, for her alone._
"What does that mean?"
_The song will remain with you till the time._
_The time?_ "What time, Lord?"
_You will know._
Brandon set his guitar back onto its stand and stared at the strings as if he'd never seen them before. Why had his life become such a kaleidoscope of confusion? Why couldn't God just give him his voice back? Give him a relationship with Dana? What was God doing?
Something in his gut said answers would come soon—but not the ones he wanted.
THIRTEEN
TWO DAYS LATER, THE GOD OF AWKWARD MEETINGS PAID Brandon a visit. He was in Seattle strolling through Pike Place Market looking for original photos of old guitars. He looked up right after he paid for a shot of a Gibson Les Paul from the forties and saw Dana walking toward him. Great. His heart rate picked up. What was she doing down here on a Monday afternoon? Shouldn't she be at the radio station? Next to her walked a woman who looked vaguely familiar.
God was in all things? Then why force him to bump into her? If Dana was done with him, why couldn't he be done with her? Whatever. He'd get through it. This was inevitable, wasn't it? No, it wasn't. If he was finished with the Warriors, there would be no reason to see her ever again. Yeah, right. As if it could be that easy. She and her dive-into-your-soul emerald eyes were in his life forever and ever amen. _Accept it. Deal with it. A little hello, small talk, how are you, how are the Warriors—have you seen any of them lately? How are things at the station? And get out of there. Not a big deal._
He gave a halfhearted wave as the two women clipped toward him. If Dana was uncomfortable seeing him, it didn't show. "Hey," she called out from twenty feet away.
"Hey."
When Dana reached him, she gestured to the woman next to her. "Brandon, I'd like you to meet a recent acquaintance of mine. This is Sandra. Sandra, this is my friend, Brandon." She turned to Brandon. "Sandra is part of a national radio campaign and is in town visiting our station as part of the promotional push. She'll cut some liners for the client and maybe even some liners for my station and a few of the other stations in our group. I'm showing her a few of the sights around Seattle."
Brandon stared at the woman. Tall. At least five foot nine. And he knew her. He'd at least seen her face before. Without question, but from where escaped him. One of his concerts maybe? No. Something caught in his spirit. It wasn't at a concert, it was somewhere else, but he had no recollection of a conversation.
"Have we met, Sandra?"
"I don't think so, but I know who you are even without Dana making the introductions." She smiled and extended her long arm.
"You do?"
"Aren't you Brandon Scott? The singer?"
"I used to be."
"I thought so. My sister has all your music. Forces me to listen to it all the time."
Brandon laughed.
Sandra looked at him with her head tilted. "You say you used to be. Care to explain how you changed into someone else?"
"It took a great deal of work and a decision to trust God to ruin my life."
"I see." She nodded, her brown eyes narrowed, and in that instant Brandon knew who she was.
"Oh, wow. You're Sandra Aspen. From the Olympics."
"Not true. I didn't come from the Olympics. I came from Maine." She smiled. "But I did compete in the 2000 and 2004 games."
"Wow. This is wild. You won a gold and two silvers in Athens. Silver in the 100 and 200 meters and gold in the four by one hundred."
"I'm impressed. You're obviously into track and field."
"Actually I'm not. Only once every four years. For some reason I can't stay away from the Olympics. You knocked me out that year. It is a true pleasure to meet you."
"Thank you. It's good to meet you as well."
"What have you been doing with your life since the games? Those Olympics were your last competition, right?"
"Yes, I retired after Athens." A darkness passed over Sandra's eyes. "I've been dabbling in various things since."
She looked down and Brandon's mind locked on to the image and froze it in his brain. Yes, he knew her from her track-and-field days. But he'd seen her much more recently. It was her in his backyard. In the vision. Along with a song that ripped his soul apart with its power and beauty.
"Are you okay, Brandon?" Dana touched his shoulder.
"I'm fine."
"You don't look fine. You look as white as that cloud over our heads all of a sudden and like you're about to faint."
"Yeah, I do feel a bit strange. Probably bad sushi for lunch."
A compulsion rose up in him to sing the song for her. Not a good plan. With his raw and raspy voice? No thanks. Wouldn't make Dana look good. Him either. But the feeling only intensified. He couldn't. Impossible. Not even in private, let alone here in the middle of Pike Place Market. And to a complete stranger? Huh-uh.
_You can. You are the Song._
_I can't. My voice is gone. Plus, I don't remember the song. I don't remember the words. I don't have my guitar . . ._
_Remember what I told you?_
Brandon pressed the heel of his hand into his temple as if he could force the idea from his mind. But the impulse continued to grow at an exponential rate.
_Okay, let's make a fool of myself._
"I need to ask you a question, Sandra."
"All right." She folded her arms and gave him a curious look.
"I'll warn you, this might sound very strange."
"Don't worry. You wouldn't believe some of the questions I've had over the years."
"This one might be the winner."
"Really." Sandra glanced at Dana and then back to Brandon. "Lay it on me. I'll let you know if it is."
"Recently were you by yourself in a park with two swing sets and a merry-go-round? Next to a lake with a long, old, piling-style dock jutting about fifty feet out into the water? And a green rowboat was tied up to it?"
Sandra's eyes went wide.
"You pulled out a granola bar or PowerBar or something, then stuffed it back in your pocket without eating it. Right beside this little bed of yellow and blue flowers."
Sandra tried to smile but it died a second later, and her eyes narrowed and her voice grew soft. "How do you know all that?"
"I know, I know." Brandon took a step back and held up his hands. "Kinda creepy, but I swear we've never met before. And I have no clue how to be a stalker. You can ask Dana."
"Then how—?"
"Are you . . . ?" Brandon hesitated. "I take it if you've listened to my music you believe in God?"
"Sure. I'm no churchgoer, if that's what you mean, but I'm a spiritual person and I believe there is a God, yes."
Brandon dropped his head as if it could make the compulsion go away. He had no wish to put Dana in an awkward position and even less desire to make a fool out of himself. "Sorry, I shouldn't have told you—"
"I repeat, how did you know about the merry-go-round, and lake, and green rowboat?"
"Here we go." Brandon gave Sandra and Dana a weak smile.
Dana tilted her head and frowned at him with a please-go-away-now look. "What do you think you're doing?"
"The Wild Goose is leading and I'm going to follow."
"Wild Goose?" Sandra pointed at Brandon and turned to Dana. "This guy is your friend?"
Brandon glanced around. No one was close enough to overhear their conversation, but if he sang they would.
"I had a vi— I had a dream and you were in it. You sat on that bench in that park, and from what I saw you weren't having the greatest of days. And while I watched . . . while the scene played out, I heard a song." He hesitated and opened his palms. "And I'd like to sing it for you."
Sandra folded her arms. "Did you say it was a dream or a vision?"
"A vision."
"Brandon Scott had a vision about me." She put her hand on her hip and cocked her head. "I know you're hyperspiritual from listening to your music, but you're starting to get a little freaky."
"As you might be able to tell, my voice is pretty scratchy these days." Brandon cleared his throat. "That's what I meant by 'used to.' I can't sing anymore. Or I should say I can barely sing. I was . . . injured . . . in the throat and it destroyed my voice. But I feel like I'm supposed to sing this song for you."
"Right now?" Sandra glanced around at the shops and the people strolling up and down the street. "You're one of those freak-out, charismatic, squirm-on-the-floor types, aren't you?"
"No. I'm not, but I feel like the Spirit—"
"You feel like the _Spirit_ is telling you to sing. Like the Spirit of God? The Holy Ghost and all that? What, are you going to start dancing around and speaking in tongues?" Sandra held up her hands. "You're right about the weird question thing. You definitely win the gold."
Sandra took three slow steps backward. "I'll talk to you later, Dana. I'm headed back to the hotel. I'll talk to you never, Brandon." She continued to walk slowly backward, apprehension on her face.
_Sing._
_Now?_
_Yes._
Why not? He didn't have much of a life left anyway. He would play the fool, not care what anyone thought. Brandon opened up his mouth, and as he did it felt like his pride spilled out and dropped onto the concrete at his feet.
But it didn't matter what his voice sounded like. This wasn't about him; it was about this lady, Sandra, and what the Spirit had given to him to give to her. He didn't remember the words or the melody—didn't have a clue where to start—but again, it didn't matter. He glanced at the people milling through the market on either side of Dana and him and pushed from his mind any concern about what they would think about his ragged voice. He breathed deeply and sang.
As the first words hit the air, astonishment spun through him. This couldn't be. His voice sounded strong and clear and stunning. The tone was deeper and richer than he'd ever experienced. His heart raced. This shouldn't be possible. But just as it had been up in Edmonds, it was happening.
_"Push your body, push your talent, take it to extremes."_ When he finished the first line of the song, he stopped.
Sandra stared at him in awe. Her face grew a shade lighter. "Wow."
Brandon stared at her as she eased back toward him.
"Why'd you stop?" Sandra came alongside Dana. "And I'm not getting the voice-is-gone thing at all, honey. I've listened to a lot of your tunes, and you never sounded that good. Ever."
Heat rushed through Brandon's body. He wasn't imagining it. She'd heard it too. This new voice God had given him.
"Don't just stand there with your mouth hanging open like a junkyard dog. Let's hear the rest of it." Sandra beckoned with her fingers.
Brandon started over, this time closing his eyes and singing it as if he and the Olympian were the only ones in the world.
_"Push your body, push your talent, take it to extremes,_
_"Will they love you, when it's shaken, no longer their great dream?"_
As he finished the second line, he heard Sandra pull in a quick breath.
_"Can you leave it, lay it down, when the race comes to an end,_
_"When the cheers have vanished, and the spikes are tarnished, will they still call you friend?_
_"There is one who longs to love you fully, and draw you deeper still."_
When he finished the fifth line, he opened his eyes. She was two feet away with tears in her eyes, staring at him. He couldn't tell if her face held anger or deep longing. A few more seconds revealed it as the latter.
_"Hope reborn and dreams uncovered, destiny fulfilled._
_"Take his hand and run the distance, the path is lined with gold,_
_"But getting there requires a death, then beauty will unfold."_
By the time he finished, she sobbed with her face in her hands. Dana took her by the arm and led her away from the market to Victor Steinbrueck Park overlooking Puget Sound, right off Western Avenue. No one was in it, and once they reached the center of the small grass lawn, Dana took the lead.
"Looks like God might be doing something here," she said gently.
Sandra nodded and took the tissue Dana offered her. "When I stopped running, others started. Away from me. Everyone wants to be famous, you know?" Sandra looked up, her eyes red. "Everyone wants to be loved. And I believed they loved me. I believed he loved me for who I was, not for what I did. And when I came home and found that note . . ." She broke down again. When she raised her face a few minutes later, every shred of toughness had disappeared.
They sat in silence as Sandra leaned into Dana and Dana held her tight.
"If it's okay with you, Brandon and I are going to pray for you."
Sandra nodded again, and for the next five minutes Dana and he prayed and listened to what the Spirit was saying about Sandra and prayed some more.
"I don't understand it. I feel hope for the first time in . . ." Sandra wiped her cheeks.
"Me either," Brandon said. "No, I'm not kidding."
Sandra smiled at him with a mixture of laughter and tears.
By the time they finished, a lightness sparkled in Sandra's eyes and a tangible peace surrounded her.
"Strangest and best question I've ever been asked." She reached out and hugged Brandon and he hugged her back. "Thank you for everything."
As she strolled off, Dana's eyes stayed wide for a long time. "Wow, that was something."
"What part?"
"All of it." Dana turned for a few seconds in the direction Sandra walked, then turned back and stared at him like he'd grown wings.
He grinned at her. In a way he had. He was the Song again. "That look means something."
"I've never heard you sound like that. Ever. I don't know how to describe it." She shook her head. "Your voice . . . never . . . I mean . . . you know I've always loved your voice, so don't take this the wrong way. But compared to what you sounded like before, this is a million times beyond."
"Are you serious?"
"That was the most beautiful voice I've ever heard. You're healed."
"In a way, maybe." Brandon gazed out over Puget Sound. "But not like you're thinking. This is something else."
"What do you mean?"
"I'm not exactly sure. I'm trying to figure it out, but I have a feeling when I sing his songs, I get the voice you heard. When I sing my own, I get the raspy voice you're hearing right now."
"And you have no idea when he's going to give you the next song?"
"Exactly."
He turned to go, but before he could step away, Dana reached out and tugged on his arm. "Hey, can I tell you something?"
Her eyes were almost as soft as they'd been back at Well Spring when they'd talked about a coffee date. Was he getting a glimpse of how he suspected she really felt deep down about him, about them, or just some leftover emotions from the time with Sandra?
"Anything."
She glanced at the ground, out over Puget Sound, and finally back at him. "I want us to be close. I mean . . . at least closer than we are now. I'm just . . . it's just that . . . I think we need to wait and—"
"I think we just need to—"
"No." Dana held up her hand and made a quarter turn. "Stop. Let's just keep it right there for now. Okay?"
No, it wasn't okay. Brandon couldn't shake the feeling they were supposed to be more than close, or closer—whatever that meant. As unyielding as it might sound, for him, their relationship needed to be all or nothing. And he wouldn't apologize for that. They were supposed to be together like they were four years ago. Engaged. On their way toward spending the rest of their lives together. But Dana wasn't ready to get even within a football field of that door. Brandon nodded. "Okay."
"Thank you."
"Um-hmm."
She walked away for two steps, then turned back. "This thing with Sandra? I think it's going to happen to you again. Soon."
FOURTEEN
THE MONTBLANC PEN IN HIS HAND SHOOK. NOT FROM fear the words he'd scrawled on the pages in front of him weren't true. He knew they were from the Spirit. And not from what the words portended for the five of them. His hand shook from the adrenaline that flowed from his head and heart into the palm and fingers of his right hand. From anticipation of what the five would think and feel, and how they might be inspired when they read the letters. How these letters might guide them and bring freedom.
He straightened the six or so pages in front of him and stared into the flame of the oil lamp that sat on the cherrywood desk. How long would his own flame continue to burn? Years? Decades? Months? There was still so much to do. But if his time on earth was only days more, it would be all right. All would be right. In this age or the next. And these letters were only a small part in the grand play where all the world and all the heavens were certainly a stage, and he was simply playing his part. William indeed had it right.
He turned back to the page and stared at the paragraph he'd just written. Had those words come from his hand? He knew they had, of course, but he didn't fully recognize what was written there. He smiled. Good. It confirmed the words weren't coming entirely from him but from the Spirit as well. And they would need these words. If not now, someday soon.
Was he worried the Warriors would interpret what he'd written correctly? Yes. And no. It wasn't his place to fret about how each of their letters would be received. His job was to write them. And pray they would hear the Spirit's voice as they took in the contents and then decided how to act on the information.
He sighed and set the pen down. _Someday soon._ The words circled his mind like a blue heron circling high above a lake, watching, waiting to streak down, strike hard, and snatch a fish from the water. Years of life left in this mortal body? Yes. He felt it. Which made the letters unnecessary. So why did he feel compelled to write them?
He slumped back in his chair and sighed. One more letter to write, and it wouldn't be recorded with pen and paper. He walked outside and vowed to finish it, then put all the letters in the box before dawn crept across his windowsill.
FIFTEEN
ON TUESDAY MORNING, BRANDON DROVE EAST ON I-90 toward the little town of Hyak on the top of Snoqualmie Pass. His seven-year-old mountain bike, which had logged maybe seventeen miles on it, sat tied to the top of his Toyota Tundra. He needed to get away. Think. Do something metaphorical and physical at the same time.
Should he go to Well Spring with the others? After yesterday's weird display of God's love down at Pike Place Market, Brandon's definite no had turned into a definite maybe.
He needed to figure it out. Figure himself out. Let Reece and the others know if he was going this week or not. So he was about to head into the darkness to see if there was any light at the end of the tunnel. Literally.
He would take a ride on the John Wayne Trail, the perfect adventure for a mid-July Seattle day. The mountain bike trail was a stretch he could hop onto just west of Hyak. A few minutes' ride would take him to a two-mile train tunnel first carved into the Cascade Mountains back in the early nineteen hundreds. Over two hundred thousand hikers and bikers went through it every year, and Brandon figured since it was only twelve miles from his home, it was about time he partook of an adventure in his own backyard.
He stopped at the entrance and looked at the archway. The tunnel had closed in January of '09 for eleven months because chunks of concrete had started raining down from the ceiling. But it had been fully repaired. Supposedly. He laughed to himself. If this was the way God wanted him to go—so be it.
He coasted into the tunnel and came to a stop twenty yards inside. The light from behind him still gave a smattering of light here, but twenty yards ahead there was only blackness. Wow. Only two miles long and he was freaking out. He needed to get it together. But it was a perfect analogy for his life. No light. Only darkness ahead. And only a tiny bulb on his head that he hoped wouldn't wink out halfway through. Should he go back to see if he had another flashlight in his trunk?
_No._
The voice of the Spirit was soft, but the word was clear. He needed to get going.
As he eased forward it felt like he was entering the Mines of Moria in _The Lord of the Rings._ Should he stop? Should he avoid the trolls while he still could? Ridiculous. He was going through. He flipped on his helmet light and was surprised how little of it penetrated the darkness. Brandon turned and looked back, and the sunshine seemed to invite him to return to the entrance. It felt strangely like a tug-of-war. What was wrong with him?
He pushed off and slowly pedaled deeper into the tunnel. The tunnel curved slightly to his left, and in a few minutes the remaining light from the tunnel entrance was gone. Utter darkness. Apparently he picked the right analogy. Headlamp wasn't nearly bright enough. Should have brought a spotlight.
He'd heard a pinprick of light from the other end of the tunnel could be seen, but either his eyes weren't working like they used to or someone had turned off the sun at the other end. Brandon pedaled on, listening for sounds of other riders or walkers and hearing nothing but the spin of his tires on the asphalt.
How long had he been under the mountain? It felt like days when in reality it had probably only been ten minutes. Brandon guessed he was doing five miles per hour, which meant he should cover the length of the tunnel in another ten or twelve minutes. He should have brought a watch.
Finally. He saw light far in front of him. And whatever was at the far entrance appeared in the opening in the shape of a cross. Amen. He was ready to get back into the light.
He pumped his pedals till his quads burned and the opening grew larger every second. As he exited four minutes later, a palpable weight rose off him. He'd never been afraid of the dark—but then again, he'd never been in a pitch-black tunnel two miles long.
Brandon coasted to a stop and gazed down the trail that ran straight ahead. The clouds he'd seen when he entered the tunnel had left, and the sun was out in full force. He looked back at the tunnel and into the darkness. He'd been inside for probably twenty-five minutes. What would it have been like to work for years inside the mountain?
A lone biker sat on the edge of the trail, his arms around his legs. He looked to be in his early thirties. A dark-green backpack sat next to him, and as Brandon's brakes squealed, the man turned. He stared at Brandon, nodded, then turned back around.
Brandon set his bike down and ambled toward the man. "How're you doing?"
"Me?" The man got to his feet and brushed dirt off his dark-gray biking shorts. "Really good, thanks. If life got any better it'd probably take two of me to handle it."
"Nice line." Brandon glanced behind him. "Did you come through the tunnel, or are you about to go through?"
The man pointed west away from the tunnel, down the gravel road. "I came up the trail, so I'm about to go through. My first time."
"Darker in there than I thought. I'd heard you could see light from the other end, so I figured I wouldn't need that strong a light. Wrong. I almost went back to my car to see if I had an extra flashlight. Only would have taken ten or eleven minutes, but I had this weird feeling I wasn't supposed to. Once I got to the heart of the tunnel, I wished I would have ignored the feeling and gone back." Brandon laughed.
"So it was good?"
"It's a rush. But not sure you'd want to turn off your light when you're in there all alone."
"That'd feel like death, I'm guessing." The man cocked his head and gazed at Brandon in a way that was . . . off.
Brandon stared at the man, and as he did a song began to play in his head. _Here we go again._ At first there was only music, no words. Great crashing cymbals and soaring violins filled Brandon's heart, and then the other instruments slipped away till all that remained was a piccolo playing a song that could turn a desert into an ocean.
The second movement of the piece started, and as it did Brandon's mind filled with cascading images of the man sitting next to him. Not good. If the images were from God, God would have to show up and do something powerful. Brandon waited for the words of the song to come, and when they did the images he'd seen all made sense.
_Life is stolen, lives are shaken, so deep and to the core,_
_Pain is spreading, his life is shredding, this is eternal war,_
_Fear has crushed him, horrors rushed him, illusions, but so real,_
_He needs awaking, not this taking, with blood about to spill,_
_Daughters yearning, the future burning, before their sun can shine,_
_Grant him grace, extend our mercy, a touch of the divine._
A few minutes later the song ended. It didn't take someone with the professor's brain to figure what this guy was about to do. How was Brandon supposed to get into this? With Sandra, Dana had been there to break the ice. Here he was dealing with a total stranger. "Hey, pal, don't kill yourself, okay?" probably wouldn't be the most effective intro. Cold sweat broke out on his forehead.
"I don't suppose you heard that?" Brandon asked before he could stop himself.
"Heard what?"
"Nothing." He held out his hand to the man. "I'm Brandon, by the way."
"Good to meet you. I'm Garen." The man shook Brandon's hand.
"Is this a solo trip? Any wife or kids still coming up the trail?"
"Nope, all by myself today, but I am married. For almost seven years and not even a hint of itching going on." Garen scratched his forearm and grinned.
"Nice." Brandon swallowed hard and tried to smile.
"Plus two of the most gorgeous daughters you'll ever set eyes on. They're just six and four, but I still oil up my shotgun every other Saturday night. I'll be ready for those boys who'll be sure to be coming over when they reach the teen years." He winked. "What do you do?"
"I'm kind of a musician."
"A songwriter?"
"I do write songs."
"I figured you probably weren't on the singing end of things with a voice like that." The man smiled. "Unless the Bob Dylan style is making a comeback."
"Not that I know of. No, I don't sing much anymore." Brandon rubbed his throat. "Hey, Garen, are you a Beatles fan?"
"Kind of. I know some of their songs."
"A friend of mine loves 'em. You know the song 'Yesterday'? It's the most covered song in the history of music. Do you know how McCartney came up with it? Apparently he woke up one morning with the song in his head. The whole melody was there and he had no idea where it came from. He thought he'd heard it somewhere and asked around to see if he'd picked it up unconsciously from someone else. But he didn't. It was his. From a dream. _Boom._ Just appeared in his head as if from nowhere."
"Didn't know that."
Brandon picked up a piece of old wood—probably off the old railroad trestle. "I can relate to that story."
"How's that?"
"Same thing's been happening to me lately."
"Getting songs like that, you mean? In your dreams?"
"Not in my dreams, but yeah, I'm having songs kinda pop into my brain, I guess you could say." Brandon grabbed his knees and squinted down at the river below them. _Keep going. You haven't scared the guy off yet._ "And sometimes it happens at the weirdest times. Like after I've ridden through an old abandoned tunnel on the John Wayne Trail."
"Okaaay." The man drew out the word, but the look on his face said he would humor Brandon at least a little longer. "So what kind of songs do you get?"
"Most of the time they're about specific people."
"I'm not sure why I'm asking this because I think I already know the answer, but why are you telling me this?"
"I think I might have just heard a song about you, and I want to tell you about it, but I don't want the idea to freak you out."
"You don't even know me."
"Yeah, I know. But just like James Paul McCartney had this song pop into his head unannounced, I had a song pop into my head unannounced just now. And like I said, I have this strange feeling it might be about you."
"All right." Garen scooted a few inches to the left and narrowed his eyes.
"And I'm thinking I'd like to try it out on you, you know. Sing a few lines and see what you think."
Garen craned his neck in all directions as if looking for something. "The cameras are trained on me right now, aren't they? Are you like some bizarre magician or mentalist? Undercover weirdo?"
"Look, you say the word and I'll get back on my bike and get out of here right now."
"This is too strange."
"I know. And it's going to get stranger."
"How?"
"I think the reason the song popped into my head is something or someone much bigger than me is behind it." Brandon stared at the man. Were those tears?
Garen dropped his head and mumbled, "Yeah, why not? Sing me your song."
When Brandon finished he turned to Garen. The man's head was in his hands. "Who are you?" Garen looked up and wiped his red eyes.
"A man. A friend maybe. Most of the time I'm not sure anymore."
The man stared at Brandon long past uncomfortable. Tears continued to stream down his face. A few other bikers passed them, but if Garen noticed he didn't give any indication.
"I had one goal when I came up here today." Garen picked up a rock next to him and tossed it over the edge of the bank toward the river. "Only one." He reached inside his pack and lifted out a pistol and held the gun up to his head.
"I was going to end it. Ride five minutes or so into the tunnel, get off my bike, and _boom_. Good-bye." He lowered the gun to the gravel between them but kept his forefinger on the trigger. Brandon could see the safety was off.
"I was counting down from sixty to zero. When I reached three I was going to head for the tunnel and get it over with. Do you know what number I was on when you came pedaling up?"
Brandon shook his head.
"Three." The man wiped his nose. "I'm kinda glad you didn't go back to your car for that extra light. You know?"
Brandon stared at the man and gave a slow nod.
"Please take that." Garen pulled his finger from the trigger, set the gun down between them, and patted it.
Brandon slid his hand over the gun, lifted it, and set it down on his other side.
The man smiled. "You're not a gun guy, are you?"
"Not so much." Brandon chuckled. "Could you tell from the fear in my eyes or the sudden rivers of sweat pouring off my forehead?"
"And the way you picked it up." Garen tilted his head back and closed his eyes. "You know, at first I wasn't going to stop here. But at the last second I decided I would and take a moment to burn the memory of my wife and daughters into my mind." He turned and squinted against the sunshine. "Just in case there really is a heaven. I want to remember them."
"What happened?"
Garen closed his eyes and pressed his lips together so hard his face shook. "I had an affair. I can't tell my wife. It would destroy her."
"And leaving her like this won't?"
Garen opened his eyes and laughed, a sad little laugh that said killing himself was worse. "Yeah, it's more selfish this way, I suppose. This is crazy, but your song did whatever it was designed to do. I'm going to have a conversation I swore I would never have."
"Do you really have a shotgun?"
Garen shook his head and tossed another small stone over the side of the bank.
Brandon watched it splash into the stream. "Probably a good thing."
"I agree."
"Can I pray for you?"
"Pray?" Garen gave Brandon a crooked smile. "I liked the song. But I'm not much of a praying sort."
"You don't have to say a thing. And you don't have to agree with a single word. Just listen."
"Yeah. Okay."
After he finished, Garen wiped his eyes again. "You're a preacher, huh?"
Brandon smiled at the idea. He supposed in some ways he was a preacher. "No, not like you're thinking of it. Like I said, just someone who loves songs. Just someone Jesus knows."
"Do you think he knows me?"
"Without question." Brandon laughed and pulled a scrap of paper out of his day pack and wrote his number on the old Red Robin receipt. "Anytime day or night, you call me, okay? I'm there."
Brandon got back on his bike and pushed off. Just before he entered the tunnel, Garen called for him to stop.
"Hey, just wondering. You ever thought about being a singer? Your voice is pretty rough when you talk, but when you sing . . . wow."
Brandon shook his head and smiled. "Stay strong, Garen. He sees you out of the corner of his eye, and his eye will be on you the rest of your days."
On the way home Brandon tried to sing, but his voice was as bad as it had ever been. But this time it didn't matter. Before he reached home he'd left a message on Reece's cell phone and on Doug's. Both were the same: "I'm going to Well Spring."
SIXTEEN
"IT'S TIME FOR US ALL TO GO IN TOGETHER."
Doug clasped his hands and leaned his head back as they sat around the fire pit at Well Spring on Friday evening. When he brought his head back down, the look on his face was more intense than Dana had ever seen it. This was a man ready for war. "We need this foray into the spiritual realms if we are to be ready for Zennon and his army when he launches his final assault."
Battle. Army. War. Dana shook her head. That's all Reece and Doug had said to them for the past few weeks. Nothing more. Not any details of where or how or when Zennon would attack or what each of their roles would be in it. They'd said Brandon's part was critical. But wouldn't all their parts be critical? And why hold back the information if they knew more than they'd told? Because they didn't know? Or because they didn't want to tell Marcus, Brandon, and her?
She glanced outside as dusk brought darkness down on the ranch. She tried to shake the feeling that the fading light was only from the day slipping away and not from another kind of darkness come upon them. She should feel hopeful. Something had convinced Brandon to join them here, and he seemed even more settled than when he'd sung the song for Sandra. But Dana didn't feel hope. Only dread that hung on her like a watermelon-sized stone.
"When is this battle coming? And what is it going to look like? I don't understand why you're not telling us. And why haven't you read this new prophecy to us?"
Doug answered by standing and walking over to the couch and sitting next to her. He ran his hand over the top of his gray hair and turned to Reece. "What do you think?"
Reece nodded. Doug nodded back and pulled a folded piece of tan paper from his pocket.
WHEN IT IS TIME, YOU WILL JOIN THEM,
THE FOUR; THE TEMPLE, THE LEADER, THE TEACHER, AND THE SONG,
THEY WILL NEED YOUR STRENGTH FOR THEIR LAST BATTLE TOGETHER,
FOR THEIR GREAT ENEMY IS MOUNTING A FINAL STRIKE AGAINST THEM AND WILL HOLD NOTHING BACK,
AND YOU WILL STEP BOLDLY BEFORE THE TEMPLE AND HE WILL RECEIVE YOU,
AND YOU MUST TAKE THE LEADER INTO THE GATEWAY OF DEATH,
AND IN THE GATEWAY ONE WILL REMAIN, WHICH WILL BRING GREAT SORROW, BUT SET IN MOTION THAT WHICH MUST BE,
AND YOU WILL EMBRACE THE TEACHER FOR HE IS THE FRIEND OF THE RESTORER,
AND ONE YOU WILL TRAIN WHEN THEY ASK IT OF YOU—AND ONLY THAT ONE WILL YOU TRAIN,
YOU ARE A WARRIOR OF WARRIORS, LIVE IN THE TRUTH OF WHO YOU ARE,
AND RIDE WITH THE WIND.
No one spoke. Doug leaned back on the couch; Marcus and Brandon stared at him with narrowed eyes as the words of the prophecy settled like weights onto Dana's soul. _"Take the Leader into the gateway of death"?_
Brandon finally broke the silence. "No one is taking Dana through some gateway."
Reece shook his head. "No, they are not."
"But if that thing is true—"
"It isn't clear that the Leader is the one who will stay in the gateway." Reece stood.
"Then who is the one—?"
"We don't know that 'great sorrow' means death."
Brandon stood as well. "It's a pretty good guess, bub!"
"My friends," Doug said.
Marcus opened his palms. "And who is this warrior the prophecy speaks of?"
"Friends," Doug repeated.
"I'd like to get back to this gateway of death someone is supposed to take me through." Dana leaned forward.
"Friends!" Doug stood, and all of them went silent and focused their gaze on him. "It is time to go in. Trust now. He holds us all in the center of his hand."
Doug sat again and patted the back of her hand like a grandfather and it helped. A little. But not enough. Going in? After hearing that? It felt off. More than off, but when Doug offered his hand, she took it, as did Brandon on Doug's other side. As soon as Marcus and Reece joined hands, Well Spring vanished and her vision went dark. But a moment later she streaked toward a wall of stars so thick, she didn't see how they would get through it. The sensation of her spirit accelerating faster than her mind could grasp wrapped itself around her, and her worry melted away. Joy flooded every microscopic part of her being and she wished for the ride to last for hours.
The five of them slalomed through the stars like a galactic skier racing near the speed of light, but too soon they slowed and their trajectory changed. When she felt ground beneath her feet, Dana expected her breathing to come in gasps, but all that came out was laughter.
"I never want to get used to that." Brandon grinned.
Dana looked into his eyes and nodded. His smile was almost back to being the old Brandon's. Almost. Something was missing and she could pretend she didn't know what it was. He missed her. Whenever she looked at him, she saw his—should she call it love?—for her. She saw it right now. It was unsettling and reassuring at the same time. Because he did love her. And how could she deny she wanted to be loved? By him. She _wanted_ to be noticed. Fought for, as he'd already proven he was willing to do.
So what was wrong with her? Why wasn't what he'd already shown her enough? Was it time to give in? Maybe. No! It wasn't. She shook the arguments from her mind. This wasn't the time or place to try to untangle the spaghetti-like thoughts twisting through her mind. _Let it go._
She turned to look at Reece. The big man stared back at her with his brilliant blue eyes once again restored as they always were in the spiritual realms. He wasn't any less in the physical world but here he could see, and she missed being drawn into his eyes like a father draws a daughter.
"It's good to see you, Dana." He smiled and she returned his with one of her own.
They stood in the center of a quaint, open-air town square paved with thick gray cobblestones. A soft wind swirled through the square and brought the smell of burning leaves. There was no sound, and gray clouds that matched the color of the stones at their feet were washed across the sky.
"Where are we?" Brandon asked.
"So it begins." Doug sighed and his eyes took on a sadness so deep, tears rose inside Dana. Something was very, very wrong about being here, and the joy she'd felt during the journey was gone.
"What begins?" Marcus shifted his weight back and forth on his slender frame. Concern was etched into the professor's face, which probably matched her own. Whatever she felt, it was obvious Marcus felt it too. She turned and looked at Reece. Confusion was splayed on his face as he stepped toward Doug.
"We shouldn't be here, friend." Reece grabbed his beat-up darktan Stetson and shoved it down farther on his head. "I'm getting an extremely bad vibe about—"
Before Reece could finish, a noise like massive stones smashing into each other shot through the air around them. In the next instant the gray clouds turned darker. A smoky presence filled the edge of the square and moved toward them. Inky blackness swirled around the figure, then melted into a solid body. The demon they knew as Zennon.
His dark hair almost reached his thickly muscled shoulders. He stood fifty feet away from them, a mocking smile on his face. He'd changed. Far larger than the last time they'd seen him. Close to seven feet tall now. His features had grown sharp and even more handsome. But hard. His eyes darker, with an intensity that sent a chill through Dana. Seconds later three more demons—each a head taller than Zennon—appeared on his right and left.
"I didn't think you'd show, old man." The demon paced slowly in front of them.
"You can't win, Zennon." Doug's voice was calm. It was obvious he was somewhat surprised at the appearance of the demons but not entirely.
"Win what?"
"This war."
"The war? _The_ war. You mean tossed into hell at the end of the age with all the others who decided to follow Lucifer? We will see, won't we? But that battle is centuries in the future. Right now, all I care about is this war between you and me and your pathetic Warriors Riding. This battle, here and now, which I can most assuredly win. A battle I am winning already." Zennon pulled a long black sword from his belt. "Are you ready to die, Doug?"
"If he wills it." A sword shimmering with blue light appeared in Doug's hands.
"Then let us begin."
Reece stepped in front of Doug and took him by the shoulders. "What are you doing?"
"What I have been called to do. Nothing more."
"This isn't what I expected."
"Nor I."
"He said he didn't think you'd show, like you knew you were coming here."
"He might have known. I did not."
"You didn't know we were coming to face Zennon?"
"Not us. Me." Doug drew a deep breath. "That part is clear to me now. But no, I didn't know this is where the Spirit was going to bring us. Just that I was to follow his lead."
"Great. Lead followed. Now let's get out of here. I have a feeling it would take all of us to defeat these three, and I don't think we're ready for this kind of battle."
"Leave? No. Not yet." Doug placed his hand on Reece's cheek. "It is all right, friend."
"It's not. He's far stronger than we've ever seen him. Can't you sense it? The enemy has given him more authority and power. More skill."
"There is no power greater than the One."
"He's going to kill you, Doug."
"If the Lord wills it."
"You can't die." Reece's face went pale.
" 'Every man dies. Not every man really lives.' " Doug smiled. "From _Braveheart_."
Zennon scraped the tip of his sword along the stones at his feet and raised his voice.
"This has been so touching, but enough."
Doug raised his sword and stepped toward the demon, but Reece grabbed his arm. "I can't let you do this."
"You must. Do not intervene. It will be all right, I promise. Trust me."
Pain was evident on Reece's face, but he nodded. Doug covered Reece's hand with his own and eased it away, then strode toward the center of the square to meet Zennon. When they both reached the middle of the cobblestones, they circled each other twice before Zennon's blade flashed toward Doug.
Doug blocked it easily, then stepped back two paces and raised his left hand. A ball of blinding white light was unleashed and streaked across the six feet between them. But before it reached the demon, Zennon raised a hand and the ball exploded in a shower of red light.
"Not bad, Lundeen. I see you're going to make this last longer than I thought you would. Maybe stretch it out to thirty or forty seconds instead of five."
"You won't win, Zennon. This battle or any other. Your destruction is coming and the power of the Christ will overcome you once again."
His face contorted with rage, Zennon leapt toward Doug and swept his sword in a wide arc. "Now!" the demon screamed as the blow slammed into Doug's sword. The impact sent Doug staggering back but he kept on his feet.
Zennon strode toward him to press the moment and unleashed another three strokes of his dark sword: at Doug's head, his legs, his body. Each time, Doug blocked the assault, but each time with less speed.
"Getting weak this quickly, old man?"
Zennon didn't wait for an answer and rained blows down on Doug from above, then the side, then straight ahead. The clash of their swords rang through the square like a twisted symphony of cymbals and both began to breathe heavily.
But suddenly Doug spun to his left with a supernatural speed and sliced at Zennon's right side. The demon blocked the attack but not fully, and the blow tore into the upper part of Zennon's leg. Dark-red blood spilled out and the demon's face turned black.
He roared with fury and attacked Doug again. But his rage made his assault less disciplined, and Doug not only parried the demon's blows, he drew blood twice more. Once on Zennon's right arm and once on his left hip.
Hope rose in Dana, but then she looked at Reece. He sucked in rapid breaths as he clenched and unclenched his hands. Fear radiated from his face and eyes, and in that moment Dana realized Doug couldn't win alone. Even though Reece's mentor had drawn first, second, and even third blood, his strength was waning, and if Doug's strikes had hurt Zennon, there was no visible evidence to back it up. Sweat glistened on Zennon's body and face, but he seemed just as fast and strong as when the battle started.
"Enough." Zennon grinned, wiped blood from his thigh, and licked it from his palm. "Does not taste the way yours will, Lundeen." The demon raised his sword and raced toward Doug.
A battle cry erupted from Reece's mouth and he sprinted toward Zennon, but the two demons with him stepped in front of Zennon and drew their swords in perfect synchronization. Reece didn't slow. Just before reaching them, he spun and whipped his sword around his body like a discus thrower.
The move startled the two demons, and when Reece's blow struck, it knocked the sword out of one of the demon's hands and sent the other one back two steps. Reece didn't hesitate. He drove his sword into the heart of the demon that had dropped his sword, and as if it were one fluid motion he slashed at the throat of the other demon. But Reece's blow was blocked as the two circled each other.
A thick voice came from the demon. "The chance to take down the mighty Reece Roth." The demon grinned and stepped toward Reece, his sword swinging from one side of his body to the other.
"Your last chance." The instant Reece spoke the words, he feinted high with his sword, and the demon took the bait. Reece dropped to a knee and his sword blurred from the speed with which he wielded it. The blade severed half the demon's torso and he collapsed onto the cobblestones.
Reece spun to face Zennon, the Temple's eyes on fire. "C'mon, Zennon, take me down."
"Nice try." Zennon laughed at Reece but kept his eyes fixed on Doug. "I could so easily, you know. But this is not the time. Now say good-bye to your dearest friend."
Reece leapt toward Zennon, but before he'd covered half the distance, Doug and the demon vanished.
"No!" Reece leapt to the spot where they'd disappeared, bowed his head, and went completely still. A few seconds later he rose back up. "There." He pointed across the square at an eight-foot-tall, thick bronze gate embedded in a stone wall at least forty feet high. "We have to get through."
He started to sprint toward the gate and the rest of them followed, but an instant later a swarm of twenty or thirty demons appeared in their path. Reece turned his head and shouted to Brandon, Marcus, and her. "We have to take them out fast!"
Swords appeared in all their hands and none of them hesitated. In less than two minutes, every demon had been destroyed. Reece tossed his sword to the ground and it clattered on the stones at their feet. He took six massive strides toward the gate and glanced at his hands. Instantly two fireballs appeared. But their intensity went far beyond the ones Brandon or she had ever conjured in the past. Both were white-hot and the heat coming off them stung her face.
The big man hurled both fireballs at the gate at the same time with a speed that stunned Dana. They exploded into the gate, and the structure shuddered like paper in a strong wind and the stones shook under their feet. While the fire still spread across the gate, another two streaked through the air. As two more appeared in Reece's hands, he glanced at Brandon and her as if to say, "What are you waiting for?"
In the next fifteen seconds, twenty-six fireballs detonated against the bronze gate. Although it shuddered violently each time, when the flames and smoke cleared, the gate still stood strong.
Reece closed his eyes. "What do we need, Lord?" After only a few seconds his head snapped up and he riveted his gaze on Brandon. "Song, you must sing. It's the only weapon that will take down the gate in time. Sing!"
Brandon staggered forward as if he knew he couldn't refuse. "But . . . no, I can't—"
"You must." Reece's eyes were ice. "We have to get to him."
"My voice is gone."
"It doesn't matter. Sing anyway."
"I can't," Brandon rasped out. "Don't you understand? I can't sing with my own voice. All I've been able to sing are the songs I've heard from the Spirit, that have been given to—"
Reece grabbed Brandon by the shoulders. "But in here you can. You have to be able to. If you don't, Doug will die."
"My . . ."
"Now!" Reece screamed the word and his face turned red with the effort.
Brandon started to sing, but it wasn't with the stunning voice Dana had heard in downtown Seattle. It wasn't even the voice he had before the demon had put a jagged gash in his throat. It scraped out of his mouth and the sound made her gasp. It was horrible. Ten seconds of mutilated melody eked out of Brandon's mouth.
Brandon stopped and then tried again. Another ten seconds passed, but this time his voice was even worse. He tried once more, but after a few seconds Brandon stopped. Reece's eyes were frantic. He stared at Brandon and was about to speak when a thick voice oozed out from behind the gate.
"If you want in so bad, then join us."
A great creaking sound filled the air and they all spun toward the gate. It quivered for a few seconds and then swung open. They rushed through it. Doug lay alone in the middle of a small, raised wooden stage twenty feet away. His body convulsed and blood covered his clothes. His eyes were closed and a sheen of sweat covered his face. His gray hair was splayed across his forehead. Zennon was gone.
Reece reached him first and clumped to his knees on the rough wood. "Doug!"
The only response was a soft moan.
Reece glanced at them. "Join hands, we have to get him out of here."
They slid back into their bodies at Well Spring, and Reece lurched up from his chair and crumpled to one knee on the stones around the fire pit. He staggered to his feet, stepped around the pit, and took Doug in his arms, glancing wildly at the rest of them.
"Talk to me!" Reece continued to spin his head back and forth. "I can't see how bad it is. Only darkness near his chest. Tell me."
Dana knelt next to Doug and fought back tears. "I think his ribs are crushed. And he's bleeding from a deep wound over his heart and on his head. Reece, I think he's dy—"
"No. Don't speak it. We have to get him to St. Vincent."
"No," Doug's quiet voice sputtered. "That's not needed." Blood bubbles spilled over his lips. "It has arrived, Reece, in all its glory."
"What?" Reece's voice shook.
Doug laughed, a weak laugh that made the blood bubbles pop. "My chariot. The one taking me to heaven."
"No, we'll teleport to the hospital."
Doug gazed at Brandon. "This is not your fault."
Brandon's body heaved with sobs. "I'm sorry, Doug. I'm so sorry. I should have been able to—"
"No, it's a lie." Doug gasped for air. "Don't give in to it. Promise me."
Brandon nodded, but his face said he would have a difficult time keeping the promise.
"When the time comes you must sing with everything inside you. Your whole life will be in that moment and the time is coming soon."
Doug's body was racked with coughs. Then he tilted his head slightly toward Reece. "Don't hold it against him, friend."
And with that, Doug Lundeen was gone.
The next morning, Dana woke at first light and slipped into a thick gray sweatshirt and matching sweats. The air bit into her face, but it didn't occupy her thoughts for more than a second. They were consumed with questions about Doug's death. They'd always been stronger than Zennon in the past. Why not this time? It didn't make sense. Doug was stronger than any of them. He should have been able to break free. His death was a dream. A nightmare. In a few seconds she would walk into the main cabin and find Doug sitting in front of the fireplace with a volume of George MacDonald's _Unspoken Sermons_ in his hands and a giant cup of tea next to him on the coffee table.
Reece only spoke four sentences the entire day, and all of them were directed at her even though Brandon and Marcus were both in the room when he said them.
"I've talked to Doug's family. The funeral will be in ten days in Colorado Springs. I'm assuming you and Marcus will be there. I don't care what Brandon does."
SEVENTEEN
"HAVE YOU SEEN ENOUGH, MASTER, TO SET ME FREE FROM the authority of this cretin?"
Zennon bowed and kept his head down as the rest of the council muttered obscenities. Some directed at Zennon, some at Caustin. All of them felt the issue was not worth taking the time to address in a council meeting. But Zennon had pushed for the audience. Sitting under the imbecilic Caustin for one more moment was like being doused with the Holy One's fire.
"He's done nothing!" Caustin slammed his hand onto the table.
"Doug Lundeen is dead." Zennon rose and faced Caustin. "Reece Roth blames the musician for the death, which will drive a wedge between them and create a rift nearly impossible to breach."
"So what?" Caustin stuck out his thick chest. "So what!" He turned to the Master. "He kills Lundeen and thinks the battle is over?"
"No, fool." Zennon gripped his sword. "It has just started. But everything is moving exactly as I have foreseen and will not stop till they are all destroyed and hundreds of thousands of the Warriors' followers have been turned."
"What of the new prophecy?"
"It is nothing."
"You do not know that. If they—"
"Enough." The low, guttural voice of the Master turned Zennon and Caustin toward the front of the table. "You both waste our time with your petty arguing. There will be restraint between the two of you till this is finished or you will suffer greatly." The Master paused. "Zennon, the destruction of Lundeen is to be commended. Until your next report, leave us."
"Yes, my Master." Zennon left the room, his body shaking. Not the outcome he'd anticipated. He'd done enough to warrant release from the fool's authority. The door of the council chamber shut, and he leaned back against the wall and closed his eyes and tried to quiet the rage that surged through his veins.
An instant later his windpipe was cut off and he whipped open his eyes. Caustin had his hand around Zennon's neck and a thin short blade descended toward his eyes. Zennon blocked the blade and slammed his fist into Caustin's nose and his grip loosened.
Half a second later Zennon held his knife to Caustin's throat and pressed it deep into his skin. "You think yourself a warrior near my skill. You are wrong. The only reason I won't gut you right now is because the Master would want answers as to why I disobeyed him."
Caustin growled. "The council is on my side. The only thing that holds them back from letting me annihilate you is the death of Lundeen. That's nothing. He was old. He wasn't the one of the new prophecy. His death will only rally them—"
Zennon pressed the blade deeper and pulled it a millimeter to the right. A dark line of blood sprang out on Caustin's neck. "Talk less, Caustin. You'll live longer."
"I suggest you make some real progress before you try to speak nonsense to the council again."
Zennon shoved Caustin to the ground. The day was coming when his blood would flow freely. But far from soon enough.
EIGHTEEN
DANA'S MIND COULDN'T GRASP IT. SHE SAT NEXT TO REECE in a church on the outskirts of Colorado Springs and tried to accept the fact Doug was gone. The heat of the early August afternoon was winning the war over the church air-conditioner, and she wiped her forehead.
Dana glanced at Reece on her right. If she was in a daze, he was probably comatose. His mentor and best friend gone. Why? Why would God send them into a place for Doug to be killed? It made no sense.
She looked again at Reece and then pressed into him and wrapped her arms around his shoulders. "Would it be terribly cliché to say Doug is at this moment being flooded in inexpressible joy? That our mourning is not for him but for us?"
"Yes, it would be. Horribly."
"I'm going to say it anyway."
"I'm glad you did." Reece gave a sad smile.
"It seemed like he almost knew it might happen."
"It doesn't lessen the pain." Reece drew in a deep breath. "But you're right. He's dancing now. His body is restored and life has come into every fiber of his being. And we'll be okay."
Reece's words floated down on her like snow, melting away before she could let them sink in. _Would_ they be okay? Doug had been so instrumental in everything they'd done. And what about Brandon? He had just started to show flashes of becoming himself again and then this happens? And why couldn't he sing? What happened to him in there? And how much of his despair and inability to act had to do with her rebuff of his attempt to rekindle their romance? No. She wouldn't let herself take even one step down that road.
"Now, one of Doug's friends would like to say a few words."
The pastor's voice snapped Dana out of her contemplation, and she watched a heavy-footed Reece trudge to the podium. He stood for a good twenty seconds before speaking.
"My name is Reece Roth, and I had the great and humbling honor to be able to call Doug Lundeen my friend. Doug did not use that word lightly, nor do I today. For Doug, when he called someone friend, it meant he was willing to lay his life down for you."
Reece's head tipped forward and he paused. "Many of you here today I know. Many I do not. But it is not a cliché to say all of us—known or unknown—are bound together this day by an extraordinary man. I've come to learn that Doug Lundeen had the ability to make everyone he grew close to feel like he was their best friend. If the men here were of the marrying age, my guess is Doug would be the best man at every one of our weddings."
Reece continued his heart-stirring eulogy, but Dana couldn't focus. Where would the Warriors go from here? Until now, she hadn't realized the confidence Doug had given her. Knowing Reece had someone he trusted and could rely on for wisdom with every decision made her feel like she was on a solid bridge as they crossed the canyons of their destiny. Now it felt like they were walking on a rope bridge with most of the slats missing.
The rest of the service was a blur, and soon Reece, Marcus, Brandon, and she followed the other mourners into the church's large reception hall. More precisely, she and Marcus followed. Brandon seemed to drag himself into the hall. And he kept a sizable distance between Reece and him. It was obvious Doug's death tore at Brandon like a saw across his heart. She knew because she knew him. And she knew that while his mind and heart were buried with guilt over what he hadn't been able to do, an equal measure of another emotion stabbed him which was even more brutal. Worthlessness. If he couldn't even be the Song inside spiritual realms, what good was he to the Warriors? She'd tried to talk to him about it outside in the foyer before the service had started, but the conversation was decidedly one sided.
"Stay in the truth. Reece is wrong to blame you for Doug's—"
"Sure."
"It's true. You tried to sing with everything in you. I saw it."
"Okay." Brandon studied the floor.
"Why can't you believe that?"
"Okay."
"Not okay." Dana yanked Brandon's arm and he looked up at her. "Reece is only blaming you because he's trying not to blame himself. He thinks he acted too late. He thinks he should have engaged with Zennon right from the—"
"What am I, Dana? Tell me." She stared at him but didn't respond. "Answer? I'm nothing." Brandon stepped back and looked at the cream-colored ceiling. "Worthless once again. Doug says I'm key to whatever Zennon has in store for us, but I'm not buying it."
"Are you kidding? Think about what you've done for Sandra, and Garen, and those people down in Edmonds."
"So what? Even if I sing a few songs of heaven for people, what happens when that's over? I want more of a life than just that."
Dana squeezed his arm. "You're not worthless. The enemy is trying to resurrect your old wound."
"Feels pretty new right now."
They'd talked more, but the conversation went in circles and nothing was close to resolved by the time they were ushered into the sanctuary.
Dana glanced around the reception hall. Poster-sized photos of Doug covered the walls, and it struck Dana how accomplished the man was—and how she had no idea of the things he had achieved. After the four of them meandered through the room for a while, chatting politely with people each of them knew, they gathered along one of the side walls and gazed out at the friends and family paying Doug last respects.
Dana turned to Reece. "I don't think I've ever asked how you and Doug first met."
Reece stood like stone. If he'd heard her he gave no indication.
"Reece?"
Again he didn't answer. His face turned forty-five degrees to the left as if his gaze was fixed on that side of the room.
"Reece?" She gave his arm a slight squeeze.
He started and turned. "I'm sorry, Dana. Did you say something?"
"Only three times." She rubbed his arm. "Are you okay? What are you . . . um . . . staring at?"
Reece bent down and lowered his voice. "Is there a woman on the far side of the room who is looking this direction? I think she's holding a cup of coffee or tea or punch and is by herself."
Dana scanned the wall in the direction Reece faced, and her gaze stopped on a woman who stood along the wall at the back of the hall. She wore a black gold-embroidered silk kimono, along with a crystal-embellished leather belt. Her white heels with black ankle straps looked like they might be Nicholas Kirkwood. She looked young, early twenties at the most, and Reece was right. She stared directly at them.
"Yes." Dana looked away. "She's Asian, dark hair almost to her shoulders, average height, thin frame. Attractive. And I'd describe her countenance as confident but subdued."
"Marcus?"
"Intelligent would be my first descriptor. And Dana's perception of confidence is accurate, I believe. This young woman stands alone in a gathering that is predicated upon interaction with fellow mourners, yet she shows no indication of being uncomfortable in her solitude."
Reece didn't ask Brandon for his impression.
"Why, pray tell, are we so interested in this female?" The professor pushed up his glasses.
"The aura surrounding her is striking. Bright gold light is radiating off of her like a fountain. But it's also tinged with hints of dark red. It's different from any other I've yet seen and definitely powerful."
"Is the aura a you're-on-our-side-powerful or a we-could-be-in-for-a-battle powerful?" Dana asked.
"I would guess the former."
"Do you believe it would be pertinent to implement an engagement strategy with her here and now?" Marcus said.
"One more time, Professor, for those of us with pea brains." Brandon snorted. "How many translators does Kat have to have to understand your dinner conversations?"
"I was simply asking if we should—"
"No. That was not simple." Brandon held up a finger. "Here's simple: 'Hey, think we should try to meet her?' "
Dana glared at Brandon and he glared back. It wasn't fair for him to take out his pain on Marcus by snarking at him.
"Is she still looking our direction?" Reece asked.
Dana glanced up. "Not only looking at us, she's coming this way."
The woman seemed to glide over the floor, and her shoes made no sound on the hardwood of the reception hall. She stopped a few feet in front of them and nodded at each of them before resting her gaze on Reece.
"Hello, Reece Roth."
Reece tilted his head as if trying to find a spiritual frequency that would show him more about this woman. "Have we met?"
"Yes, we have. But it was long ago. I've heard stories of you since I was a child and have continued to hear them into adulthood."
"From who?"
"A mutual friend."
"Does this friend have a name?"
Her eyes turned sad. "From Doug." She looked down. "I'm deeply sorry for your loss."
"Thank you." Reece extended his arms to either side. "These are my friends: Dana, Marcus, and Brandon."
"It is truly an honor." The woman nodded at each of them.
"Might I ask your name and how you knew Doug?"
"Of course. My name is Miyo." She bowed. "Doug was my—"
"Miyo?" Reece leaned forward. "Is it really you? But you're a little girl."
She smiled and her eyes almost closed. "I was, yes, certainly when we met, but now I've matured to the ripe old age of twenty-three."
"I'm . . . You . . . I remember you well. Has it been that long?" Reece rubbed his jaw. "It was astounding the spiritual maturity you had at that age. What were you when we met? Eleven?"
"Ten."
Reece went stiff. Likely because it was the same age as when his daughter, Willow, was murdered nearly three decades ago. But if he'd lost his composure, he regained it a moment later.
"Doug loved you very much."
"Yes, we were able to spend a good amount of time together as I grew up."
"Did he tell you about my sight? Do you know about—?"
"Yes. He spoke to me often about Warriors Riding and what the Spirit has done and is doing in the world through the four of the prophecy."
There was respect in Miyo's dark-brown eyes, and yet Dana instinctively knew this woman had a strength and self-assurance that was rare for someone her age.
"Did Doug continue to train you as you grew up?" Reece asked.
"Indeed." Miyo bowed again. "My grandfather taught me many astounding things."
The tone of her voice certainly wasn't one of arrogance, but it wasn't humble either. She might have been describing the weather.
"Are you in college?"
"I graduated from college when I was nineteen. Since then I've been working in the publishing industry."
"As?"
"An editor. For my father's small publishing house."
"Did Doug tell you he and I spoke recently about you coming to Well Spring someday?"
"He did tell me that, yes." She glanced at each of them.
Reece shifted his weight, then grew still, his spiritual eyes fixed on Miyo. "Were you aware that for the past six months he's been suggesting you join the ministry?"
"Yes." Miyo again glanced at the rest of them, not with a look that wanted their approval, but one of mere curiosity as to what they might think. "And what was your reaction to that suggestion, Reece?"
"I told him I thought you were too young, but it's something I might be open to, and we should talk about it again in a year or two."
"I see."
"But I believe you would benefit greatly from coming to and going through one of our training weeks at the ranch. There is much you could learn, I believe. After that we could talk again about the idea."
"I see," she said again and hesitated. "I appreciate your invitation to come to Well Spring."
"Will you come?"
As the words left Reece's mouth, he was surprised by how much he wanted the answer to be yes. Probably because she was related to Doug. And if Doug had trained her, then they shared more than just a bloodline. There would be pieces of Doug throughout her soul, heart, and spirit.
Miyo was young, probably almost as green as Dana, Marcus, and Brandon had been when they first came to Well Spring. But that didn't matter. If Reece was honest, he would love having her as part of the Warriors. But that was his emotions talking. Wisdom would say get to know her first. See how she responded to a weekend of Well Spring training. And then explore the idea of her joining the others and him for greater things.
"My grandfather gave his heart to you." Miyo took Reece's hands. "Your friendship was one of the great treasures of his life here on earth. Because of this, I have a great love for you as well. I don't believe this is the last we will see of each other, Reece Roth. And I believe that next time will come very soon."
The red and gold glow around Miyo grew brighter, and a sense of joy and laughter seemed to spill off of her and surround him. But as he reached out his hand toward her to say good-bye, the glow around her vanished.
"Wait a minute, hold on, everybody," Brandon said.
Reece turned toward Dana. "Did she just—?"
"Yes, she did. Gone. And I think you know I don't mean she walked away. I'm assuming she used a technique we've all grown familiar with over the past year and a half."
Marcus chuckled. "It's apparent Doug taught Miyo more than just the rudimentary elements of the extraordinary spiritual life in his classroom."
"How much do you really know about her, Reece?" Dana asked.
"Doug said she was the most spiritually attuned person he'd ever met. And that I would benefit from knowing her. I scoffed at the idea at the time."
Marcus cocked his head. "After seeing that demonstration, I would have to conclude you've just entered a no-scoffing zone."
An hour later the four gathered outside the church. "Thank you for coming. All of you." Reece didn't look at Brandon when he said it, but it was a start. Dana wanted to squeeze Brandon's hand as if to tell him Reece would come around, but she worried the signal would be crossed and he'd read something into the gesture she didn't mean. Or wasn't ready to mean.
They stood in silence for a minute before Reece turned and faced west. "I want us to stop by Well Spring before we head back to Seattle. There's something I believe we need to do all together. A place we need to go."
"And where would that be?" Marcus said.
"I think you can guess. We need refreshment. Hope. Restoration. A time of healing from the loss of our fellow Warrior. Direction from the Spirit on where we go from here."
Dana took Reece's hand and pretended she could grasp it hard enough to squeeze the sadness out of his voice. "I'm thinking you're thinking of taking us to a place you can't find on a map."
"That would be accurate." A sad but hopeful smile appeared on his face. "Let's go."
NINETEEN
IT WAS PROBABLY BRANDON'S IMAGINATION, BUT THE AIR felt heavy. His soul certainly did.
After a quick late dinner on Saturday, they gathered at Well Spring's fire pit and watched the flames shoot into the sky. The last time they'd sat around this pit they'd gone in with Doug, and his empty chair loomed large in Brandon's mind.
Reece said he was going to take them to a place of refreshment. That they needed it. Understatement of the year, probably the decade. But the way Reece had treated him since Doug's passing made Brandon wonder if coming to Well Spring had been the right decision. If he hadn't come, Doug might have still died, right?
But at least Reece wouldn't blame him for it and launch guilt at him like it was a spear. Doug said it wasn't Brandon's fault. But if not his, then whose? He should have been able to sing. He'd sung for the couple in Edmonds, for Sandra, and for Garen. So why couldn't he do it inside a spiritual realm?
Brandon shook his head. No. No more questions that were impossible to answer. He wasn't going to let the guilt take him. Dana was right about his role in Doug's death. He had done everything he could to sing. But that made it worse because his best effort amounted to nothing. Worthless.
And now they were gearing up for some massive assault from Zennon, and Brandon wouldn't be able to wield his greatest weapon against the demon because it had vanished. Great. Just spectacular.
"It is time." Reece raised his head and held out his hands to Marcus on his right and Dana on his left. Brandon didn't wonder why Reece had set it up this way. There was no way the big man would take Brandon's hand.
Moments later, the four stood on the shore of a small lake Brandon guessed to be a mile and a half long and half a mile wide. Rolling hills on the other side were spotted with tall pine trees and sparse patches of green shrubs and wildflowers. Directly across the lake, a large rocky hill fifteen hundred feet high shot into the sky with two lone pine trees sitting along the top of the ridge. The lake was glass and gave a perfect reflection of the hill and trees.
As he soaked in the view, peace settled on him even though he didn't deserve it.
_It's my pleasure to give you my peace, Brandon. Take it in. All of it._
As contradictory as it was, the voice of the Spirit sounded in his mind both soft and loud at the same time. For the first time since Doug's fight with Zennon, Brandon let all thoughts slip away, and he stood and basked in the glory of God's creation. If only he could stay here forever.
To their left, far off in the distance, a series of mountains covered with a dusting of snow sat under a smattering of white clouds. The way the mountain ridges ran, Brandon saw what looked like the form of a lady lying on her back, her hair shooting out from her head, her legs raised slightly.
"Lady of the Lake." Brandon pointed at the ridgeline. "Can you see her?"
"You're right. I see her too." Dana laughed.
Marcus bit his upper lip and nodded. "Yes. I see her." He shifted his gaze from the lady to the rocky hill across from them and turned to Reece. "Over the years when you've encountered others in the spiritual realms, how often are they of the enemy and how often are they of God?"
"That's an intriguing question. I've never considered it." Reece looked down for a few moments, then raised his head. "I would say more often than not when I've met another being inside a soul or spiritual realm, they've been evil. Why do you ask?"
Marcus peered across the lake at the top of the ridge. "Because I think we are about to have one of said encounters with a visitor, and I would like to know if we need to be on guard or not."
Dana moved a few steps away from the others and shielded her eyes from the sunlight, and Brandon did the same. The professor was right. A tiny figure high above them strolled along the ridge to the right of one of the pine trees. From this distance it was impossible to tell if it was male or female.
"So you didn't give out an invitation for someone else to join our party?" Brandon said.
"No."
"I'm guessing this is one of those times where you'd like to be able to see with those spiritual eyes of yours and get a feel for what kind of Beach Boys music she's putting out."
" 'Good Vibrations' by Brian Wilson, off _Pet Sounds,_ 1966." A hint of a smile appeared on Reece's face as he answered Brandon. It vanished a moment later, but Brandon saw it. It was the first time Reece had given any kind of warmth toward him since Doug had died. It gave him hope. Exactly what Reece said they all needed.
"What are you sensing, Dana?" Reece asked.
"That whoever it is, it's female and not evil."
"Brandon?"
Again, hope stirred inside. The first time he'd asked Brandon's opinion on anything since the death almost two weeks back.
"That she knows us."
"Professor?"
"I would toss my proverbial hat into the same ring as Brandon. And then I'll go a step further and confess I have an educated guess as to her identity." The professor clasped his hands and stared at the figure and went silent.
"Hello?" Brandon smacked Marcus on the shoulder with the back of his hand. "Care to share it with the rest of the class?"
Marcus opened his mouth, but before he could speak, bright-green light flashed across the ridgeline and blocked the person from view. The same light flashed again an instant later, halfway between them and the ridge, and a final time right in front of them. When the light faded and their eyes readjusted, a woman stood in front of them, her face split by a thin smile.
Miyo. She glanced back over the lake to the ridge she'd come from. "Even more beautiful a view from this vantage point."
"What are you . . . How did you . . . get here?" Reece stood with hands on hips, surprise on his face mixed with a scowl.
"Don't look so stunned, Reece. You think you're the only one Doug taught how to travel within the spiritual realms?"
"I know there are others Doug trained and I know he trained you. What I'm surprised about is your ability to—" He stopped as if catching himself from stepping off a cliff.
"To what?"
Reece glanced at the ridge, then back to Miyo. "Seeing you move from there to here in the manner in which you did was . . . entertaining."
"More like a shock given the look on your face."
"Entertaining." Reece grimaced.
"Yes, of course." She grinned at him. "I take it you don't know how to travel like that. Which surprises me." Miyo spun in a half circle and her swirling black-and-sapphire top flowed around her like it was part of her body. Even Brandon knew her clothes were designer made. She glanced at each of them. "Teleporting in the physical world is a lot harder than doing it here."
"It's not something we've delved into at this point," Reece muttered.
"Is that a euphemism for 'I don't know how'?" She laughed, not in a mocking way, but one of playfulness. "I thought my grandfather would have taught you all his secrets."
"Apparently not." Reece stared at her.
"It seems he was holding out on you."
"I hardly think so."
"Then based on the experiential evidence, your thinking might not be completely accurate in this area." She smiled again and walked over to the trees and examined the fruit thoroughly before choosing an apple near the center of the tree. Miyo rubbed the apple on her dark-blue pants and took a bite.
"We can eat them?" Dana stared at Doug's granddaughter.
Miyo turned and smiled. "As you've no doubt heard from Reece or Doug, we are not human beings having a spiritual experience; we are spiritual beings having a human experience. This is our true nature. And yes, one day we will have resurrected bodies to go along with it, but just as wounds we receive here are carried into the physical world, many elements of the physical world and things we can do there are reflected here."
Brandon studied Reece's face. Again their mentor seemed surprised. Was this another new revelation for him?
None of them spoke, and after a few more moments of awkward silence, Miyo said, "Tell you what. I'm going to take a quick walk along the lake. You can talk about me behind my back, and after a short while I'll return and we can get down to business." She turned without waiting for a response and strolled down to the water's edge.
When she was out of earshot, Dana said, "Who is she? I mean, we know she's Doug's granddaughter, but I'm guessing you know more than that. Give us a little background."
"Doug's son married a woman from Japan when he was in the service. Miyo was born there along with a brother whom I've never met. The family moved to the US when Miyo was four or five, if I remember right, and they ended up a few hours from Doug and his wife. Doug took an interest in Miyo—said there was a connection immediately—and he always spoke her name with great tenderness, great affection, and great respect."
"Anything else?" Dana twirled her finger around a lock of her light-brown hair.
"That she was strong in the Spirit from a very young age. That if she stayed on the narrow path, she would be a formidable warrior."
"From what we've seen so far, that seems to be the case," Dana said.
"What do you think of her?" Reece asked Marcus.
"Her abilities seem considerable." The professor gazed in the direction Miyo had walked. "But what I want to know more about is her heart."
"Well spoken," Reece said.
A few minutes later, Miyo strolled back, a smile on her face. "It's so beautiful here." She stopped a few feet from them and set her gaze on Brandon. "So, musician, what's your opinion of my getting involved somehow with the Warriors Riding?"
Brandon jerked his thumb toward Reece. "I'm still agreeing with what Reece said at the wedding. Thinking you're a little young to be stepping into our arena."
"Tim's first letter, chapter four, verse twelve," Miyo said.
Brandon turned to Marcus. "Help us out, Whiz-Brain."
" 'Don't let anyone look down on you because you are young.' "
Miyo cocked her head at Marcus. "Impressive. Your reputation precedes you."
"What reputation would that be?"
"My grandfather profiled each of you. And I—"
"Profiled?" Brandon said. "I've been profiled?"
"In all your glory, Brandon Scott." Miyo smiled. "He explained a great deal about each of you, yes, and about the things the Warriors Riding have done. Your stories have inspired me and encouraged me greatly in my own journey." She bowed in the beautiful style of the Japanese.
Reece took a step toward her. "We would be honored if you would join us tomorrow at Well Spring Ranch for the day. It will give us a chance to get to know you better and you to know us."
"I would like that. And it will give me the chance to make my deliveries. I have something for each of you."
TWENTY
"MIGHT I GIVE YOU YOUR LETTERS NOW?" MIYO LOOKED around the fire pit at each of them late on Sunday afternoon. Marcus had, of course, been curious as to what Doug's granddaughter wanted to deliver, and it seemed that question had now been answered.
"The letters were written by my grandfather, as you might have anticipated. One for each of you." She picked up the flat wooden box she'd kept by her side most of the day. It appeared to be six inches wide by a foot long and made out of myrtlewood. A lacquer finish made the box shine with an almost unearthly light. Appropriate since the box was undoubtedly Doug's.
Miyo lifted the lid and removed what looked like four envelopes. A fifth remained in the box. She handed Brandon his letter first, then Dana, and then one to Marcus.
Marcus judged by the weight of the envelope that the letter was only one page. On the envelope—in what he estimated to be eight-point font in a decorative script—was his name: _Professor Marcus Amber_ and underneath it, _My friend_.
"When did he give these to you?" Marcus asked.
"He didn't." Miyo sat back in her chair as a wistful look filled her eyes. "A few days after he died, my father asked me to help him go through Grandpa's things, and we found this box in his study sitting in the center of his desk. We opened it and found six letters. Dated recently. One was addressed to me. I read mine and at the bottom of the note were instructions for me to give each of you your letter as soon as I could."
"Thank you," Dana said.
"You're welcome. My hope is they bring you hope as the one he wrote to me did." A look of consternation passed over Miyo's face. "But I'm afraid they will also bring you trepidation."
"You gotta like this lady, Prof." Brandon kicked Marcus's chair. "She utilizes terminology almost as indecipherable as yours."
"Please tell me you see the irony in that sentence," Marcus said.
Miyo waited till Brandon's chuckles faded, then stared at the musician with a look that shouted, _Get serious._ She certainly knew how to command a room. Twenty-three in age, but far older in experience.
"I suggest each of you open your letter in privacy. Mine said I was free to share what my letter contained with the four of you if I chose, but of course the instructions in your letters might be different. In any event, you might want to keep its information to yourself." She turned to Reece. "If you don't mind, I would like to give you your letter when the two of us are alone."
"Fine." Reece stood and shoved his hands in his pockets. "Let's do it now."
Reece and Miyo walked to the big cabin on the north end of the ranch that he'd had built a year ago to accommodate the surging size of the groups that came to Well Spring for training. They sat in the corner of the large room where the sun streamed through the picture windows to warm their faces.
He stared at the glow around Miyo that outlined her body. It shifted from gold to silver to white and back to gold. He'd never seen anything like it on anyone else. Granted, his new spiritual eyes didn't always allow him to see people with this much detail, if at all, but of the people he had seen so far, Miyo was the most fascinating.
He saw her reach toward her chest and pull out a rectangular object that had a faint, thin line of light around it. It had to be his letter. Fire seemed to drip off her finger as she ran it along the edge of the envelope. "Can you see what I have in my hand?"
"I can see the outline of an envelope."
"So your sight allows you to see objects?"
"Sometimes yes, sometimes no. Usually just an outline around the object that allows me to figure out what it is."
"Are you ready?" Miyo leaned forward.
"You're sure Doug wrote it?"
"Why do you ask that question when you already know the answer?"
Reece didn't respond. The honest response would be that he didn't want to read words Doug had penned probably only weeks ago. Plus, he would need Miyo to read them, and he wanted to be alone when he heard them.
Also, Doug's words would undoubtedly stir up the feelings of loss that stung his mind and heart like a series of unending needle pricks. Feelings of anger. Despair. Bitterness. He'd already been through the gamut of emotions over the past ten days and again at the service, and he didn't want to go through them once more.
Miyo leaned farther forward. "I realize this likely will not help, but I faced the same emotions of loss when I read my letter."
Great. She was a mind reader as well. No, not true. Just sensitive to the obvious.
"I'll need you to read it to me." Reece sighed.
"Your message is for your eyes only, just as my message is for mine alone, just as it is for the rest of the Warriors."
"If I had eyes I'm sure that would be true. But since my newfangled vision doesn't allow me to do things like read, I'll have to rely on your narration. I'm sure Doug would understand."
"I disagree." The sound of ripping filled the small room, and Reece saw Miyo's hands and the faint outline around the envelope twist and then light spill out of its end and rain down like a cluster of Fourth of July sparklers. Whatever was contained in the letter had power. "There's a thin flash drive in here. Doug recorded your letter. I'll plug it into my laptop and hit Play and leave. All right?"
Reece nodded. A few minutes later she had things set up, and then Miyo's footsteps faded across the floor. As the door to the large room clicked shut, Doug's voice came over the computer's speakers. Reece's eyes watered and he allowed himself to sink into the last message from his mentor and friend.
_"Reece, my old friend . . ."_
Doug stopped to laugh and Reece couldn't decide if he loved the sound or hated it.
_"We had some great adventures together, didn't we? Indeed we did, but they are nothing compared to what is to come and what we will do together throughout eternity. Do not forget that—this is only one age of many more to come, and I can't wait till you join me on the other side._
_"Please indulge me for a moment. I've always loved it in TV shows and movies when the person on the tape or in the letter says, 'If you're listening to this tape or reading this note, then I am dead.' So now I've said it to you."_
Doug laughed again and it made fresh water come to Reece's eyes.
_"I'm sorry for your loss because I know you loved me. But cry for you, not ever for me, because you know where I am now. I have run the race, I have finished the course, and I believe I have run well."_
Doug paused and Reece heard the sound of a river in the background. Was it the one at Well Spring? Is that where he recorded this? That would be fitting.
_"This might be hard to accept at first, but you need to receive Miyo as my replacement in Warriors Riding. She walks in the power of the Spirit like no one I've ever seen, and that includes you, friend. She is young, yes, but only in body and years, not in her soul. I have taught her all I know._
_"You were always one for keeping a journal of all the things you've done, all the secrets you've learned, all the experiences of the worlds the Spirit opened up for you. I've kept a journal for the past thirteen years as well. I felt it was time to record the things I've learned. But I didn't use pen and paper or a computer. Miyo is my journal. Everything I've learned over the years is now in her and part of her. She carries my words so well._
_"I wish I could say you_ must _make her part of the Warriors—that without her you will face some battle where she is a critical component to your success, but I don't know that for certain. I haven't heard it spoken from the Spirit even though I believe it to be true. So it is your choice whether to grant my wish or not. Nonetheless, I will say she is true of heart and spirit, and I believe she would be a fine addition to your team._
_"Who knows, you might even grow to trust her to the point where you'll have her read your journal back to you. I'm certain you haven't memorized everything between its pages. It is highly possible you've forgotten some of the things it contains, which you might need to be reminded of in the future and be of help in your time of need."_
He thought of his journal, which Doug had found in Reece's backyard after Zennon's attack a year ago. He carried the journal with him everywhere now, even though he couldn't read it. Maybe Doug was right. Maybe he would let someone read it back to him someday. Not Brandon. Dana? Marcus? Possibly. Maybe even Miyo. He shook his head and focused on Doug's recording.
_"You have given me life, Reece Roth. So much life, friend. So many adventures of the spirit and soul. And soon we will continue those adventures in ways that will make our time on earth seem shorter than the blink of an eye._
_"Go forward in full strength, Reece. I know you think you need me. That you won't be able to face the coming battle with Zennon without me. This is not so. You have the Spirit. He will guide you in all things._
_"One more thing. Forgiveness. And blame. I've heard those words over and over again these past few weeks. I don't know what it means, but by the time you read this letter, my imagination says you will._
_"For you, I believe it will be years till we are joined together again, but for me, I imagine I will turn the moment I walk through the gate into heaven and see you coming through the door only an instant after me._
_"As always, I am your friend. Now, through all time, and beyond time."_
Reece sat in the silence and let the emotions of the moment wash over him. Forgiveness? Could he forgive Brandon? If Reece didn't it would leave a crack for the enemy to enter into. And if Doug and Miyo were right about the coming battle with Zennon and whoever else the demon brought to the arena, Reece needed to get that crack filled soon. He leaned forward and took his head in his hands. Forgive. He didn't know if he had the strength to do it.
Regarding allowing Miyo to join the Warriors, his emotions were a fifty-fifty mix of yes and no. It didn't feel right, but he couldn't tell if that was because of his pride at realizing she knew things he didn't or if she wasn't ready for it. So young. Yet did that matter? Maybe she was ready, but were they ready for her? He would think and pray about it. An image of Doug filled his mind. Reece already knew the answer to his mentor's request. Why hadn't he seen it? It was obvious.
Reece slogged across the wood floor and out the door. In minutes he found Miyo overlooking the river.
"No wonder Doug didn't tell me. I would have rejected the idea immediately." He smiled and shook his head. "You're the one, aren't you?" Reece cocked his head. "You certainly stepped before me with boldness."
The glow around Miyo brightened. Like a spiritual smile, only he was able to see.
"The one what?"
"The one of the new prophecy."
"Yes, Reece. I am."
TWENTY-ONE
BRANDON OPENED HIS LETTER DOWN BY THE RIVER. IT was written in longhand, and he stared at the pattern of the words for a long time before reading them. If Miyo was right, the letter would bring hope and despair. Hope he could use. But despair? He'd already seen that on the menu too often over the past month, and he'd eaten more than his fill. Did he have a choice? He could burn Doug's letter and pretend it didn't exist or toss it into the river and let it float away. Why not? He crumpled the letter into a ball and lifted his arm, ready to fling it into the undulating current.
He'd come to Well Spring like Doug and Reece had asked, and the result was disaster and his utter failure. Had his inaction killed Doug? No. But that didn't matter to Reece. And didn't matter any longer to Brandon. Any guilt he'd felt from that lie was gone, but it had been replaced with another conviction he knew was the truth. A poster appeared in his mind with the headline _Worthless_ , and his picture was underneath.
He sighed, uncrumpled the paper, and read the letter. He owed Doug that much.
Dear Brandon,
I fear for you as I pen these words. Ever since your battle with the religious spirit, I've been seeing the same thing over and over again. It's an image of you surrounded by darkness. And the darkness is unbelief. Unbelief that you have the strength to do what must be done in the coming war. Unbelief that you are still the Song. And a deep conviction that your presence among the Warriors Riding matters little. That you have nothing to offer.
If this is true, I ache for you because you have believed the lie. Whatever pain you now carry, hold on to it no longer. I have told you this before, but allow me to say it one last time: You matter. You are the Song. It is your destiny. Night comes swiftly, but the day is not yet over. Do not lose heart. You will be restored to your former glory and beyond it. You will sing again, and when you do, great healing will come, far more than you can conceive of.
Seek the King now, Brandon, and the answers will come. Listen for his voice and he will speak to you. Great freedom will manifest if you are willing to have ears that hear.
Believe with me. With everything you hold dear, believe with me.
Your friend,
Doug
Restored? Hope surged inside Brandon, but before it could take root, he crumpled up the letter for a second time and tossed it into the river. Believe with Doug? Nope, sorry, he'd been ejected from the spiritual Super Bowl and didn't want to get back into the stadium. He wasn't the Song any longer. And a sentimental letter from Doug wouldn't change that.
Dana sat on a small rise a quarter mile west of the main cabin that overlooked the ranch and fought an aversion to opening her letter. Did the others feel the same? Maybe, but probably not for the same reason she did. She didn't want to read Doug's words because she didn't think they would surprise her. And if she was right, her letter wouldn't contain much of the hope Miyo spoke of—only a liberal dose of foreboding. She turned the letter over again and again, trying to work up the nerve to read it. Finally she slid her finger under the flap of the brown envelope and tore it open.
Dearest Dana,
You have fought well and led with such strength. I am so proud of you. But as you might already realize, your ability to lead will soon be tested like it has never been before. I told you and the others, Brandon is the key to the coming war. But your role is no less critical than his. You each have your part to play, so take courage, dear heart, for the Spirit is indeed with you.
Also, you must open yourself to what lays inside the deepest part of your soul: your feelings for Brandon. I know you are scared. I know you fear that if you give him your heart again, he will treat it in a way that will not allow you to survive. But this is a risk I feel you must take. Not for me. Not for Brandon. But for you. Don't let your self-protection turn into a weapon for the enemy to use against you. Against the Warriors.
Rejoicing as I think of the day we will be together in eternity,
Doug
Great. Doug poking into her personal life from the grave. Or from the heavens. Risk her heart again? No. She knew him too well. Knew that even though he'd sacrificed himself for her during the battle with the religious spirit, in some ways the sacrifice was for himself. Because of his need and desire for her, it was highly possible there was a part of him that rescued her because he didn't want to lose what she gave him.
All through their courtship and engagement, she'd met all his expectations just like she'd done all her life in all her relationships. Dana Raine. The perfect girl, always straight As in high school, summa cum laude in college. The top salesperson when she sold radio, exceeding goals as a sales manager, exceeding them now as the station's general manager. Even as the Leader in the Warriors Riding, she'd done more than anyone had expected.
But what would happen if she gave her heart to Brandon and she failed to be perfect for him? Did he really love her for her, or for what she gave him? He was an amazing talent, charming, funny, charismatic, and kind, but there was still a significant part of him that was all about Brandon. Even his reason for breaking off their engagement was about himself. Crushing her heart because he was worried about her leaving since his mom had left when he was young. Didn't he ever think about the fact she had the same fears from being abandoned so often as a child?
She let out an aggravated sigh. Why did she let herself think like this? It wasn't helpful. But she couldn't stop it. Maybe if life were normal, she could take the time to figure out what she really wanted and how she really felt. But life wasn't normal.
Dana sighed again and rubbed her lips with the back of her hand. It was all so mixed up and confusing because part of her still needed him. What _did_ she want? She didn't know. Didn't care. Or better said, she didn't want to take the time to care. Her mind was too caught up in what Doug's letter had said, because he was right.
She did sense her role would be bigger than she wanted it to be, and while Doug said she would be able to accomplish whatever it was she was supposed to do, she didn't share anything close to his level of faith.
The ache of Doug's absence struck Marcus again as he sat in front of the fireplace on the outside of the main cabin and held his letter. Too soon—far too soon—for him to have gone. Already he imagined the day coming when he and the rest of the Warriors would soar together with Doug through the heavens.
Dear Marcus,
Do you see it? The change inside? I do. You have chosen so well and are seeing the fruit of those choices in your life, in Kat's life, and the lives of your daughters. Without you the Wolf would not have been defeated back in June.
Now, as I sit writing these words to you nearly two weeks later, I continue to ponder what role you will have in the coming melee. It seems—if I am hearing correctly from the Spirit—that your friend Simon will play a significant role, which means you must play a role with Simon. I believe this involves bringing him to Well Spring. And bringing him to another place as well, I don't know where. Ask the Spirit, he will tell you. There is much more to Simon than you can imagine.
And you must pray, Professor. With great intensity. For your fellow Warriors. And especially Simon. For while I sense he will be your salvation once again, there is also darkness surrounding him.
Your friend across time,
Doug
Marcus folded Doug's letter and placed it back in the envelope. He would most certainly pray. And getting Simon to Well Spring? That would be a challenge given the last words the magician had spoken. But Marcus would find a way. There was no question in his mind that he had to.
TWENTY-TWO
THEY GATHERED LATE ON SUNDAY EVENING AROUND THE kitchen table, and Reece got right to the point. "I assume each of you has read your letter and worked through what it contained."
Brandon and Marcus nodded, as did Dana. Were their letters as ominous as hers? She didn't really want to know.
"Good." Reece clapped his hands together. "You can share the contents if you wish—all, some, or nothing." He turned toward Miyo. "From mine I want to introduce an idea from Doug that I believe will bring strength to all of us. But a decision on this idea ultimately isn't mine. It is ours."
"And that idea is?" Dana said.
"That Miyo would join Warriors Riding and take her grandfather's place at our side."
"Wow," Brandon said and faced Miyo. "You want that?"
She didn't answer and turned her eyes to Reece.
Reece folded his arms. "Doug wanted it."
"Sorry. Not seeing it." Brandon glanced at Miyo, then back to Reece. "No offense, Miyo, but the prophecy says there are four Warriors. Not five. Four. So unless the prophecy changes, she can't—"
"Knock it off, Brandon, you sound ridiculous. Doug wasn't part of the prophecy either, but he certainly was one of us." Reece shifted toward Dana. "Thoughts?"
"I don't know." Dana folded her arms. "It seems a little premature."
Another woman in the Warriors? Yes, long overdue. It would be refreshing to have another female around. But Miyo? Something didn't feel right. Yes, there was strength in Doug's granddaughter. It almost rivaled Reece's. And it was clichéd to say Miyo was an old soul. But she was. She held wisdom in her that spoke of deep pain and exhilarating highs and multiple acts of courage. In other words, she met all the qualifications, but still, Dana's mind balked at the idea of Miyo joining them.
_Lord?_
An answer came from the Spirit so fast Dana blinked.
_Yes, dear heart. It is right._
_But I don't want—_
_Life isn't always about what you want, Dana Raine._
Heat rose to Dana's face as Reece clasped his hands behind his back. "All right. So far we have a yes vote from me, a no vote from Brandon, and an abstain from Dana who needs time to—"
"No."
"No, what? You're voting no?"
"I don't need time. I believe she should join us."
"What changed?"
"Just . . . I . . ." Dana shoved her hands under her thighs. "I think the Spirit is saying she should."
Reece nodded and turned to the professor. "Marcus? Thoughts about Miyo joining us?"
"I concur with Dana."
"Excellent," Reece said. "Brandon? Do you want to give us the real reason you don't want Miyo to—"
"You don't need my reasons now." Brandon sprawled back in his chair. "It doesn't matter what I think. Majority rules."
"No, unanimity rules." Reece leaned toward Brandon. "Your vote?"
"Sure, why not. I mean, it's good."
Reece frowned. "You're sure?"
"I'm sure."
Reece started to say something to Brandon but stopped, scowled, then turned to Miyo. "Welcome to Warriors Riding."
"I'm honored." Miyo glanced at each of them and held Brandon's gaze a fraction of a second longer than Marcus's. "Thank you."
Reece opened his watch and felt the face. "It's late. I suggest we all get some rest."
Dana stood and went to the restroom. When she finished and walked back into the living room, everyone had left except Brandon. He stared at the dying coals in the fireplace, his body wrapped in the thick quilt that always rested on the end of the couch.
"So everyone else left?"
Brandon nodded and continued to stare straight ahead.
"Aren't you going to bed too?"
"Nah." Brandon sat up and let the blanket fall to his sides. "I'm going for a hike."
"Now?"
"Yes. Now."
Dana looked at her watch. "It's quarter to twelve."
"Yeah, late." Brandon shrugged. "But it's a short ways to where I'm going. Just a half mile or so up the river. Or maybe down to the post. I need to hear from God. Doug said I would. I tried to shut the desire down, but who am I kidding? In Peter's words, where else would I go? But that's not saying I'm doing peachy. Either I hear from the Spirit tonight or I'm going home."
"How long will you be out there?" Dana frowned.
"You're worried about me, huh?" He gave a sad smile.
"Yes, I am." She didn't elaborate but returned his smile and guessed her eyes probably held more warmth for him than they had for a long time. Doug's letter had opened a door she wasn't sure she wanted to open any further, but she wasn't sure she wanted to shut it again either. "What do you hope to find?"
"An answer. I've tried to bury the question, but it keeps shoving its ugly head up into my face 'cause of that stupid letter from Doug."
"What's the question?"
"Same as it's been since we were last here five weeks back and I destroyed my voice." Brandon stood and folded the blanket. "What am I supposed to do with my life now? Do I have any purpose left in this group? Am I worth anything? And of course what role do I have in this supposed coming attack from Zennon?"
Brandon picked up his North Face jacket and slipped it over his T-shirt.
"It'll be cold out there. You might want more than that." Dana smiled and gave his hand a quick squeeze before she could stop herself.
He blinked, his face went soft, and he stared into her eyes like he did in the old days when they'd discovered their mutual love of old jazz records and drinking cream-laden coffee in Dana's backyard gazebo as rain pounded down on the roof like thousands of miniature drummers.
Oh boy. One hand squeeze was all it took, huh?
"Can I ask you something?" Brandon said.
"Umm . . ."
"Is your thaw a result of Doug's letter?"
Dana put her head down for a moment, then raised it. "You should get going."
His countenance shifted and his eyes got hard again. Brandon ambled toward the sliding-glass door and opened it, then turned to her and didn't step through. "Can I ask you something else?"
Dana didn't answer.
"Why were you hesitant about Miyo taking Doug's place?"
"Why were you?" Dana asked.
"She's too young. We barely know her. And I like things the way they are. Add a new member to a group, and the dynamics of the band and the music they make turns out way different than it was before." Brandon slid the door open farther. "Your turn."
Cold wind sprinted inside and chilled Dana. "I don't know why."
"I do."
"No, you don't." Dana scowled at him.
Brandon gave her that smile she'd loved when they were dating. Part kindness, part mischievous, and a splash of being able to read her feelings like a billboard. The smile she'd loved back then. Not now.
"Yes. I do know. But I'm not going to say it."
"Why not?"
"I doubt you could handle it." Any hint of a smile was gone from Brandon's face.
"Try me." She yanked her arms across her chest.
Brandon eased one foot outside onto the patio and breathed deeply before answering. "You're worried about abdicating your position as the number one female on the team."
"What are you talking about?" Dana's face went hot.
"It's clear Miyo's got leadership oozing out all over her. You're worried she's going to lead better than the Leader."
"Shut up, Brandon." She hated him knowing her that well. "Have a nice hike. I hope you freeze."
Brandon stood at the sliding-glass door as Dana disappeared down the hallway toward the cabin's main bedroom. He shouldn't have said it. But it was true. She didn't want Miyo taking the gold medal. So much of Dana's identity was wrapped up in performing for people. Being number one. Getting results no one else could. Her greatest strength was also her greatest weakness. Her greatest wound. Be everything people expected her to be. And Brandon had played into it. Called her the perfect woman when they dated. Praised her for it so many times.
Whenever he did, she'd tell him that she wasn't perfect. And now he finally understood why. What if she _wasn't_ perfect? Would he still love her? That had to be her greatest fear and the foundation of the wall between them. And now it was too late to prove to her that she didn't have to be perfect. Impossible situation. If only he could stop loving her, life would be so much easier.
He slung the thoughts to the back of his mind, slid the door shut, and trudged up the trail along the river, carrying one of the ranch's green folding chairs with him. A quarter mile should do it. He just wanted to be sure he was far enough away not to worry about the others making an unlikely surprise appearance, which would be a shocker this time of night. But with the Warriors, and with Miyo now hanging around, anything could happen.
Dana's comment about the temperature was an understatement. Within minutes Brandon's feet and hands went numb, and his face felt like he wore a Frosty the Snowman helmet. He picked up his pace and it helped. Within a few minutes he found an open spot in the trees where he could see the river.
Brandon set up the chair, then sat and stared at the black water flowing past him thirty feet below. The chair was like ice and its cold seeped into his legs and back up his torso. But he ignored the cold, closed his eyes, and turned inward.
"I need to know, Lord. Will I sing again like I used to? Doug said I'd hear from you, so let's go."
No answer.
He looked up at the trees silhouetted against the stars, and the image of a tree house sitting between their trunks thirty feet in the air shot into his mind. He grunted out a laugh. Maybe that was the answer God was trying to give him: build a tree house somewhere on the acreage in his backyard, put in lights, heat, running water, and live in it like a hermit. Forget everything and everyone in his life. If only God would let him off that easy.
Brandon slumped forward and closed his eyes. "How can I be the Song if I can't sing in the spiritual realms when I need to, let alone the physical? And what are these songs I'm getting for other people? Yeah, I'm singing for a few minutes, but it's not even my voice!"
Brandon didn't need to look at his watch to know an hour had passed. Then two. Still nothing from the Spirit. At four o'clock he rose stiffly and picked up the chair. The Listening Post flashed into his mind. Everyone would be asleep by now. Why not go there and sit in the spot where miracles had happened in the past?
He settled down at the post with his back to the cabin and looked up and down the river. A sliver of the morning sun crept over the north ridge, and still there was no answer. But minutes later as the light edged down the sides of the mountains and across the stream, Brandon heard a sound like he'd never experienced. Music. A song. So faint he couldn't distinguish it from the chatter of the river. But it was there. A sensation of warmth surged inside, and he sniffed in a quick breath. The sound of it pierced his heart like a laser.
"Lord?"
_Listen._
Brandon strained to hear the song. It floated toward him and it seemed to come from the mouth of the river. He turned his head and stared at the current as if it were the instrument that played the tune. Then the music encircled him and suddenly grew louder. It came from his right and left, above and below, as if he were hearing the song in 3-D surround sound.
He'd never heard anything like it. Each note was as pure and clear as if the music was from another realm. And the melody was far more than haunting. Shattering. Full of freedom and sorrow in equal measure. A lost song, a melody that could crush mountains and birth worlds. Its richness sliced through his spirit with soul-splitting pain and immense pleasure.
It only lasted a minute. Maybe less. But even if it had gone on for hours, it wouldn't have been close to long enough. As the tune vanished, Brandon felt like his life had been sucked out of him, then it rushed back in with so much force, he lurched forward, then it faded again. He gasped.
The song so powerful that its absence felt like death. All he wanted was to hear the song again. He sat for half an hour, waiting for its return, begging the Spirit to bring it back, but the song didn't come.
"Will I hear the song again, Lord?"
The answer was soft but immediate. _Yes._ And laughter seemed to be in the answer.
"When?"
_And you will sing it._
The idea immersed him. "When?" he asked again.
The Spirit didn't respond this time, but he didn't have to. Knowing he would hear the song again was enough. The warmth tinged rays of the early-morning sun fell on his face and brought hope. He hadn't felt like this for what seemed like ages.
"What is the song, Lord?"
_It is a song of immense healing._
"For who?"
_It is a song to be sung once. For one person only. And for that person, extraordinary restoration will come._
"Who is the song for?"
_The one who needs it more than any other._
The words from Doug's letter flashed across Brandon's mind, and his body grew warm. _You will be restored to your former glory and beyond it. You will sing again, and when you do, great healing will come, far more than you can conceive of._
Brandon sat stunned in the midst of the revelation. He would be healed. Not now. Not yet. But restoration would come for his voice. He would be the Song once more.
After another ten minutes, Brandon shuffled up the long stone path back to the main cabin but hesitated before going in. If any of the others were up, he wasn't ready to tell them what had happened. It was too raw. Too glorious. He glanced through the sliding door. The fireplace was cold and no lights were on. He was probably okay.
Brandon slid the door open and stepped inside. The sound of the river faded as he closed the door behind him, and the silence inside the main room smothered him. He glanced at his watch. Five thirty. Too late to go to bed. Too early to start breakfast. Too tired to read, too wired to sleep. A light snapped on behind him and Brandon spun as adrenaline surged through him.
"This will help you see better. I don't need it, but you might."
TWENTY-THREE
"WOW! ARE YOU TRYING TO GIVE ME A HEART ATTACK?"
Reece sat in a back corner of the main room in a sweatshirt and jeans. His thick stockinged feet rested on the ottoman in front of him. Steam rose from his _Jefferson Airplane_ coffee cup cradled in his hands. A leather book sat next to him. His journal? Brandon hadn't seen that in ages.
"Trying, yes. But not succeeding obviously." Reece pulled his legs off the ottoman and sat forward. "Coffee's brewed if you want some."
"Yeah, okay." Brandon rubbed his head and blinked against the lamplight that seemed to burrow into his brain. "What are you doing up?"
"I think that should be my line."
"I never went to bed."
"Hmm, that's a long night." Reece took a long sip of his coffee.
"I needed time to think."
"I understand."
"Do you, Reece?"
"More than you know." Reece let out a low whistle. "Do you want to talk?"
Brandon ambled into the kitchen, found hazelnut creamer, and poured himself a cup of coffee. He raised the cup to his nose and breathed in the aroma. Nothing like a cup of joe to wake a guy up after he'd been up for twenty-three hours straight. He gave Reece a furtive glance. Maybe if he ignored the big man he'd go away.
"As I already said, you're not in this alone, Song."
"And as I already said, don't call me that anymore." Brandon set his coffee on the kitchen counter and stared at Reece. Why couldn't the guy still be asleep? Brandon wasn't ready to talk to anyone—especially Reece—about what had just happened out by the river.
Reece didn't respond but continued to somehow stare at him through his scarred eyes.
"I'm not the Song, so do me a favor and let's stop talking about it."
"Is that what you heard out there?" Reece slowly rose and strolled over to the sliding-glass door and faced the river. "Or are you hiding your glory?"
"What's that supposed to mean?" _Here it comes._
"You have the look about you of a man who heard something he desperately wants to hear again." Reece continued to face the river. "And my guess is what that man heard was music and the thought that he might one day become the Song again."
"You and your X-ray spiritual vision."
"Yep."
The room went silent.
What was the point in trying to keep what had happened from Reece? For some reason God told the man with unsettling frequency what had happened or what was going to happen in Brandon's life. It'd been that way since the Warriors began. But that didn't mean Brandon had to be happy about telling Reece anything.
"What if you're right? What if that man heard a song at dawn's breaking that went to the core of his heart?"
"I'd say the Spirit would be doing a powerful work in that man's soul and spirit."
"I don't know." Brandon slumped into a chair next to the cold hearth.
"You do know."
"I'm not up for an interrogation this morning." Brandon squeezed his coffee cup. "Have you forgotten you blame me for Doug's death?"
Reece shuffled into the kitchen and poured himself another cup of dark-roast coffee. "What did you hear out there? Am I right about it being music?"
"How do you know I heard anything?"
"Because I think you would still be making like a statue down at the Listening Post if the Spirit hadn't revealed something to you. A man who stays out all night isn't going to leave till he gets an answer."
"How did you know I was at the Listening Post?"
"Just because I don't have eyes doesn't mean I can't see."
Brandon had to smile. A man with spiritual eyes who could often see angels and demons all around them and could see some kind of outline of Brandon down at the Listening Post. "You're right. I did hear music."
"Tell me about it."
Brandon described the song he'd heard and what it had done inside his heart.
"Is this the first time you've heard a song like that?"
Brandon shook his head. "I've been hearing songs for the past four weeks. Sometimes visions as well."
He told Reece about what had happened with the couple in Edmonds, and Sandra, and the guy named Garen on the John Wayne Trail.
" 'And they sang a new song before the throne and before the four living creatures and the elders; and no one could learn the song except the one hundred and forty-four thousand who had been purchased from the earth.' " A small smile crept onto Reece's face. "From the book of Revelation."
"What are you saying? That I'm hearing the songs the 144,000 hear?"
"Not possible. Those songs are for their ears only. But maybe you're hearing songs for _your_ ears only. Ones only you can sing. Songs coming from heaven."
Reece spread his hands. "Think about it. What if everyone has songs written for them in heaven? Specific songs only for us? What if there are hundreds and thousands of songs for every soul who has ever lived and they're waiting to be sung to each of us throughout eternity? Songs of joy and sorrow and comfort and battle, freedom and glory?"
Reece's voice grew more animated. " 'For the Lord your God is living among you. He is a mighty savior. He will take delight in you with gladness. With his love, he will calm all your fears. He will rejoice over you with joyful songs.' "
"Zephaniah 3:17," Brandon said.
"Yes. And whose songs do you think God is singing? And do you think it's possible that an infinite God has only a finite number of songs—and he sings the same ones for everybody? Or does the God who has names for all the stars and knows each hair on the heads of everyone who has walked this earth create intimate songs for each individual?"
Brandon sat stunned as Reece talked.
"What if God is teaching you a few of those songs?" Reece paused and opened his hands wide. "I'm seeing into the spiritual realm. I think you're hearing into the spiritual realm."
Brandon nodded. Reece was right, but his mind couldn't help but spin toward thinking about the song he'd heard by the river. If the ones he'd heard back in Seattle were the songs of heaven, then the new one was straight from the throne room.
"The one I heard out there was . . . so much more than the others." Brandon didn't know how else to describe it.
"Have you asked the Spirit what the song means?"
"Yes." Brandon allowed a thin smile to reach his lips.
"Healing is coming for you, isn't it?"
"Yeah. It is."
Reece leaned on the kitchen counter, still as granite. Brandon shifted and drew in a long, silent breath. Should he ask the question? Or let it lie dormant a little longer?
"What about healing between us? Forgiveness?"
The question hung thick in the air like dark smoke, and for a time Reece seemed to grow even stonier, if that was possible. Finally he took a breath of his own, blew it out in a slow stream, and started to speak. But before the first words escaped, the moment was stolen as the front door of the cabin swung open.
TWENTY-FOUR
DANA STROLLED INTO THE CABIN FOLLOWED BY MIYO. Dana studied Brandon's face. She knew the look. They'd just interrupted a conversation Brandon wanted to finish with Reece. But Brandon looked better. Much better. It was clear he'd gotten an answer he'd been hoping for during the night or early-morning hours. A few moments later, Marcus stumbled down the stairs from the loft, his brown hair a mess, the skin underneath his eyes puffy.
"Everyone seems to be up early today," Reece said. "Good."
"I wonder why." Marcus rubbed his head and glared at Reece and Brandon. "It couldn't have anything to do with the rather loud ponderings emanating from your vocal chords at an hour where silence is the socially acceptable and preferred behavior."
Brandon wiggled his forefinger at the professor. "You manage to talk like a vocabulary teacher even when you're still half asleep."
Reece ignored the comment. "Brandon and I had an interesting discussion just now about what the Spirit is doing in him. Healing is coming. And we will need it. We will need everyone to be healthy. Regarding our next gathering, I'm sensing we need to reconvene here at Well Spring sooner than later. To be more precise, I'd like us all back here by Thursday night."
He looked at Dana. "But I know some of you have work. Can you get the time off from the station?"
"Sure. I still have plenty of vacation time built up and things are running extremely well, so long weekends are doable." It would mean working more hours the days she was there, but that was fine. The station was close to beating projections by seven percent this month. With a concentrated effort she knew she could get it to eight.
"Marcus?"
"I teach only on Tuesdays and Wednesdays during summer quarter, so my schedule can accommodate that as well."
"Miyo?"
"I've taken a leave from my job. I have no commitments for the next two months." But the intensity in her dark-brown eyes said the coming four days wouldn't be simple.
Marcus must have noticed the look in Miyo's eyes. "What will your priorities be during the coming week?"
"You might have noticed there was one more letter in the box when I gave all of you yours." Miyo pulled an envelope from her back pocket and tapped the edge of it against her palm, then put it back in her pants. "And there's a bigger package that goes along with it."
"Who is it for?" Dana asked.
"I don't know."
"There's no name on it?" Brandon frowned. "No instructions from Doug?"
"Just a first name. And my grandfather did give me instructions. But they don't offer much help."
She opened what Dana presumed was Miyo's own letter and read from it.
_" 'You must deliver the letter to him as soon as you and your father discover the box that contains all the letters. I don't believe he will remember me as he's been through quite an ordeal. But he needs to remember. Just as you and all the Warriors are critical pieces in the coming battle, he is as well. I didn't realize it was him till recently. I'm not sure why I didn't figure it out till now._
_" 'Funny how our lives are intertwined isn't it?' "_ Miyo smiled delicately as she continued to read. _" 'Marcus would call it quantum entanglement, I believe, or string theory, or some such thing. I'll call it God's way of weaving a magnificent universe-spanning tapestry where we all are of the pattern he is weaving. Find him. Deliver the letter as soon as you can. My prayer is it will start his restoration and put him in a position to play his role well.' "_
Miyo looked up from her letter. "I have no idea how to find this man. My grandfather never spoke of him. I searched his computer files, journals, cell phone records . . . but there doesn't seem to be anyone out there he might know with this name.
"There is certainly the option of opening the envelope and reading the letter, but I'd rather not do that for two reasons. First, I doubt the contents would give me much clue, and second, my grandfather specifically said in his instructions that the contents of each letter were for the recipients' eyes only."
"What's the name?" Brandon said.
Miyo glanced at each of them before answering, her eyes questioning. Dana knew what it would be before the word was spoken and silently agreed with Doug that God certainly was weaving a fascinating tapestry.
"The name is Simon."
TWENTY-FIVE
"ARE YOU IN THERE, SIMON? I AM NOT AN ENEMY."
Simon stared at the back of his front door. It was a woman's voice. Confident sounding. And young. Not yet out of her twenties, he guessed, and stressed and felt all messed. Not his enemy? Maybe not. But maybe she was. Maybe she was Zennon. Couldn't tell these days, couldn't tell these daze. He smiled at his own joke.
Yes, he could tell, yes, he could, yes he could. And he should. He was free. Except for the fact the humming in his head shot into his mind at least three times a day. No, not free. It felt like a rope was attached to his soul and the person holding it on the other end could yank him back anytime he wanted to.
"Simon, are you in there? I have something for you. From an old acquaintance of yours."
He padded over to his front door slowly enough that his feet didn't make any sound on his floor. He peered through the peephole. Intense brown eyes, they could be spies, full of lies. But he didn't think so. Something about her was true. Her eyes had the same thing in them that the professor's did. The Spirit's light, much delight. Showed that she'd traveled in the spiritual realms. That made her dangerous.
She stared at the peephole as if she knew he was looking at her. "I am a friend of Marcus Amber's."
Was she? No way to know for certain. But how could she have found him unless she was? Simon pounded his knuckles together. Should he speak? Why not? What could she do? Break down the door, fling him to the floor? No, no, no. He didn't have to open up for her.
"Who are you? What is your name?"
"My name is Miyo. A friend of mine apparently was also a friend of yours, and he said I must deliver these to you."
"Tell me about 'these' so my mind doesn't squeeze."
"A letter and a package, neither of which have been opened because they are only to be opened by you."
"Who is it from? Who is this acquaintance?"
"He asked me not to say."
"Don't play games. Tell me the name of the man who gave you this."
"I'm honoring his request."
Simon twisted the knob of his front door and pulled it open a crack. "Why should I let you in?"
"I already told you."
He opened the door wider. The woman didn't move. She held a business-sized envelope in one hand and a large manila envelope in the other. "Both of those things are for me?"
"Yes."
Simon opened the door all the way and still the woman didn't move. That he liked but his pulse still spiked. "What did you say your name was?"
"Miyo."
Simon shifted his weight from one leg to the other. "I used to do a trick with an unsealed envelope. I'd read the contents before anyone opened it, then a spectator would unseal the envelope and confirm I'd gotten every word right." Simon rubbed his fingers. "I could attempt that with this letter if you like."
"He said these are important." Miyo extended both envelopes to him. "That you needed to read them right away."
"This he of whom you speak . . . if I wanted to talk to him after I read what he wrote, would that be possible?"
"No."
Simon raised his eyebrows.
"He's dead, Simon."
"I see." He ran his tongue over his lips. "Any other plea?"
"He said he hoped you would remember him."
Simon's eyes widened. "No one knows me. No one. Only Marcus. I've been gone too long, no one still sings my song." He frowned. Song? A song for him? He didn't have a song.
"Good-bye, Simon."
The woman bowed and strode away. As she did the sun seemed to bounce off her shoulders in a strange pattern of light, and it raised a memory that faded too fast for him to hold on to it. A memory from the days when he . . . The reference point slipped from his mind and he couldn't locate it again.
Simon closed the door, walked over to his tiny kitchen, and set both envelopes in the center of his small table. Sunlight from the window high on the east wall of his apartment seemed to spin in circles as if a whirlpool were drawing him to the contents of the large envelope.
He stared at the envelopes for a few minutes, then settled into a chair and placed his hands on either side of them. The envelopes didn't move. They didn't mock him. They just sat there and stared back in his direction, daring him to rip them open.
Simon reached Ravenna Park a mile and a half north of the University of Washington just before dusk. No one stood or sat or played on the grass or hit tennis balls back and forth on the courts. Good. He needed to be alone to examine the contents of the envelopes. Not in his apartment. Too confining. Not in a bar or restaurant or coffee shop—he didn't want prying eyes. He needed open spaces—a place where he and his mind would have no distractions.
He eased up to one of the picnic tables and frowned before sitting down. Why did it feel so ancient and familiar to do so? When was the last time he'd sat like this at a picnic table, unable to face a life that cut like a knife? He ran his finger along the envelope's seam twice before sliding it under the flap and tearing it open. He sighed, closed his eyes for a moment, then opened the letter and read.
Dear Simon,
You revolutionized my life. I deeply regret I was not given the chance to tell you why on this side of eternity. I would have enjoyed that and enjoyed meeting you in person.
I can't imagine what kind of reaction seeing your manuscript again after all this time will elicit in you—it might be powerful; it might be painful—but I believe the Spirit has told me to give it to you. From what I've been able to learn from Marcus, I believe a gift has been stolen from you—the most precious one you were ever given—and this might be the catalyst that brings it back.
When Marcus first told the Warriors about a street magician, I suspected it was you, but I always thought of you more as an illusionist. However, I came to realize that many illusionists perform close-up and parlor-style magic as well. It wasn't until the end that I knew for certain it was you who had been trapped in multiple realities and somehow made it back to this world.
Before I explain how I know you, let me say what you did for Marcus dealt a major blow against the enemy. Well done, Simon, well done.
Long ago—as you might recall—I held the title of publisher for a small imprint located just outside of New York. I vividly remember the day your query came across my desk. It was on a Thursday in late May—the 31st, if I recall. I was of course swamped with work as usual and had an anniversary happening later that evening to distract me, but a feeling told me to slow down and take my time with this one before sending out our standard rejection letter. I did slow down and it transformed the way I saw the physical and spiritual worlds. I've never been the same.
Simon set the letter down and swatted his head as if that could stop the humming sound that had grown louder. "Get out of my head!" But the noise continued. What was this man talking about? He'd never written anything down—not even a journal—let alone an entire manuscript. Revolutionized this man's life? He didn't need this stupid letter; it would only serve to fetter.
He slipped off the bench and stumbled down the slight hill in front of the picnic table and tried to ignore the feeling that he did very much need the letter—that the letter needed to be fully read, for souls were to be fed, nothing to dread. Simon ignored the humming and staggered back to the letter and snatched it up.
From the moment I finished the first page—if I recall correctly it was just after lunch—I did nothing but fill my teacup and use the restroom till I finished your book. The experiences you documented and backed up with Scripture stirred my heart and spirit in a way I could not explain. Two days later I read the entire manuscript again. You can't imagine how hard I searched for you when I never received a response to my letter offering publication! After I found your book in the mail, it was as if you simply vanished.
But not being able to find you did nothing to abate the allure of what you had written. I pressed into the deeper things as you suggested, but not alone as you also counseled. I gathered a small group of men around me, and we learned together about the greater things of the Spirit. Oh, the adventures your book sent us on! The worlds you opened and the depth of the Trinity we began to experience was astounding. It is fascinating to me that the circle has now completed its cycle.
Do you remember who you are, Simon? Are you willing to act out of that strength once again? And if you aren't, are you willing to find the answer to the question of who you once were?
Simon set the letter down a second time and tried to slow his heart. He didn't know why it pounded like a drum. Fragments of memory flitted through his mind. An image of him at a typewriter, an open Bible and stacks of open books, him addressing a thick envelope. No, that couldn't have happened, couldn't be him. Maybe in one of the alternate worlds he'd existed in, but not this one.
Simon refolded the letter and slid it back into its envelope and set it on the picnic table. The sun was close to slipping below the tree line. He should go. He loved parks when the sun shone and turned the grass brilliant shades of green—when parks grew dim, though, he didn't like being in them. But he had to at least look at what was inside the large manila envelope.
Simon lifted the package and jiggled it up and down. It was heavy. He set it down, stood, and circled the table. Why did it frighten him? Yes, this Doug Lundeen's cryptic description of the package was part of the reason, but something deep inside said it was far more than that. That he was attached to the contents in a way that would spin him down a corridor as dark as the ones Zennon had trapped him in for all these ages past.
He finally slid a thick bundle of papers out of the envelope and set them on the picnic table. The edges were yellowed and a few of the pages were cracked. On top was a title page.
_Going Deeper and Deeper Still: A Manual for the Follower of the Ways of Christ Who Wants to Explore the Unexplored Spiritual Realms_ by Simon P. Donelson.
Simon's face grew warm. This had to be a joke. He'd never written anything. He pulled the rubber band off the stack and slid off the cover page. The next page was a table of contents.
• Soul Travel
• Traveling Like Philip
• Becoming Unseen
• Speaking to the Dry Bones
• Going Deeper into His Love Than Ever Before
• Fighting for Freedom
• Healing for Others
• Putting on the Armor of Light
• Swords and the Sword of the Spirit in Spiritual Realms
• Arrows of Power
• Wearing the Cloak of Strength
He leafed through the manuscript, still refusing to even consider that he was part of this. A few of the chapter titles had been lined out with a red pen and retitled. Notes were scribbled in the margins on almost every page. At first he thought the notes were editorial comments, but as he looked closer, Simon realized the person who made them—Doug presumably—was recording his own experiences after trying the things this manuscript contained. Just as this Doug said he'd done.
The last page was a letter with a sticky note on top of it. The sticky note read:
Simon, this is a copy of a letter I sent you after reading your manuscript. I assumed you never received it as I didn't hear back from you. Then again, maybe you did. In any event, I wanted you to have it.
September 2, 1962
Dear Mr. Donelson,
Allow me to forgo common pleasantries and say your manuscript has consumed me. The concepts are fascinating and have captivated my imagination. While I find myself vacillating between believing and not believing what you propose is possible, I without question feel the body of Christ needs to explore the ideas you are promoting.
There are numerous grammatical errors throughout the manuscript, and I would suggest giving your book a different title, as the one you have now is cumbersome, but these are small issues and easily remedied.
Please contact me at the phone number below at your earliest convenience.
Warm regards,
Doug Lundeen
Simon set the letter down and stared at the fading light. He needed to talk to the professor as soon as possible.
TWENTY-SIX
"YOU MUST HELP WITH THIS, FOR I AM AMISS." SIMON rubbed the bridge of his nose with both forefingers on Wednesday afternoon and paced in front of a cherry tree in the quad at the U-Dub. Marcus had never seen Simon this agitated. He suspected whatever Miyo had given the magician was the catalyst.
"I thought you were out of my life," Marcus said.
"No! Not anymore, must step through the door, tired of hiding, must talk about Warriors Riding."
"You want to discuss the letter Doug Lundeen wrote to you."
"Yes, of course, must get on that horse." Simon kicked at a leaf on the ground, then broke a small branch off the cherry tree and pointed it at Marcus. "Help me. Please."
Marcus gave a slow nod. "Tell me what the letter said."
Simon paced again. "He says I wrote a book and it makes me uneasy—"
"And quite queasy?"
Simon stopped pacing and glared at Marcus. "That is not funny. I don't want to rhyme. I can't help it."
"I'm only attempting to shock you out of this dither you've worked yourself into." Marcus patted the air with his palms. "Relax. It will be okay. Now, what did the letter say?"
His face devoid of color, Simon handed him a thick manila envelope and stared at Marcus. He'd never seen that look on Simon—the look of a little boy who just heard his first ghost story. He leaned forward and Simon tapped the package. "Open it. Take it out and look at the name on the front."
Marcus slid the stack of papers out and stared at the top page. "Is that your last name?"
"It used to be. One of them, anyway. I can't remember exactly who I was here. At least not most days, and today is a most day."
"Did you read through this?" Marcus riffled through the pages, stopping occasionally to read a few sentences.
"I've read the whole thing. Twice. And it's not mine." Simon rubbed his forehead hard enough to leave a red mark. "I didn't write that, Marcus!"
"Then who did?"
"I don't know why this Doug person would send it to me." Simon paced again and pulled his silver coin out of his pocket. "It makes no sense, Doug is so dense." He stopped and drilled Marcus with his gaze. "I didn't. I didn't write it. I didn't."
"Then I fail to understand why you would be this upset."
"Because what if I did?" Simon's eyes widened. "It would change everything." He pointed at the manuscript. "Read the table of contents."
Marcus did and when he finished, his heart thumped double-time. Was it possible?
Simon pulled a wrinkled envelope out of his back pocket and handed it to Marcus. "Read it. My letter from Doug, made me want to crawl under the rug."
As Marcus read the letter, it stunned him. When they'd met at Reece's home back in mid-July, Doug had hinted at the person who had taught him all he knew. It was Simon? Unbelievable. And yet at the same time, it somehow made imperfectly perfect sense. It explained how Simon could be so instrumental and insightful in Marcus's life—and if Simon had written the manuscript, it explained the reason why Zennon would have been so intent on taking him out. And why Reece felt the magician was so important in the coming war. If Simon could remember who he was, the results could be staggering.
"Look at me, Simon."
The magician stopped rolling his silver coin and complied.
"You need to come to Well Spring with us. We're going there this weekend. No is not an option."
TWENTY-SEVEN
"IS SIMON STILL COMING?" DANA ASKED.
She sat with Reece, Miyo, Brandon, and Marcus around the fire pit at Well Spring early on Thursday evening after a quick dinner that had been filled mostly with small talk. Not usual for them, but it was a nice break from their usual intense conversation that was often good but could also be exhausting. It was refreshing to simply sit and talk about nothing in the place where God seemed to show up in great measure. And she allowed herself to enjoy being around Brandon without thinking one moment into the future about her and him and what might or might not come. Nice to just _be_ for once.
Marcus tossed a piece of wood on the fire, which sent a stream of red sparks into the air. "He's given every indication he'll arrive sometime tomorrow evening."
"You think he'll show?" Brandon asked Marcus.
"Yes. Why wouldn't he?"
"From what you've described, he doesn't seem the overly social sort." Brandon tried to balance a small piece of kindling on his palm.
"You think he needs to be here, Professor?" Reece spoke over folded arms.
"You've indicated Brandon is critical to our success against whatever is coming our way. I feel the same about Simon. We need him. I more than feel it. I know it." Marcus picked up a long stick and poked the fire. "And he will need us."
"So be it." Reece stood. "I'm going to go for a hike. Clear my head. Try to hear from the Spirit what we're supposed to do if Simon shows and figure out exactly what this battle is. What are the rest of you planning?"
"Finishing up the paper I'm presenting at the university next week." Marcus stood and ambled toward the main cabin.
"I'm thinking of taking my camera up a ways into the mountains and getting some shots before the sun sets," Dana said.
"Veg out," Brandon said.
"You mean waste time?" Reece kicked at a rock near his boot.
"No. I mean relax."
"Yeah. Right."
Brandon stood, shook his head at Reece, and strode off along the river. Dana let the silence linger till Brandon was out of earshot.
"You have to stop blaming him, Reece. And stop blaming yourself."
Reece folded his arms and didn't answer.
"Reece?"
"You're right."
"And?"
"I'm working on it." He turned toward Miyo. "What are your plans?"
"I'm going in." Miyo stared across the river to the chalk cliffs north of the ranch, her eyes like stone.
Reece clasped his hands together and gazed at Miyo with his sightless eyes. "By going in, do you mean—?"
"I don't think you need to ask what I mean." Miyo laughed and the early-evening sun lit up her black hair like polished ebony. "You know exactly where I'm going."
"Into the spiritual realms."
"See?" She tilted her head down slightly. "Told you."
"Who's going with you?" Reece stood like a rock except for his mouth.
"No one." She lifted her head. "This is a solo run."
"It's extremely rare for one of us to go into any kind of spiritual realm by ourselves. Why do you think the Spirit is leading you to do this by yourself?"
"Rare for you, maybe," Miyo said. "Not rare for me."
"I'm not your mentor, Miyo, or your father or your grandfather. But I do have experience and lessons I've learned in the spiritual realms over the past thirty years that will save your life. And one of the fundamentals is the same as the old scuba-diving adage: Never dive alone. Always take a partner."
"I don't need a partner for this excursion."
"I disagree."
"I appreciate you offering your opinion."
Reece tilted his head back and took in a long, severe breath. "Where exactly is your excursion going to take you?"
"Into the hinterlands." She glanced down and rubbed her hands back and forth over her knees. The light from the sinking sun flashed off her purple nail polish, which matched her eye shadow. "Always interesting things to see when I do that."
"What are the hinterlands?" Reece cocked his head and put his hands on his hips.
"The classic definition is the land directly adjacent to and inland from a coast, or a region remote from urban areas, backcountry. It comes from the word _hinter_ or _behind,_ which comes from Middle High German, which developed from the Old High German word _hintar_."
"I see, but I'm thinking you're not using it in that way."
"True. I mean it more in the sense someone familiar with _World of Warcraft_ would define it."
" _World of Warcraft_?"
"It's an addictive online role-playing game," Miyo said.
"And what is their definition?"
"The Hinterlands are both a center for the Wildhammer dwarves to the west at Aerie Peak and the forest trolls to the east. It is an ancient region with pine trees, troll ruins, and one of the few remaining highelf settlements."
"So you're off to see dwarves and trolls and elves?"
"No. I never went in for those role-playing video games. I enjoy the real thing. And I would substitute the words _demons_ for _trolls_ and _angels_ for _elves_."
"So you're off to some unknown spiritual realm to engage in battle by yourself?"
"Not unknown. I've been there many times."
"For what reason?"
"The Spirit told me to." Miyo lifted her head. Her eyes were intense, and although her words and tone of voice could have been taken as lighthearted, her countenance said the opposite. She glanced at Dana. "Does he grill all of you like this?"
"Usually not. He must like you."
She turned back to Reece. "I'm twenty-three, not twelve."
"In the short time I've known you, I've decided I definitely want you to reach twenty-four."
"And you think I won't because . . . ?"
"I believe you're reckless." Reece spread his feet and folded his arms. "And cocky."
"Based on?"
"Everything you've shown me so far points to that conclusion." Reece turned his face into the sun. "You've never had any problems in a soul or any other spiritual realm?"
"I didn't say that. I said I don't need anyone tagging along."
"As I indicated, that's not wise."
"Where did you latch on to that view?"
"From your grandfather."
"Hmm." She clasped her arms behind her back. "Interesting."
"Not the same advice he gave you?"
"When I started out, yes. I never, ever went in alone. There were never any exceptions. But that changed."
Reece still stood like one of the Easter Island statues. "When you decided it should change?"
"Not a chance. I never even thought about breaking that rule till my grandfater said I was ready to go in by myself."
A breeze brought a strong aroma of pine to their noses, and it took Dana back to camping as a kid. But this wasn't camp. It was a confrontation she'd never seen before. Brandon, Marcus, and she had been so overwhelmed when Reece had first trained them, they'd never challenged or questioned him. Miyo was a very different animal. She wasn't mesmerized by Reece's knowledge and experience because it was clear by now hers likely exceeded his. Maybe by a wide margin. She respected him, but she wasn't going to give a millimeter simply to appease him.
"With age comes wisdom, Miyo." Reece tilted his head down slightly. "I'm offering some of mine."
"Maybe you're not ready to go in alone yet."
"You're joking, right?"
"I never backed out of the arena, Reece. From what I've been told, you did. Got off the field to build that photography business of yours. Maybe if you'd stayed in, you wouldn't be a few grades behind."
The silence that followed was like a snow-covered forest in the dead of winter. Reece stayed in the silence for at least thirty seconds. When he spoke again his voice was tinged with irritation. "As I said before, I am not your mentor but—"
Reece stopped, turned his head in Dana's direction, and rubbed his upper lip. She'd learned this was a clue he was seeing something in the Spirit with his new eyesight. She expected the resulting emotion on his face to be anger, but instead it was surprise. "Do me a favor. Take someone with you this time. Not that I'm saying you need to. Maybe he or she needs it."
"Agreed," Miyo said softly and turned to Dana. "Would you like to have a little adventure?"
No, she wouldn't. It would mean having to face the issues about Miyo that Brandon brought up the other night. Or at least shoving them down deep where they belonged. But at the same time, Miyo was someone she could learn from. "Sure, I'll go."
After they'd strolled away from the fire pit, Dana said, "Don't mind Reece. He's a little overprotective of you."
"Why?"
"I think it's because you remind him of someone," Dana said.
"Who?"
"His daughter."
"My grandfather told me Reece had a daughter and that she died young. But he didn't say much more than that."
"Zennon."
"The demon who killed my grandfather." Miyo's eyes darkened. "What about him?"
"Twenty-six years ago Reece took his wife and daughter into a soul with him and he made a mistake. They ended up in a different soul than Reece thought they were going into. Zennon murdered both of them there."
"Oh wow." Miyo sat back. "Zennon has certainly made his mark among the Warriors."
"Reece said his daughter—her name was Willow—didn't fear anything. Not in a bravado way, but she had strong confidence. A strength in the way some people would describe as an old soul in a young body. He was so proud of her and loved her so much. He was training her at a young age just as Doug trained you from a young age. She was bold. Confident. Ambitious."
"You mean often too driven for her own good and sometimes confident bordering on cocky?" Miyo pointed at herself.
"Maybe something like that."
"I am confident. But not cocky. Maybe early on. But not now." Miyo sighed. "Is there a good spot to go in from?"
"Everywhere on the ranch is good. Since Reece owns the place, there's never an interruption. But I say let's go in up the river a ways."
"He owns Well Spring?" Miyo frowned. "Really? My grandfather never told me that or much about Reece's working life."
Dana led them up a path directly in back of the cabins on the western edge of the property. It wound up a gentle slope for two yards and ended at a small clearing Brandon, Marcus, and she had created together six months ago.
"Photography was extremely good to him over the years. So when he sold his company eleven years back, it meant he never had to work again. He could probably buy twenty ranches this size and it still wouldn't dent his portfolio much."
"Photography?"
"He owned one of the most prestigious lines of galleries in the world."
"Reece is Roth Photography? You've got to be kidding me."
Dana burst out laughing.
"What's so funny?"
"That's exactly the reaction I had. I never put the pieces together till I saw his camera bag out here fifteen months or so ago."
"Couldn't be the just-off-the-street, classic-rock-T-shirt look Reece sports, could it?"
They both laughed. Dana looked at Miyo. "A bit of contrast to the way you dress. I'm guessing the fashion gurus get advice from you."
"I'm just being me. No agenda in it. I don't wear Emilio Pucci and Roberto Cavalli because they're trendy. I wear them because I like them. I hate the attention it brings."
"Really? Sorry to be blunt here, but I had to assume you dress like you do to get a reaction out of people."
"If I dressed down in order to stop the reaction of people, I'd be just as guilty as the people who dress up to get a reaction. In either case I'd be playing small. If everyone in the world was blind, I would still dress like this."
"Playing small?"
"Most people live in fear of what others will think, how they'll react, and it holds them back from being their true selves." Miyo stared deep into Dana's eyes. "Where do you play small, Dana?"
She almost gasped. The question went to her heart like an arrow. But it was the right question—one she needed to face. She played small at work. With the Warriors. At home. Basically everywhere. But there were times she didn't. Those moments didn't come often enough. "Is my jugular vein sticking out so far you just had to go for it?"
"Sorry. I've been told more than once my tongue is one of the bluntest instruments people have ever seen."
"I like it." She did. Miyo said what she thought. No typical female games. Refreshing. But it didn't mean Dana had to like Miyo becoming a star among the Warriors.
"Why did he sell his galleries?"
"He says he liked it too much. Not the photography, the business side of it. Creating an empire. Crushing the competition. The rush of growing something huge. Making lots of money for the sake of making lots of money. And probably more reasons. He rarely talks about it, and then only after I push him to."
They reached the clearing and peace came over Dana. Two chairs sat in the small clearing, and the view the spot gave of Well Spring always made her relax. They both sat and rested in the silence for a moment.
A few minutes later, Miyo held Dana's gaze and there was kindness in it. "You're sure you want to go with me on this ride?"
"Positive."
"Because the roller coasters I ride on don't come with seat belts."
Dana grabbed the sides of her chair and smiled. "Don't worry, I know how to hang on tight."
TWENTY-EIGHT
MIYO GRABBED THE CHAIR'S ARMRESTS, SPREAD HER FINGERS over the edges, and squeezed. Then she laid her arms in her lap and slowly leaned her head back till it rested on the back of the chair and closed her eyes. "Ready?"
"Aren't you forgetting something?"
Miyo kept her head back, rolled it toward Dana, and opened one eye. "Not thinking so."
Dana held her hand out, but Miyo just stared at it. "What? You want me to hold your hand? I like you, but aren't we a little old for that?"
"We always hold hands when we go in."
"Really?" Miyo opened her other eye and laughed.
"Always. I thought it was something we had to—" Dana stopped herself.
"Fascinating." Miyo sat up and studied Dana. "You think it's like some connection point so you both go to the same spot? That if you weren't touching you'd spin off into different realms?"
Dana stared at her. It was exactly like that. It's what Reece had taught them. It's why they lost Marcus last year in a spiritual realm when the crevasse opened up and the professor couldn't reach them, and he'd nearly been sucked into one of Zennon's alternate realities. But obviously it wasn't an issue with Miyo. Had Doug taught her an advanced technique?
"You don't touch?"
"First, since I can't really remember the last time I went in with someone, there hasn't been the option to hold someone's hand. Second, I'm not sure what the purpose of doing it would be. Unless it strengthens the— No, you're right." Miyo looked up as if she was remembering. "We used to do that when I was in my early teens, but when I was about sixteen my grandfather said I'd grown beyond needing to do that." She frowned. "But if it makes you feel better, I don't mind doing it."
Yes, it would make her feel better. Dana felt like she was six years old talking to her babysitter, and here she was fourteen years older than Miyo. Dana's face grew hot and she hoped her embarrassment wasn't obvious to Miyo. If it was, Doug's granddaughter didn't act in any way like she'd noticed it.
"Yes. It would help."
"Then let's do it." Miyo grasped Dana's hand and Well Spring vanished.
Every time Dana had traveled into a soul or into another spiritual realm, there had been a sensation of movement, a changing, a sensation she was swimming. With Miyo, one moment they sat on the chairs hearing the sound of the river in the distance, the next they stood in a forest of thick alder trees. Lush moss and ferns carpeted the ground, and a smattering of sunlight filtered through the emerald leaves. Large, round boulders dotted the landscape.
"How did you get us here so fast? It was almost instantaneous."
"Not almost." Miyo tilted her head and stared at her. "This was unusual for you?"
"We've never traveled this fast."
"Then you've placed a limitation on yourselves. Time is a restraint embedded in the soul and body. Our spirits have no such limitations, and since our spirits are what travel into souls and spiritual realms, the journey from the physical world into the spiritual does not need to take any time unless we choose for it to."
"You sound like Marcus."
"I'm looking forward to the day Marcus realizes many of the theories in his books are not theories but realities."
"He's realized some of them."
"Far fewer than he knows." Miyo glanced around the forest, then turned back to Dana. "How many armies have you spoken into existence such as Ezekiel did?"
"I think Reece or Doug might have mentioned the possibility at some point."
"In other words, none."
"Are you always this direct?" Dana grinned.
"Too much?" Miyo narrowed her eyes. "There I go again. My apologies."
"Not needed. As I said earlier, I like it." Dana squeezed Miyo's hand. "I'm not really a play-the-game type girl."
"I knew that about you the second I met you."
For the first time since Dana had met her, Miyo gave an unrestrained smile where her eyes and smile were in perfect concert with each other.
"You're beautiful when you really smile."
"Really smile?"
"A smile with your guard down."
"I see a heightened sense of perception is one of your gifts." Miyo shook her head and smiled again.
"Sometimes. I lead a radio station in Seattle. Often success is more about knowing people than knowing numbers."
"I bet."
Dana studied the forest. The beauty of it captivated her, but something was out of place. Not out of place. Missing. Ah, that was it. There was no sound. No birds, no sound of water from a far-off stream, no buzzing of insects, no breeze through the leaves above them. The forest was still as if it were frozen.
"Why do I feel like we're the only things here that are alive?"
"We should be." Miyo stopped on the edge of the clearing and motioned Dana to do the same. "But I can't be certain. Let's be watchful."
They padded over the forest floor, both turning their heads back and forth. Five minutes later they reached a small clearing thirty or forty feet across. Long, wispy grass leaned to the left and covered the meadow, and with the sun now directly on them, the temperature of the realm seemed to rise five degrees.
The tree in the center of the clearing made a perfect half circle as if it grew out of two separate places in the ground and met seamlessly in the middle. The arch was ten or eleven feet wide at the base and seven or eight feet tall.
"An elegant tree," Dana said.
"That's more than a tree. It's a gateway. Do you want to go through?"
"A gateway to where? We can see right through it. There's nothing on the other side."
"You know how in the Field of Doors the doors appear to go nowhere? When in reality they take you into a person's soul?" Miyo moved her right hand under her left in a fluid motion.
Dana nodded. "Like Marcus when he went through the door of his memories. The inside was so much bigger than the outside."
"Marcus went through his memory's door?"
She nodded. "Changed his life."
"I bet. I've heard of those but have never seen one. I suppose the only time you would see one is if you're viewing your own." Miyo pointed at the tree. "It's the same thing here as with Marcus's door. This is a gateway or a door into another realm." Miyo motioned Dana forward. "Shall we?"
Miyo winked and held out her hand. Dana smiled and took it. As they approached the arched tree, a thin line of light appeared on either side of the trunk. After two more steps, the air in between the half circle of the tree began to shimmer.
"Ready?" Miyo asked.
"Sure." Her heart pounded but she had no fear of stepping through—only anticipation. Two more steps. One more.
Just before they stepped into the shimmering air, Miyo leaned back and yanked Dana's hand hard. Both of them stumbled backward and Dana fell to the ground.
Miyo kept her gaze riveted on the gateway as she helped Dana up. "Sorry."
"What was that for?" Dana brushed herself off and stared at Miyo.
"Are you okay?"
"Fine, but what—?"
"Something's not right." Miyo's gaze roamed all around the tree. "Can you feel it?"
"No."
"It's there. Believe me, whatever is on the other side of this gate is not our friend." Miyo glanced back at the archway. "We need to get geared up before we go through there."
"We're still going through?"
"Sure." Miyo smiled. "But first, are you still certain you want to be here? This is my mission, not yours. This trip has just turned from one of discovery into one of battle. We can leave right now."
Dana didn't want to go on. She wanted to be safe and warm and cozy and have a perfect little life of no struggles and no worries, where she had a man who truly loved her for who she was, not for what she did. But that wasn't reality and never would be. Life wasn't white chocolate and wedding invitations and happily ever afters. Not hers anyway.
"Absolutely."
"This is no time to posture, Dana. I can see it in your eyes and feel it pulsating off your spirit. You're scared."
"I'm terrified, yes. But I don't posture." Dana narrowed her eyes. "Ever."
"I believe you."
Dana glanced at the air in the archway. It had grown thicker during the time they'd talked. It looked like the frosted glass in the wall of her shower back home. Only this glass swirled like liquid.
"Is that going to continue getting thicker?"
"Yes, and it's easier to navigate the thinner it is. So we should go through in the next few minutes. I got stuck one time in something similar for seventeen hours. It wasn't fun." Miyo looked at Dana from under her eyebrows. "Still good to go?"
"Yes."
"Then let's get armored up. We'll be glad we did."
Miyo tilted her head back, closed her eyes, and held her slightly raised arms out to her sides. A soft yellow light appeared at Miyo's feet and moved up her legs as if it were water flowing the opposite direction gravity would take it. As the light moved past her knees and over her waist, it changed, growing thinner and brighter till Dana had to squint against its brilliance.
In seconds, Miyo was surrounded and she opened her eyes and turned in a slow circle, gazing at the landscape and then at the arched tree. "Much better. I think we'll be glad we put these—" She stopped and stared at Dana. "We don't have time to waste. When I said a few minutes I meant it. You know we're not supposed to spend too much time inside any kind of spiritual realm. Ever."
Dana gawked at the light swirling around Miyo. "How did you do that? And what is it?"
"You don't know?" Miyo laughed, and the light around her seemed to grow thicker. "It's light. Pure light of God. Didn't Reece ever show you how to do this?"
She shook her head. Dana had the distinct feeling Reece would be as startled as she was at Miyo's revelation.
"How do the four of you protect yourselves when you're inside?" Miyo frowned. "What things did he teach you?"
"He started with showing us how to send our spirits into a soul. Then teleportation. Then—"
"It was a rhetorical question. I'll get you started on your armor and you can finish it." Miyo raised her hands and held them wide and then six inches from Dana's body. Slowly, a paper-thin light formed and spread around her feet just as it had a moment ago on Miyo's. And the pressure was like a spa bodywrap but the feeling was far better.
Warmth and strength surged through her body, and part of her wanted to burst out in laughter. The light inched up her legs as it had done with Miyo. By the time it reached Dana's stomach, a powerful sense of peace filled her mind.
"What is this?" Dana didn't need to ask the question. She now knew exactly what it was—not because Miyo had told her, but because it had become a part of her—but she had to say something.
"It's armor, Dana."
"Armor? Made of light?" The question seemed silly once Dana asked it. Why couldn't armor be made of light? Maybe it was impossible in the physical world, but what would stop God from doing it here?
"Yes. Light. Made of his power and strength and invulnerability." Miyo seemed to examine the thickness of the light surrounding Dana with the precision of a surgeon. When she came to Dana's right shoulder, Miyo moved her hand in a circle a half inch above the light and it thickened. "I thought you read the Bible."
"Your point?" She glared at Miyo.
Miyo grinned in return. " 'The night is nearly over; the day is almost here. So let us put aside the deeds of darkness and put on the armor of light.' "
"Romans," Dana said, feeling like she'd heard the verse for the first time.
"Ah, so you do read the Word." Miyo tapped her forehead.
"Don't mock me."
"I apologize."
"I never took that verse literally." Dana stared at the light cocooned around her and laughed with a joy she couldn't keep inside. Of course. That had to be another part of this. The joy of the Lord was strength.
"Sometimes the Bible is taken far too literally; sometimes it is not taken literally enough. As you can see, this is a case where the latter is the truer of the two statements."
"This is amazing. Why didn't I ever see that?"
"The Word of God is living—it's not a stagnant book. It's animated. Things will come alive to you that you have missed for years. Still others will take years more before you see them."
"But still—"
"Don't feel bad. I just discovered this armor two years ago." Miyo's eyes grew distant. "And believe me, it would have saved me a great deal of pain if I'd learned it earlier."
"I thought you were going to teach me how to do this for myself."
"I can't teach you. I can only show you—which I've done. Now it's time for you to practice the technique."
"How?"
"The only way any of this works," Miyo said. "Think about it. How have each of your battles been won so far?"
"Belief."
Miyo nodded. "If you had the faith of a mustard seed, Dana, you could toss mountains into the sea like they were pebbles. I showed you so you could believe it was possible. Now it's time for you to believe."
Dana stared as the light around her body faded. Slowly at first, then faster like it was being sucked into an invisible drain under her feet. In ten seconds it was gone. She felt vulnerable. "Where did it go?"
"I created it, which gave me the power to release it. Now you're going to create it and you'll have control over the armor."
"I'll try."
"There is no try."
"Yoda." She pointed at Miyo. "I thought you were a geek when you made that comment about _World of Warcraft_. This confirms it."
"You must be one, too, if you know the quote." She pushed back her black hair.
"Not me. Brandon. When we were—" Dana stopped. She didn't need to be spilling all her secrets to this woman. Besides, the subject of Brandon wasn't one she needed to be worried about right now.
"I suspected you two had a history together."
"No you didn't."
"It's pretty obvious." Miyo smiled.
"What is? I don't—"
"Don't what? Let your eyes always linger on him a fraction of a second longer than is normal?"
"What!" Dana scowled playfully and shook her head. "Don't you mean the way he lets his gaze stay on me?"
"Uh . . . no." The smile stayed on Miyo's face.
"That's it? Just 'no'?"
"Let's concentrate on you putting on your armor, okay?"
Dana shook herself as if that could get rid of thoughts of Brandon. Armor? Right. But she had no idea how she would make it happen, and Miyo didn't seem to be offering any coaching other than to believe. But that was fine. Dana had seen and experienced enough over the past year and a half to know leaping off a cliff with the flight plan already in place was the exception, not the rule.
She closed her eyes, pushed her doubt away, and pictured a cocoon of light surrounding her feet and moving up her legs. Instantly her feet felt surrounded in the same warmth she'd experienced a few minutes ago. She opened her eyes and stared at the liquid light swirling around her toes and arches and ankles. "Oh wow." But a moment later the light faded and seemed to soak into the wild grass at her feet.
"What happened?" She turned to Miyo.
"You lost concentration. You let your thought of astonishment crowd out your belief. With the thought of wonder came the thought something along the lines of, 'I can't believe I'm really doing this.' Am I right?"
She was exactly right.
"It will help if you let go of the idea that you're doing anything. You're not. He is the one creating the armor. You're only tapping into the power that is already residing in you. You have all the power of the God of the universe at your disposal. We have been seated at the right hand of the Father in the heavenly places. Think about that. You don't have the power of Dana. She's dead—crucified with Christ. But the Dana that is now alive with Christ has incredible power. So creating a small armor of light around your body is nothing. Go again."
This time the light started at her feet and streaked up her legs and torso like wildfire. In seconds, her entire body was surrounded by light—thicker across her chest and over her head, thinner around her hands and fingers. It felt stronger than the earlier armor Miyo had created and Dana said so.
"Yes. The armor you create for yourself will always be more powerful than armor created by another. The only one who knows your weaknesses better than yourself is the Spirit. And since you are creating it in unison with him, the result is a protection perfect for your spirit, soul, and body."
"Amazing." Again came the thought of how incredible the light was, and the armor started to fade. But Dana torched the thought before it had time to take hold, and the light thickened again to the level it had been.
"Good. You're learning quickly." Miyo padded around her in a complete circle on the soft grass. "Well done."
"Can the enemy pierce this armor in battle? Will it hold up?"
Miyo stopped when she completed the circle and her face grew somber. "I'm going to give you a chance to find out."
"So we're going in."
"No."
"What? I thought—"
"Look at the opening."
It still swirled, but now at an eighth the speed it had earlier. It had turned to a dark gold reminiscent of honey and just as thick.
"We wouldn't be able to get through that, would we?"
"Getting through would be extremely easy. Getting back out would be the challenge. And what's inside is not our friend."
"Then why would you take me in there?"
"The Spirit told me to." Miyo paused. "I'm not an outlaw, contrary to what Reece might believe. I'm not doing these things on my own. This is not a playground. I only ever do what the Spirit tells me to do. The Spirit told me to invite you, and Reece mentioned it before I could. He saw it, too, and was true enough to admit it.
"You try going into spiritual realms without the Spirit's invitation and at best you'll get severely hurt. Worst case is you'll be headed into eternity earlier than the divine design called for. So I have to assume God wants you to learn something inside that realm."
"Then why did you make it seem like a suggestion for me to come? Like it was my choice and I could take it or leave it?"
"You can take it or leave it. That's the Spirit. He's never going to force you into anything. While I believe there is a specific destiny God has planned for each of us, I also believe we have free will. We have choice. If I presented my invitation in a way where you couldn't say no—' _God told me you have to come in with me!_ '—then you'd either have to say God didn't tell me that and act against it, or disobey. Besides, sometimes I'm wrong. Sometimes I think the Spirit has told me something he hasn't. I figure if God is part of it, it'll work itself out."
"But doesn't that keep you from fighting hard for things he's told you to fight for?"
"No. When I say I hold decisions loosely, I mean other people's decisions. When it comes to my own actions and obedience, I'm fierce."
Dana stared at the archway as she mulled over Miyo's words. "So if you were supposed to take me in there, does that mean we can try again sometime?"
"Most certainly."
"When?"
"Tomorrow."
"Why does the look on your face concern me?"
Miyo stared at her, a little smile at the corners of her mouth. "If I'm hearing the Spirit right, what you will learn inside there will be really freeing for you, and really hard."
TWENTY-NINE
TRISTAN BARROW PACED ACROSS THE NARROW RIDGE, HIS boots tearing into the loose shale at his feet and sending it falling into the river canyon below him. His six-foot-six frame moved like a lion, his thick blond hair and broad shoulders completing the picture of a world-class athlete.
Orson—to Tristan's left—shifted the weight of his chunky body back and forth and stared straight ahead. Jotham stood on his right, his short lean frame twitching as if ready to strike. To either side of them were two more angels. In the distance, on the other side of the canyon, Tristan saw a small cloud of dust rise from three figures that moved toward them.
"I don't like it." Orson folded his arms and glared at the three beings. "What's the point of having even a shred of discourse with him?"
"Let not your heart be concerned. His goal for this encounter is knowledge. To poke and prod at us. Not battle."
Of this, Tristan was certain. Both Orson, Jotham, and the two others had been under his authority for seven centuries of human time and were proven warriors who had joined him in more than six thousand battles. If this encounter came to war, so be it. He had not even a sliver of fear that he and his warriors wouldn't emerge victorious. Their enemies knew it as well. Which was why swords would not be drawn. Today.
A jagged wind surged up from the canyon below and buffeted them like a sandstorm. A current of evil designed to instill doubt and fear. None of his warriors would succumb to the lie, but it was irritating nonetheless.
"I don't like this either." Jotham reached for the hilt of his sword and massaged the leather-wrapped hilt. "We should destroy them the moment they appear."
"Patience," Tristan said. "We are here to listen." He turned to his left. "Rantor, take a position twenty paces farther out." He turned to his right and issued the same order to the angel there.
When the three figures were two hundred or so yards away, they vanished. An instant later the ground shook with the strength of an earthquake, and the three figures stood across the canyon from them, thirty yards away.
The one in the middle took out a gold coin and flipped it in the air, caught it, and stared at the markings on its surface. He glanced up at Tristan, then back to the coin.
"I like the human's worship of this mineral." Zennon rolled it around his fingers. "It is quite beautiful. But its beauty is nothing like the garden before the earth was corrupted."
"Don't waste the moments I have given you." Tristan's voice was ice. "If you have words to speak, say them now."
"Quite right." Zennon grinned. "By the way, old friend, I'm sorry you didn't arrive in time to keep Brandon Scott's throat from being slashed open. How is he doing? Still dedicated to the cause? Rumor says not as fully as he once was."
Tristan still stood like granite, his hands at his sides, his fingers loose. "Why did you ask for this time, demon?"
"Demon?" Zennon stopped twirling the coin and looked at Tristan in mock amazement. "You're not seriously using that word, are you? Have you been truly humanized from walking around in those flesh suits too often?"
"Get to the reason you've come."
"You don't remember me, do you, Tristan?" Zennon frowned. "From the old days, I mean."
"Why did you call us here?"
"Come now. Think back. I was a lowly angel in those days. And you were the mighty Tristan, the great avenger. I asked to be in your battalion. I came to you and pledged my loyalty. You took your sword and offered me your strength. I asked for more. To have power equal to yours. To stand by your side for eternity. But you refused. You said I needed to do more to earn that kind of power."
Tristan didn't answer.
"Good. I see in your eyes you do remember. Do you also remember calling me your brother? Your friend? Is that why you were assigned to Reece and the other Warriors? Because of our history? I'm simply curious."
Again, Tristan didn't respond.
"We explored the universe together. Past the Milky Way to the outer reaches. We were like brothers, Tristan Barrow. I wanted to be like you. And then the renting came. And you seethed with anger at our leap into freedom. You even cried out in rage when you discovered I'd gone with the Morning Star. Do you remember?"
Tristan tensed. "Lucifer is only a depraved imitation of the true Morning Star."
"He hasn't lost any of his beauty, contrary to how man has painted him. Who would want to follow a monster? Remember when the battalion used to watch him go through his exercises? None could match him. His power. His speed. His strength.
"He still does them. And he will win. Why? Because the Master isn't relying on humans who have shown such weakness again and again over the centuries. He relies on us who have sworn loyalty to him till the end."
Zennon stepped up to the edge of the canyon so the front of his feet hung over the side. "Do you know why I turned? I asked him to give me what you would not. He answered by taking my shoulders and waiting till I lifted my eyes to his and held his gaze. Then he said, 'You shall have the power you crave and more. And I will not delay.' " Zennon tilted his head back. "It was a glorious moment. I believed him. I embraced the Morning Star in that moment and my heart was his.
"He asked that I bow to him and pledge my strength, and I did. He asked that I follow him to the depths of Sheol and the heights of heaven, and I swore I would. He asked me to pledge my life to him, and I agreed. And then he asked me to worship him, and I did. He raised me up and held me like a son, and in that embrace I felt power flow into me like I'd never known. A power you could have given me but refused."
Zennon paced along the edge of the cliff, and with each step the rocks under his boots shattered. He lifted his hand toward a massive column of rock to his right and it exploded in a shower of baseball-sized chunks. In the next instant, Zennon whirled and flung his hand toward the angel on Tristan's left. A boulder the size of a bus hurtled toward him like lightning.
Tristan spun to his right and threw a bolt of light like a javelin at the boulder. It pierced the stone in the center and reduced it to dust long before it reached Rantor.
"I see your reflexes are still in working order." Zennon stared at his palm. "But I'm not so sure about them." Zennon pointed at Jotham and Orson. "Or him." He jabbed a finger at the angel on Tristan's right. "Or him."
Zennon motioned to the soldiers on either side of him. "If you tried the same attack on my friends, they would not have needed me to come to the rescue. And when we next meet in battle, I assure you, you will have too much to occupy yourself to have time to come to the aid of your friends here, or the humans."
"Are you finished?" Tristan asked.
"Are your precious Warriors—these tents of flesh you've grown so fond of—truly ready for what you must sense is coming?" Zennon swept his hand over the horizon. "No. They are not. And because they are not, they will be destroyed.
"One more thing." Zennon steepled his fingers. "Do you wonder if I'm more powerful than you now? If I could defeat you in battle?" Zennon laughed. "I think you're worried I would dance in the pool of blood that poured out of your side if I had the chance to face you alone.
"But this isn't a war between you and me. The humans are irrevocably intertwined. And as I've said, they are not anywhere near ready. Give them to me now. Lift your protection of them. Hand them over to me and there will be no war between us."
"They have defeated you multiple times."
"Those were skirmishes. You know this. Yet you haven't told them. They think they've won great victories."
"They have." Tristan laid his hand on his sword. "And they will. They are complete."
"Oh, you think adding Miyo will make a difference?" Zennon shook his head. "Hardly. She's too young, too impetuous. Brash. Cocky. Splattered with pride. You're resting so much hope on her and she will fail. All of them are deluded about their skills and ability to stand against me, and you continue to let them believe the lie. You who say you are of the truth. We are not so different, my commander." Zennon spit on the ground and rubbed it into the dirt with the toe of his boot. "This will be you very soon."
Tristan again remained silent.
"Come now, old friend. There must be words of response waiting to explode against me. I know you. I feel it radiating off of you like the sun. You long to see how much stronger I am than you and if you have a chance of winning."
"This is over." Tristan's words rang out over the canyon and echoed back to them like a cannon shot. "Go, demon, in the power of the One!"
Zennon and the demons at his side vanished.
"What was that?" Jotham spat out the words. "How could you take that refuse from Zennon?" He lifted a hand and flicked it toward the spot where Zennon had stood. The ground exploded in a geyser of rocks, and when the dust cleared, that part of the cliff was demolished.
"Unnecessary anger does not befit a warrior."
"Righteous anger always befits a warrior."
Tristan stared at Jotham but didn't speak.
"Fine." Jotham jerked his neck back and forth.
"Your chance for retaliation will come, brother. Soon." Tristan paused and looked at the rest of his warriors. "That was time well spent."
"To have him insult you and the rest of us was time well spent?"
"We learned two critical elements about the coming war. First, that Zennon is worried about Miyo, so we must guard her well." Tristan's hand went to the hilt of his sword. "And second, that Zennon longs to meet me in single combat."
The angel smiled, bowed his head, and raised both palms. "If it be your desire, I will answer the call with all that I am."
THIRTY
THE NEXT DAY AFTER BREAKFAST, MIYO AND DANA AGAIN stood in the clearing with the arched tree in the center. The forest was just as still. The shimmering light in the archway was clear again.
"Still feeling good about this?" Miyo pointed at the gateway they were about to step through.
"The adrenaline pumping through me right now is about to burst out of my veins."
"Good. That means you're on high alert. You'll need that."
"Are you taking me into something I can't handle?"
"We won't know till we're back at Well Spring," Miyo said. "One more time. Are you sure you want to do this?"
Dana stared at Miyo and then at the arched tree. She was far from sure. Her nerves made her response come out in a squeak. "I'm sure."
Miyo laughed. "That's not real convincing."
Dana glared at her. "Let's go."
"Yes, let's."
They both covered themselves in light-armor, and when she finished, Miyo studied Dana's construction.
Miyo circled her. "Well done. You've learned faster than anyone I've taught." Dana couldn't help but smile at the compliment.
"Now make it a bit thicker all around."
Dana closed her eyes and pictured the light around her as more substantial, and seconds later the warmth intensified and the pressure on her skin grew.
"Excellent." Miyo turned to the gateway. "I can't tell you much about what we'll find once we pass through. It changes every time. But I will remind you that the greatest battle is in your mind. Okay?"
An icy chill shot through Dana's body as she stepped through the shimmering air in the archway, but it vanished as their new surroundings came into focus. They stood on a tropical white sandy beach with medium-sized waves crashing onto the shoreline.
Both of them wore khaki shorts. Miyo had on a black tank top. Dana glanced down at the _Life is good_ T-shirt she wore. True. Some of life was good. But not all. And she had little doubt what they were about to walk into was one of the not-all parts. Because something about the scene was extremely familiar, and the feeling it stirred in her was not good.
A few clouds dotted the sky and a breeze pushed at them from the front, carrying with it the scent of suntan lotion. The day was hot and the sun bright even though it was on its way toward setting. She guessed it was around four o'clock if there was time in this realm. The beach was empty where they stood, but she spotted adults, children, and teens playing in the water and sand fifty yards ahead of them. The brightness of the sun made Dana's armor almost imperceptible and she frowned.
"It's still there, Dana. Trust me. Trust yourself. Trust the Spirit. Even though you can't see the armor as well, can you still feel it?"
Dana nodded. "But not as strong." She gazed down the beach at children cavorting in the water, and the sand filled with women reading books under bright-red beach umbrellas or tossing Frisbees and baseballs with their kids.
Dana scowled. If the scene was designed to give her a false sense of tranquility and lightness, it wasn't working. A dark current of dread pricked at her as whatever this reminded her of tried to surface.
"Are you ready?" Miyo asked.
"Sure."
As they walked toward the people, Miyo said, "Remember, the enemy's greatest strength is deception. Illusion. Making what is true invisible and making visible that which is not true. If we react to those external and internal images, he will use those emotions against us, and in an instant we can make agreements about ourselves that aren't true. Let's lock this truth into our minds right now: emotions are not reality."
After a minute they approached a dark-red lifeguard tower. A small group of five or six people stood at its base. Most of them pointed at her, gave sad little smiles, and whispered to each other.
"Steady, Dana. Concentrate."
Dana's face grew hot. Why were they pointing at her? She had to let it go. It wasn't real. But she couldn't shake the feeling it was entirely real. She turned to Miyo to ask for an answer and gasped. Her friend wasn't there. Dana spun in a circle but Miyo had vanished.
"Miyo!"
"Problem, ma'am?" a male voice called. The lifeguard sitting at the top of the tower. Tall, dark haired, tan with a ripped six-pack. He stood and jammed his fists onto his hips.
The words sputtered out of Dana's mouth before she could stop them. "My friend just—"
"Friend? Oh, Dana, I'm so sorry to be the one to break it to you. You have no friends. Not true ones, anyway." The lifeguard grinned and swept his hand in a wide half circle. "Just like back in high school." He paused as if waiting for some kind of acknowledgment from her. "C'mon, Dana, you have to remember this scene we've created for you. No one can bury a memory that deep."
Seconds later the memory flooded her. Mid-July after her ninth-grade year. She and the rest of the girls from her youth group were gathered on this beach—no, not this beach, one _like_ this beach—where they all watched the sun melt into the horizon.
Her youth leader, Sherri, stood as the girls sat crisscrossed in a semicircle around her. Nineteen years old—still young enough to understand high school girls but old enough to really be somebody—Sherri had started the youth group with just Dana.
"I think God brought us together, Dana. I see a uniqueness in you. Strength. He wants to build something special and you're the one I want to help me. And besides, I just like you."
She'd been chosen. Singled out. Loved for who she was. Sherri and Dana met every Wednesday for five weeks, getting to know each other, praying together, talking about who Dana could invite, discussing how the meetings would go. Sherri made her feel like her pappy did, but this was someone who wasn't supposed to love her but still did, and loved her deeply.
Dana started asking all of her friends to come to the group, and soon there were almost ten girls gathering at Sherri's apartment every week. Sherri seemed to praise her more for each new girl Dana invited. By the time she'd brought sixteen girls, they'd moved the meeting to Dana's house, and Sherri spent at least a couple evenings a week hanging out with Dana, goofing off, going to movies or talking on the phone. Mentor, friend, confidant, spiritual leader, big sister, all rolled into one.
But as the year went on and the number of girls coming grew, Sherri called less often—their dates were spread out further and further, and during their meetings, Sherri didn't ask how Dana felt about things much anymore. And the look she used to give Dana now went to Kendal and Morgan and Emma.
Sherri dug her feet into the sand. "All right, girls. I know it seems like school just got out, but September will be here in a flash, and that means I'm going to need some of you to be my key advisers as you head into your sophomore year. But it will take some time." She smiled and pointed to Kendal, Morgan, and Emma. "Will you three girls be willing to meet with me one extra day per week?"
All three shifted in the sand and cried, "Yes!"
Dana's stomach felt like lead.
"Great! I'll call all of you tomorrow." Sherri glanced around at the rest of them and pointed down the beach. "Okay, girls, let's get that campfire lit before the light fades!"
As the other girls shuffled off, Dana went up to Sherri. "Can I talk to you for a minute?"
"Sure."
"I'm not . . . I don't understand."
"What is it, Dana? You can tell me."
"I thought maybe I would be one of the council members, you know? 'Cause I've been here since the group began. I mean, we kinda started this thing together and—"
"Oh, Dana." Sherri laughed. "Don't think that you're not very, very important. You are."
"But I like hanging out and it doesn't seem like you have much—"
"Time for you lately?"
"Yes." Dana dropped her head and studied the sand. "And I'm feeling like the reason you don't is because I'm not . . . not doing enough for you." She dug her toes in the sand. "That that's the reason you . . . Like when I was inviting my friends to come to the group . . . you and I were doing a lot together. So I'm thinking maybe—"
"Oh, Dana, don't take it like that. You're awesome! It's just that . . . well, some people are feet and some people are elbows and some people are heads. We're all the same body but with different things to do, you know? And I just think these girls are best at brainstorming and leadership-type things, okay?"
"I think I can maybe be a leader. In school I've been on—"
"Tell you what." Sherri smiled. "You get some more girls to come to the group during the first half of the year, and we can talk about you maybe joining the other council girls and me after winter break, okay?"
Sherri patted Dana's arm and strolled off to where Emma, Kendal, and Morgan waited halfway to the campfire.
When the calendar reached November, Dana had brought ten more girls to the group, and Sherri started spending time with her again. Lunch dates, an occasional movie, and she was invited into the inner circle. By the time June appeared, Dana had introduced fifteen more regulars.
But in her junior year, Dana was buried in AP classes, track, the school paper, and she stopped inviting girls. And Sherri stopped calling. By December, Dana stopped going to the group. Sherri never called to ask why.
Dana snapped herself back to the present. "Those memories have no hold on me." She spun to glare at the lifeguard, but he was gone. The beach was empty except for a teenage girl around fourteen with shiny brown hair and sky-blue eyes.
"Hi, Dana." The girl smiled, crossed her legs, and patted the sand. "Sit down."
"I'll stand, thanks."
"You don't remember me, do you?"
Dana stared at her as flecks of recognition peppered her mind. "You look like—"
"Alene Richardson."
"Yes."
Alene laughed. "I am her, but we both know that's not really true. But God thought it would help you work through things if there was someone from those days who was in the group, who truly understood how painful it was."
"I see."
"Will you sit?" Alene patted the ground again. "It won't be easy, but it will be so good. You've now been taken back into the wound so we can get it healed."
Dana sat and as she did, Alene said, "To start, I think you're honest, Dana. Too honest to make statements like, 'That memory has no hold on me.' "
"Okay. That's true."
"I mean, even when you figured out that performing to get people to love you was a trap, you kept doing it. Because by that time it was a habit you just couldn't break. Since then you've always had to perform better than anyone else. I remember you in high school running the 1600 meters and being so driven to win. And then on the school paper so determined to get the editor position. Then in college in your photography classes having to get straight As.
"Same thing with your friendships, always being the one to come through for them. When you were a salesperson starting out in radio, your entire focus was to become the best. Same thing as a sales manager, and now as your station's general manager. Even with the Warriors—you are loved because you perform well."
"What?" A chill raced down Dana's back. "It's not just because—"
"No time for lies here. What would happen at the station if you stopped performing? Fired. What would happen to all your friends if you stopped coming through for them? Do you think Miyo would still like you if you stopped picking up her training so quickly? What about Reece and Marcus and Brandon? Ah yes, Brandon. Take a close look at him. You always met all his expectations, and even that wasn't good enough for him. Because you're not good enough. And certainly not good enough as the supposed Leader."
Dana stood and staggered back three steps. Alene stood and took a deliberate step toward her.
"I don't even have to tell you to take a close look at Miyo, because you already have. She leads like a lion. You've done a few good things in spiritual realms, but compared to Miyo you're a bunny rabbit. It would take years to become the leader she already is. And face it, when the Warriors truly see Miyo's skills, they're going to discard—"
"Stop it!"
"They'll leave. Just like Sherri left. Like your new, uh, _friend_ Miyo just did. Not very nice to skip out like that. But I'm guessing she figured it was better to get rid of you now rather than drag out the process."
The Spirit's voice stirred deep inside. _Fight it, Dana._
Fight it? With what? Her armor of light was gone from sight, and even though she still felt it, she also felt it getting thinner, as if Alene's gaze was melting it.
_Know the truth._
Dana blinked and dug her feet into the sand. Yes, the incident on the beach had happened back in high school. Sherri wasn't a friend. But Reece, Doug, Marcus, Miyo, and even Brandon were her friends. But even if they weren't, it didn't matter. She was called friend by the King of kings. And he didn't love her because she was useful or executed well. He loved her for her. Nothing else.
"I don't have to perform. I don't have to be perfect."
Alene flicked her finger repeatedly toward Dana in cadence with her voice and walked in a slow circle. "Miyo is not your friend. She has her own agenda. So does Reece. You think he would be your friend if not for the prophecy? And for what you've done for his little band? He's using you."
Dana dug her feet farther into the sand and pushed the lies from her mind. "I bind you by the blood of the Messiah. I know who I am and I know what you are. Get away from me by the power of his rule." The pressure around her increased—her armor thickened.
As Alene circled again, her form shimmered and Dana blinked. Alene was gone and the lifeguard stood in front of her again. He grinned and wagged a finger toward her.
"Your days of performing in hopes of getting a man are over. No man wants you any longer, Dana. You're too old now. You're frustrated. Damaged goods. How many guys have dumped you since your first little romance with Johnny boy your freshman year?"
The guard drew closer as he continued to circle. "Brandon says he dumped you because of his own wounds. You don't truly believe that, do you? When are you going to wake up and understand that it's because he finally got to know the real you? And found out you'll never be able to come through for him, never be able to drop the walls really. Not enough for someone to want to marry you. And just like all the guys who have gotten to know the real you, Brandon vanished."
The words pounded against Dana's mind, and the thickness of her armor again shrank as the lifeguard's eyes grew darker.
"No, he's interested in me again."
The lifeguard burst into laughter. "The only reason he's showing a shred of interest is because he's even more damaged than you. Grasping at anything to make him feel better. Let him get close and you know how it will turn out. Dumped again. Brandon is for Brandon. You know this is true." The lifeguard was only a few feet from her now.
"I am not alone. And I'm not loved for exceeding people's expectations."
"Always have been. Always will be. We're coming for you, Dana. And we can't be stopped."
"Yes. You can." The words sputtered out of her mouth.
"Are you kidding?" The lifeguard's white teeth seemed to glow even in the bright sunshine. "And let me tell you a little secret. Even if you do get out of here, Miyo will leave you in the real world too. She will turn on you. Mark my words. She will abandon you in the moment of your greatest need."
Dana slashed at the thought and replaced it immediately. "A lie. Miyo is my friend. And I am his beloved and he is my shield and my strength. Go, in the name of Christ."
"Nice try."
"He will never leave me, never abandon me, even till the end of the age." She stabbed her finger toward the demon. "I am his workmanship. Fearfully and wonderfully made. I have the power of the risen Christ flowing through my body, soul, and spirit. And you cannot stand against that power. In the name of Jesus Christ, go and be judged by the Alpha and Omega!"
Darkness flashed over the lifeguard's face.
"Jesus. Lord. Lion of the tribe of Judah. He is my shield. My fortress. I am more than a conqueror. And I won't listen to your lies any longer." She took a step toward him. "King. Warrior. Savior. Jesus!"
Strength pulsed through her and the armor around her felt like steel. The lifeguard staggered back, his eyes flashing dark light. "When you are left utterly alone in the midst of the war, we will kill you. It is coming. We are nearly ready, and when we are, you will die."
Dana almost laughed. This time the words made no impact. They didn't raise any emotion of fear. She felt her side. The armor of light. Even thicker now.
"Go!" She pointed at the demon again. _"Now!"_
The lifeguard vanished, and the instant he disappeared, Miyo appeared beside her.
"Let's get out of here," Miyo said.
"Where did you go?"
"You know the answer."
She stared at Miyo as the realization washed over her. "You were there the whole time but blocked from speaking."
"Yes." Miyo smiled, her dark eyes lit up with joy. "You agreed with the lies. You gave them power. In order for your eyes to be opened, you had to break the agreement that you are only loved when you perform well and meet expectations. And by the way, believe me, I am your friend."
They both slipped back into their bodies and Dana let out a long sigh. "Wow. That was like nothing before. I expected the battle inside there to be one with swords and fireballs and—"
"As I've said before, the battleground is in our minds. That's where the war will be won or lost." Miyo stood and squeezed Dana's shoulder. "You were excellent in there. I had no doubt. Take some time to celebrate what you learned about the battle and about the strength you carry so well. I'm going to take a shower."
Dana sat by herself at the same spot above Well Spring where Miyo and she had gone in from yesterday. Not the lesson Dana expected, but most certainly the one she needed. She took her time meandering back to the cabin she and Miyo shared. When she reached it, she went inside and sat on the bed. Shower? No. But she did want to freshen up a little.
She tapped on the bathroom door. No answer, so she eased into the bathroom, assuming Miyo would still be behind the closed door that separated the shower from the rest of the bathroom. In the same moment Dana stepped inside, Miyo stepped through the shower room door into the main part of the bathroom. When Dana saw her, she couldn't help but gasp.
THIRTY-ONE
"YOU'RE BUILDING A WHAT?" MARCUS ADJUSTED HIS GLASSES and stared at Brandon. He wasn't sure the musician was serious.
"Like I just said. A tree house."
"In your backyard?"
"Yes."
"A tree house akin to the ones kids construct using old two-by-fours and scrap lumber?" Marcus pulled his New England clam chowder out of the microwave, gave it a quick stir, then placed it back in for another minute.
"Not this one." Brandon grinned. "I'll have you over for a glass of wine when it's finished."
"Have me over?"
"Not just you. Kat, your girls . . . we'll have a little party."
"This sounds like a formidable structure."
"Two stories. Room for six on the first floor. Double-pane windows. Lights. Heated." Brandon slipped off his stool and gestured with his hands. "Spectacular structure."
"You're serious."
"Very. It should be done soon."
"Why are you building it?"
"Two reasons. First, I've always wanted to build one, but my stepmom wouldn't let me, so I'm fulfilling a lifelong dream."
"And the second reason?"
"Because of a hope I can't get rid of."
"And what is the nature of this hope?"
"That's a secret." Brandon twisted his forefinger and thumb in front of his mouth as if to lock his lips.
"It doesn't involve a member of the female species, does it?"
Brandon walked to the refrigerator. "Want to eat down at the Listening Post? I'll give you a few more details about the tree house."
"Negative. I'm going to my room. I need to finish a letter to Kat."
"Letter?"
"I've been writing to her every third day since I told her about what happened with Layne. The unmerited grace she extended set me free, and the letters are a way to thank her for it."
"Why don't you just e-mail her?"
"No, no." Marcus shook his finger. "These letters aren't for her to read—"
"That makes sense. Write her letters, then don't let her read them. Excellent. Love it. You're an insane romantic, Professor."
"They aren't for her to read yet." Marcus pulled his chowder out of the microwave and doused it with pepper. "They are simply thoughts about her, about us, my memories of Layne . . ." Tears tried to surface, but not tears of lament, tears of gratitude for the eight years he had with his son. "After I accumulate a year's worth of letters, I plan to bind them into a book and give them to her as an anniversary gift to commemorate one year of my new freedom from regret."
"Wow." Brandon nodded. "I take it back. I really do love it."
The musician pulled three hot dogs and a Dr Pepper out of the refrigerator.
"Fueling your body with health food today, I see." Marcus shook his head.
Brandon rubbed his flat stomach. "Gotta give the metabolism something to do."
"Enjoy." Marcus poured himself a glass of ice water. "Are you going to eat in here?"
"Nah, I'm going to look for Miyo. I want to see if our newest member can take a little good-natured challenge."
THIRTY-TWO
MIYO STOOD IN THE DOOR FRAME OF THE SHOWER ROOM, a large towel wrapped around her chest, hips, and upper legs, but her back, shoulders, and arms were bare. Rough dark splotches covered her shoulders and biceps as if her skin had been burned. Thin jagged lines and half circles were spread across her back as if someone with a serrated blade had played a sick game of tic-tac-toe there.
"Don't you know how to knock?" Miyo spat out.
"Oh my gosh." Dana lifted her hand and covered her mouth. "Miyo, I . . ." What could she say?
"Seen enough?" Miyo spun back, fire in her eyes.
"I did knock, but there was no answer, so I—"
"Fine. Now leave."
"I'm sorry, I thought you'd still be in the shower." Heat rose to Dana's face. "How did you get—" She didn't finish the sentence. Dana knew exactly where she'd received the scars. And why Miyo had bristled at Reece treating her like a schoolgirl the day before with regard to entering spiritual realms. Miyo had paid dearly for her experience.
"Would you like to examine my legs too?"
"No, I—"
"Then what do you want?"
In that moment, Dana's triumph over the lifeguard took hold. She didn't care if Miyo was more skilled and more knowledgeable and better equipped to lead. It was still a struggle to keep the thoughts of needing to perform out of her head, and there was still a part of her that resented Miyo for coming into the Warriors like she had, but the victory had provided enough that Dana had to ask. She wanted to learn, to grow stronger, more accomplished.
"Will you train me? Like you did this morning but on a regular basis?"
"Train you?" Miyo yanked her towel tighter.
"Yes."
Miyo flicked her hand at Dana as if to shoo her out of the bathroom. "Now I have to . . ."
"Have to what?"
"Leave. I'll be out in five minutes."
Dana sat again on her bed and tried to think of what to say when Miyo came out, but all she could focus on was the idea of being trained by Doug's granddaughter. When Miyo emerged from the bathroom four minutes later, her anger had vanished. She sat next to Dana on the bed and clasped her hands on her lap.
"The new prophecy Reece and my grandfather spoke of was given to me. That I would join the Warriors. And that I would train one of you."
Dana stared at her. Of course Miyo was the one of the prophecy. It was obvious. Why hadn't they seen it immediately?
"Why haven't you told us?"
"About the training, or that I'm the one of the prophecy?"
"Both."
"In time I knew you'd figure it out. And because I didn't know which of you I would be training. My grandfather's letter said it would be the first of you who asked."
"But why didn't you go to Reece and tell him that you were supposed to—?"
"I know who I am, Dana. But the rest of you do not. I'm twenty-three. Headstrong in many ways. Blunt to a fault. I couldn't train any of you till I'd earned your respect. Maybe I haven't earned Brandon's or Marcus's yet, but I believe I have yours. And now that you've asked, your formal training can begin."
"I can get the others to agree to train with you as well. Even Reece."
"Yes, I believe you could." Miyo smiled. "You are the Leader. But this is not the time. The prophecy says I'm to train one. Only one. You are the one. Not the others."
"Why?"
Miyo rose from the bed and ran her fingers through her wet hair. "I can be ready in fifteen minutes."
"To start training?"
"No." Miyo patted her stomach and went to the tiny kitchenette in their room and opened the small cupboard. "To start lunch. I'm starving."
As they sat at the Listening Post and ate their lentil soup, the sound of the sliding door opening floated toward them. A few seconds later Brandon glided down the path with three hot dogs, a bag of Doritos, and a Dr Pepper in his hands. How he stayed trim eating as much garbage as he did had always confounded Dana.
When he reached them, he sat in a chair next to Dana and across from Miyo. "Mind if I join you?"
Dana shook her head as did Miyo.
"Good." Brandon took a large bite of his hot dog and talked with his mouth full. "Saw you two out here and decided it's time to learn from the Mighty Miyo."
"Is that right?" Miyo took another spoonful of soup and glanced at Dana. She didn't think Miyo would take easily to Brandon's mocking tone.
"What in the world would you ever have to learn from me?"
"Hey, if Doug said you should be in, and Reece says the same, then you must be a superstar warrior." He rubbed the side of his dirty-blond hair and grinned. "I'm sorry, I'm just teasing. And I want to apologize for last night. It wasn't right. I am truly glad you're part of us. So I'm hoping this can be a new start."
"But even though you have fully accepted me, you're still skeptical of what I can bring."
"Yep." Brandon took a swig of his Dr Pepper. "You would be too, wouldn't you? I mean, you're young. Not that much life experience."
"Yes. Very possible I would have the same doubt you have." Miyo nodded and set her soup to the side. "I suppose we'll simply have to look for opportunities where you can learn more about me."
"Why wait? Why don't you tell me about a few of your experiences?"
Dana sensed Miyo's body tighten as she leaned forward and zeroed in on Brandon with her gaze.
She waved her hand in front of Brandon. "Try to ignore him. It's been a tough couple of months, and it makes him provoke people."
Miyo sat up straight and looked at Brandon as if he were a child. "I know you believe you have fought great battles in the spiritual realms, and in one sense you have. I would never seek to diminish what you have accomplished and the freedom you have given others. But the resistance you have faced is minor compared to what I sense is coming. And you're not anywhere close to ready."
"Really." Brandon laughed. "I don't think you know anything about the battles we've faced over the past year and a half. I think you're the one who has been taught a trick or two but hasn't figured out much more than that."
Miyo turned and looked toward the chalk cliffs across the river. "You don't know my story."
"Maybe not. But I know her story." Brandon motioned toward Dana. "I know Reece's. And I know mine and Marcus's. I know the experiences and training it took to get the Warriors to where we are today."
"I imagine you've learned a few skills, and it's clear you have passion, but you have much to learn, Brandon. If we were to spar with one another, the outcome would be certain."
Miyo's eyes flashed with intensity and Dana knew where this conversation was headed. Brandon wouldn't back down from a challenge like that.
"Yes, I believe it would," he said. "But I am loath to humiliate a girl."
"But perhaps you would be open to humiliating a woman." Miyo stood and stared at Brandon for at least ten seconds. "Let's do this."
"What are you looking for? A fight? A duel?"
She nodded, a thin smile on her face. "Absolutely."
"Don't do it, Brandon." Dana waved her palms back and forth, one on top of the other. "You have no idea what you're up against."
He ignored her. "What are you thinking? Are we going to do pistols at high noon?"
"No. That would be far too clichéd for my tastes, and for yours, if I'm reading you right. I suggest something in the spiritual realm since that's what your doubt centers around."
Should she warn him again? Nah, this would be a good lesson.
"Fine. Let's go." Brandon turned to Dana. "Are you going in to see this?"
She nodded and smiled. "Wouldn't miss it for all the tea in Colorado."
Thirty seconds later the three of them stood on what looked like high-desert country under a reddening sky. Miyo didn't waste any time and circled Brandon in a wide arc with slow, rhythmic steps. Her eyes were like coal.
Brandon glanced at his right hand, then his left. A fireball materialized in each. "We can stop this at any time." He tossed them in the air. "But if you're feeling like being the catcher, I'm happy to step onto the mound."
"I don't think it's a good idea for me to hurt you even in showing you how mistaken you are." Miyo dropped her gaze. "We shouldn't have come here."
"I'm touched by your kindness. But let's go ahead and play ball. Let me just toss a few and see how you like my heat. I think I can bring a bit of warmth into your life."
"That is an unacceptable proposition." The hint of a smile showed on Miyo's face. "As well as an impossible one."
"Really. Is this where you make a speech about me never even getting close enough to scratch you? How my skills pale in comparison to such a seasoned warrior as yourself? How you will engage me in battle to the fullest extent I care to go but will at the same time keep me from harm?"
"Thank you." Miyo bowed as she extended her hand to Brandon with a flourish. "Now that you've made the speech for me, we can begin without further delay."
"You're sure you want to continue?"
"Positive. Throw them, Brandon."
"I can't do that." Brandon dropped his hands, but the fireballs still burned bright. "Now it's time for me to apologize for doing this. What say we go?"
"Throw them."
"Do you understand what I can do with these things?"
"I know what I'm dealing with, and you could no more hurt me than hurt the sun."
Whether she'd provoked Brandon into action or he was tired of talking, he reared back and slung both fireballs toward Miyo. The angle looked like they'd strike near Miyo's feet. Dana knew there was no way he'd throw them anywhere near her body. He'd grown so adept at controlling the size, shape, and velocity of the fireballs, she had no doubt they would tear into the ground exactly where he wanted them to without any danger to Miyo.
This way he probably imagined he could show Miyo what he was capable of without coming close to hurting her. But Dana guessed he was about to realize his imagination was severely uninformed.
As the fireballs streaked toward her, Miyo moved so fast Dana couldn't follow her. An instant later she stood four feet closer to Brandon, holding one of his fireballs in each of her hands. She'd caught them? How?
Miyo squeezed her hands and the fireballs vanished. An instant later she planted one leg in front of the other, flicked her fingertips toward Brandon, and he was covered by . . . What was it? Liquid? Light? It was a dome of translucent . . . She couldn't describe it, but it encircled Brandon for five yards on every side.
Before it stopped moving, he conjured a fireball and flung it into the base of the dome. It didn't even shudder.
Brandon stared at Miyo for ten seconds before uttering just one word. "Wow."
"Have you seen enough?"
He nodded and a second later Dana watched the scene fade from sight.
After Brandon slid back into his body at the Listening Post, he sat on the chair for a few seconds with his eyes closed. What an idiot. He'd made a fool of himself and his life was still a joke. Couldn't sing. Couldn't perform any longer. Couldn't come through when Doug's life depended on him. And he'd just gotten his butt kicked by a twenty-three-year-old hotshot.
Sure, he was supposedly hearing the songs of heaven and heard the song of his coming healing and restoration, but how long till that scene would play out? Months? Years? What was that Proverb? "Hope deferred makes the heart sick"? Yep, and some days it felt like he was lying in the proverbial hospital bed. Yes, God was going to give him his voice back, but why did he have to take it away in the first place?
He rubbed his face, sighed, and then opened his eyes. Miyo stared directly at him but said nothing. Her eyes didn't gloat. She didn't say, "I told you so." And the look on her face was not one of satisfaction but one of concern for him.
"You have skill, Brandon."
"No. Sorry. Not going to let you do it. I didn't give you a ticket to the patronizing party, so I can't let you in the door."
"I've been training intensely since I was ten years old. You've been training for less than a year and a half. The skill you've gained in that time is considerable. You are already a strong warrior. In time you will be a great one."
Brandon started to respond but was interrupted by Reece's voice booming down at them from the main cabin.
"Come on up and settle in. It's time for us to have what I believe will be an intriguing meeting. Arriving in less than twenty minutes at Well Spring Ranch will be the one and only Simon the magician."
THIRTY-THREE
FROM THE MOMENT MARCUS PICKED UP SIMON AT THE Colorado Springs airport in Reece's old Chevy pickup, the magician had talked nonstop about why he shouldn't have come to Well Spring. How it wouldn't be good for him, for them, for the future, for the past. How Zennon was coming after all of them. Only a smattering of it made sense, and for the past half hour, Marcus had tuned out the conversation. He believed the magician needed to come, and nothing Simon could say would change that.
His feeling was confirmed when they stood looking down on the main cabin of Well Spring and Marcus sensed a thin, translucent mist coming off Simon. His imagination? Marcus didn't think so. He couldn't see the haze, but he had little doubt it was there. All doubt vanished when he felt something cold bump up against his chest. Immediately he called on the power of the Spirit to banish anything of the enemy from grabbing hold of him. The mist vanished, but Marcus took an uncertain step to his left.
"Are you all right this night?" Simon peered at him through half-closed eyes.
"Sure. Yes. I'm fine. Are you?"
"Yes."
But the magician's voice betrayed him. Something had just come over Simon or emerged from within him. Marcus couldn't tell. But whatever it was made him uneasy. Marcus firmly believed the Warriors needed Simon, but it was now abundantly clear Simon needed them just as much.
When they reached the main cabin, Marcus opened the door and motioned Simon in. They eased down the short hallway together to the edge of the great room. The other Warriors were already gathered—Brandon sat in front of the fireplace leafing through what looked like a coffee table book filled with pictures of the Oregon coast. Dana was on her laptop, probably editing her photos, Reece was in the kitchen somehow peeling a slew of potatoes, and Miyo stood in a corner of the room with her arms folded as if not willing to do anything until Simon and he arrived.
Simon stopped and motioned Marcus to do the same. His gaze darted from the floor to the ceiling to the walls. "Just promise me we're still in the real reality," he whispered. "Because those two giant warlords standing in the corner over there are really, really, freaking me out."
"You see two warlords?" Marcus glanced at the corner, saw nothing, and then looked back to Simon.
"No, of course not. What? You think I really am crazy?" Simon rubbed his hands on his pants and whispered a touch louder, "Sorry, just nervous meeting the big-time spiritual warriors, you know?"
"There's nothing to be—"
"Afraid of? Maybe not, but this Well Spring nation is filled with intimidation."
"You're going to be fine." Marcus gave Simon what he hoped was a comforting smile, then turned and raised his voice. "Fellow Warriors, it is with great pride that I introduce you to the man you've heard much about and the one who not only kept me from entering into a great darkness but gave me the knowledge to make a choice that has given me much freedom. My friend and brother, the magician, Simon."
After a smattering of applause, Marcus introduced everyone, and Simon gave a slight nod to each of the Warriors.
"It is a great honor to be here." Simon grimaced and Marcus could tell he was fighting the urge to rhyme.
"We are the ones who are honored." Reece strolled from the edge of the kitchen to the center of the room. "I won't need to finish prepping for dinner for another three hours, so why don't we gather at our favorite Well Spring spot and get to know each other a bit."
Fifteen minutes later, the six of them sat around the fire pit watching the crackling logs and watching Simon. The small talk about travel and a brief description of Well Spring by Reece had ebbed and Dana guessed the conversation was about to turn serious.
"I've described in detail to the other Warriors what you saved me from, but if you'd acquiesce to making any additional observations, I know they would welcome it." Marcus pushed his glasses up on his nose.
Simon nodded as he reached into the front pocket of his black jeans and pulled out a silver coin and laid it on the fingers of his right hand.
Marcus had talked about Simon's silver coin, so it shouldn't have surprised Dana to see the magician pull it out and roll it around his fingers. But he did it the exact same way Zennon did, and she couldn't stop the revulsion that stirred inside her at the sight.
When the silence grew awkward, Marcus seemed to read her mind with his next question. "Why do you carry a coin like Zennon has? Why imitate him with the coin roll?"
A bitter laugh escaped from Simon. "I'm not imitating him. He's imitating me. I taught him the roll. So I carry the coin as a reminder of Zennon." He stared at the coin. "Of what he stole from me. Of what he did to me. Of where I've been and where he took me. Of where I will not go ever again. Where I do not belong—a reminder to stay strong."
"When did you first meet him?" Brandon asked.
Simon held the coin between the tips of his thumb and forefinger, tossed it into the air, and it vanished. The man certainly had skill in sleight of hand.
"Just like that, I was gone. For a long, long time. I paid in full for my supposed crime."
"What happened?" Dana said. "How did you end up in the alternate realities?"
Simon leaned forward, knees on elbows, and stared at Marcus. "Did I ever tell you I sat on that same ledge you sat on overlooking a lush green valley? You must have imagined I did."
"No, I haven't."
Brandon tossed another small log on the fire, but that was the only movement around the fire pit.
"And I made the choice to live in one of the realities. And for days I was happy. But it didn't last. I longed for the past when happy did last. But I couldn't go back. So I chose another reality and another, deeper and deeper into the pit. Couldn't escape. Not even Houdini could have escaped. I should have asked him about it, but of course at that age I didn't know I'd need it later on."
"What?" Brandon gave a flick of his head. "Did you say you should have asked Houdini?"
"Houdini was a fascinating man."
"Uh, are you saying you knew him?" Brandon stirred the fire and glanced at the rest of them with a Simon-is-crazy look.
"I did." Simon stared into the fire. "He made a lasting impact on me even though I was young."
"You mean you know of him through others?" Marcus leaned forward as if to offer protection to his friend. "You've studied his life."
"No." Simon winked at Brandon, then turned to Marcus. "I met him. Spoke with him."
Marcus frowned. "Your age would preclude you from knowing him except through the knowledge of others, since he died in 1926."
Simon's eyes lit up. "I'm impressed. Everyone knows who Houdini was, but few these days know the year he passed. Do you know the day?"
Marcus shook his head.
"October 31," Brandon said.
"Well done!" Simon grinned at Brandon and rubbed his hands together. "Now for all the money and the grand prize of substantial size, tell me how he died."
"Everyone thinks he died performing the Water Torture Cell thanks to that lame Tony Curtis movie," Brandon said. "But that was Hollywood. The truth is much more boring. He died from a punch. Some kids came backstage and asked if he could take a hard blow to his stomach. Houdini absentmindedly said yes, so the kid punched Houdini in the stomach three times, and it ended up rupturing his appendix."
Simon grinned and glanced back and forth between Brandon and the others. "Again, well done, that was indeed fun. Brandon, did you do magic when you were young?"
Brandon smiled slightly and a dreamy look came over his face. It was the same look Dana used to see when he played songs for her when they dated. It surprised her. She'd never heard him talk about doing magic when he was a kid, but it was obvious he'd enjoyed it.
A natural connection point between Simon and him, and she could see from the movement of the magician's shoulders that it relaxed him to be with someone else who understood—even in a small way—the world that was so much a part of his life.
"I did. I got an Adams magic kit for Christmas one year, probably around eight years old."
"And did you learn any of the tricks?"
"Yeah, quite a few of them. I was into it all the way through seventh grade. I got really good at the cups and balls, actually. It was my favorite trick. The kit had a set of three plastic cups. After I showed it to my grandma, she got so frustrated she slammed those cups so hard, thinking that was the secret, that she cracked one of them." Brandon laughed. "I should have kept up with it."
"Why didn't you?"
"It turned out the girls seemed to think magicians were geeks and the musicians were cool. So I switched."
"Ah yes, 'tis true, I'm afraid, the right decision was likely made."
"Might we revisit the Houdini comment?" Marcus interjected. "About your knowing him? He died a significant number of decades ago."
Simon held out his hands and tapped three of his fingers together. "Yes, quite a few."
"You're looking good for someone ninety-plus years old, Simon."
"Thank you, Brandon Scott. I appreciate that."
"When were you born, Simon?"
"Before any of you, of course." Simon pointed at Reece. "And that includes him."
"What are you telling us?" Dana asked.
"No time to explain it all. Makes me thin and makes me tall." Simon waved his hands. "Something now that must be seen, while lessons and knowledge can still be gleaned."
"It might be painful to speak of, Simon, but I believe there is healing in explaining more fully what happened to you." Reece stood and folded his arms.
Simon shifted in his chair like a little boy who had been kept inside from recess. "Time manipulation. You haven't studied that?" He stared at Reece. "Inside alternate realities time shuts down, and the body doesn't age. Spiritual cryogenics. He kept me on ice, wasn't very nice. To keep me from whatever it was I was supposed to do."
"You're saying—" Marcus began.
"Yes, yes! I'm saying it. Already said it. Aren't you listening? I was in the spiritual realms. Outside of time."
"So when you went in, you were in your early fifties and still that age when you escaped fifty-one years later?"
"Faugh!" The magician let out an exasperated sigh. "Think, Professor. Didn't you notice that when you slipped in and out of your alternate realities? That no time had passed when you returned?" Simon flicked his hands toward the fire. "Can we move on now? There's something I must show you."
Simon snatched up a long, flat piece of kindling leaning against the gray concrete of the fire pit and stuck it into the center of the fire with his right hand. When he pulled it out, a tiny burning ember was balanced on the end of the stick. He held it up to his face and blew on the ember till it glowed bright red.
"We'll get back to my new little friend in a moment, but for right now keep a steady eye on my left hand. That's the spot where you're going to wish you'd watched with greater intensity." Simon opened his palm and spread his fingers wide. Then he slowly turned his hand over and showed the back, then leveled his palm, then brought his fingers together to form a loose fist.
"Ready? Drum roll please. Don't miss this. Don't look away, not tomorrow and not today." Simon brought the stick with the burning ember over the top of his hand and dropped the bright coal into the small opening between his fist and his fingers. His face contorted in pain, but he kept his hand closed tight.
He dropped the piece of kindling and grabbed his left wrist with his right hand. It was the moment of distraction, but Dana wasn't fooled. She kept her gaze riveted on Simon's left hand. It had to be painful, but the magician didn't cry out.
A moment later, Simon released his wrist and waved his right hand twice over his fist. Then he opened it and pointed at its center. The ember had vanished. There was no burn, no red mark, not even a hint of soot on his palm. Then he showed his right hand was empty as well.
"No curtains, mirrors, trap doors, or even smoke. Well, I guess there's a little smoke. Or should have been when I stuffed that hot coal into the folds of my skin." He showed both hands front and back completely empty.
"What? That's impossible," Dana said.
"No, it's very possible." Simon grinned. "You just witnessed it."
"Let me see your hand again."
Simon extended his hand and Dana stared at it, but even inches from her eyes there was nothing to indicate the coal had touched any part of his skin.
"That trick's a keeper; it had to tweak your peepers." Simon slapped out a quick drum beat on his legs.
"That's incomprehensible." Marcus stared at Simon's hands. "How did you accomplish that?"
"Quite well, that one I performed quite well." Simon glanced around the circle at the stunned faces and laughed. "This stuff isn't real. It's an illusion. It's deception. You are missing something that is right in front of you. You think you're seeing one thing, but you're really seeing another."
"How many years did it take to learn that trick?" Dana said.
"Not years. In fact, less than days is how this one plays. If you had three bucks and the willingness to practice for a couple of hours, you too could have this miraculous power."
He glanced at Brandon, then back to her. "I wouldn't be surprised if Brandon was given the tools to perform that trick in his kiddie magic set." Simon winked at the musician. "You probably even know how it was done."
Brandon winked back. "That I do."
"Really?" Dana turned to him and Brandon nodded.
"And what is the lesson you're teaching us?" Marcus said.
Simon's voice grew quiet, and it seemed he was listening to the words he spoke as if he was hearing them for the first time.
"You were given the ability to perceive what the natural man cannot. The deception with the ember was right there in front of you the whole time, and you never knew it. The curtain hung in front of you and you couldn't figure out how to bring it down. But if you are to be victorious against him, the curtain must be pulled away."
Both Reece and Miyo had remained silent the whole time, and it didn't surprise Dana. Reece was undoubtedly seeing things about Simon in the spiritual realm none of the rest of them could. And Miyo was likely tuning into the Spirit and trying to figure out exactly who Simon was. She hadn't heard the story of what the magician had done for the professor, so she wasn't biased to like him. It would be fascinating to see Simon's story unfold over the next few days.
THIRTY-FOUR
HE NEEDED TO HEAR GOD'S VOICE. NEEDED TO. HAD TO. Simon sat at the Listening Post after dinner leaning forward with his elbows on his knees. It was a good place to be alone. God was here. He sensed it. So why wouldn't God speak?
Simon turned over the deck of cards in his hands, opened the flap, and pulled out the Queen of Hearts. He wasn't ready for the King. Didn't deserve the King. Wouldn't deserve the King ever again. He'd bowed to the wrong throne. The scrape of shoes along the stone pathway startled him. Simon turned to find Marcus standing ten feet away.
"Good evening, Simon."
"Good? It is? I hadn't noticed." He took the Queen and launched it fifty feet out over the river and watched it float down and land in the center of the current.
"That's an impressive throw." Marcus slid into the chair across from him. "Care to share your assessment of Well Spring so far?"
"Full of life with little strife."
"I agree. For me it's a fortress of solitude."
"Like Superman's place?"
"Something like that." Marcus smiled. "I'm curious about one of your mannerisms. Might I inquire as to why you speak in rhyme so often?"
"You may question like a dancer, but I might not always answer."
"I think I know why." Marcus picked up the hatchet next to the fire pit and a small log and split it into kindling. "I think it's a way to keep your mind occupied against the constant pummeling from yourself and from the enemy about what happened to you. But I also think it's part of his continued influence over you. That you can't stop from rhyming sometimes."
"What are you saying, Professor?"
"You assisted me greatly in making a choice that brought me great freedom. Motivated to a significant degree by your desire to prevent another person from entering into the choice you made and the subsequent consequences."
"No doubt you could tell me what you're saying in a way less roundabout."
"How do you deal with the fact that you made a choice you regret with such vehemence?"
Simon went silent.
"What was your choice, Simon? The one that took you out?"
He shook his head. No. No. What was Marcus thinking? That question wasn't allowed. Didn't the professor know? It wasn't part of the show. It couldn't ever be asked because there was no door to that memory that could ever be laid hold of. It was locked shut and tucked away in a place no one could ever find, no matter how long they searched. Gone forever!
Simon gave a soft whimper and wished that was true and the memory wasn't pounding on the door almost every second of every day, screaming to get out and bury him again. He scraped the card in his hand against his forehead as if that could brush the memory to the ground.
"What was your choice?" This time the professor's voice came from galaxies away because the door had already opened and Simon had already fallen through the doorway and was hurtling into the darkness of the choice he'd made fifty-one years ago.
Simon's eyes had been closed on that ancient rainy Monday evening in early March, but the lamp to the left of his old leather, overstuffed chair cast enough light through his eyelids to keep him from falling asleep. Or was he asleep? His brain wouldn't answer. A series of dull thuds echoed in his muddled brain. Was he dreaming? Could be. Didn't know. Didn't care. His arm twitched as the thudding in his brain continued.
No, he was awake. Might as well admit it. He squeezed the wine glass in his hand and opened his eyes. Was it day two since the accident? If he made it to day three, he might make it to the funeral. He might be able to pour out all his grief on those who came to offer him their pity and condolences. Sure. And he might learn to build human-sized butterfly wings and soar away from all this in the next thirty seconds.
_Stay strong in my strength. I am with you._
No. He didn't want to be strong. Only fifty-two years old and his life was over. All he wanted to do in this moment was pour more red wine into his glass, then lift it to his mouth and feel it trickle down the back of his throat where it would do magic on his mind. The pounding increased and Simon realized the sound didn't come from his head but from the front door.
_Stay in me._
Why couldn't God leave him alone? Just for an hour. Let him drown in his sorrow.
"Simon!" The voice was oddly familiar but he couldn't place it. Thoughts of high school and college peppered his mind. A classmate from eons ago? Grade school? No, it was a time far back, yes, but from days more recent than high school. College? It didn't matter. He wasn't going to open the door for anyone ever again.
"Simon, let me help you." The voice was softer this time but no less insistent. "Let me in. Please."
Should he? Whoever it was would probably tell him it would be okay, that his wife was in heaven now waiting for him to arrive so they could skip together in fields full of poppies or some such inane platitude he would have to nod and agree with. From a person who had probably never experienced this type of ripping of the soul.
"Leave me alone!" Simon screamed as he sat forward in his chair. The wine in his glass sloshed over the rim and splashed onto the armrest and then onto his tan carpet. He stared at the wine as it soaked into the carpet fibers. How could it look like anything but blood? He wouldn't clean it up. He'd leave it there forever as a reminder of what God had done to his life. Done? Allowed to happen? Either way was stark evidence of God's betrayal of him.
The crash was an accident? Impossible. If every hair of every head was numbered? All the stars of the universe were known by name? If that was true, then accidents could not exist. They were planned. And God was the planner.
_A lie. Do not go down that path._
He knew the Spirit was right. The thought was poison. And wrong. Knew it better than most. He had an enemy that would target everything in his world for destruction, including his wife. He'd written about it extensively in his manuscript that would never be read by anyone. He'd lived it for years now—fighting the spiritual forces and principalities in high places, exploring unbelievable spiritual realms, doing the things in the Bible he thought were impossible in the modern age. But how did that fact change _anything_? It didn't. It made it worse.
Was there something he could have done to keep the enemy from taking her life? Was it his fault? He didn't know. Didn't even start to care. He was done listening to the Spirit. At least for a decade or two. Quench the Spirit? Yes, he was about to show himself how. His mind continued to spiral as he lifted the wine glass to his lips.
The Spirit spoke once more, but Simon ignored it and the words faded into whispers that didn't reach his heart or mind. But the rapid knocks on his door and the voice behind it were more difficult to brush off.
"Simon." The voice was soft now. He blinked and looked up at his front door. This guy wanted in. Clearly wasn't going away. Why not grant him entrance? Nothing mattered anymore.
"Come in. It's open."
The door opened only a few inches, then stopped as if the person behind it was either respectful of Simon's condition or fearful of entering.
"I said come in." Simon raised his glass as the door swung wide. "All the way."
The man stepped through the doorway. Dim light from the lamp at Simon's side cast just enough light on the figure to make out the man's features. Could it be him? The lines on his face and the graying of his hair spoke of the years that had passed, but it had to be him. Simon sat stunned, a mixture of wonder and long-forgotten memories swirling through his mind.
"Aaron?"
"Hello, Simon."
"It's really you."
Aaron nodded. "Why did we ever lose touch with each other?"
Aaron. The one who rescued him that day a million years ago after his dad almost destroyed his heart. The one who brought him to the magic club and who had taught him all those tricks for all those years. The one who had been the big brother and dad he'd always wanted.
"I can't believe you're standing here. I've followed your show in Vegas off and on for years. It seems they love you down there."
"Yes, the town has been good to me."
"It's been so long."
"Far, far too long since we've seen each other. I read about your wife's passing in the newspaper. Which is why I'm here. I have no words to say. I wouldn't know where to begin except to say my heart is torn for you." Aaron eased forward and pointed at the couch next to Simon's chair. "Do you mind if I sit?"
"Yes, yes, of course." Simon stared at his friend in amazement as he settled onto the couch. "You've aged well."
"Don't humor an old man. I haven't. And if you don't want to see it in more detail, keep these lights low." Aaron's eyes darkened and he pointed at Simon's glass of wine. "How much have you had so far?"
"Half a glass at most, but it will be much more in the coming days and months, I suspect."
"You don't want to do that. It's not the answer. You know this."
"Do I?" Simon swirled the wine. "What happens if I get riproaring drunk every day for the rest of my life? Will God send me to hell for it?"
"No, but this is not you, friend." Aaron stood and stepped close to Simon's chair. "This is not a choice the true you would make and one I will not allow you to continue making. As I just said, it is not the solution."
"You don't know my pain."
"No, I don't, but I know where giving in to this kind of pain leads." Aaron extended his hand. "Just for this moment, let me have the glass, and I'll tell you of a better way to ease the pain."
"Tell me."
Aaron smiled. "What is the best part of being a magician, Simon?"
"Knowing how the trick is done."
"And what is the worst?"
"Knowing how the trick is done."
"Yes." Aaron stepped next to Simon's end table and picked up the bottle and waggled his fingers toward Simon's glass. "Please?"
Simon handed Aaron his glass, and his old friend set both the glass and the bottle of wine on the floor in front of the couch and sat again. As he did so, something inside Simon lurched as if he'd been grabbed by two hands, but he shoved the feeling aside.
"And why is the worst part knowing how the trick is done?"
"It steals the wonder."
"Exactly!" Aaron poked the air. "We are no longer astonished. We've met the man behind the curtain and we marvel no longer. We cease to be children and the world becomes dull and plain."
"Yes."
"But from time to time we capture our wonder once again. How, Simon?"
"When another magician fools us and takes us back to the moment where we believe—if only for an instant—that the magic is real."
Aaron nodded, a tiny smile at the corners of his mouth, and Simon knew the escape his friend was offering. A chance to go to a place where he could be a child again. "You're still meeting with the old group, aren't you?"
"Yes. I fly up once a month to be with them." Aaron's smile grew. "I won't pretend to understand the depth of your anguish, Simon. But come do a little sleight of hand like in the old days. The meeting starts in forty-five minutes. Come with me. Escape into that world of wonder. Take your mind off the devastation that wants to consume you. You don't have to remember any longer. You can forget. I can show you how."
"Still my friend after all these years."
"It's even better than that."
"How so?"
"You're sure you want to ruin the surprise?"
Simon nodded.
"I'm growing old. I can't do the show much longer. I had no sons to pass it on to, so I need to find a successor."
Simon shook his head.
"Yes, you, Simon." Aaron sat forward. "I want to teach you all my illusions. My most closely held secrets. I want you to headline my show in Vegas when I retire."
"You're not serious."
"Deadly. But we can talk more about that later. For now simply come away for a few hours and let the pain lie in a corner of the mind where we will shut the door without using wine."
Aaron was true to his word. Right after his wife's service, Simon spent three weeks in Las Vegas and worked four hours every day perfecting Aaron's illusions. He spent another week performing alongside Aaron onstage, and at the end of a month, Aaron said the time had come to turn over the show.
"I'm not ready. It takes years to perfect a Las Vegas show." Simon sat in what would soon be his dressing room in the Sahara Hotel on the Las Vegas strip.
"You _are_ ready." Aaron winked. "Almost. There's one more illusion I'd like to show you before I fade into the back row of the audience."
Aaron led him through the hotel to the theater where Simon had labored for the past four weeks. In the center of the stage was a thin black box—barely wider than a man—that rose at least fifteen feet high from the floor. When they reached it, Aaron opened a hidden panel and motioned toward the box.
"Let's go inside."
Simon stared at the small enclosure. It would barely fit him, let alone both of them. He looked back at Aaron in question.
"Don't worry. We will both fit, and after you've gone through, you will be astonished like you never have been before. I promise you that." Aaron smiled. "I've been waiting to show you this for an extremely long time."
Simon's heart pounded, although he didn't know why.
"Are you ready?" Aaron motioned toward the box. Simon gave a slight nod and stepped inside.
THIRTY-FIVE
THE INSTANT SIMON STEPPED INTO THE BLACK TOWER, all light vanished and then exploded back on him so bright, he shielded his eyes from whatever the source of the light was. After his eyes adjusted, he found himself standing on a cliff overlooking a large valley that flowed with lush green trees and a river set in the center of the land. The scent of lilacs played on the wind. A palpable sense of peace settled on him.
"Do you like it?" Aaron's voice sounded behind him.
Simon turned. "What is this?"
"A gift." Aaron opened his arms toward the valley. "The greatest gift that can be given to any man or woman."
"I don't understand."
"You will." Aaron pulled a gold coin from his pocket and laid it on his palm. "Watch the coin with all your concentration, old friend."
Aaron adjusted his gold coin till it sat in the exact center of his hand. As Simon stared at the coin, it began to fade, then seemed to melt into Aaron's palm. A moment later it simply wasn't there.
"Impossible." Simon didn't feel the astonishment of a child. He felt fear. Because this was not a trick, not an illusion. "I don't—"
"I've brought you to a place where the magic is real, Simon."
"What is this place?"
"Like I said. A gift." Aaron eased to the edge of the cliff and gazed down on the valley. "Let me ask you a very important question."
"What?"
"Do you feel the pain? Of your wife's death?"
Simon searched his feelings and frowned. It was gone. He felt at peace about her death. Impossible. The past month of working nonstop with Aaron on the show had buried his sorrow deep, but every morning and every night it ripped into his mind like a giant serrated blade that felt like it would slay him. He knew learning the show was itself an illusion—a momentary covering of the pain, but it was his only way to cope with the sorrow.
Aaron stepped closer. "This is a place where the illusion remains. Where it is real. The valley is a gift from God that removes the pain but not the memory. The only part that remains is the joy of knowing you will see her again."
"How can it remove the pain?"
"When I say remove, I don't mean the pain is gone. It is still there."
An image shot into Simon's mind of his wife sitting on their back deck in north Seattle, a glass in her hand toasting him, her laughter filling the summer evening. Sorrow seared his mind and Simon started to sob. But Aaron waved his hand and a few seconds later the overwhelming grief vanished.
"I'm sorry to do that to you. But I want you to be assured that you will lose nothing of your love for her or your memories of her." Aaron smiled. "But the pain will vanish forever."
"Are you saying I can stay here?"
"Yes. Where every part of your life is the same as it is now. Your show, your friends, everything."
"What's the catch?"
Aaron nodded as if he'd anticipated the question. "You're right to ask. Although this place is a free gift of God, there are consequences to all our choices, and this choice is no different."
"Tell me."
"As you can see and feel, this place is one of joy and hope." Aaron pursed his lips. "But you can only come here once. If you choose to leave for any reason and go back to the real world, you can never return here. And that means you need to choose now if you're going to stay."
"What about my affairs? My house, my things?"
"You will have them all here."
"But won't the people back . . . ?" Simon spun in a slow circle, expecting to find the door to the black tower that would lead them back onto the stage in Las Vegas, but there was no door. "Won't they—?"
"They will not see you again. You will live out the rest of your days here if you choose to. Happy. At peace."
"But I wouldn't have a chance to say good-bye."
"Good-bye to whom, Simon? First, you'll still have them all here. Second, is there anyone that must hear from you, do you think? My old, and your new, assistants?" Aaron shook his head. "They are not your friends. It's not show friendship; it's show business. They were acquaintances. Your uncle lies in a nursing home and doesn't know your name. Your parents are gone. You have no children. No brothers or sisters."
"The friends from my church."
"Yes. They were true friends. Were. But how long has it been since you've seen them? Will you miss them? No. You'll have them here. Will they truly miss you?"
"What happens to my body?"
"It will remain where it is, in the physical world."
"So I'm not really here?"
"Your spirit is here. But not your body. While you are here your body will not age. It will remain with me till such time as you want to return."
"But what happens if you . . . ?"
"I think you've realized I'm not ever going to die, Simon." Aaron's body grew taller and thicker, and light seemed to radiate off of him like the mirrors of a lighthouse. "I think you've suspected it since the day we first met."
Simon nodded and the words came out of his mouth before he could stop them. "I will stay."
The sensation of fog descended on Simon's mind, but it was a sweet mist, a mist of forgetfulness, and he breathed it in deeply.
Simon jerked his mind back to the present and locked his gaze onto Marcus's. "I can't be in that memory. A place I can't go, too much of the show. Don't ask about that ever again if you claim you're my friend."
"My apologies." Marcus studied Simon's face. Fear was mixed with sorrow and deep regret, but terror was by far the greater of the two emotions. "I didn't mean to cause you pain."
"It's okay." Simon squeezed the sides of the card in his palm and it leapt to his other hand with a perfect flip. "So many parts of my mind are ones I can no longer find."
"I won't ever ask about the alternate realities. I promise."
"But you want to ask me something else. I can see it in your eyes."
"I can't help it." Marcus smiled wide. "I'm a physics professor."
"What?"
"Where was your body kept for all those years?"
"You want the history of that mystery, eh?" Simon shook his head. "Wasn't in an exotic or high-tech location as you might suspect. Zennon, of course, wanted to keep an eye on me, so he stored me in the back of his huge Las Vegas warehouse filled with all his other full-stage illusions. I was lured into one of Zennon's boxes and I stayed in that box till the day I left."
"Escaped."
"I didn't escape, Professor. I went to sleep one night and woke up in the morning in that black-colored box."
"Why would he let you go? Why keep you all those years? Why didn't he just kill you?"
The magician pressed his temples. "I'm part of his plan."
"What plan?"
"I don't know." Simon continued to massage his head. "But there's the tiniest piece of me that suspects at one time, long ago, I might have walked strong with the Spirit. That I really did write the manuscript Doug Lundeen says I did." Simon's voice was more stable and coherent sounding than Marcus had ever heard it. "Does that sound crazy to you, Professor?"
"Not at all. I believe it's true. I've believed it all along. But it doesn't matter what I believe. You must remember who you are."
Simon dropped his King of Hearts and shuddered as he picked it up off the stones at his feet. He flipped the card back and forth between his hands again.
"Look at me." Marcus waited till Simon stopped looking at the card and held his gaze. "Restoration is coming."
"How can you know that? How can you say that when you don't know for certain about the veil and about the curtain?"
"I do know. I believe the Spirit has told me restoration will come for you. I choose to believe this. And I invite you to join me in my belief."
Simon turned back to his card and spun it on his fingertip like a basketball. "How do I know you're not Zennon again? And this whole place"—Simon waved his hand toward the river and the white chalk cliffs and the cabins of Well Spring—"isn't designed by him to steal my soul once more?"
"You were in devastating pain when he attacked you and offered a solution to that sorrow. You were vulnerable and open to suggestion. He exploited your weakened accessibility."
The magician didn't answer. "Even so, the choice was still made . . . for which I have paid dearly. I accepted Zennon's solution."
"Let me repeat, restoration is coming." Marcus waited till Simon met his gaze. "Just as it came for me, it will come for you."
"When? When will it come? When I die and to heavens I fly?"
"Oh no." Marcus smiled. "Many ages before that."
Simon stared at him for a long time before speaking, and when he did, his eyes were full of tears. "Do you promise me that?"
"With every molecule that makes up my being." Marcus took the King out of Simon's hand and grasped both the magician's palms. "You will be restored."
"Thank you, Professor Marcus Amber." Simon's head bobbed up and down. "So what happens now?"
"I think you already know."
Simon swallowed and rubbed his hands. "I suspect that tomorrow, you and the rest of the Warriors are going to ask if you can enter into my soul."
THIRTY-SIX
"WHAT DO YOU THINK OF SIMON?"
Reece sat alone with Miyo at the Listening Post on Saturday midmorning and let the warmth of the tenth day of August soak into him. Doug was right. She was wise far beyond her years, and he wanted to get her take on the magician separate from the others.
"You first." Miyo seemed to shrink back in her chair. "What did you see last night?"
"I saw the outline of his coin. It left a trail of light like phosphorescence in the ocean. As if his hand is wrapped in a million tiny stars."
"Evil?"
"I don't think so. It feels neutral, but I'm not one to say anything is neutral in the heavens or on the earth." Reece leaned forward, elbows on his knees. "But Simon is not of the enemy. I'm not worried so much about Simon as I am about what cloaks his soul."
"I agree, he is for us. And he is a son of God. But there is also much darkness and confusion that swirls around him. He speaks of a curtain? Simon has a curtain around himself so thick, I can't start to see past it."
"As might we all if we'd lived in over four hundred different realities." Reece rubbed his hands. "All I could see was the faintest outline of light around his body. Whatever he carries, it weighs on him like a coat made of concrete. He fights it, but without much success."
"Have you considered asking him if we can go into his soul?"
"Yes."
"And?"
"I asked him early this morning, and he's agreed."
"You're kidding."
Reece shook his head. "From talking to the professor a little bit ago, it seems Simon wants restoration more than he wants to avoid the memories from his past."
The shuffle of feet coming down the white stone path filled the air a few minutes later, and soon all the Warriors sat with Simon in a circle, ready to enter the magician's soul.
"Simon?" Brandon called out the magician's name for the third time since they'd arrived inside Simon's soul, but again, there wasn't a response. "Where is he?"
Dana didn't answer and neither did any of the others. The question was rhetorical. She spun in a slow circle trying to take in the kaleidoscope of images that surrounded them. They stood on the top of a building at least forty stories high. Spread out for miles in every direction were other buildings almost as tall. Every one of them was lit up like a multicolored lighthouse.
The streets below were filled with people laughing and milling about as they entered and exited the buildings.
"I'm getting why Magic Man would go Las Vegas inside his soul, but isn't this a little over the top?" Brandon said.
"Where do we go from here?" Dana asked.
"Down," Reece said. "Let's see if we can talk to any of the people on the street."
By the time they'd exited the building's lobby and reached the street, all the people in each direction had vanished.
"Nice disappearing act," Brandon said. "Any other ideas?"
"You know him the best, Professor," Dana said. "Where do we go?"
"No idea." Marcus pointed at a door across the street bordered by three sets of neon lights: bright yellow, bright red, bright orange. "And since I have little indication of where to go, why not start here?"
They reached the door and Marcus turned the handle. But the instant he did, the door and building vanished.
"It makes sense," Reece muttered.
"What makes sense?" Brandon asked.
Reece pointed up and down the street. "Try all the doors up and down the entire block."
The Warriors spread out. In five minutes all the buildings were gone in every direction. Nothing remained. They now stood on a desolate field of loose gravel and sand. It was hot. Not unbearable, but uncomfortable compared to the coolness they'd felt when they first arrived.
"All of it, an illusion."
"There has to be something here." Brandon gazed in each direction. "His soul can't be entirely empty."
"There." Miyo pointed toward a slight rise along the horizon. "Can you see it? Ten, maybe fifteen miles away."
Dana stared in the direction Miyo pointed and saw nothing. Brandon voiced what she was about to say.
"I don't see a thing. Talk to us."
"It's a small cabin. One light on in the window. A few evergreen trees." She turned to her left. "Reece?"
"I see it. That's where he is."
Marcus turned toward Miyo. "I would surmise based on your earlier demonstration that you can get us there instantly."
She smiled and nodded. "Let's go."
As soon as they landed outside the dark log cabin, Dana saw Simon through the window. He sat on an ottoman and tossed playing cards at something beyond her sight.
Reece knocked and Simon opened the door a few seconds later.
"This is very strange." The magician took time to lock gazes with each of them.
"Why is that?" Reece asked.
"Because I know what you're doing. You're all inside my soul, aren't you?" Confusion passed over his face. "And somehow I have no doubt I used to do this kind of travel, still a mystery to unravel." He ushered them in but stayed standing. "Does that strike you as odd?"
"Not at all." Reece took a slow spin around the cabin, and his gaze landed on a large stack of posters sitting on an oak table. "What are these?"
"My collection. Priceless. Houdini's King of Cards poster. An original of Carter's most famous. Thurston. All the greats. I guard them. Protect them. And look, look here." He lifted up the corners of the first four posters and pulled them off the stack. "Do you see this?"
It was a poster of Simon. He stood on a lavish stage with his arms raised as if lifting by magic a woman five feet over his head. He was dressed in a tuxedo and a wide smile split his face. It was evident from the dress of the crowd looking up with astonished faces that the poster was from the late sixties or early seventies.
Reece glanced at Miyo who nodded at him. The big man did the same with Marcus and Brandon. When Dana had nodded her assent as well, Reece widened his feet and instantly a sword appeared in his hands. He raised it above his head. "Here we go."
Simon's face went white. "What are you doing?"
Reece brought his sword down hard on the posters. They exploded, and as they did, the cabin vanished in a flash of light. Where the table had stood was now a small fountain made from a series of granite stones. A soft green moss surrounded the fountain that still sat on the small hill the cabin had sat on. Below the rise, jade grass swept out in every direction and ended miles away at the base of snow-covered mountain peaks.
Brandon gazed at the surroundings, then back to the fountain and grinned. "Living water, I'm guessing."
Next to the fountain sat a flat stone roughly the size of the table the posters had sat on. On the stone rested what looked like a yellowed manuscript, and on the manuscript sat a pen made of wood.
Simon stared at each of them as if he were Rip van Winkle waking from a hundred-year sleep. Which probably wasn't far from the truth. He turned to the stone table, picked up the manuscript, and ran his thumb down the edges of the pages. "I didn't think I'd ever see this again. I didn't remember . . ." He hesitated, then gripped it tightly with both hands. "I wrote this, didn't I? Every sentence. Every word. There is power here. And here." He pointed to his heart. "Unfathomable power. Because of who lives there." He looked at each of them for a long time before speaking again. "This manuscript can change the world. And with the power of the Spirit, it will."
The moment Reece's spirit slipped back into his body, he sat forward. "Well done, all of you. Simon, how do you feel?"
"Are you kidding? New. I feel new." A grin split his face. "Reborn. Every adjective you can think of. I don't know how to thank all of you."
They chatted about what had happened in the magician's soul for another four or five minutes, but eventually everyone headed for their cabins. Only Miyo remained.
"Reece, might I speak with you for a few minutes?"
"Of course." Reece waited until the sound of the others' footsteps faded away. "What would you like to talk about?"
"Even after what just happened, I still feel Simon is tied to Zennon. There was great victory just now, but I feel that whatever role Simon has in this play has not been fully acted out. Put another way, what Simon just experienced is a start, but there is more healing needed. And in the meantime, I think Zennon is still pulling some of the strings inside his soul."
"In other words it was too easy."
"Yes. I can't shake the sense Zennon is still going to use the magician against us somehow."
"I trust him, Miyo."
"I do too. No question. I'm simply saying we must be careful." She stopped and brushed back her dark hair.
"Of course. But I'm more open to Simon than I was before. Being in another's soul and understanding more of his story tends to make that happen."
"I think it's clear the magician has a good heart, but Zennon's attack is still coming. And he won't stop till every one of the Warriors is dead or he's sent to the pit. We must stay vigilant in every way. Alert. Strong."
"I agree."
"So while it's good that Simon is getting healthy in the midst of the approaching war . . ." Miyo grew quiet and closed her eyes.
"Don't stop now, friend."
Miyo opened her eyes and leaned forward, and when she spoke, her voice was close to a whisper. "I believe the Spirit wants me to say something to you, but my intent is not to pry."
"Say it."
"If you hold on to the blame you've carried toward Brandon, and more accurately carried toward yourself, it will grow inside your soul. And this is not the time to allow that kind of growth."
She was right. Why couldn't he let it go? His grip tightened on the stick of kindling in his hand. Brandon wasn't to blame. Reece himself was. He'd hesitated. He'd stayed back when Doug had waved him off, even though Reece knew he should have ignored his mentor's request. Doug's death was senseless. He should be sitting here right now, the three of them strategizing together, trying to hear from the Spirit on how to get ready for Zennon's attack.
Why could he forgive himself for causing Willow's and Olivia's deaths but couldn't forgive Brandon or himself? He didn't know. Yes, he did. He needed time to process the loss of his dearest friend. The one who had stuck with him during the years he'd been absent from the arena and the one who had drawn him back in with strength and truth and mercy. Doug had helped him find life again, and Reece had imagined many more years together embracing that life. The Warriors were not the Warriors without Doug. He just wasn't ready to move on. But that didn't change the fact he had to.
"You're right, Miyo. I will let it go. I will forgive. It must happen." But he couldn't. Not in this moment. It had taken almost twenty-seven years to forgive himself for the deaths of his wife and daughter. It wouldn't take that long this time. But it would take time.
"It's good to hear that. You are the Temple, and as your health goes, to a great degree goes the health of the Warriors."
A thin, light-green mist passed over the fire pit, then swirled past them. It smelled . . . sweet, and Reece rubbed his chest right over his heart as the cloud vanished. His chest was tender but a good kind of tenderness. Strange.
"Are you all right?" Miyo asked.
"Did you see that?"
"What?"
"In the Spirit. I just saw a mist sweep past us."
"I didn't." Miyo stared at his chest. "But if I'm seeing in the Spirit now, the left side of your chest looks sunburned."
"It's fine. It's nothing."
"You're sure?"
"Positive."
That night Brandon sat on the small deck off the building where they trained new students. It was late, but Brandon wasn't tired. He turned to study a waxing moon that seemed ready to settle down on the ridgeline of the mountains across the river.
The clomp of feet coming up the small set of stairs to the deck pulled his attention away from the view. It was Dana. Why? She'd avoided any chance of the two of them being alone. She slipped into the wooden chair next to him without looking his direction and pulled her arms across her chest.
"Hi." Brandon looked at her, but she only nodded and continued to stare straight ahead. But something about her body language betrayed her secret. This wasn't a chance meeting. She was here with a specific purpose in mind. And her wall was down.
"Nice of you to stop by for a visit."
"Thanks."
"Is there a reason you came by?"
Dana shifted in her seat. "What do you think of Simon now that you've seen him up close?"
No problem. A warm-up of small talk was fine. "He's different than I expected. Definitely twitchy and affected by something unknown going on inside his brain. But I like him." Brandon wiggled his fingers like he was about to make the kindling at his feet rise into the air. "Makes me want to take up doing sleight of hand again."
"Really?"
"Yeah. He inspired me with the hot coal trick. And since I won't be wasting my time going out on dates, I figure I need to find something else to fill the evening hours."
"Nice segue into the awkwardness that always lingers just below the surface between us, Song."
"How many times do I have to repeat, I'm not the Song."
"You'll always be the Song."
"You sound like Doug and Reece."
"Look at what the Spirit has been doing in you."
Brandon stared at her till she turned and looked at him. "Now remind me why you came over here?"
Dana pulled her eyes away and pressed her lips together. She waited so long to speak he almost asked her a second time.
"You say you know me, right?"
"Yes."
"And I know you." The volume of her voice dropped in half and the tone of it grew soft. This was going to be really good or really bad.
"Okay."
"I'm going to tell you something, but you have to promise me you won't say anything about it."
"I promise."
"I love you. I think I always will."
Brandon's body went hot with a good kind of heat but in the next moment it turned to ice.
"But I can't chance it."
Brandon waited. Everything in him wanted to ask her what she couldn't chance. But asking would break the moment and her wall would go back up.
"If we know each other, then you understand why I can't risk giving you my heart again, even if I do have feelings for you buried so incredibly deep. Because if I let those feelings surface, you won't be able to handle it."
"What do you mean?"
Dana glanced at him long enough for him to see tears in her eyes. "You don't need me to answer that question, do you? Really?"
She turned again and her eyes pleaded for him to say no. And he did, because she was right. He didn't need her to verbalize that Brandon Scott was still not worthy of her. Not till he could let go of needing to be worth something. No, that wasn't the right language. He was worth everything because of the love of the Trinity. But that knowledge wasn't enough to keep him from trying to find the answer outside of the Father, Son, and Holy Spirit. He'd died to so much of himself, but if he faced the mirror with eyes wide open, he'd see a man who was still focused on what he'd lost, and what he wanted to become again, and what she could do for him, and not enough on what he could bring and give and lavish on her.
A smoldering anger rose up inside. He was angry at her, angry at himself, angry at God. Restoration was coming, it was coming, it was coming. He was tired of hearing it over and over again, always off in some future he couldn't grasp. He needed restoration to come now.
Dana didn't speak and neither did he as she rose from her chair, shuffled down the stairs, and faded into the night. As she did, a thin, green haze appeared between Brandon and the moon. The smell of vanilla, similar to the scent from his backyard _fothergilla gardenii_ shrub, filled the air. He frowned as the haze shimmered and then vanished along with the smell as quickly as they had come.
THIRTY-SEVEN
"I BELIEVE OUR LIVES ARE ABOUT TO CHANGE."
Reece paced in front of the fireplace late Sunday morning, more animated than Dana had ever seen him. As if a megadose of caffeine had been injected directly into his veins and the high was at its peak.
"I've figured it out." He took off his dark-tan Stetson and tossed it onto the hearth. "I wondered why the Spirit asked us to come here to Well Spring for these days together. Certainly meeting Simon and assisting in his healing was part of it"—he nodded toward the magician—"but there had to be more. Now I believe I know what it is and what the Spirit has been trying to tell us. I woke up at four thirty this morning and it rolled out like a scroll." Reece clasped and unclasped his fingers in rapid succession. "Also, I believe I know where, when, and why Zennon will attack us."
Reece stopped moving and put his hands behind his back. "After lunch—let's say around two—I'll lay out the map that will take us where the Spirit wants us to go. And if you grasp it with a tenth of the passion I feel inside, we are going to turn the world upside down, and nothing Zennon does will be able to stop us."
"Mexican food is the perfect meal," Reece announced as they all sat down to lunch.
Perfect? Marcus didn't agree. Sautéed mushrooms and shrimp with pesto sauce over angel hair pasta was the perfect meal. But Mexican did come close, especially the way Reece made it. Even Kat, Abbie, and Jayla now ate Mexican after Marcus had started using Reece's recipes at home.
"Could you pass the salsa?" Miyo said.
"Which one?" Marcus asked.
"The hot one, of course."
"I'll take some after you," Simon said.
Miyo glared at the magician as she scooped out a spoonful of salsa and dropped it on her plate. She slammed the jar down on the table and didn't pass it on. She'd seemed agitated all morning, but this was the first sign of outright hostility.
Marcus continued to study her eyes. She now looked at Simon with both confusion and anger as if the magician had done something horrible to her. As she continued to gaze at him, the look intensified.
"Are you feeling okay, Miyo?" Marcus said.
Miyo nodded but placed her hands in her lap and just stared at her food. Marcus started to ask what she'd felt, but before he could get the words out, Brandon grinned at Miyo. "Gearing up to send that fire into your mouth, Warrior Girl? Yeah, you better. This is Reece's specially concocted hot sauce. Spread it on the side of a house and it will peel the paint off faster than the most powerful pressure washer on the planet."
Miyo glanced at Brandon, Reece, and then drilled Marcus with her gaze as if trying to tell him something. Then, without a word, she shoved herself back from the table. She stood quickly and the motion flung her chair backward. It slammed against the wall and she half strode, half jogged from the room.
"Wow!" Brandon leaned back, his hands locked behind his head. "It's that powerful, Reece? Just looking at your fire sauce drives people insane with fear."
Marcus pointed at Miyo's plate. "I would propose it wasn't the fear of the sauce but something else that caused Miyo to propel herself from our presence. Something strange has been happening. In the air. I've been meaning to talk to you about it. Like a spiritual mist—"
Brandon snorted. "Most of the time you're a certifiable genius, Prof, but every now and then you say something so obvious and bonehead simple it makes me think I can keep hanging around you a little longer." The musician grabbed the sauce, spun off the lid, and stared into the jar. "I feel no fear. You're right. Miyo's reaction has gotta be coming from something else."
"My suspicion is it's tied into this haze I—"
"I'll talk to her." Reece put both hands on the table and made to stand up.
"No, let me." Dana pushed her plate to the center of the table, stood, and walked to the door. "I have an idea what this is about, and it's definitely a woman-to-woman thing."
After Dana left, Marcus again tried to tell them about the mist he'd felt on the night Simon arrived, but neither Reece, Brandon, or Simon paid him any attention.
THIRTY-EIGHT
AT TWO O'CLOCK THAT AFTERNOON, REECE LED THE FIVE of them up to the lookout spot on the hill where Miyo and Dana had gone in from the week before. But this time Miyo was missing. No matter. Her absence wouldn't dampen the mood. Something stirred inside Dana as if the energy and excitement Reece had been throwing off since his morning announcement had been transferred to her. Whatever their mentor was about to announce, it would be big.
"Look down." Reece pointed down the hill. "Look at Well Spring Ranch spread out before us. It has launched a worldwide ministry. Changed hundreds and thousands of lives. But what we've done so far is only the beginning."
A light wind rolled up the ledge as if on cue, and the smell of pine spoke to Dana of adventure. The scuffle of boots drew her gaze to the path below them and she frowned. It was Miyo. Dana had tried to locate Miyo after she bolted from the main cabin during lunch and couldn't find her anywhere.
Their eyes locked and Dana gave her a questioning look. Miyo looked down and stopped five yards away from the rest of them and acted like she was a cat among a gathering of rabid hounds. But the look on her face wasn't one of fear but of anger. She folded her arms and glanced from person to person as if expecting one of them was about to attack.
"Hey." Dana waved at Miyo. "You okay?"
Miyo nodded. "I'm fine. But right now I need some space. Don't bother asking why. I won't explain it."
Brandon lifted his forefinger and middle finger together. "Scout's honor, Miyo. I promise I'll get Marcus to take a shower tomorrow."
Miyo didn't laugh. Didn't smile. "I appreciate that."
"Why don't you join us?" Reece motioned her up next to him. "This is important."
"I'll listen from here."
Reece continued to face her for at least thirty seconds. Probably trying to see what was going on with her with his spiritual eyes. Dana certainly wasn't getting anything. But if he got something he didn't speak it aloud.
"Okay then, let's start." Reece turned his back to the ranch and smiled. "Here's how we're going to change the world. I've always said the Warriors were supposed to stay small. And we were. But that was a season, and like any other season, it's coming to an end. A new one is about to be born.
"Dana, being in the position you are at the radio station, leading teams in the corporate world will help you understand where the Spirit is taking us better than anyone. The days of playing small are over. We need goals. We need clear objectives. We need an effective strategy for this ministry. Up till now we've operated on a wing and a prayer. It's worked well. But we're entering into a new phase of the ministry, and we will be buried if we don't know where we're headed a month from now, a year from now, five years from now. And none of us will be able to lead that charge as well as you. You are the Leader. You are exceptional. We need you now more than ever."
As Reece spoke, something cool seemed to surround Dana's chest. It felt like a mister she'd walked through at a restaurant in Arizona a few years ago. Whatever it was smelled almost sweet. But was it good or evil, or even neutral? No time to think about that now. She ignored the sensation and concentrated on Reece's words. Yes, this felt good. She would have a chance to lead the Warriors like never before. She would develop teams. Inspire them. Guide them.
This was her glory, her strength, and it was nice to have Reece recognize it once again in front of all the other Warriors. But a moment later Dana felt odd. Part of her was thrilled at Reece's words, but another pulled at her like taffy, which said this was completely wrong. No, it was the enemy, trying to steal this away from her. She would not give in.
Reece turned to Brandon. "You understand this too. You were a god in the music industry. We need to tap into your experience and use it to take Warriors Riding further than any of us have imagined we can go. You know how large events work. How to promote. How to create a following."
He turned to Marcus. "You have at least a feel for how a major business like the University of Washington runs. And can teach people better than anyone. You will teach our teams how to function on a massive scale."
"And, Miyo, I don't know if you've had any life experience in building a business, but nonetheless I am looking for your wisdom as we map out our future."
Miyo stared at Reece but didn't answer.
Reece's voice grew in excitement. "I had a strategic plan for my photography business. It's what allowed it to grow into one of the largest chains of high-end photography galleries in the world—and certainly the most profitable. It's far past time we tried to accomplish the same with Warriors Riding. Let's get down to specifics." Reece pointed at Marcus. "Professor, have you talked to Carson Tanner lately?"
"Yes, I have."
"Did you talk numbers? How many people he's reaching these days with his show?"
"He did volunteer that his audience has increased twelve percent since he changed the focus of his broadcast, blog, and e-zine to a message of freedom."
"Outstanding." Reece smiled and rocked back and forth on his boots. "And how often is he promoting our ministry?"
Marcus frowned. "He's not. He offered to, but I explained that's not what we do. That we are not about getting big and never—"
"Never say never. As I said, that's all about to change, and Carson's help will be critical."
Marcus's brow furrowed more. "That's not what I've been sensing from the Spirit—"
Reece ignored him and raised his voice a notch louder. "We need Carson to start pumping the training weeks and our CDs and DVDs as often as possible." He turned to Dana. "What is it you always say about advertising, Dana?"
"Frequency sells."
Reece turned back to Marcus. "We need frequency on Carson's show. If we're going to grow this ministry like God has just told us to, we need continual exposure.
"Dana, I want you to work with Carson to develop a marketing plan using his outlets and influence. Develop a series of radio spots, get us testimonials from our followers, get us going on some promotions and cross promotions with other ministries, get a fully functioning website going, everything."
"Love to. And with my radio contacts, I can get some serious exposure for us on a significant number of stations, networks, and podcasts all across the country to go along with Carson's show."
The feeling of disharmony in Dana seeped away as she pictured how she would orchestrate all the elements they would need. Reece wanted leadership? Watch out.
"Sounds like you've come up with a serious no-wings cliff jump." Brandon grinned. "I love it. It's about time."
"I agree. And in some ways it involves you more than anyone else, Brandon. You've been down lately. We all understand why. But this project won't allow you any time to dwell on what has been, only what is to come."
"I almost believe you." Brandon leaned forward. "Lay it on us."
"This ministry is ready to explode, and we're going to light the fuse with an event that will be seen by millions. We are going to rent Safeco Field in downtown Seattle. We are going to ask our friends who have been through our training and taken our message of freedom throughout Puget Sound to fill that stadium and join us in a celebration of what God has done and what he will continue to do. We are going to broadcast this event to our allies around the world. It will be shown in homes, churches, arenas, and on the Internet around the globe."
Reece was almost dancing now. "It will be a time of rejoicing and a time to lay out the next phase of our ministry and what God is calling every one of our partners across the world to engage in. We will take our rightful place at the head of the charge the Spirit is leading against the forces of darkness."
Reece spun and looked out over Well Spring. "This no-wing cliff jump, as Brandon puts it, is to reach twenty-five million people with this message."
Brandon shifted his weight. "And my role in this—?"
"Don't you know?" Reece spun back and laughed. "You haven't figured it out yet? You are going to sing."
"Come again?"
"You heard me."
"Do I get to lip-synch?"
"You are the Song. What heaven gave you the other day down at the river is the song you will sing on that stage in front of millions. It will be your moment of restoration and usher in great healing in your soul and the millions of souls you'll sing to. You will be healed in front of the world."
Brandon smiled and nodded. "If only—"
"No." Reece stepped toward him. "We will give no quarter to doubt. Think of what Doug wrote to you, what God himself confirmed. This is your moment. Our moment. Where we become known to the world."
"If that could happen . . ." Brandon rubbed his face and glanced at each of them. "We have to do this. Have to."
Dana stared at Reece and struggled not to break out in joyful laughter. He was right. This gathering would be epic. She looked at Marcus. He looked more like he was a taster at a lemon factory than a warrior ready to enter into a grand, new arena. "Professor?"
Marcus glanced at her and then turned toward Reece with combative eyes. "If we go ahead with this, where would we get the money to rent Safeco Field?"
"No ifs, Professor. As you know, I have money. I stockpiled more than I know what to do with from my photography galleries. And I still bring in tens of thousands of dollars a month from my sales and licensing agreements. I don't care about the money. I care about reaching the nations."
Marcus's countenance grew hard. "We _are_ attaining great reach into the nations. We don't need this. It's wrong. Our method has always been—"
"How many times do I have to repeat myself? That's changed. Last night and this morning everything changed." Reece put his arms behind his back and paused for a moment. "We've been on the enemy's radar for a long time, but this move will expand our ministry even more exponentially than it has already and deal our adversary a crushing blow."
Reece turned to Miyo. "And one of the reasons we'll be better equipped for what will certainly come against us is because of you, Miyo. You will war for us in the spiritual realm, because the prophecy that was spoken over you is clear to me now. The attack Zennon is going to bring will attempt to shut down the gathering before it starts. And then he will attack again during the event itself. You must head up our resistance."
Miyo's only response was a sigh and an almost undetectable nod.
"There is a time for everything. We've had our season of being small. That is no longer our time. Believers who have only heard smatterings about us will get a chance to fully understand our message."
Dana studied Miyo as Reece continued to speak. The earlier look of anger had been augmented by a fierce determination. And yet Dana didn't have the sense the topic of their conversation was what bothered Miyo. It was deeper. Something they'd done earlier that day? Yesterday? Nothing came to mind.
"Thoughts on this, Miyo?" Reece asked.
"None." She tilted her head back and pulled her hood over the top of her head.
"No opinion? I'm supposed to believe that?" Reece laughed.
"You can believe whatever you want to believe."
"Do you want to be here right now?"
"No." Miyo folded her arms and fixed her gaze on the ground. "I don't."
"Then why are you here?"
"Because this is where I'm supposed to be. This is where the battle lies and where I am needed."
"Whatever the battle is at this moment, it lies inside you." Reece stepped toward Miyo and she stiffened. "We need to break whatever is coming against you. Right now."
"No." Her gaze darted to each of them. "You don't."
"I believe the Spirit is saying we have to."
"Then you would be mistaken." The scrape of Miyo's black boots on the path seemed to fill the sky as she stepped back two paces. "It's time for me to go."
"Miyo, stop." Dana stood and took a few steps toward her friend. "Tell us. We can help. What is going on? This isn't like you."
"I'm fine." Miyo turned. "Like I already said, I need some space and some time." She half walked, half jogged down the path.
"Do you want me to go after her?" Dana asked.
"No. Let her go," Reece said.
"Wow," Brandon said. "I know we're from the land of strange at times, but it looks like Miyo has a cabin there bigger than any of ours. What's the deal with her?"
"What did you see when you looked at her, Reece?" Dana said.
"Not as much as I'd like to." Reece rubbed his hand over his eye sockets. "My special kind of seeing has been dimmed today. No doubt an attack of the enemy. But from what I _could_ see, there was nothing around her that would give a hint as to what she is wrestling with. The only thought that struck me is that although everything we've seen from Miyo has been strong and full of truth, it's also true we've only known her for seven days.
"Yes, she is Doug's granddaughter. Yes, she is in some ways far more experienced than any of us in the spiritual realms. But at the same time, she is young and susceptible in some ways that those with more life experiences are not."
"Nice speech," Brandon said. "Why don't you just say what we're all already thinking in a language a bit less eloquent?"
"Because it's not what you're thinking." Reece paused as if not wanting to say too much but not wanting to say too little. He faced the path Miyo had walked down. "But I will say this. Stay alert. Be cautious. Be wise."
"What does that mean?"
"As you well know, God has his plans, but the enemy has plans as well. So for the time being, we must not let Miyo catch us off guard."
Great. Easy for the men to say. They didn't have to go to sleep with Miyo lying in a bed three feet away.
THIRTY-NINE
"WHERE ARE YOU GOING?"
After bursting into their cabin late on Sunday night, Miyo stuffed a few pieces of clothing into a workout bag, grabbed a blanket and a coat, and snatched a pillow off her bed. Dana hadn't seen her since she walked off the side of the hill hours earlier.
"Out."
"You're not sleeping here tonight?" Dana snapped on the light next to her bed, pulled off her covers, set her feet on the floor, and started to walk toward Miyo.
"Stop." Miyo pointed to the corner of the room behind Dana. "Stand over there."
"What is wrong with you?" Dana took another step toward her friend.
"Stop!"
The strength of Miyo's voice halted Dana and she stared at Doug's granddaughter in complete confusion. "Talk to me. Why are you acting like this? Why did you act like we were all lepers earlier today? Don't you understand what the Spirit is leading us all to do?"
"I'll be fine. But tonight I'm going to sleep by myself."
"Where?"
"I'll be back in the morning, I promise." Miyo's eyes were dark and commanding. "Now please, stand in the corner for just a moment."
"All right." Dana backed into the corner and watched Miyo shuffle along the back wall till she reached the front door of their cabin. "I realize my actions must appear very strange to you. But don't worry. I'll explain everything to you tomorrow."
On Monday morning, Dana was ripped from her sleep by the sound of her door slamming into the wall of her room. She pried open her eyes to find Miyo silhouetted in the doorway against a graying dawn, hands on her hips, her legs spread a little more than shoulder-width apart. The air that swirled in from outside was cold and smelled foul.
"What stinks?" Dana rolled over and pulled her blankets over her head.
"You have to come with me. Now."
"What are you . . . What time is—?"
"No time. That's the time." Miyo's voice grew in intensity. "We have to move." The clomp of her boots across the wood floor echoed through the room. "I told you I'd explain my behavior from last night. Now I'm going to."
Dana opened her eyes a little wider and looked at the clock on her bed stand. Four thirty. "Can you explain it to me in the morning?"
"Now, Dana. We have to go."
"How long have you been up?"
"I never went to sleep. Something has been stabbing at my brain like an ice pick since Simon arrived at Well Spring, and I've finally figured out what's wrong. And you are a key to fixing the problem before it grows beyond my abilities. Get dressed. We're going in."
"You didn't go to bed all night? Then why did you take a pillow last night when you left?" It was a stupid question, but more of Dana was back in her dream floating down a slow-moving river in the heart of summer than was awake. Couldn't Miyo turn off her rampaging energy at least till seven?
"Sixty seconds and we're going in whether you're wearing what you want to or not."
Dana swung her legs over the side of her bed and plopped her feet on the floor. Wow. Cold. It helped wake her up a little, but it was far from enough. "I suppose a quick cup of coffee is out of the question."
"You'd be supposing correctly." Miyo grabbed Dana's Seattle Space Needle sweatshirt off the dresser and flung it at her, then fished her hiking boots out of the corner of the cabin with her toe and kicked them over to Dana.
"You could have handed those to me."
"Thirty seconds."
"Why the countdown?"
"I'm serious."
Dana pulled off her pajama bottoms, pulled on her jeans, and struggled into her sweatshirt and socks and hiking boots. "Are you going to explain to me what is going on? Why this is so urgent?"
"Not yet. It would take too long. I will when there's time." Miyo strode through the door and looked back over her shoulder. "Ready?"
Dana nodded as she zipped up her sweatshirt and trudged toward the front door. For the next three minutes, Miyo led Dana at a rapid pace past Well Spring's softball field, the ropes course, and the outer cabins they used to house the students during training weeks. Once they reached the edge of the property, Miyo's pace increased till they were moving close to a slow jog.
"Where are we going?"
"Someplace safe."
"Safe for what?"
"Safe to go in from."
"Anywhere on the ranch is safe, I told you that."
"We're almost there. Seven more minutes at the most."
While they hiked on, Dana tried to make conversation about Reece's plan to grow the Warriors and how powerful it would be, but Miyo didn't comment, so they trudged along in silence. Six minutes later they arrived at a thick grove of aspen trees. Miyo pushed through them to the other side. A small clearing appeared that wasn't visible from the path.
"No one would spot this from the trail."
"Exactly." Miyo motioned toward a large boulder to Dana's right. "Why don't you lean up against that rock." Miyo pointed to the left. "I'll use this one."
"Why do we have to go in?" Dana sat back against the boulder and the coldness of the rock seeped through her sweatshirt. "Is there a reason we have to do this so early, and outside?"
Miyo settled back and stared at Dana. "If you have ever trusted me, you need to trust me more now."
A sensation grew inside Dana like wildfire that what they were about to do was a very bad idea.
"Do you trust me?"
"Yes, but I don't like this. It doesn't feel right."
"Do you trust me?" Miyo asked again. Her voice was softer but it lost none of its fervor.
"I don't like this." The spark of apprehension inside Dana burst into a small brush fire.
"I know." Miyo clenched her fists and shook them lightly. "I understand why. And I'm sorry. But I don't have time to explain it to you right now."
"Will you explain it to me once we go inside?"
"Yes. Fully. I will answer all your questions that the Spirit will allow me to." Miyo raised her voice. "Ready?"
Dana nodded even though everything inside her was saying no. Just before their spirits shot out of their bodies, a scream ripped through Dana's soul that said she had made a decision that would lead to her death. She tried to stop from going, and for a second she thought she'd succeeded, but it was too late. Something grabbed her and yanked her on.
Every time she'd gone in with Miyo, the trip had been instantaneous. Not this time. At first it felt like she was being pulled through molasses and every second the syrup grew thicker. Then like she was being pulled in every direction at once. Pain shot down her back, legs, and arms and seemed to grow exponentially. But just before she got to the point where it was too much, the pain vanished and she found herself standing on solid ground, breathing heavily.
She stood surrounded by a series of tall, evenly spaced boulders that formed a circle twenty-five or thirty yards across. It would be tough to squeeze through any of the gaps between them. The sand at her feet was fine and the color of honey. A gray sky hung low overhead.
Miyo stood facing her twenty yards away, her eyes like ice.
"Why did it feel like it was tug-of-war back in grade school and they chose me to be the rope?"
"Because there is part of you that desperately does not want to be here. Because everything inside you was screaming not to go and now you're scared. Because the enemy doesn't want you to be here. But like I said, Dana, you can trust me. This is where you are supposed to be. Where you need to be."
"You still haven't told me why you brought me here." Dana widened her stance.
"I'm about to explain it." Miyo began to circle Dana as if they were in one of their training sessions and ready to spar. Instantly it made sense. This was part of her instruction. Woken up and forced into battle without time to fully wake up. Without warning. Without explanation. And put in an arena where she couldn't run.
"So this is a training exercise. I get it. Why couldn't you tell me that? I would have gone without hesitation."
"You wouldn't have come if I'd told you that." Miyo continued to circle—her feet gliding across the thin layer of sand, ready to pounce—and perspiration broke out on Dana's forehead. The look in Miyo's eyes was chilling. "You would have found an excuse not to come. In fact, I'm surprised you came this easily."
"Why?" Dana backed away. This might be a training exercise, but everything in her shouted it was much more. She instinctively called on the Spirit to provide a sword. It appeared in her clutches an instant later, and she grasped it with sweaty hands. "Answer me. Are we here for training? Or something else?"
"You know we are not here for training." Miyo gripped her own sword that had appeared right after Dana's.
"Then what is it?"
The lifeguard's words came back to Dana in a rush. _Let me tell you a little secret. Even if you do get out of here, Miyo will leave you in the real world too. She will turn on you. Mark my words._
"It is what is necessary." Miyo continued to circle and Dana continued to back away toward the towering boulders behind her.
"Why are you doing this?"
"I'm sorry." Miyo drew her sword and pointed it at Dana's heart. "This won't be easy for me. But I have no other choice. I promise you would do the same were our roles reversed. It must be done."
"Miyo, think about what you're doing!" Dana stared at her friend in disbelief.
Miyo dropped her gaze. "I thought about it all night." When her gaze met Dana's again, all compassion and friendship was gone. She looked at the sky, raised her sword, and dug her feet into the soft sand under them as if a gun were about to fire at the start of a one-hundred-meter dash. Her jaw tightened and her lips parted slightly, revealing clenched teeth. Miyo's breathing grew rapid as a strong wind came out of nowhere and whipped through her hair, pushing it behind her like a dark stream.
Miyo crouched down, her knees bent, her eyes on fire. She rocked back slightly, then pushed off and sprinted toward Dana. Her feet threw up little curtains of sand, and a fierce battle cry erupted from her mouth.
Dana snapped herself out of the daze of bewilderment and disbelief that surrounded her and raised her sword. But what would that do? Miyo was quicker and knew far more moves than Dana had even heard about. She tried to raise light-armor around her, but the disconnect of seeing the one who had taught her the technique streaking toward her with death in her eyes destroyed her concentration. She had to somehow avoid Miyo's attack long enough to think. Find some plan of battle that didn't involve sword-to-sword combat.
_Jesus!_
A quarter second more and Miyo's blade would sweep toward Dana's torso. Had to move. Faster than she ever had before. Because if she didn't, she would die.
FORTY
ZENNON BURST THROUGH THE DOOR OF THE COUNCIL chamber and scanned for Caustin in the ill-lit room. Where was he? The table was full. All twenty seats were filled so he had to be here. There, his back turned, near the middle of the table.
In two strides, Zennon reached his rival, spun him around in his chair, and backhanded him hard across the face. Blood seeped from Caustin's eyes and nose. "You told me to report again when I felt I had made significant progress, so I am here. Are things progressing to your satisfaction now?"
Caustin's eyes didn't leave Zennon as he stood and faced him.
"Well, fool? Have you no words?" Zennon leaned in and brought his face within inches of his adversary's as he ran his finger along the edge of his sword. "Or would you like to express yourself with your blade, and me with mine?"
Caustin clutched the hilt of his sword but didn't pull it from its sheath. "I'd like nothing more."
"Answer Zennon's question." Their Master's guttural voice rumbled from the end of the table.
Caustin's eyes burned with rage. "Progress has been made."
"As if I needed your approval at this point." Zennon stepped away, turned toward his Master, and bowed. An asinine gesture and beneath him, but required. "My lord, the mission you sent me on has almost been accomplished. May I kill Caustin now?"
His Master gazed long at both Caustin and him before speaking. "You have done well. And your zeal is warranted. But we will wait for the outcome before I will allow either of you to act."
Zennon bowed lower. "My lord, allow me to exact my vengeance now. As you know from my last report, Doug Lundeen is dead. Reece Roth and Brandon Scott have been subdued by the warfare and the demonic strongholds launched against them. Marcus Amber has resisted, but I have foreseen him being of no consequence this time. Simon is still fully immersed in my deception, and Lundeen's granddaughter is about to—"
"Silence."
Although the word was spoken just above a whisper, it reverberated around the room as if shouted.
"Do not anger me, Zennon." The Master stared at Zennon till he dropped his gaze. "We will wait."
"Yes, my lord." Zennon bowed again, then turned to leave.
"Stop."
"Yes, Master."
"Report again in six days."
"Yes, my Master." Zennon bowed again, strode for the chamber door, and turned when he reached it.
Caustin pointed a gnarled finger at Zennon. "If you are not victorious, you are mine."
Zennon stood in the stone doorway of the council room and fixed his gaze on Caustin. "It will be with immense satisfaction when I grind you to your knees as you weep with pain, and then listen to you plead for your life as your lifeblood flows from your veins like water."
FORTY-ONE
EVEN THOUGH MIYO WOULD PROBABLY BE EXPECTING THE move, Dana had no choice. It was the only one she could execute perfectly without thinking about it—and at this moment she needed all her mental strength to find a way out of this nightmare.
She thrust her sword at a forty-five degree angle to block Miyo's strike while at the same time started a roll forward, inches to the left of her opponent's upper-right leg.
As she dove into the roll, Dana pulled her sword down low and aligned it with her body. If the roll worked well, she would avoid Miyo's attack, complete the somersault, and be back on her feet while Miyo's momentum carried her at least four feet in the opposite direction. If the roll worked perfectly, Dana's blade would reach its target and inflict at least minor damage to Miyo's left leg.
It worked perfectly. Dana completed the somersault and spun to face her attacker. Miyo turned on one leg and glanced at the other. The fabric of her pants was sliced open and the flesh of her leg was exposed. Blood seeped out of a long gash on her thigh. Miyo glanced at the cut but gave no indication she felt any pain.
"Well done." There was surprise and respect in her eyes. She glanced again at the wound and dabbed at it with the sleeve covering her wrist. "A move executed with perfection and the only one that could have saved you. And you made it into more than a defense and drew first blood. This shows mental strength and shows your synapses are capable of firing as fast as your reflexes even under severe stress."
Relief flooded Dana. It might only mean she would live a few minutes longer. But Miyo wouldn't attack again without a healthy dose of caution. And those few minutes might give her time to devise an escape. The answer flashed into her mind. Of course! Well Spring. She would send her spirit back to Well Spring where she might be able to get to the cabin and Reece and the others before Miyo could catch her. And who knows? Maybe Miyo's warrior skills weren't as developed on earth as they were in the spiritual realm. It was her only shot, and the look in Miyo's eyes said Dana didn't have time to consider any other option.
Dana focused inward and her spirit started to leave the realm, but a second later she felt like she'd hit a wall of three-feet-thick glass and was tossed back like a sack of concrete.
"It won't work, Dana. I've blocked you and it is impossible for you to return without my permission. I brought you here and the only way you're going to leave is with me."
"Let me go."
"I can't do that."
"Tell me why you're doing this. We can talk, figure this out. The enemy has a stranglehold on you. This is not you!"
"It is the true me. Truer than I've ever been."
"Is this about Doug? I'm not the reason your grandfather died."
Miyo's answer was a steady advance. Her eyes were full of rage, but also of ice, as if killing Dana would be executed without a hint of remorse. Maybe because of Dana's minor success. Maybe because Dana had brought up Doug. Didn't matter. Rage meant lack of control. And lack of control meant the stroke of her sword during the next attack would have less precision to it. Dana would use that lack of accuracy not to defend herself, but attack—a strategy Miyo wouldn't expect.
Dana shoved down the panic that pressed up from her stomach like a geyser. If this didn't work, she would be dead. But if she didn't try it, the result would be the same. In a moment she would know if Miyo was as good a teacher as she claimed to be.
She waited till Miyo had moved to within three feet—well within reach of her sword. Again, Dana's move was perfect and hope surged in her. But this time the teacher didn't underestimate the student. Miyo's defense was faultless. It was as if she'd expected Dana's attack. And her countermove followed so fast, Dana stood no chance.
Miyo slid her sword down Dana's forearm and sliced hard on the back of Dana's wrist. She cried out and dropped her sword and instinctively clutched her wrist. _Foolish! Never drop your sword._
Miyo kicked Dana's sword fifteen feet to the left and held the tip of her own blade at Dana's throat. "I would ask you not to resist, friend, but I know you can't do that. But out of respect for our friendship, I will ask anyway. If you place your hands behind your back and close your eyes, you will make this easier for both of us."
No. She refused to die like this. Dana spat into the sand at Miyo's feet, then dropped to her knees with her head down as if to submit to Miyo. A second later Dana swung her leg out like a whip and cut Miyo's legs out from under her.
Again she caught her opponent off guard, but this time it didn't buy Dana any extra time. Before Miyo hit the ground, she was rolling forward and lifted her leg straight up. Then brought it down on Dana's shoulder like a falling redwood and followed up with a blow to her ribs that felt like it crushed three of them.
Dana tried to strike out, but Miyo was behind her, pinning Dana's arms to her sides. Dana struggled with everything inside, but Miyo's grip was like iron.
"Fight it, Miyo! Don't let it control you! Talk to me!"
Miyo didn't answer.
_Jesus, I need you! Come!_
But there was no sense of the Spirit's presence. No tinge of hope for victory or survival. Dana struggled again to no avail. She looked back and stared into Miyo's eyes. "Before you kill me, don't you have anything to say?"
Miyo answered quickly and in a voice just above a whisper. "Do you want to be free?"
"What?"
"Do you?"
"Of course. But what you're doing is not—"
A gust of wind whipped sand into Dana's eyes and she slammed them shut. An instant later something hard smashed into Dana's skull and darkness swallowed her.
FORTY-TWO
DESCRIBING THE PAIN AS AN EXPLOSION IN HER HEAD wouldn't come close to accurately describing what Dana felt. Because the pain wasn't just in her head. It extended down her neck into her torso, arms, legs . . . How could her legs feel like they were on fire while at the same time acutely aware that the little toe on her right foot felt like the nail was in the process of being ripped off?
Then a thought struck her. She was alive. If she was dead she wouldn't be feeling this pain. Right? Or was she in a spiritual prison like one of Simon's alternate realities?
Miyo. A demon? Based on her actions, yes, maybe. No. The thought was ludicrous. But Dana couldn't comprehend what she'd done. Twenty-four hours earlier she would have sworn Miyo was the epitome of the warrior Dana wanted to be. But now? If she wasn't a demon, what was she? A tool of the enemy who infiltrated their ranks to destroy them? It seemed just as impossible. Yet with what Miyo had done to her, Dana had no other explanation.
Something hard pressed down on her feet and she tried to open her eyes. Were they open? She couldn't tell. If they were, all that was visible was darkness. After a few minutes, images of microscopic green strands circled through her imagination as they rose from her body. She was inside her body and outside it at the same time. Thin translucent fingers reached inside her body, took hold of one of the strands, and pulled it out like the unraveling of a tapestry, where one strand was connected to all the other strands.
A lilting melody played in her head—or was it outside her?—from an ancient sounding flute. Then a far-off drumbeat joined in. Time seemed to slow and seconds took minutes to pass. And still the ethereal hands worked to pull the strands out of her body. Each time one of the green strands left, it felt like another piece of her flesh was being ripped out. The process lasted for hours—maybe days—and still the microscopic organisms seemed to fill every part of her.
Finally the last fiber was gone and Dana breathed a sigh of complete exhaustion even though she'd done nothing. For the first time since she and Miyo had left Well Spring and entered into this realm, she felt peace.
_Jesus?_
_I am here._
_Am I alive?_
_Yes, dear child._
A voice broke into her conversation with the Spirit. "Rest, Dana. It is what you need more than anything else right now. There will be time to talk later. You are not alone."
"Miyo?" It sounded like her, but how could it be? "Is that you?"
The owner of the voice didn't answer and Dana slipped back under. When she came to the second time, Dana heard a brook to her left, and the air smelled like it was early morning with the hint of a flower she felt like she should know from childhood.
She opened her eyes for a moment and caught a glimpse of Miyo before a sting of pain shot through her head and forced her to close them again. Her worst migraine was nothing compared to this. This couldn't be heaven, so Miyo must not have killed her.
"Good morning."
"Miyo." Dana risked opening her eyes again and paid for it with another twinge that shot through her head like a grenade going off inside her skull.
"Don't talk till you're able to without pain. And keep your eyes closed if you can. You've been through quite an ordeal."
"I'm alive."
"Very much so." Miyo stroked Dana's forehead. "Although keeping you that way took a toll on both of us, I'm afraid."
What was she wearing? Whatever it was felt heavy, like the lead-lined jacket she wore when she was ten and had to get X-rays on her wrist. And it was hot. Her forehead felt wet with sweat.
"Sleep if you can."
"But you have to tell me—"
"I will, all of it, just like I promised. But not yet. You need more rest first. It will help you heal faster." Miyo prayed a short blessing over Dana, and before the prayer was finished, Dana slipped back under.
When she woke for the third time, her headache had vanished. She opened her eyes and kept them open. Above her was an archway of red stone. It reminded her of a trip to Sedona she'd taken after her junior year of college. That would explain the heat. Next to them was a wide brook that flowed swiftly with crystal-clear water.
"What happened to me? Where are we? Why aren't we back at Well Spring?"
"You were deeply infected." Miyo pulled a damp white cloth across Dana's forehead. "I'm sorry. What I did to you had to inflict a great deal of pain. But I'm proud of you. You fought well and embraced the freedom that was offered. And you have advanced a great distance in your training."
Miyo grinned and rubbed her arm where Dana had landed more than one blow. "Far better than I could have hoped for. You have become a strong warrior. Or better said, you always were a strong warrior and the warrior has been more fully released, far more quickly than expected. My grandfather was right about you."
Dana lifted herself up on her elbows, but Miyo eased her back down and Dana didn't resist.
"Rest a little longer. It's okay. We must go soon, yes." Miyo paused and glanced around. "But there is time. The Spirit has given the stones of this place healing properties. Extracting the virus out of you has no doubt taken its toll. Lie on the stone for a while longer and let it soak into your body and bring relief."
Dana sank back into the stone. It didn't make sense. It didn't feel hard. In fact, no bed had ever felt this soft, and whether it was her imagination or real, heat seemed to seep out of the stone into her back and then down her legs in waves. And with each pass she felt stronger.
She stared into Miyo's dark-brown almond-shaped eyes. They were more tender than she'd ever seen them and they spoke of more compassion than her words could have. "I thought you were going to kill me."
Miyo smiled, dipped the cloth into the stream again, and squeezed out the water. "No, I like you far too much to do something like that. And I love you even more."
"What was inside me? You used the word _virus_."
"In human terms it is best described as a virus. A spiritual virus." She pressed the cloth onto the back of Dana's wrist where Miyo's sword had sliced it open. It stung for a moment but then seemed to pull away the pain and stiffness.
"Human terms?"
"You were infected."
"And in spiritual terms?"
"You let in a significant amount of warfare from the enemy."
"Are you saying—?"
"Yes. Warriors Riding has been attacked. Infiltrated because our guard was down."
"Guard down?"
"You've become adept at seeing the attacks coming at you from the outside but were vulnerable to an assault from the inside."
"You're saying one of us—"
Miyo shook her head and knelt closer. "Not one of the Warriors."
"Simon?"
Miyo nodded, dipped her cloth in the water, and brought it back to Dana's wrist.
"That can't be. He's not evil. He saved Marcus, which saved us during our battle against the spirit of religion. I can't believe he—"
"I doubt Simon has any idea of the warfare he carries. It would devastate him if he knew. I'm certain Zennon offered the warfare to Simon before or during his time in the alternate realities in a way that seemed to be right and an answer to his pain, and he took it in. I imagine it has lain dormant for many, many years. But now it has been set loose on us. And you took the bait, friend."
Dana gave her head a tiny shake. "Bait? I didn't take any—"
"Ask the Spirit, Dana."
She squeezed her eyes together in an effort to push beyond the pounding headache now assailing her. "I . . . I don't see—" But she did see. The lure was her chance to shine as the Leader of Reece's new version of the Warriors Riding. To be the A student once again. To be lauded for her skills and leadership prowess. To perform well and be loved for it.
Miyo took the cloth from Dana's forehead and dipped it once more in the stream, and this time placed it on her forehead.
Dana closed her eyes. "What about you?"
"I resisted and narrowly thwarted the attack. I've learned to guard myself at all times with the armor of God I taught you to build. I always keep a thin layer of it around me. That gave some protection. Even so, it took everything I had to fight off the warfare. It weakened me. If it came at me a second time, I don't know if I could do it again so soon."
"It was sweet and cool and promised me . . ."
"Yes."
"How did it get in? What did I do wrong?"
Miyo hesitated. "It's time for us to leave here."
Dana grabbed Miyo's wrist. "Tell me."
"I'm not your judge."
"But you know something."
"I know the only way the warfare can get in is through an opening. A crack in our souls. Those cracks come from sin. Things we are holding on to. I don't know what it is in you. Hardness of heart? Having to prove yourself? Needing to perform? Those are only guesses. But whatever it is, it allowed the enemy to more easily get past your defenses. You offered him a seam, and he was able to worm his way through and plant thoughts and images and promises and suggestions and warfare inside you."
Dana closed her eyes again. Of course she had cracks. Everyone did. Her two biggest? Miyo nailed one of them. Needing to succeed. Perform. She thought she'd finally defeated it on that beach inside the spiritual realm she'd gone to with Miyo. Obviously not. The second crack was Brandon. To all outside appearances she'd forgiven him completely. Given up every shred of bitterness. Let go of all her woundedness over his breaking of her heart. But it wasn't true. There were still shards left she hadn't fully acknowledged till this moment.
"I need to give up being the Leader."
"Our greatest strengths are so often our greatest weaknesses."
"And I have to forgive him completely."
"The Song?" Miyo said.
"Yes."
Miyo squeezed her hand. "We need to go."
"Back to Well Spring."
"No, it's not safe there."
"But we have to warn the professor. Warn Brandon and Reece—"
"Do you know the moment the warfare came on you?"
She blinked. "It . . . it was when we stood on the hillside, listening to Ree—" Dana blinked. "You're not saying Reece is already infected, are you?"
"What do you think?" Miyo stood and folded her arms. "He does a complete 180 on the direction and focus of Warriors Riding right around the time the warfare was unleashed?"
"It's hard to believe Reece couldn't resist, as strong as he is in the Spirit."
"I agree, which is why I want to go to a place where we can know for certain if he's been infected."
"Where?"
"To a spiritual realm I hear you've already been to."
Dana raised her eyebrows.
"The Field of Doors," Miyo said.
"The gateways of all souls."
"Yes. We need to see Reece's door."
FORTY-THREE
MOMENTS LATER, THEY STOOD ABOVE THE FIELD OF DOORS on the dais where the other Warriors and Dana had gathered when they were here the first time. The air temperature was just above cold. A hint of jasmine tickled her senses, and the brightness of the sun and the blue of the sky made the place feel like early spring.
"Does it look different from the last time you were here?" Miyo asked.
Dana studied the field. In the distance to the right were the same green cliffs, thousands of feet high. Waterfalls still divided the mountains in sporadic sections. As before, an arid plain spotted with massive red-rock bridges and formations sat to her left. And in front of them were the doors—thousands of them stretched out as far as she could see. But there were slight differences.
"The colors aren't as bright in certain places and the air isn't quite as clear."
A man approached them from fifty yards to their right. His robes covered his feet, adding to the illusion that he floated over the surface of the huge dark-wood platform.
"I still can't believe that's what they wear in heaven." Dana pointed at his robe. "Seems a little clichéd if you ask me. Something out of a bad Sunday school painting."
When he reached them twenty seconds later, he stopped and gave a slight bow. "First, this isn't heaven. Second, would you prefer I wear jeans and a T-shirt?"
Dana felt her face flush.
He laughed and his eyes radiated kindness and joy. "There is no shame and are no secrets here, Dana Raine. So don't allow the world of men to creep into your mind in this place."
"You remember me." She blinked and frowned.
"Of course." He turned and winked at Miyo. Even without them speaking, Dana could tell the two were friends. "Few humans visit us, so those who do are remembered. But even if I'd met millions of other spirits, I would remember you. You are the Leader."
"Yes . . ." Dana looked away and tried to compose herself.
"I see you are still struggling by comparing yourself to your friend." The man smiled. "We don't recommend that. It is a trap that must be released."
"I've been learning that lately." Dana pointed at her head. "I know it here."
"But not yet so well there." The man pointed at her heart.
"Yes."
"There is a difference between seeing a path on a map and walking it with your feet touching its surface." He didn't wait for a response. "If I understand correctly, you had an encounter recently in the heavens with a number of demons, yes?"
She nodded.
"You refused to give in to Zennon when he pretended to be the Christ in Revelation. You were the one among the Warriors Riding who remained strong and led Brandon and Reece back into the truth."
"I suppose that's true." Dana gazed over the Field of Doors as a feeling of confidence grew inside.
"Every evidence in front of you said you were in the presence of the Christ. Your fellow Warriors said the same. And yet you refused to bow. To give in. And you pressed into truth despite the resistance. What would have happened to Reece and Brandon if you hadn't led well? Where would they be? In the same place Simon was for so many years? Or simply destroyed?"
She smiled at him in thanks, but he wasn't done.
"Are you still allowing the enemy to put doubt in your mind as to the strength of your gifting?" He folded his arms, glanced at Miyo, then looked back at Dana. "Allowing him to taint it by tempting you to compare yourself to another daughter of Eve?"
He shook his head. "You cannot play Miyo's role and would not like it if you stepped into it. Just as she was not born to lead in the same way as you and could not wear your yoke."
Dana only nodded again.
"But there is a deeper truth you are beginning to know and need to know fully."
"The beach scene before my sophomore year. Expectations."
"Listen to me with ears that will hear." The man stared at her and she seemed to lose herself in his flashing green eyes. "He is not disappointed in you and never will be disappointed. There is no performance he requires. No expectations you need to meet. You are his daughter and loved without reservation."
Something snapped inside Dana and tears flooded out of her. After what felt like hours, she rose and stared into the man's radiant eyes once again.
"Now that we have broken the hold of this sin, you need to repent of it to complete your healing."
"What?" Did she hear him right? "Sin? Repent?"
"Yes." The man smiled. "If you consciously allow yourself to continue to allow a thought to stay in your mind you know not to be true, a thought that keeps you from living fully in your glory, yes, I would call that sin. And to repent means to turn from one way of thinking and embrace another. I suggest you turn for good from thoughts that are lies and believe fully that you are loved simply because of who you are."
Without thinking—without knowing if it was all right—Dana grabbed the man in a hug. It must have been okay, as the man hugged her back, and warmth and acceptance radiated into her. When they released, Miyo took her by the arm.
"We can't take too much time here." She turned to the man. "I'm sorry, we can't stay longer."
"I understand. May the Spirit go with you in power and in love."
"And also with you."
Miyo asked Dana to close her eyes, and the instant she did, she felt a rush of wind from behind. She was lifted into the air, but seconds later felt solid ground under her feet again. She opened her eyes to find herself surrounded by doors in the same astounding variety she'd seen the last time she was here.
Massive doors. Small ones. Thick and thin doors. Ancient-looking ones and ones that looked brand-new. Some of stone, some of wood. Some that appeared made entirely of various types of vegetation and some of crystal. But the one directly in front of her and Miyo caught Dana's attention more than any of the others. Something pulled at her as if it wanted her to come closer.
This door was taller and wider than most. Thick redwood logs cut into a circle served as a platform. Rough-hewn stairs were cut into the platform and led up to the door itself, which was made out of rich brown boards in a variety of light and dark shades. Not straight up and down, but woven together in a fascinating pattern.
"I feel drawn to it. It makes me feel safe and apprehensive at the same time. As if danger and glory and life and hope and risk are all wrapped up in a package. And I feel like I know the person whose door this is."
"Yes, it is the door of someone you've grown close to."
She voiced what she already knew. "It's Reece's."
Miyo nodded.
"It's just like him. Strong and full of mystery and hope and the unknown."
"But it's not just like him."
"I think it's stunning." Dana reluctantly pulled her gaze away from Reece's door and looked at Miyo.
"It's all the things you've said, but it isn't right." Miyo glanced around the field at the other doors near them. "Many of these are wrong now. It is spreading."
"What do you mean 'wrong'? What do you mean 'it's spreading'?"
Miyo didn't answer. She circled Reece's door like a lioness sneaking up on its prey, her feet barely making indents into the thick grass that circled Reece's door.
"Look at the grass closely."
Dana bent over and studied the blades. Some of them were lighter than the others, and some were thinner and light brown as if dead. "The grass is dying."
"Yes." Miyo studied Reece's door and spoke without turning. "We need to see what Reece's door looked like a week ago—before Simon came."
"How would you hope to do that? Some sort of spiritual-realm photo album?"
"Did my grandfather teach you anything about time manipulation?"
"Doug and Marcus talked about it when we were all at Reece's house a month ago. The conversation lasted maybe thirty seconds. I thought he might be kidding."
"Kidding? We have the Spirit of the God of the universe in us. The God who created the earth. The God who moved time backward as recorded in Isaiah thirty-eight. The God who says we can move mountains with the faith of a mustard seed. The God who—"
"I get it. So are we going?"
"Yes." Miyo looked at Dana from under her eyebrows. "This might feel a little strange."
Without warning Dana's mind felt like it was pulled out of her skull, down through her torso, down through her legs as if split in two and each half emerged from her feet. Then the rest of her body followed her mind, collapsing on itself until it formed again as if she stood on her head. She felt like she was about to throw up.
But the feeling dissipated as quickly as it had come. Her eyes came back into focus, and she blinked as Miyo took her by the shoulders. "Are you all right?"
"That wasn't fun."
"No." Miyo gave a thin smile. "I'm sorry to say it never gets any easier." Miyo slumped forward, knees bent, and rested her hands on her kneecaps. She looked for a moment like she was going to welcome her lunch back to the land of light. "At least I haven't figured out how yet and if GPD knew, he never taught me."
"GPD?" Dana dabbed at her mouth as if that could wipe away the nauseous feeling.
A sad smile surfaced on Miyo's face. "Grandpa Doug. My pet name for him."
She gave her head a quick shake, and Miyo's countenance shifted back to the granite Dana had come to know. Miyo motioned toward Reece's door.
"Take a look at it now."
Dana stared at the door in astonishment. What had been solid in the present was vastly different in the past. The rich light and dark browns were no longer solid but liquid. They moved up and down the door like small individual rivers undulating and pressing against each other, widening and narrowing as they formed an intricate dance against, around, above, and below each other. It was beautiful. Free and full of life.
She stared at Miyo. "It's alive?"
"Yes. Of course." Miyo glanced at Dana, then turned her gaze back to Reece's door. "Every door is alive. They are the gateways to our souls. So they live just as a soul lives—because the gates are a part of the soul they allow access to."
"And Reece's is hardening." Dana sighed. "He's carrying the warfare."
"Yes. Carrying it and spreading it." Miyo's face grew worried. "And getting ready to unknowingly unleash it, along with a horde of demons on thousands of susceptible believers."
Realization struck Dana like a tsunami. Of course. The gathering. Which Brandon had clearly bought into. And Marcus was clearly resistant to.
"Brandon?"
"Infected, I fear."
"The professor?"
"I don't think so," Miyo said. "But I'm not sure. And we need to be."
"I agree." Dana paced. "We need to hear from the Spirit, figure out where we go from here."
"I'll tell you one thing I know for certain." Miyo bit her lower lip. "We're not going to tell Reece, but we have to go to his gathering."
"Are you mad? Why would we go and put ourselves in the center of this virus or warfare or whatever it is?"
"We might be the only ones who can stop it."
"Just the two of us?"
"Oh no, we'll have three others with us of such staggering power, the enemy will not be able to stand."
Dana knew she meant the Trinity. "I was thinking more along the lines of people."
"I know." Miyo smiled. "Don't worry. We have eight weeks to prepare. We might not be ready to face the warfare now, but by then we will be. Trust me." Her eyes grew soft and her gaze dropped to Dana's arm. "I'm sorry about your wrist."
Dana smiled and pointed toward Miyo's leg. "And I'm sorry—"
"They are wounds for the King. Do not be sorry."
Dana ran her finger next to the gash on the back of her wrist. _Yes, for him._
Miyo took Dana's hands. "We need to get back to Well Spring."
"I thought you said—"
Miyo shook her head. "No choice. Our spirits are here. Our bodies are not." Miyo's face darkened. "Let's just pray Reece and the others haven't found them yet."
They slid back into their bodies and Dana glanced at her watch. Still early. Maybe the others weren't up yet. A moment later the crunch of boots coming through the underbrush answered her question. In another ten seconds, Reece and Brandon came into view.
Miyo leapt to her feet. "Stay away from us."
"What?" Brandon opened his arms. "You have an early-morning party and don't invite us?"
Reece wasn't as flippant. "What have you two been doing?"
"What is necessary."
Brandon pointed at them. "I'm thinking something strange is going on given the gash on the back of your wrist, Dana, and the chunk of skin someone took out of your thigh, Miyo."
"We're fine."
Reece took a step toward them and Miyo grabbed Dana's arm.
"Stay away from both of us." Miyo's voice grew hard.
Brandon scoffed. "Are you going to tell us where you got your ticket for the Loony Wagon or do we have to guess?"
"No closer, Reece, or we're gone."
"Not without the power of the Spirit, you're not."
"I believe he will lend us his power if your boots come an inch closer."
Reece seemed to grow taller. "I don't know what has you secure in its talons, Miyo, but it is time to break free of it. It's time to stop trying to brainwash Dana into whatever skewed way of thinking you've allowed yourself to get sucked into."
Miyo jabbed a finger toward Reece. "Where is Marcus? And Simon?"
"The professor had to return to Seattle. A minor emergency with Kat and the girls. And Simon became agitated with the idea of being here without Marcus. So we gave them our blessing and allowed them to go."
Dana stared at Reece. _Gave our blessing? Allowed them to go?_ Not his language. The comments sent a shiver down her spine.
"Whatever is bothering the two of you, we can work through it. But for the moment we need to put it aside and focus our energies on the gathering."
Dana dug her feet into the ground. "We're not taking part in the gathering, Reece."
Frustration passed over his face. "There are four of the prophecy, Dana. Without you, the Warriors are incomplete. Do not let the enemy plant lies in your soul. Do not accept them."
"You've been infected, Reece. So have you, Brandon. With warfare orchestrated by Zennon that is taking you both down a path of deception."
Reece didn't answer. He turned to Miyo as his face darkened. "I didn't see this coming. Not from you. So gifted in the things of the Spirit. And a legacy from your grandfather to be envied. And yet you have fallen. You've been deceived. Come back to the light, Miyo." Reece reached out his hand. "Let go of your ego and youth and the deception you have accepted as from the Spirit. I see the light around you trying to overcome the darkness. Allow it to happen. Allow the Spirit to take control and return you to the truth."
Suddenly Reece strode toward them, his long legs chewing up the distance between them like he was running. Just before he reached them, Dana felt Miyo's arm on her shoulder, and the woods vanished.
FORTY-FOUR
ON TUESDAY EVENING, SIMON WALKED INTO LUCID ON the Ave and headed for the back of the lounge to try to make sense of the past few days. He'd been set free. Without question he had thrown off many of the cloaks of deception he'd worn for decades. And yet he still felt like he was standing on a stage with seven illusions to perform but the memory for only two.
Even knowing two was wonderful. After living backstage for more years than he wanted to count, knowing even one trick would feel like Eden. And he would learn the routines once more, and ride again in the spiritual realms.
The clink of glasses and the smell of beer filled his senses, and he tried to relax. He slid into a booth near the corner, ordered a pale ale, and studied the room as he waited for his waitress to return with his drink. Two young men and one woman—students it looked like—huddled at one of the tables over their laptops and talked rapid fire about something. Another table held four women who looked to be in their midtwenties and giggled like it was their first time in a bar.
The rest of the place was empty except for three musicians pumping out a nice assortment of acoustic jazz. Good. He needed a place to gather his thoughts. Some people needed silence. Simon needed noise. Something to compete with all questions pinging around his brain, asking how he'd allowed Zennon to deceive him for so long. Asking what Simon was supposed to do now that he had an idea of who and what he'd been. And why Marcus thought he was important to Warriors Riding. Before he'd left Well Spring, Reece invited him to the gathering, but Simon wasn't sure if he'd go. More than anything he wanted to have time alone to process everything he'd been through.
He pulled out a pad of lined paper and started to jot down his impressions from Well Spring. Get them organized. Record what he remembered from the old days that had inspired him to write the manuscript. Jot down what the Spirit was saying now.
_So good to have you back, Simon. I've missed you._
Simon smiled at the clear voice of the Spirit. It would take time, but the professor was right. Restoration had come. He pressed his pen to the paper, but before he could start to write, a familiar voice sliced into Simon's soul.
"Simon."
His chest tightened and his gaze stayed fixed on his paper. He didn't have to turn to know whose voice it was. He prayed for clarity and closed his eyes. He felt the being slide into a seat two tables down.
"Hello, old friend. It's been such a long, long, long, long time."
Simon continued to stare at his paper and prayed again.
"Are you going to pretend you didn't hear me?"
Simon turned and bit into his upper lip. Zennon sat in a corner of the room ten feet from him, looking exactly the same as he had when he'd introduced himself as Aaron to a brokenhearted twelve-year-old boy. Hair just as dark. Eyes just as penetrating.
"Leave me alone."
"Of course. My apologies." The demon rose from his seat, sauntered toward Simon, and stepped past his table. But a second later Zennon spun back, his dark eyes blazing, and slid into the seat across from Simon. "But I cannot. It's so good to see you again. I can't leave without catching up. I'm sorry I didn't come visit you when you were . . . um . . . in the other place. How long were you in your last reality?"
"You know exactly how long." Simon gripped the edge of the table and tried to keep his hands from shaking.
"True. But do you? And how do you know this isn't just another reality I've created for you?"
"I escaped from those realms forever. I'm never going back." Sweat covered Simon's forehead and palms. "And the Warriors went into my soul. Set me free. I know who I am again. Your illusion is finished."
"Yes, you have to feel grand about that." Zennon leaned back and spread his arms along the seat back of the booth they sat in. "Do you remember all the magic we used to do together? Sessions that would last until the dark hours of the night?"
Zennon took out his gold coin and placed it in his left hand, then closed both hands into fists. A second later he opened them and the coin had vanished from his left and appeared in his right. "That was one of the first vanishes and reproductions I taught you. Do you remember?" Zennon extended his hand. "Do you want to hold my coin?"
"Your coin?" Simon narrowed his eyes. "I have the power of the Spirit inside me and he is greater than you, and what you can do, with a power—"
Zennon laughed. "You're no threat to me. You must know that." Zennon pointed at Simon's shaking hands. "Relax. You're of no consequence now that you've served my purpose. Although I must give you credit. You played that part so well."
"What purpose?" Simon's stomach tightened.
"Why, old friend, you have to have suspected." Zennon leaned forward and smiled. "You already know you didn't escape. There was no heroic breach of the alternate-reality wall. So you have to ask yourself, why did I let you go?"
"I . . ." Simon's mind went blank for a moment. "It doesn't matter. I helped the Warriors gain a victory over you. And then I taught them at Well Spring the nature of deception and how to look past the illusion and—"
"Oh my, you're not serious." Mock astonishment splashed across the demon's face and laughter spilled out of his mouth. "You really think you were at Well Spring for God's purposes? How interesting. I love that. It makes everything so much sweeter."
"What are you saying?"
"Before I tell you, be honest with me." Zennon leaned forward and clasped his hands in the center of the table. "You really don't know?"
Simon started to answer, but Zennon cut him off.
"You're the key to my plan. This gathering your precious Warriors are planning? That's not of God. Not at all. That's my event." Zennon rapped the edge of his clasped hands on the table. "You see, I planted warfare in you long ago. I offered it to you on the ledge that day, and you took it and cherished it and it embedded itself deep in your soul.
"And then I let you go. And you got involved in Marcus Amber's life. And gained his trust, which allowed you access to Well Spring and the other Warriors. There you passed the warfare to Reece and Brandon. Marcus unfortunately isn't offering much of a crack to sneak through these days. And Miyo is a little too paranoid to fool. Then she yanked Dana back from the abyss—which I will probably kill her for doing."
Zennon leaned in till his head was inches from Simon's. "No matter. Reece and Brandon are the ones I need. Reece's bitterness toward Brandon for not saving Doug, and Brandon's lack of ability to think of anyone's restoration but his own have served me perfectly. Think back to your last day at Well Spring. Even with your brain full of fog, you had to think it strange the way Reece suddenly decided to revamp his ministry, and you had to wonder why they went after the missing Dana and Miyo like they were hunting game. Why they 'allowed' you and Marcus to leave like they owned you. Why all the way back to Seattle, Marcus talked in riddles about his concern for the rest of the Warriors. And then when you pinned him down for an answer, Marcus told you he feared greatly for his friends. That they had been attacked by some kind of mist that burrowed into their souls with demonic warfare."
Simon stared at the demon and tried to breathe. It felt like all the air had been sucked out of his body and a massive foot stood on his chest.
"You did it, old friend. It was you!" Zennon smiled and flipped his gold coin into the air, where it vanished. "You know how most decks of cards come with an extra card that shows the rules of poker or offers a discount on your next pack? Those are the cards people throw away. That is you, Simon. Your chance came and went back in the sixties before you chose to sleep your life away in other realities. All you're good for now is as a pawn in great wars far beyond your comprehension."
Zennon cupped his palms together, and when he lifted them a red deck of cards rested in his hands. He flipped the top card over and pointed at it. "At best you're the joker. Wild, unpredictable, and rarely needed in card games. If the jokers are lost, no one really notices, just as no one noticed when you were gone for decades."
Zennon gave an exaggerated shake of his head. "You are a forgotten, utterly useless being. You wrote a manuscript. As of late you remember doing it. So what? You're not living what is written in it and probably never will come close to living it ever again."
"Get out."
"I could take you away, you know. To someplace you wouldn't remember. And you could be a king again." Zennon showed the front and back of his hand. Empty. A second later a King of Spades appeared at his fingertips. "I would do that for you. You have to admit, there were times when you liked living there."
"Get out. Leave me."
"By what—?"
"By Jesus Christ. The Son of the Living God. And his Spirit who lives in me."
Zennon shoved himself back from the table hard, stood, and his eyes turned black. "There is no place for you in this world, Simon. Maybe in the next, but not this one. Give it up before you destroy anyone else. You say these pretend Warriors are your friends? Then stay away from the gathering before you ruin someone else's life like you've ruined theirs."
Shame and self-loathing washed over Simon. Was it true? Had he brought warfare on the Warriors? Simon shook his head like a dog after a bath. If it was true, there was no question—he had to stay away. Had to. Had to. Had to. Heat filled him. As much as he wanted to believe Zennon's accusations were a lie, he knew they were true. Yes, he knew who he was: the joker. And he needed to get as far away from the deck as possible.
FORTY-FIVE
"REPORT."
Zennon bowed before the Master, then glanced at the only other one at the council table. Caustin.
"All things are in place, my lord. The musician is poised, ready to sing the song of heaven for himself. Simon is buried even deeper in deception because I allowed him to discover a slice of who he is again—but now he sees his depravity—which will prevent him from searching for who he is fully. More important, he knows the attack against the Warriors came from him, burying him in guilt and shame, and he will go nowhere near the gathering.
"Miyo has some skill, but her understudy, Dana Raine, is far from ready to face my full wrath. If they choose to show themselves during the gathering, they are only two and cannot hope to stand against me. Reece Roth is now being steered like a ship and I am the rudder. He will unleash my army and its warfare on more than fifty thousand people who come to the gathering, and that will in turn affect hundreds of thousands more across the world. It is not possible at this point for my legions and me to be stopped." Zennon bowed lower.
"Yet I sense it in you. You want something from me."
"Yes, my Master, you are right. I request more power and more resources to build an impenetrable shield against the enemy."
"Against who?"
"Tristan Barrow and those under his command."
For the first time in centuries, the hint of a smile appeared on the Master's cratered face. "Is it possible your old friend has you worried? This surprises me."
"No, my Mas—"
"Scared he's going to come to the rescue like last time, eh?" Caustin pulled his ragged fingernails across the table. "And this time take you out? Admit it. You're terrified."
Zennon pressed his thumb hard into his sword blade. Calm. The moment was almost upon him. He felt it. "I am not frightened of Tristan Barrow. I long to meet him in battle with such intensity that the tang of blood from his soon-to-be-slaughtered body is already on my lips. But there is a far greater purpose here than—"
"Wah, wah, wah. You looooong to meet him in battle." Caustin laughed. "You sound like a freak the way you talk, Zennon. Just admit it. You're petrified of him. You're—"
The Master lifted a finger to silence Caustin and leaned back. "Why do you feel you need this?"
"Because those who are overconfident in their abilities and positions of power are often undermined by that arrogance." Zennon resisted the urge to look at Caustin.
"It would require a considerable amount of resources to hold back the angel and those with him."
"Enough strength was provided to hold back Michael for twenty-one days in centuries past. I don't require anywhere near that kind of force. I only need three hours."
"A well-spoken answer. You will have what you need."
"Thank you, my lord."
"Is there anything else?"
"I have no desire to overstep my position, Master, but I do have a final request."
The Master smiled again at Zennon, glanced at Caustin, then back to Zennon and nodded.
Zennon's first stroke sliced off Caustin's left arm. His second tore off half his rival's leg. Caustin's knife bit into Zennon's upper left arm, but he barely noticed it because he was busy severing Caustin's head from his body.
"Talk to me." Tristan stalked the thick, green mountain ridgeline in long strides as Jotham and Orson half jogged to keep up with him. "Something feels very wrong. I've been blocked from getting any kind of read on Zennon for the past three days."
"We as well." Jotham almost growled his answer.
"This is not good." Tristan spun to look at his second in command. This had never happened before. Zennon was skilled. Formidable. Cunning. An enemy to be taken very seriously. And Tristan and his team always had. But this sudden cloud of silence meant they had to take Zennon more seriously than ever before.
"Tell me of the Warriors Riding."
"Marcus Amber is strong," Jotham said. "As are Dana and Miyo."
"How bad are Reece and Brandon?"
"Not good. Both."
"And Simon?"
"The Warrior's journey inside his soul was a start."
"But he has far to go."
Jotham nodded.
Tristan turned and strode up the mountain. This was disconcerting. He needed to take time to go see Dana and Miyo. Speak to them. Offer them hope. They would need all the faith and courage they possessed, plus a great deal more.
FORTY-SIX
"YOU HAVEN'T HEARD ANYTHING FROM DANA OR MIYO?" Kat slid her plate to the side of their kitchen table and leaned forward on her elbows toward Marcus.
"Nothing." Marcus swirled his plate still half full of spaghetti. His stomach was far from amenable to food at the moment. It hadn't been even slightly receptive since returning from Well Spring.
"You've called—"
"Called, e-mailed, stopped by Dana's house. Nothing. They disappeared from Well Spring and maybe from this realm as well without any explanation of where they've gone or why they went there."
Kat grabbed his hand and stopped him from swirling the noodles around his fork. "It's only been a week."
"Only? With what's going on with Reece and Brandon, that is seven days too many."
"I still don't understand—"
"The Temple and the Song are out of equilibrium. Imbalanced. It's all discombobulated. Every last nanobyte. They're both fixated on this gathering. It's all they talk about. Every moment is dedicated to developing the program, getting sponsors, negotiating the contract with Safeco Field, talking to lighting people, sound people, film crews, people who will help stream the event around the globe. They keep saying they want to bring freedom to the masses."
Marcus slammed his fist down on the table harder than he intended. "I can't put my finger on it, but there's something wrong with this idea of taking the Warriors big. There's something wrong with Reece and Brandon, and there's something wrong with the fact I am now the only member of Warriors Riding who seems to be thinking straight."
"Then it seems the only option is to—"
Three sharp raps on the front door stopped Kat from finishing her sentence.
She raised her eyebrows. "You want to get that?"
Marcus answered by rising from the table and marching toward the door. He swung it open and blinked twice. "Dana? Miyo?"
"As you might recall, we've met before." Miyo motioned past him. "Can we come in?"
"Yes. Of course." Marcus stood aside and they walked by him into the entryway.
A few minutes later, Dana, Miyo, Kat, and he were settled on the back deck in a tight circle of chairs.
"So you're here to enlighten us as to what you feel is transpiring in the heavens and on earth?"
"Precisely," Miyo said. "But it might be easier if you simply ask your questions, and we'll try to answer them as succinctly as possible."
"Why haven't you been in touch?"
"Dana and I needed concentrated time of uninterrupted solitude to hear from the Spirit on what we're supposed to do next."
"Does that include me?"
"It does now." Miyo scooted her chair closer.
"Why now and not earlier?"
"We had to be one hundred percent certain you hadn't taken on the warfare Simon was carrying."
"Simon? Warfare?" Marcus fiddled with his glasses. "I don't understand."
"You're about to." Miyo raised her palms and stared at Kat and him for a good five seconds. "Simon infected Brandon and Reece."
"Infected them. What do you mean?" But as he thought about it, Marcus knew exactly what she meant. It was the mist he'd felt the first night when he and Simon stood outside the main cabin.
"In simplistic terms, the warfare and demonic oppression Simon is carrying has been transferred to the Temple and the Song. We trusted Simon, we allowed him to get close to us because of what he did for you, and we let our guard down. It's like a cold or a computer virus. We didn't have our defenses up. We weren't cautious enough, and his warfare shifted onto us."
Marcus gave a tiny shake of his head and glanced at Kat. "I can't believe this. Simon would never—"
"It's not his fault. I doubt he has any idea what he was carrying."
Kat frowned. "What has it done to Reece and Brandon?"
"We believe it's stolen their identities."
"Stolen?"
"Masked them. Clouded them. They took the bait and they're not living out their true selves. They're living out of the flesh."
"How do you know Reece and Brandon are . . . ?" Marcus didn't need to finish his thought. Miyo's raised eyebrows confirmed what he knew to be true. It explained everything. Why Reece was now obsessed with growing Warriors Riding into a monolith. Why Brandon had become fixated on relaunching his singing career and becoming a star once again.
"Explain why I wasn't . . . to use your term, _infected_ at Well Spring."
"To continue the analogy, your immune system is extremely strong right now." Dana offered a gentle smile as she looked between Kat and him. "You know your identity. What you went through recently alone and with Kat has made your spiritual defenses strong. The demonic needs a crack to enter through. It needs permission. An agreement. Some dark longing inside that will entice a person to embrace the lie the enemy is offering."
"Such as?"
Dana held out her hand and counted on her fingers. "Bitterness. Unforgiveness. Entitlement. The need for adoration. The need for control. Fear. A hundred different things. And the enemy always offers a compelling solution."
"And what is the result if the warfare is let in?"
"The same effect it had on Simon for so many years."
"As you just said, the loss of identity." Marcus blew out a low breath.
"Yes. The magician forgot who he was, as has Reece, as has Brandon."
"Reece has slipped back into the businessman who created a photography empire. In control of everything and gaining his identity from how large he could grow it." Marcus laced and unlaced his fingers.
Dana nodded.
"And Brandon has become the musician once again acquiring all his self-worth from the adoration of others."
"Precisely."
Marcus adjusted his glasses again. "Neither of you were affected."
Dana glanced at Miyo. "I was. But the newest member of Warriors Riding rescued me."
"Rescued how?"
"She took me into a spiritual realm, subdued me, and prayed the warfare off of me. Fought it off. Pulled it from my soul piece by piece." Dana bowed her head. "My sin was subtle but potent. I believed I was only worth loving if I was perfect. Achieved great things. Led well. Exceeded expectations. On top of that, I vowed to never give my heart to Brandon ever again. A vow can be a dangerous thing."
"Pride," Miyo whispered.
"Your sin?" Kat asked.
Miyo nodded. "I have a friend who owns a home on the Oregon coast who says acquiring great wealth or renowned abilities at an early age is often a detriment to one's soul, and I agree. Pride has been a struggle for me. I was strong enough to resist the attack. But just barely. I knew the warfare on Dana was the weakest of the three, so she was the one I chose to rescue. If I'd gone after Brandon or Reece, I likely would not have succeeded. The warfare is growing stronger in them. It is not wise for me to be around them for any length of time till this is over."
Doug's granddaughter smacked the armrests of her chair. "We have to fight this. Stop the gathering from happening or be there to stop the warfare from spreading."
Kat frowned. "How will it spread? I'm not sure I understand."
Marcus took his wife's hands. "We opened ourselves to Simon, let our guard down because we trust him. Fifty thousand people will be in the stands and even more across the world, trusting Reece and Brandon. They will open themselves to what they have to say. And if there are any cracks in their souls, if they are in a state of weakness . . . if they are open in any way to the sweet lie of the enemy, the oppression will invade them as well."
Kat's face went white as she realized the scope of damage the gathering could inflict on hundreds of thousands of believers.
Miyo clapped her hands. "Now it is time to make our plans. Any thoughts, Professor?"
"Two." Marcus opened his notebook and pawed toward the back few pages. "As I've been praying over the past three days, the following things have become abundantly clear: First, I didn't know why, but I've felt the need to develop a small team of allies who would pray for whatever was going on in the Warriors. Now I know what it is. They must pray for us from this point on up through the night of the event. Second, I have to make sure Simon gets to Safeco Field the night of Reece's gathering."
"I'm not thinking having Simon there is going to help our side of the equation."
"Trust me, Miyo. It is critical."
"Can you explain why?" Dana glanced between Marcus and Kat.
Marcus looked at her over the top of his glasses. "The short answer is Doug's letter told me I needed to, and as I mentioned a moment ago, I feel like the Spirit has confirmed that."
"And the long answer?"
"There isn't one." The idea of Simon not being there gave Marcus an image of the Pacific Ocean going dry. "There is no doubt in my mind. Simon must be there."
After twenty more minutes of discussion, Dana and Miyo stood to leave. They had decided Marcus would continue to meet with Brandon and Reece regarding the gathering, and Marcus said he would attempt to explain the warfare that was on them. The women said it was a waste of time, but he had insisted.
As Kat and he walked them to the front door, Miyo reached into her tote bag and handed him a book wrapped in a light brown cloth.
"What is this?"
"Open it."
It was a leather-bound notebook. Marcus ran his fingers over the worn cover. "Is this—?"
"Yes. Reece's journal. I was compelled to grab it the morning we left Well Spring. Who knows, maybe this is why. Maybe you'll find something inspirational in it to tell your prayer team."
"When do we meet next?" Marcus said.
"I think until the gathering we need to meet every other day. We're only seven weeks out. Thoughts?"
"Agreed. And be praying for me. I'm meeting with Reece and Brandon tomorrow."
"You won't convince them."
"I have to try."
FORTY-SEVEN
MARCUS GRITTED HIS TEETH IN UTTER FRUSTRATION. Dana and Miyo were right. This was pointless.
"Let me repeat, implementing the gathering is not the right decision for the Warriors. Did you hear me? You've both been infected by Simon. Don't you comprehend what I've told you? The decisions you're making are a result of warfare and demonic oppression you've let in because of your sin. Don't you see? You took the bait. You have forgotten who you are!"
Marcus spoke to Reece and Brandon as the three of them sat on the back deck of Reece's wooded home northeast of Seattle, but his words would have made more of an impact on two marble statues. They'd been arguing for twenty-five minutes, and not a shred of progress had been made.
"Enough, Professor." Reece stomped his boot on his dark stained deck. "Wake up. I don't need the enemy playing with your head like he's done with Dana and Miyo. The Spirit has told us to do this, so we're doing it. I know who I am."
"You've lost your spiritual sight, haven't you?" Marcus jabbed a finger at Reece. "It's gone cloudy or vanished altogether. Why do you think that has hap—?"
"Be quiet. It's an attack of the enemy. Nothing more."
Marcus spun toward Brandon. "You have to fight this, Song. You're caught. Deceived. Think about what you're feeling! You want to be the rock star again. Revive your career. But that's not the true you. You are a leader of _worship_ , Brandon, to point to the One. Not to yourself."
"You don't understand, Marcus. This is my path. My destiny."
Reece jumped in. "Brandon knows what the Spirit has spoken to him of his restoration. It was confirmed by Doug. There is no doubt. We have continued to pray for Dana and Miyo, but their silence confirms they are still mired in deception. We have tried multiple times to reach them and they have not responded. At this point I'm assuming they won't. We haven't given up on them being there, but it's clear the enemy has them in a stranglehold at the moment.
"Back to you, Marcus. The gathering is happening in less than seven weeks and you need to be sharp. You're going to make sure Carson is pumping this thing for all he's worth, especially during the last three weeks, correct?"
Marcus lied and nodded. He'd spoken to the talk-show host after speaking with Dana and Miyo and had explained why all promotional materials and ads for the gathering had to be pulled.
"Speaking of the other members of the Warriors, do you know where Miyo and Dana are?" Brandon leaned forward and stared at Marcus with intense eyes.
"Yes."
"Where?"
"As I've already said three times this evening, I intend to honor their request for that information to remain unknown."
"They need to be at the gathering."
"That is their choice."
"Are they coming?"
"I will not answer for them."
"Friends," Reece said, "we're not making progress at the moment, so let's stop while we are still being civil to each other. Is there anything else before we break?"
Marcus grabbed his satchel. "Yes, I want to read you something."
"From what?"
"From your journal."
Reece stiffened but didn't ask how Marcus had come to have possession of it. "Fine."
Marcus cleared his throat and read without looking up.
The most potent attack of the enemy will always come against our identity. He does not want us to know who we are. He does not want us to know our talent, our true heart's desire, our destiny, our path. For if we know these things and live out of them with passion, we become extremely dangerous to him. If we live in our true, free, Spirit-infused identity, he will do everything possible to thwart our realization of that knowledge.
Once we discover our glory, our gifting, our calling, the evil one will seek to cloud it like a dark fog, to taint it, spin it, twist it to such a degree that we forget who we are and become only a shadow of what the Lord has made us to be. He will lead us back into captivity, back into who we were before we stepped into the freedom and power of our true self.
He will tempt us to question who we are. To doubt what God has spoken of. It is the attack he used against the Son during his time of fasting in the desert. " _If_ you are the Son of God, tell these stones to become bread" . . . Then the devil took him to the holy city and had him stand on the highest point of the temple. " _If_ you are the Son of God," he said, "throw yourself down."
_If_ you are Reece Roth of the prophecy. _If_ you are loved unconditionally, irrevocably, by the great I Am. _If_ you are the mentor of Warriors Riding. _If_ you have the power and strength and courage to carry out your destiny.
Lies. Because there is no "if" in the kingdom of the One. Know who you are. Know who you are. You must know who you are, Reece!
Marcus shut the journal and glanced up. Neither Brandon nor Reece looked like they'd heard any of the words he'd just read. Both were back to being marble statues. Finally Reece spoke.
"Give me what is mine, Marcus." He held out his arm ramrod straight.
"Know who you are, Temple. What you have become is not the true Reece. You are not a man who must control his world. You are not a man who needs to fill his emptiness with a vast empire of success to prove his worth. You are not a man—"
"Hand me my journal now, Professor."
Marcus set Reece's journal on the coffee table between them and slid it to the center. He stood and walked out of the room without anyone saying another word.
FORTY-EIGHT
DURING THE NEXT SIX WEEKS—AS LATE AUGUST SLIPPED into September, then into the first days of October—Miyo stayed at Dana's home in Seattle. They trained together, prayed together, and tried to rest in the knowledge that God was God and he would prepare them for Reece and Brandon's gathering.
Dana worked most days at the station even though her mind was barely in it, and Miyo did business for her dad's publishing company as well as she could remotely. They also continued to meet every other day with Marcus and Kat.
At first the days moved slowly, but the final three passed by in what felt like seconds. Two nights before the gathering, Miyo appeared in the door frame of Dana's family room and smiled. "I want to take you to one more place."
"Now?"
Miyo nodded, shuffled over to the couch, and sat next to Dana.
"I thought we were going to rest up."
Her friend smiled. "Exactly."
A few minutes later they sat on the end of a small cape that jutted out into an almost wave-free, light-blue ocean. They didn't speak. Didn't move. Simply soaked up the peace that floated through the air like dandelion spores.
Dana glanced down two hundred or so feet below them to a trail that meandered back and forth from the water up the side of the cape to where they sat. Was that a man? She turned to Miyo. "I thought you said no other soul knew about this place."
"That's right."
"Then who is that?" Dana pointed to the man who jogged up the trail toward them.
"Don't be concerned. It's a friend."
"A friend of yours or mine?"
"Both."
"Who? I don't think I have any friends who travel these parts."
"You'll see." Miyo rose and brushed off her shorts.
The man seemed to cover the distance between them in giant strides, and while he was still a hundred yards away, Dana realized Miyo was right. It was a friend. And a warrior. A few seconds later the massive form of Tristan Barrow stood before them.
She smiled and pointed between Tristan and Miyo. "You know each other?"
"Yes, Dana. We know each other well." The angel fixed his gaze on Miyo. "How is she progressing?"
"Beyond my expectations." Miyo spoke in a low voice without emotion. "She is ready."
"Good. She needs to be."
"And you?"
"I'm fine." The angel spoke the words with firmness, but there was also hesitation in his tone.
"You are fighting well, Miyo." Tristan rubbed his blond hair and glanced at Dana, then back to Miyo. "You set a critical captive free at significant personal risk."
"Thank you." Miyo's tone didn't match the words.
"You're angry with me." The angel cocked his head.
"Why won't you help us?"
"Help you?"
"Fight this war for us. Come in and take out Zennon once and for all. Take down—"
"You need this explained to you?" Tristan frowned.
"Yes."
"It is not the way the Spirit works. The Spirit gave Ezekiel the power to speak life into dry bones, but God was not the one who spoke. God gave Moses the power to split the sea, but the Lord was not the one who raised his arms. In more circumstances than you know, we war for you. But in this battle we are called to war _with_ you. It is with great rarity that I understand the Spirit's ways, but it is with great frequency that I trust him. I suggest you do the same."
Miyo frowned. "But you will be there to war with us."
"We hope to be, yes." Tristan turned to go.
"Hope to be?"
"Yes, hope." Frustration passed over Tristan's face. "Zennon has been given power far above his normal authority."
"What does that mean?"
Tristan didn't answer for more than twenty seconds. "That our every intent is to be there to fight with you."
"That's not filling me with a great deal of comfort," Miyo said, concern etched into her face.
Tristan gazed at the darkening horizon. "So much responsibility has been placed in the hands of humans. It has been this way throughout the ages. The Creator gives you great respect with his invitation to play a significant role in the larger story. The accomplishment of his will could not happen without you."
"You have to explain that to us."
"It means I suspect an opportunity to fight in the coming battle is not up to us. It is up to you and the other Warriors. The key to unlock that door is in your hands."
FORTY-NINE
_B E READY. THIS WILL BE THE MOST SEVERE BATTLE YOU HAVE ever faced._
The words from the Spirit stopped Dana cold as she pulled into the parking lot of Safeco Field on Sunday evening. Since joining the others of the prophecy, she'd often debated if she heard God's voice when the Spirit spoke, or if she was making words up in her mind. Not this time. She held no doubt these words were from the Spirit. They shook her to the core. Because she'd felt this night was coming from the moment she started training with Miyo.
It shouldn't be a surprise. Of course there was a purpose to what she had been learning. Armor of light. Greater skill with a sword. Calling down the fire of heaven. Creating a shielded dome of light. And she knew facing Zennon again was part of Miyo's prophecy, and now Dana was part of that prophecy. But somehow she'd convinced herself it would be in a distant future when she would use her new skills. Now the future had landed with a crash into the present, and she felt far from ready.
Dana gripped her steering wheel as if it could keep her from falling into the chasm that seemed to have opened up beneath her. "Will I die?"
_You will have to fight with everything you are, everything you have been, and everything you ever will be. There is no one else._
She asked again, "Will I die?"
Again no answer.
"Lord, speak to me."
_I am with you, to the end of this age and beyond. With me, death no longer remains._
Dana stepped from her car and stared at the people already meandering toward Safeco Field. She wanted to stand on the roof of her car and scream at them, that they were walking into a trap, into an arena where the lions were prowling and ready to strike. That it was a stadium of war.
She shut her door and stared at her car. Funny. She didn't lock it, as if it didn't matter because she probably wouldn't be seeing it again. No, not true. God was in this. With her. With Miyo. With Marcus. Dana tried to convince herself the victory was theirs but had no success. Miyo, the professor, and her against the world. More than the world. Against Reece and Brandon. And if that wasn't plenty of kindling and logs for the bonfire, they were about to face Zennon and whatever forces he'd brought with him as well.
_You are the Leader._
The Spirit didn't speak the words to comfort her but to state the reality of the prophecy that had become her life for the past year and a half. Maybe had always been her life. Maybe her entire life had led to this moment. Predestination? She didn't know. Dwelling on it wouldn't change anything. Did she have a choice to get back in her car and pretend the war about to break loose didn't exist?
A part of her wanted to. A part of her could easily pretend none of the past eighteen months had happened, that it was all in her mind, that both prophecies were figments of a man's creative imagination. That everything that had happened to her and Warriors Riding was a series of dreams and hallucinations. If she was offered the choice Simon had been given, would she have chosen to stay in this war-ravaged world?
Dana shook the thoughts from her mind. She couldn't start down that road because she would never get off. She needed to find Miyo. Get some time together before the gathering started. Surround themselves with the thickest armor of light possible and pray like they'd never prayed before.
_Your time is nearly here, friend._
The voice in his mind was so soft, Simon wasn't sure he'd heard it. He rose from his couch, slipped on a light Windbreaker, and paced across his tiny apartment, his gaze fixed on the worn tan carpet. The smell of his earlier meal of chicken still hung in the air, and Bing Crosby filled the room with the sound of "Just One More Chance." The image of a battle flashed into his mind so fast he couldn't make out any of the details.
_Yes, it is almost here, Simon._
The voice of the Spirit still speaking to him all these years later.
"Lord."
A knock at the door snapped Simon's head up. Had to be the professor. Simon glanced at the tiny cuckoo clock on the wall. Time to go. Join Marcus and Dana and Miyo at the stadium. The professor had tracked him down, convinced him the warfare was not his fault, somehow convinced Simon he had to come to the gathering. He shook his head. It seemed right—he trusted Marcus—but the shame and guilt he carried were still so heavy.
He didn't want to be there, might be another snare, but Marcus had insisted. They had argued with great intensity, but in the end Simon had agreed.
_Go._ The peace of the Spirit wrapped itself around him and he walked to the door.
After they got into Marcus's car and headed for Safeco Field, Simon rolled his silver coin around his fingers and turned toward his friend. "A battle is coming tonight, Professor."
"Yes. We will fight." Marcus nodded. "And I believe there will be something for you tonight at the gathering, Simon. Specifically for you."
Simon's mind spun. Pictures of lightning bolts raining down on a barren field were mixed with images of thirty-foot waves smashing into a blood-red brick wall that shuddered and moaned. Then scenes of him on the mountain ledge with Zennon once again and slipping out of this reality into the ones he'd been trapped in for decades.
"I can't do this. I shouldn't be there."
"Stay strong. 'We are more than conquerors.' " Marcus reached over and took Simon's forearm. "He is more than with us. He is inside us. You know this. You wrote it down in detail. Remember who you are and resist the lies."
"It's not easy to throw off a fifty-one year enchantment in eight weeks."
"What do you want, Simon?"
"I want to be free."
"So be it, and may it be so."
Dana and Miyo met at the back of the stadium at six o'clock.
"Why couldn't we come here together?" Dana asked.
"I already told you. I needed time alone."
"You could have been alone at my house."
Miyo stared at her. "Do you really want to have this debate right now?"
They stood 150 yards from a security entrance and stared at two guards who lounged near the door they had hoped to enter the stadium through.
Miyo glanced at Dana, then back to the guards. "Lord, make seeing eyes blind."
"Here we go again," Dana muttered.
Miyo smiled. "Reece told me you studied Luke together and that the Spirit made seeing eyes blind for Marcus in that church when he confronted the demon ushers."
"You think—"
"The Spirit is going to do the same for us now?" Miyo pursed her lips. "I'm counting on it. Let's go."
Ten minutes later they were through the door and huddled in a supply room deep in the stadium.
"We'll stay here till show time," Miyo said. "Once it starts we'll work our way backstage and follow the Spirit's lead."
"Like I've said for weeks now, that's quite a plan."
"Yes, it is. And is the only one that has the minutest chance of working."
FIFTY
AT 7:35, DANA WATCHED REECE STRIDE TO THE FRONT OF the stage at Safeco Field to deafening applause. The stage lights bounced off the sunglasses hiding his eyes, but nothing hid his megawatt smile. He waited till the roars of the crowd subsided, then stepped closer to the microphone.
"Welcome, Seattle! Welcome to the rest of you around the world! Welcome to _freedom_!"
The crowd exploded again.
"I wish you could see what I see tonight. I see revolution. Great change. Great power. Great battles that will be waged and won, not only tonight, but for months and years and decades to come! Warriors Riding has played small for too long. _You_ have played small for too long! It's time to make a plan. Make things happen. Set the path and the vision for our lives and take control!"
Reece spoke on for another twenty minutes about how every man and woman in the stadium and every man and woman watching and listening around the globe would be taking the message of freedom, restoration, and healing to every corner of their world. Most of it sounded right, but mixed in were frequent references to growth, success, achievement, and structure. And money. Reece had never spoken of money, but now it seemed to be one of the centerpieces of his message. He couldn't speak for more than a few minutes without the crowd shouting its approval. Finally he stopped till the stadium grew silent.
Reece rubbed his hands together, then balled them into fists and held them in front of his chest. "We are all warriors together in this battle. We are all brothers and sisters together in the kingdom. So will you now join me in a symbolic gesture of unity by taking the hand of the person next to you and joining me in surrendering the remainder of this evening to our God. Open yourself to the Spirit's message. Open yourself to freedom. Open yourself to what he wants to do inside you."
As Reece prayed Miyo's face paled and she whispered to Dana, "This is bad. I should have anticipated this."
"Why?" But an instant later Dana knew why. Reece was directly asking the people to open themselves up. Exactly what they'd done with Simon back at Well Spring. "There's nothing we can do?"
"We will do everything we can. Take heart. And look." Miyo smiled and pointed toward the back of the stage across from them. Marcus and Simon stood less than fifteen yards away, almost hidden by the thick, black curtain that provided the backdrop for the stage. "We are not alone." Miyo tugged on Dana's arm. "The moment has come. I need to show you something else."
"What moment?"
"This won't be easy to see. But you have to in order to understand what we need to do next." Miyo prayed. "Open her eyes, Spirit of the Living God." She pointed out over the stadium. "Look along the rows. In among the seats. Up in the stands and all around the stadium." Miyo prayed again. "Allow Dana to see the enemy before us."
Dana gazed over the crowd and into the stands. At first she saw nothing. Then, as if a switch had been flipped, she saw a green mist swirling through the stands, and then thousands of dark figures moving along every aisle handing the crowd something. It looked like small crackers. Some refused the wafers, but the majority of the crowd took them and ate.
"Reece's words have opened the people to this. They believe in him so much they'll embrace almost anything he says. And right now he's speaking truth laced with lies, and the people are swallowing the lies both figuratively and literally."
Dana's body numbed. "Just as I must have swallowed them back at Well Spring."
Miyo nodded. "They're letting the warfare in. And soon they'll forget who they are."
As she watched, whole sections were turned to granite. She blinked, and the same people who were stones in the spirit, moved and nodded and shouted their approval with their physical bodies.
An invisible fist grabbed Dana's chest and her breaths grew short. "It's just like Marcus saw that one day in church where the demons gave the crowd stones of duty and guilt."
"Yes, he told me about that."
"But this is far worse." Dana's hands trembled. "Can't anyone else see this? We can't be the only ones who are seeing this."
"I don't know. I believe some in the crowd can and understand what is truly going on. May the Spirit urge them to pray."
"We have to stop it."
_Stop it?_
The voice echoed in Dana's head, then turned to laughter, then spoke again.
_You can't stop this, dear Dana._
A figure at the back of the stadium at least eight feet tall strolled down the middle aisle toward them. Long dark hair flowed over his thickly muscled shoulders. He wore no shirt and his skin was bronzed and rippled with muscles. His face was flawless and strikingly handsome. Several demons with drawn swords joined him as he marched down the aisle. Just before he reached the front of the stage, he stopped and pulled a gold coin out of his pocket. He spun it around his fingers, then flicked it high into the air. It landed on the stage not more than twenty feet from Dana and Miyo.
"Hello, Dana," he called and gave a mock bow. "And Miyo as well."
Dana's heart hammered. Zennon. His evil gaze raked her body.
He waved one finger back and forth like a teacher scolding a grade-schooler. "You need to back off, Miyo. The consequences will be most regrettable if you don't." He turned his liquid-black eyes on Dana.
"Taking Reece's eyes and Brandon's voice was child's play. This is real. You need to leave now, Dana. I've always liked you and given you more space than most humans. But you've exhausted my compassion. This is my meeting, and if you do anything from this moment on to get in the way, I will end your life immediately."
Zennon walked up the steps onto the stage. The seven or eight demons with him filled in behind him. "This stadium is mine."
Miyo didn't budge. "All the earth is the Lord's."
"I was given an invitation to come, so don't make this difficult. As I said, I don't desire to destroy either of you. But if you force me to, I will."
He motioned out over the crowd. "You can't stop this. It's already been done. Simon has done his work and Reece is doing his right now. The warfare has spread. Its infection is complete and the people have embraced it. And I do not think the two of you would fare well against my most select warriors." He motioned behind him. "These are not like the ones you've faced before, Dana. These are the elite who have been under my command for millennia.
"And in case you decide to fight anyway, be aware there will be no safety net to save you this time. Tristan and his friends will not ride in on a glorious wave to rescue you. They have been, shall we say, contained."
It didn't make sense. Why weren't Zennon and his soldiers attacking them? The demon had no compassion. Why the long, drawn-out speech? Then two things hit her. Zennon's greatest weapon was deception. Fear. Illusion, Simon would call it. The ability to make things seem far worse than they were. Second, Marcus wasn't here just to watch. He and the team he'd rallied were undoubtedly praying hard and interceding for them in a way that was holding Zennon back. They couldn't break through the prayer covering. At least not yet.
At the same time, why should he attack? There was no reason. Zennon was getting exactly what he wanted. Dana turned to Miyo. The look in her friend's eyes scared her.
FIFTY-ONE
"IT'S TIME." MIYO EXTENDED HER HAND AND PULLED Dana back, away from Zennon until they stood at the far corner of the stage—directly opposite Zennon and his demons. Dana still felt exposed. Naked. She couldn't help staring at Zennon's elite warriors, their swords drawn and evil pulsating from their eyes. Palpable fear radiated off them and seemed to sweep over her in waves.
"Time?"
"To go to war. Our moment has come."
"Against them?"
Miyo nodded.
Was she serious? Did Miyo mean the two of them were about to go up against Zennon's ninjas? Didn't she hear what the demon had just said? She stared at Miyo. Her friend's face was stone but her eyes blazed with light and fire.
"Yes. Against them. I can't find anyone else to attack. Can you? And we're not here to knit."
"Just the two of us."
" 'He trains my hands for battle; my arms can bend a bow of bronze. You give me your shield of victory, and your right hand sustains me; you stoop down to make me great.' Let us be great in this moment, Dana Raine."
"We can't hope to—"
"We are not alone." Utter resolve filled Miyo's eyes. " 'You will tread down the wicked, they will be ashes under the soles of your feet.' "
Dana's heart thundered in her chest and the fear pouring off the demons wrapped itself around her soul. "I can't do that. I'm not ready. Reece, Brandon, and I barely survived the last battle with Zennon. And this is not his throwaway army. I would be dead if not for Brandon. We all would have perished if Tristan, Jotham, and Orson hadn't shown up. It's not possible for me to—"
"You are not the same woman you were then. You are far stronger now, mightier than you can imagine." Miyo turned and took her by both hands. "It is time to lead like you've never done before. You must find that strength inside you don't believe you have. Not because you'll be loved for it, but because it is who you are. Step into your glory."
Adrenaline coursed through Dana's body and her legs bounced. "I don't know how, Miyo! Yes, we could attack. But my sword will do nothing against that army."
"Did I say swords?"
"Then what? You want me to create a light-shield that will be strong enough to withstand the strength of Zennon and his demons? I'm not ready for—"
"You're letting the enemy in right now. Letting Zennon play with your mind. You're believing the lies." Miyo's face was hard as iron.
"I'm believing in reality."
" 'In the presence of the God in whom he believed, who gives life to the dead and calls into existence the things that do not exist.' " Miyo squeezed her hands tight. "And _calls into existence things that do not exist!"_
Miyo released Dana's sweat-soaked hands, took three steps toward the demons, then turned to face her and stretched out her hand. Miyo's face of stone hadn't softened, but it was now also infused with a sense of triumph and great faith.
"Believe with me, friend. Believe that you sit with Christ in the heavens. That you have been given all power and all authority of Jesus because you have taken your rightful place as a child of the Creator of the universe and the heavens and the earth. Come. Join me in this battle."
Dana forced her shaking legs to move. One step, then two, then three until she stood next to Miyo.
"The darkness cannot overcome the light. Let us speak of the light." Miyo raised her right hand toward Zennon and spoke just above a whisper. "I bring the Kingdom against the powers of evil before us. A wall of light. A wall of power between us and them. I speak it into existence by the power of the crucifixion, the power of the resurrection, and the power of the ascension of the Messiah."
As Miyo spoke, the air between them and Zennon and his army shimmered and thickened like a giant pane of glass. It rose two stories above them, then spread out to their right and left.
Suddenly words poured from Dana's mouth that were hers, but not hers. "More power, Lord. Thicker. Stronger. Able to hold back—able to contain—the forces of evil."
The wall of light grew higher. It was now three-stories tall and fifty-yards wide. The sides bent down and formed a dome of light that descended on Zennon and his demons. In less than twenty seconds they were surrounded.
Zennon shook his head at them and grinned. He lifted his hand and waved it once across his body as if the edge of his hand was a blade. Instantly the dome shattered, fell to the stage, and vanished. "You think you can do anything against me? Don't you realize by now I used every minor victory you won to bring this moment to fruition? Do you not understand the culmination of everything you think you've done for your ludicrous kingdom of God has produced this night where I will infect millions of souls with my truth?"
Zennon threw his head back and a thick, guttural laugh spewed from his mouth. "No, dear Dana. There has been no lasting victory inflicted on me by your pitiful band. All that has come out of your feeble attempts to fight me is destruction. The loss of Reece's eyes. The loss of Brandon's voice. Doug Lundeen's death. And now the spread of the virus."
Shallow breaths puffed out of Dana's mouth. Was that true? Had they achieved anything? Had they?
Miyo's whisper sounded beside Dana. "Do not agree. He's speaking nothing but lies. If you agree, he'll use your agreement against you and throw a new lie on top of the old one while you struggle to fight through the first one."
Zennon spoke again. "Now, let's watch together as Brandon Scott puts the finishing touch on this evening."
Reece held his hands high to quiet the crowd and stepped closer to the microphone. "It's my privilege now to introduce you to a man many of you already know extremely well. He's sold over eighteen million albums and has created some of the most loved worship songs over the past ten years. Join me in welcoming back to the stage after an absence that has stretched out for far too long, Grammy Award–winning singer and songwriter, Brandon Scott!"
Miyo pulled Dana close. "Now the true battle begins. We must war for Brandon with all our strength. His moment is upon him."
FIFTY-TWO
BRANDON STRODE ACROSS THE STAGE MORE NERVOUS than he'd ever been in any concert. He glanced to his left at the giant screens broadcasting his image to the crowd in the stadium. Just like the old days. But broadcasting to hundreds of thousands of people around the rest of the world wasn't like the old days. And having no clue what kind of voice would come out of his throat when he opened his mouth to sing wasn't anything like the old days.
The spotlights that poured into his eyes seemed brighter than any he'd ever stood in front of. But this was his moment, and no amount of lights or nerves or anything else would stop him. The return of Brandon Scott. His rebirth. Once again he would rule the world of Christian music.
When he reached center stage, he stopped and held his hand up to the crowd and yelled into the microphone, "Welcome, Seattle, and everyone else watching around the world! I have a new song I'd like to sing for you."
His voice shouted back at him through the monitors. It sounded raspy, but if the crowd noticed or cared, it wasn't apparent. Their roar of approval was like a tsunami. Brandon pointed one finger over the stadium. "I love you!"
And they loved him back and it filled him and lit him up like the sun. Their thundering applause and shouts grew louder. He instinctually looked around for his band and laughed at himself for the mistake. Not tonight. There were no drums. No bass. No keyboards. Just his guitar, his shattered voice, and the glory God was about to launch him back into.
He bowed his head and the shouts of the crowd faded to a murmur and then into silence. And then there was no crowd. No giant image of himself on the stadium screen. No millions watching him across the globe. Only the Trinity and him. An audience of One. Waves of peace washed over him, each more powerful than the last until he stood in utter trust and faith in the One who had brought him to this place.
He would sing the song, and it would bring him the healing he longed for more than any other gift the Spirit could give him. He would be restored in front of millions, and seeing his restoration would infuse them with the faith that would fuel their own restoration and healing.
He was born for this moment. Destined for it from before time began by the grace and power of the Father. Brandon opened his mouth to sing for himself the healing the Spirit had promised, in utter faith that his voice would be the same one that had poured forth when he had sung the songs of heaven.
_It is your choice._
Heat filled him. _What?_
_The choice is yours._
_What choice, Lord?_
_Who you will sing the song for._
Brandon frowned. What was the Spirit saying? _The song is for me. For my healing!_
_No. This song is meant for another._
_What? You said—_
_I did not. That is what you chose to believe._
A quiet rage grew inside Brandon and he stepped back from the mic. No. This was his moment. Doug had told him in the letter. The Spirit had confirmed it. Reece had confirmed it!
_Sing for the magician._
_He's here?_
_Yes._
Brandon turned and somehow spotted Simon standing next to Marcus behind the curtains to the left. This couldn't be happening. It had to be the enemy trying to steal his moment of glory. His moment of becoming whole. To wrest from him all he was meant to be once again. He would not give in.
_No, Lord. It's a lie. I'm to sing for myself, not Simon._
The Spirit was silent in stark contrast to the crowd who started to murmur. Reece opened his palms in question of what Brandon was waiting for.
"Why isn't he singing?" Dana said.
Miyo leaned in until their cheeks almost touched. "I don't know."
"But you have a theory."
"I have a feeling he's trying to decide whether to sing the song for himself or not." Miyo hesitated before she spoke again. "I believe if Brandon sings the song for himself, as his intent has been, it will bring him a kind of healing—his voice will be restored—but it will not set him free. It will release a spirit of self-glory over this arena, and we have plenty to deal with already."
"A spirit of what?" Dana turned to face Miyo.
"He who seeks to save his life will lose it. There is a part in all of us that wants to preserve what we have. We hold on to it in a desperate grip to maintain control of our lives. And we clutch for those things we've lost like a drowning man. But it's an illusion. We must let our lives go if we want to live."
Miyo took a slow breath. "If Brandon sings the song to save himself, there will be a subtle but great temptation for many others watching the gathering to do the same. He will celebrate his healing and it will provide yet another opening for the enemy to penetrate, where his thoughts of deception will resonate in the minds of the people and they will embrace the lie."
Dana's voice dropped to a whisper. "And a life focused on self takes us back to the garden."
"Yes, where we attempt to be gods, the message of true freedom is distorted, and we forget who we are."
"He has to die to self." Dana said it out loud but it was for her ears only.
Dana's words were what Miyo had just insinuated, but her friend didn't know the depth of what she'd spoken because in that moment, Dana realized why she couldn't open her heart to Brandon again. She didn't entirely trust him. And she didn't entirely trust him because life had always been about Brandon. His albums, his music, his fans, his label, his concerts—she'd never known if he could love her unselfishly. If he could put himself away and love her with his whole heart the way she had loved him. And suddenly the evening became about everything in her life, outside of her and inside, the epic and the minute, and the very, very personal.
_Sing for the magician._
Brandon clenched his jaw. _This is my moment. My restoration. I won't let the enemy steal it from me._
_Why are you trying to hold on to something that no longer remains?_
_What?_
_I took it away so you might have life._
_I don't understand, Lord. You mean my career?_
_As much as you've sacrificed, as much as you've given, there is a partof you that places your idol higher than me. And as long as you hold on to it, it will be your master._
Brandon knew the idol. His voice.
_I've never loved you for your voice, or your songs, or what you've brought millions of people. I love you for you, Brandon. Now you have a choice to love me for me. But it is your decision._
Brandon stumbled back another step as all became clear. His worth was not about what he did, what others said, the albums, the songs he could point to being sung in churches across the country, the sacrifice he'd made for Dana, or even what he'd done for Sandra and Garen. His worth came from the fact God had offered his own Son so Brandon could become a son of heaven as well; that God's Son would be shredded on the most horrific killing machine ever conceived by man so Brandon could have life.
_Yes, Lord, I love you for you. Nothing else matters. I will let it go._
Deep called to deep, and a freedom Brandon had never known before, buried him. He stepped back to the microphone, took one more glance at Simon, and began to sing. He expected an overwhelming joy to spread through him, but it didn't happen. The instant he sang, his body felt like it had been wrapped in thick foam rubber. And the rubber started to squeeze.
FIFTY-THREE
AS BRANDON BEGAN THE SECOND VERSE, A FLASH OF COLORS streaked across Reece's spiritual vision. Strange. He hadn't seen in colors since Simon came to Well Spring. An instant later the faint images in front of him were once again only black and white. But the momentary return of his spiritual sight to the way it used to be gave him hope. He hadn't expected there to be healing in Brandon's song for his sight or any other part of him, but if the Spirit wanted to give it to him, Recce's hands were wide open.
More hope came an instant later. For the first time since they'd started building toward this event, he saw outlines around the objects and bodies in front of him. In silver. Not in gold as he had grown used to. And the silver outlines were dim and sputtered as if there wasn't enough power inside his eyes to keep them fully visible. But the outlines were there. He could "see" again.
But something was wrong. Heat rose in Reece's chest. Not a physical heat, an emotional one. Of anger. Toward Brandon, because Reece shouldn't be standing here watching the Song alone. Doug should be beside him, savoring this moment with him. Reece's anger grew beyond reason, but why? He'd forgiven Brandon. It was over. But a part of him hadn't. A part still blamed the musician for the loss of Reece's closest friend.
_Enough._
The voice of the Spirit spoke in Reece's head like thunder.
"Lord?"
A moment later words from his journal that Marcus had read weeks earlier flashed into his mind:
The most potent attack of the enemy will always come against our identity . . . If we live in our true, free, Spirit-infused identity, he will do everything possible to thwart our realization of that knowledge . . . The evil one will seek to cloud it like a dark fog, to taint it, spin it, twist it to such a degree that we forget who we are and become only a shadow of what the Lord has made us to be. He will lead us back into captivity, back into who we were before we stepped into the freedom and power of our true self . . . Know who you are. Know who you are. You must know who you are, Reece!
Reece staggered back as if slugged in the stomach. "Lord . . ."
_Watch the Song._
Brandon's voice rang out strong, more captivating than Reece had ever heard it, and as the melody seeped into his head, a vision swept across his mind. He saw a lump of dough the size of a football that sat on a gray stone cutting board. A pair of tan hands kneaded the dough and as they did, another hand, slender and stark white, hovered over the bread and sprinkled a small handful of light-red powder on top of the dough. The other hands continued their work and the powder disappeared into the dough.
The scene shifted and the hands pulled a perfectly shaped golden loaf of bread out of an oven. But within seconds, thin dark lines, like tainted blood vessels, streaked over the surface of the bread. Then the loaf turned jet black with only hints underneath of the golden loaf it had just been.
"What are the blood vessels, Lord?"
_Not blood vessels. Roots._
Heat washed over Reece again. This time, from waves of remorse. "Roots of bitterness . . . which can defile many."
_Yes._
Conviction pressed in on him and Reece didn't have to ask the Spirit what the vision meant. It was obvious. "A little yeast spreads through the entire loaf. My yeast. The sliver of bitterness toward Brandon I allowed to remain. And the enemy used it to enchant me." Horror flooded him. What had he done?
The Spirit didn't confirm his words. He didn't need to. Reece stared at Brandon and whispered the words he so obviously needed to speak, and even more obviously, speak from his heart. "Forgive me for my bitterness toward you, Song. For blaming you. I was wrong."
Instantly Reece's spiritual sight returned in full force and color, and what he now saw made him stagger back a step. Demons were scattered throughout the stands, surrounding the people in the stadium. He turned. Behind him, ten yards away, stood Zennon, a grin spread across his face.
"Forgive me, Lord, for what I've done."
_You are forgiven._
"And give us strength and wisdom to fight this battle."
Peace soaked into him. He glanced around the stage and spotted the golden outlines of Miyo and Dana. Had they been there the whole time? He looked to his left and saw the outline of a figure so faint, he couldn't tell if it was human or demon, male or female. The outline was made of a gray light that dimmed and grew brighter and then dimmed again. But as he watched, the bright moments grew longer and the gray tinge to the light faded until there was only dazzling whiteness surrounding the figure. The white light lasted only a few seconds before it turned golden and grew from the width of string to the thickness of rope.
Now Reece could make out muted features. The figure was male. Average height and weight. Human. Hunched over slightly. As the brilliance of the light grew, the slouching man slowly stood straight, and as he did, he seemed to grow two inches taller. A moment later the golden light had grown so thick and brilliant that Reece knew exactly who it was: the magician. Simon Donelson. Reece was undoubtedly watching Simon's escape from dark corridors he'd traveled for so many ages.
Reece turned back to Brandon and saw images of gold and white-hot light swirling around him that shot out over the crowd like fireworks. But he also saw ink-black shapes advance toward the Song, and a moment later, Brandon staggered as if a massive weight had been dropped on his shoulders.
FIFTY-FOUR
"DANA! SNAP OUT OF IT."
She spun toward Miyo. Brandon's song had captured her so completely, everything else—Zennon, his demons, the crowd, Miyo, her own fears—had slipped into a well of insignificance. Nothing mattered except the song. It mesmerized her like nothing she'd ever heard. Brandon's voice was so clear, so pure, so strong it seemed to fill every molecule in existence. And the melody buried her in hope and triumph and healing and freedom.
"What's wrong?"
"Aren't you seeing this?" Miyo pointed at Zennon's demons and then at Brandon. "We must fight for him now. He has to finish the song before he's destroyed."
What was Miyo talking about? Yes, Brandon stood slightly stooped, but other than that he seemed calm and confident. The song continued to pour out of him as if it was effortless, and the tune continued to build in volume and power. His hands moved over his guitar as smoothly as a flowing river, and if the crowd's reaction was any indication of the impact the song was having, Brandon was breaking thousands of chains in the heavens and on earth, pushing back the warfare and demonic attack Zennon was trying to pour out over the crowd.
"Destroyed? What are you talking about? He's doing great. I don't get—"
"See with your spiritual eyes, Dana. Accept that world as more real than this one."
Something inside Dana snapped into place. Instantly the image of Brandon shifted. She blinked, trying to comprehend what she now saw. The difference wrenched her heart and she sucked in a stifled breath.
Brandon no longer stood still and confident. A thick, black cloud sat on his shoulders. His torso was contorted and his body shook from the impact of tiny flaming darts zinging at him from Zennon's demons on her right. Something still held them back from advancing. Marcus and his prayer team still? Yes. It had to be. Thank God.
But it didn't keep the darts from getting through. A thin layer of light covered Brandon's body, but it was like a patchwork with multiple openings that rendered the armor almost useless.
The darts drove themselves into his shoulders and legs and body. Where they struck they burnt small holes in his clothing and red welts appeared almost instantly. With each impact, he staggered and fought harder to keep standing.
At his feet, a thick green stalk circled around him and got closer with every second. Thin green vines grew out of it and crawled up his body. They wrapped themselves around his left arm and yanked it down in rapid jerks in an effort to pull his grip from the neck of his guitar. He didn't let go and didn't stop playing, but his voice sputtered and the words began to come out in bits and pieces.
_Open my eyes more, Lord._
A thin, translucent demon faded into view right behind Brandon. The demons weren't being held back. At least not this one. He stood behind Brandon with his hands around the musician's throat. Its jagged fingernails tore into Brandon's skin, and tiny threads of blood appeared and snaked their way down to his shoulders.
The song from Brandon's lips grew softer and his breathing more labored, but he continued to choke out the words. Dana glanced at the audience. Some had confused looks on their faces. Could they see part of what was happening? Others grimaced at her as if to ask what in the world she was doing flailing around on stage next to Brandon, but most acted like they couldn't see her and still heard the song being sung with power.
They were oblivious to what was going on in the spirit and maybe even in the physical. She doubted any of them could see the full extent of the enemy's onslaught. But a few, a remnant, stared at her with a mix of shock and fiery resolve. Somehow time slowed and her gaze was drawn to the lips of a woman and a man only ten yards from the stage who both mouthed the words _we will pray._
Still, Brandon sang on, although Dana didn't know how. The words were now garbled and a second later his hand dropped from his guitar and he reached for his throat. He pulled at it with his fingers and thumb in jerking movements. The demon laughed and squeezed tighter.
_He must finish the song, dear one._
Dana didn't consider what she would do. She simply jumped off the cliff and rushed toward Brandon, knowing the Spirit would give her wings before she hit the ground. Almost there, but when she was ten feet from him, two demons instantly appeared in front of her, grins on their faces, black swords in their hands. One waved his forefinger back and forth as a sickening voice came out of him. "Sorry, only one performance at a time. Please go back to your seat now."
The other demon laughed. The sound of it shot ice down Dana's back.
"Miyo!" Dana shouted over her shoulder and glanced at her friend, but Miyo didn't answer. For good reason. Doug's granddaughter was surrounded by demons. She spun faster than Dana had ever seen, and her blade flashed in the glare of the spotlights, blocking the swords of demon after demon. But there were too many.
More of Zennon's elite warriors had joined the battle, and it was clear even someone with Miyo's skill would not survive. Two of the demons leapt into the air while the others surrounding her slashed at her body. Dana was about to watch her friend perish.
But just before two demons took off Miyo's head, a sword out of nowhere was thrust into the fray and deflected the blades from Miyo's throat. Reece! He glanced at her only for an instant and turned back to the battle. But that instant was enough. His face had changed. She saw in his countenance that the power of the virus had been broken. Yes!
Dana spun back to the demons facing her. No time to see if Miyo and Reece could help. No time to hesitate. This was her battle. She called on the Spirit and her sword appeared in her hand. She swung it in a wide arc in front of her and let the momentum carry her into the roll Miyo had helped her perfect.
Before the demons could move, she was past them, on her feet again, and slicing her sword through their backs. They thudded to the stage and Dana spun toward Brandon. Her sword held high, she leaped at the demon that held Brandon's throat in a stranglehold.
Her next stroke was true and sliced a quarter of the way through the demon's torso. He released his hold on Brandon's throat and staggered back, his eyes now seething with rage and leveled on Dana. "You will die for that."
The demon leapt at Dana, his fingernails now razor-sharp blades streaking toward her heart. But before he could strike, Miyo's sword flashed down from her side and severed the demon's head from his body. The demon crumpled to the ground and began to fade from sight, but Dana had no time to finish watching him disappear. Brandon's face had turned stark white and the look of death filled his eyes. Still he sang.
"He's dying!" Dana spun toward Miyo, and as she did, her hope of victory shattered. A circle of demons closed in on them slowly, swords drawn, eyes full of dark fire.
"Where is Reece?"
"He'll be fine."
"What do you mean 'fine'?" Dana backed up one step at a time.
"No time to—"
"Tell me!"
"His right shoulder is cut open . . . left leg isn't doing so well. Marcus dragged him off. He'll be fine!"
Miyo stopped and spread her feet and shouted, "Now let's rock!" She unleashed a withering attack on the demons in front of her, then called back over her shoulder, "I'll hold them off but you have to shield him!"
"How?"
Dark balls of fire streaked toward them, and Miyo somehow extinguished them before they exploded on their bodies. "Can't explain!"
Dana understood. There was no time for instruction or coaching from Miyo. Again, Dana had to do this on her own. She had to be the Leader. Lead herself. Faith. Believe. Not her. Not her strength. Not her wisdom or power, but hers combined with the Spirit who lived inside her.
She raised her hands and cried out as loud as she could, "Shield him now, Lord. Your power. Your light. Your might rain down on him from above and rise up from below. Christ on his left and his right, above and below, in front and behind. Now." Then louder. _"Now!"_
A thin circle of light rose off the stage and surrounded Brandon. It was working and hope surged inside Dana. The light reached the height of his ankles, then his knees and continued to grow. But as it reached his beltline, a low voice coursed through Dana's mind.
_Do you finally realize now what a failure you are? Miyo leads, not you. If you were truly the Leader of the prophecy, you would have seen this coming. You would have led the Warriors against the virus. You would have seen it instead of being ensnared by it yourself. Miyo is the Leader, not you. There is so much darkness in you. If you were of the Light, you would have protected Brandon. But now, because of your utter failure, Brandon is about to die._
Hideous laughter filled her head and Dana gasped as if she'd been slugged in the stomach. The shield of light encircling Brandon shuddered, collapsed, and vanished into the stage floor. Brandon's image shifted back into one of him standing tall and strong and singing with confidence. Her mind clouded over and a sickly sweet sense of peace came over her.
_Yes, relax. Embrace my peace. You've fought well, Dana, but there is nothing more you can do. Let go._
Dana hunched forward. A crushing grip grabbed her lungs and squeezed and her vision grew dim, but she refused to give in.
_No, I am the Leader. Your power is nothing next to his._
The darkness continued to rush in on her, but in the next instant a sliver of light appeared a long way off. Not in the arena. Not in the sky, but inside her in the deepest part of her soul. Inside her spirit. The light grew and laughter poured out of the light, not the insidious laughter she'd just heard, but the laughter of victory and strength and unquenchable joy. So bizarre to hear the laughter of the Spirit in the midst of the horrific battle, yet at the same time it made perfect sense. Joy was strength. His strength, spilling out of her spirit into her soul and into her body.
Dana stood straight, balled her hands into fists, squeezed her fingers so hard her nails dug into her skin, and raised them to the sky. "Far greater is the One who lives inside me than anything the one who lives in the world can try to throw against me. The power of love has destroyed the power of death. I stand on the truth and the power and the glory of the One who has ransomed my life from the kingdom of darkness and has made me royalty in the kingdom of light!"
She opened her hands, stretched her fingers as straight as she could, then grabbed . . . She didn't know what. But she believed something would be there. And it was. She dug her fingers into what felt like solid and liquid at the same time and pulled with all her strength.
At first nothing happened. But she continued to strain every muscle and ligament to its breaking point. _Your power, Lord!_ A moment later something broke and it felt like the heavens opened with a flood of water. But it wasn't water.
Fire fell like rain in a circle and surrounded Brandon, Miyo, and her. The demons all around them were buffeted as if smacked by gale-force winds. They staggered back, faces contorted with rage. One lurched forward. He swung his sword toward the curtain of fire and sliced. The blade hit the curtain and the black steel of the sword melted like water, and the demon's skin was instantly scorched.
"Well . . . done." Miyo's labored breathing sounded like a steam engine as her shoulders sank and she dropped her sword on the stage. Her forehead was drenched in sweat and her face smeared with blood. Her clothes were torn and her hair looked like dark tangled twine. Blood seeped from a gash on her right arm.
Dana's face must have been filled with shock because Miyo gave her a weak smile. "No, don't worry. I'm sure I look much worse than I am. Cuts and maybe a sprain here or there, but I'm okay and there is still more fight in me than they can imagine. You?"
"I'm fine." She turned to examine Brandon. The darts now struck the curtain of fire and disintegrated. His clothes were in tatters and blood covered his body, but he continued to sing.
FIFTY-FIVE
BRANDON WAS CLOSE TO COLLAPSE. NOT CLOSE, ON THE razor's edge and leaning toward the abyss. Seconds from defeat. Keep singing? Impossible. But he had to.
_Every moment of your existence has led to this time. And the choice you make now will shape you for eternity. Will you sing the final verse?_
A realization swept over Brandon. If he finished the song, it would kill him.
_You must choose._
The words of the prophecy echoed in his head. _"And one will die before the appointed time."_ And then a verse from Hebrews appeared in his mind. _"Through Jesus, therefore, let us continually offer to God a sacrifice of praise—the fruit of lips that openly profess his name."_ The sacrifice of praise. Sacrifice. His life. A living sacrifice. Sacrificing all he was in this moment and all he would be. Death was not death. Not now. Not ever again. It had no hold on him. And he was in the middle of the Pacific Ocean, but the waves were no longer water but ecstasy and he was swimming in it.
Brandon closed his eyes and let his arms fall from his guitar as he collapsed onto his knees. He barely noticed the pain that shot up his legs from the impact. All that mattered was the song, and he continued to sing. Finish the verse. There was no other choice.
One more note he had to hold with the minuscule drop of life still left inside him. He sat back on his ankles, his arms out to his sides, and pulled in the deepest breath of his life. As he did, a voice shot into his mind.
_Stop the song now. You will live. Let it go, my son. You've done enough._
The voice of the enemy.
_Liar._
_No, it is I. Let it go. It is not too late for you to live._
It was too late. Brandon had chosen. And if the Lord willed it, he would live. If not, he would enter into glory. Brandon opened his mouth and the last note of the song erupted out of his mouth in a torrent of worship. As it rose over the arena, he opened his eyes and saw light fall like rain over the entire stadium. Then the darkness stole over him and his body sprawled lifeless onto the stage.
Dana gasped as light exploded like a star going nova and lit up the stadium in unfettered brilliance. All shadows vanished, and as the last note of the song faded, Zennon and his army were blown back as if they were brittle autumn leaves slammed by a hurricane.
The demons lay on the northwest side of the stadium, most of them not moving. Even Zennon was on one knee, his face twisted in pain.
She turned to Miyo. "Have we won?"
"For the moment. The power of the Song and the power of the song were too much for them."
"Then why are they still here?"
"Look at the people." Miyo pointed over the crowd, and Dana stared in surprise at the thousands of rigid bodies in front of them. "They haven't changed. I thought the song would heal them of the virus. Burn it out of them. But it didn't. Which means Zennon still has his claws embedded in their souls. Which gives him the right to remain. This is not good. He will recover quickly, along with his army. And I'm guessing he's going to bring in reinforcements that won't be as easily defeated."
"Easy? You call what just happened easy?"
Dana glanced down. "Brandon!" For a moment she'd forgotten about the Song. She dropped to her knees beside his still body. Reece, battered and bloody, already knelt at his side. A moment later Marcus was there too.
Strong arms lifted Brandon and a voice spoke from a thousand miles away. The Spirit's voice? No. This was human and Brandon knew the voice well. Reece.
"Wake up, sleeper. Arise from the dead."
"I'm not gone?" Pain radiated from every inch of his skin and it hurt simply to breathe.
"No, but I'm guessing you danced on the edge of death just now."
Then Miyo knelt beside him and Dana as well. He stared deep into her eyes.
"I didn't sing it for me." He smiled inside. She wouldn't have any idea what that meant. It didn't matter. He needed her to hear. "I've finally died."
"I know. More than you know, I know."
And then, whatever had hidden Dana's true eyes from him for the past year and a half was gone. He held out a weak hand and she took it in both of hers and kissed it.
"The spell has been broken," Reece said. "The light has returned. And once more the Warriors Riding are riding together." He smiled but the smile was grim.
"What's wrong?"
"Forgive me, Brandon. For hardening myself toward you. For forgiving you in my mind but not in my heart. For allowing bitterness to take root. And for leading you down a path of destruction these past two months."
"Forgiven." Brandon ignored the pain in his arm and reached out and squeezed Reece's knee with his other hand. "I finished the song?"
"Oh yes." Reece smiled and cradled the back of Brandon's head. "I suspect this moment will be celebrated in the heavens throughout eternity."
"The song wasn't mine." Brandon struggled to sit up. "It was Simon's."
Reece glanced over the top of Brandon's head. "In a moment I think he's going to tell you what it did for him."
Brandon sucked in a deep breath and slumped back. "So we won. It's over."
"No." Reece's face hardened. "If I'm right, I'm afraid it's about to get much worse."
FIFTY-SIX
DANA BLINKED AND STARED AT THE FIGURE THAT STRODE toward them from the left side of the stage. Simon? Yes. But so vastly different she almost couldn't be sure it was the same man. His back was straight instead of being slightly stooped over. The constant twitching in the magician was gone, and he looked fifteen years younger.
It was like staring into a mirror where the mirror image was clearer and stronger than the image it reflected. He held himself like an athlete in the prime of life or a king surveying his kingdom, ready to challenge all comers to whatever throne he'd ascended to. But the biggest difference was his eyes. Brilliant. Clear. And they held a depth that had never been there before. Dana saw a wisdom. A confidence. An authority that had been missing.
If the eyes were the window to the soul, Simon had just experienced a major remodel on the inside. He walked toward the four of them as if he were taking a stroll along the Seattle waterfront on a lazy Sunday afternoon.
Joy radiated from his face like a spotlight as he knelt next to them and fixed his gaze on Brandon. "I remember." The magician glanced at Reece, Miyo, and then Dana, repeating the words each time. "Not some of it as I did after you entered my soul. Now I remember it all. Who I was in ages past." He raised his head and laughter poured out. "I remember it all!"
He squeezed his arms, his head, his torso as if feeling them for the first time. "My mind, I . . ." He stared at Brandon. "You don't understand what you've done, do you? You have no idea, Song. You have set me free. You have healed and restored me beyond what you can know. What was lost has been sought out and found."
Another peal of laughter poured from his mouth and it seemed to shake the stage. "But you have done so much more because I know what I am supposed to do right now."
Simon gazed at every section of the stadium—up high, across the field in front of them, to his left and right—as if seeing it for the first time. His countenance grew sober and by the time he finished, his eyes had turned to fire. He stood and stared down at them. "Get ready. We don't have much time. Zennon will regather his army quickly."
Simon stepped to the microphone, lifted his hands, and didn't move until the murmurs floating across the stadium faded into silence.
"Good evening. My name is Simon, and I greet you, friends, in the power and authority of Jesus Christ, the slain Son of God who destroyed the power of death and wrested from Satan the keys of hell, then rose and granted immortality to all who would prostrate their souls before him. The Giver of eternity and life beyond life, to him we surrender our bodies, souls, and spirits."
Simon's voice rang out so true, so clear, so strong, it seemed he didn't need a microphone. "Many of you have been living in a dream world. I understand this better than any of you will ever know. You have been deceived, infected with a kind of spiritual virus that would drain the life out of your soul, steal your identity, and replace it with self-focused ambition and self-love.
"That is not going to happen. I'm going to show you the truth, pull back the curtain—no, _destroy_ the curtain of lies that has been draped over our souls. There are no works we can do to please God because we have already pleased him through his Son, Jesus the Christ.
"He is love. And love is patient. And kind. Believes all things. Eendures all things. The word _disappointed_ is not in that list. The word _inadequate_ is not there. The words _not enough_ are not in there. You are his beloved. Now receive his healing."
Simon lifted his hands and prayed against the virus with such force and power, Dana could only marvel. As he continued to pray, tendrils of fire spread out all over the stadium and shot into every man, woman, and child. As the fire and light surged through them, they turned from the statues of stone she had seen in the spirit earlier, to bodies of life and light. In minutes it was finished and Dana knew the virus had been destroyed. But she also could tell from Simon's movements the night was not over.
"Now I need to show all of you something. For some this will be difficult. But you need to see it." Simon's gaze went to the northwest corner of the stadium where Zennon and his demons were rising to their feet.
"We have given permission for unwanted guests to be here tonight. We have invited them with our fear and grasping for life where there is no life, and by our lack of resistance. We have agreed with them and swallowed the illusions about our lives that they told us were real. They want to destroy us. Want us to believe the illusion that they do not exist." Simon paused. "Those days of deception are over. And now you will see them. Do not be afraid."
As Simon finished speaking, Zennon appeared on the far side of the stage and struggled as if to break through an invisible barrier.
He stabbed his finger at Simon. "You can't win, Joker. You are nothing. In seconds we will break through your pitiful defenses and destroy you. And then destroy all who stand here tonight."
Simon's eyes narrowed. "You are the great illusionist, Zennon. You trapped me for longer than I could have imagined possible. But you have claim on me no longer. Nor on any of these." Simon spread his hands over the crowd.
"You think being able to see again after all these years of darkness means anything?" Zennon seethed. "You are nothing."
"You have spoken truth, demon. I am nothing. I'm less than nothing because I am no longer alive." Simon unsheathed a sword at his side and swung it in tight arcs around his body. "I am a dead man. Crucified. Buried. But I have been reborn into a glorious, powerful, and dangerous new being. All things have passed away and all things are new.
"He who is faithful and true is beyond the stars with power." Simon balled his hand into a fist and slammed it against his chest. "And this is where he lives. And you are terrified of what I'm going to show these people right now."
Simon stepped toward the demon. "I'm going to show them a world you don't want them to see. I'm going to show them a reality that will send terror screaming down your spine like acid in your blood. Because when they see the truth, you are the one who will be destroyed by the Alpha and Omega who lives inside each one of them."
Again Zennon thrashed against the invisible wall that held him back.
Simon spoke out over the crowd. "Truth in this place. Open blind eyes. Open deaf ears. Let our vision see beyond what we have seen." He raised his right hand and spread his fingers wide, then drew it down like a man pulling down a great curtain. Loud gasps broke out all over the stadium as people's eyes were opened.
"Friends. Friends!" Simon held his hands up again for quiet. "Your eyes have been opened. I implore you to keep them open in the days and weeks to come. To keep seeing with spiritual eyes and hearing with spiritual ears. But now you must grant me a favor. It is time for you to go. But as you leave, stay in prayer for us. We need your strength as we face our enemy."
Simon glanced at Zennon and his demons encased behind the wall, then back to the crowd. A third of the people shuffled toward the exits. Another third looked too stunned to move. And the final third stood in quiet defiance. It was obvious to Dana that these people knew exactly what was going on and had not been taken in at any point during the evening.
"Please, it is time to go. A war is about to begin and it is not make-believe." Simon motioned with his hands as though he could push the crowd toward the exits. "If you feel you must stay, then stay, but move to the upper seats in the stadium and war for us from there."
Dana was amazed at how quickly the stadium emptied. In less than five minutes, only a quarter of the people remained. She pulled her gaze from the crowd and looked at the demons gathered together far to their right. Miyo was right about the reinforcements. Or maybe her eyes had simply been opened wider by Simon.
Regardless, Zennon's army of demons was no longer just the ones he'd called his elite. A massive horde now strode toward them from the northwest corner of the stadium, and they were not of average height and weight. They were huge, almost as tall and broad as Zennon. She wished she had Simon's belief. Because these demons striding up to join Zennon onstage looked severely dangerous.
FIFTY-SEVEN
BRANDON STARED AT ZENNON, TRANSFIXED. REECE WAS right about it getting worse. The warlord had now been joined on stage by at least ten demons on each side of him who slashed at the invisible wall. And the wall was weakening.
As Brandon struggled to his feet with the help of Dana, Miyo, and Reece, Simon spun, strode over to him, and knelt. "Song, you are needed."
"What?" Brandon almost laughed. "I can't do anyth—"
"Yes, you can." Simon took Brandon's face in his hands. "Sing it again, Song."
Even Simon's voice had changed. A bit deeper. A tone that spoke of great love and epic battles at the same time, and none of his words were wasted. Somehow Brandon knew it would be rare for Simon to ever utter another rhyme.
"Singing the song almost killed me."
"Yes. That is true. But it didn't, did it?" Simon dropped his hands to Brandon's shoulders. "And it won't this time either." Simon's hands grew unnaturally heavy and heat radiated off them. "Receive his healing."
The warmth from Simon's hands shot into Brandon and brought a strength beyond what he'd ever felt. It raced through him and pushed hard against the inside of his legs, arms, head, body, and feet. And extreme joy pulsed through him. If he hadn't seen his feet resting on the stage, he would swear he now floated two feet off the ground. "What . . . what was that?"
"Healing. Restoration of that which once was." The magician smiled. "Which you brought to me and I now have given to you." Simon's eyes blazed. "Sing it again, Brandon." He drew his face to within inches of Brandon's. "Be the Song like you've never been before. You can't imagine what will come when you do."
Brandon glanced over Simon's shoulder. The twenty or so demons pounding away at the wall holding them back had been joined by at least another twenty of the same size. "What I see is an army of sizable demons about to break through whatever you threw up and wanting to slaughter us. Which means there's no time—"
"Which is why you must sing now." Simon released him, stepped toward the front of the stage, and pointed west toward Puget Sound. "Hold nothing back, son. Give it everything inside you. Everything you've ever been. Every dream you've carried. Every sorrow, every joy. It has all led you here. The balance of the universe has been given to you; you hold it in the palm of your hand. It is a gift from him, so take it now and live in the fullness of his glory."
"The song was to be sung only once."
"No. Only sung once for healing. And the healing has come." Simon glanced behind him at the demons. "Sung twice for battle. But you must decide now. There is little time left. They will break through my wall in less than two minutes at most and reach us in seconds after that. From that moment on I can offer no hope of victory for any of us."
"We're about to die."
"Oh no, that is not true." Simon's laugh echoed across the stage. "We have already died. There is only life for us now. But I would still encourage you to sing."
Brandon closed his eyes and began the song for the second time. His voice rang out clear and true, and the opposite sensation happened this time. Instead of strength leaving, power and hope flowed into him. He let everything around him fall away and he sang as Simon had said to, with utter abandon.
Thirty seconds into the song, the Spirit spoke in a whisper. _Open your eyes._
A gigantic, jet-black wall hung in the sky far out over the stadium and moved slowly toward them. It was half a mile wide and almost as tall.
He stopped singing in wonder and the wall slowed. Could it be? He clutched the microphone with both hands and turned to look at Simon. The magician's arms were raised to the sky, his eyes closed, his mouth moving in worship, which stood in stark contrast to the swarming demons leveling their assault on the unseen shield less than forty feet to his right.
Simon opened his eyes and gazed at Brandon. He nodded twice as a smile grew on his face that said, "Yes, it is you doing it, Song. You are the catalyst. Now you see another glimpse into the indescribable power of worship."
Unbelievable. The song, through his voice, had drawn the wall here. Brandon drew a deep breath and pushed into the next verse. Immediately the giant wall surged forward. As he continued to sing, the darkness of the wall shifted from black to gray. Then swirls of pure white began to sweep over the surface of the wall in patterns that reminded Brandon of the most exquisite marble he'd ever seen.
As he continued to sing, a faint sound started above him and seemed to sink down until it surrounded him. Was it . . . ? Yes, music. In perfect harmony with the song pouring from his mouth. In seconds the music became loud enough for him to hear all the instruments. Part of him wanted to stop. Their skill was too far beyond his. He was too human to take part in something this full of rapture.
_Not true._
The voice of the Spirit tore through him and filled him with fire. An invisible orchestra played along with him, every note containing the power to destroy or build a kingdom. He spun in a slow circle even though he knew he would see nothing. But in the next moment he did see. A gathering of luminescent beings. Male? Female? They didn't seem to be either, or maybe they were both. They held . . . what? Instruments? But they weren't instruments—the objects seemed to wrap around their bodies and seemed to be a part of the beings. The instruments were alive.
They moved as the beings played them. Shifted. Changed as the sound filled the stadium like a thousand waterfalls. And the wall continued to move closer.
The music shifted into an epic, pounding rhythm, and Brandon's confusion turned to laughter as a new verse to the song flooded his mind and he raised the mic to his lips.
_You have need of that no longer._
The microphone? How could he possibly be heard over the music without the microphone and speakers?
_Put it away. You will see._
Did he hear laughter in the Spirit's voice? Brandon set the microphone back into the stand, stepped away, and sang. He expected his voice to carry no farther than the first few rows of the stadium. But the opposite happened. It was now far louder than it had been through the speakers. Clearer. Stronger. The sound of his voice reverberated back to him from every point in the stadium.
Was it his voice? Of course. But it was different. There was no way to describe it other than to say it was more him than he'd ever been. More his true self. The one he'd known and felt in the deepest parts of him. And the part of him that would go on living forever.
The wall moved toward them faster now, but something was wrong. The top of the wall shuddered as if it had been struck. The shaking moved down the wall as if giant battering rams were pounding to get through. Thin cracks appeared at the top and slowly moved down the wall. Their speed increased exponentially and streaked down in jagged patterns.
Brandon whipped his head around and stared at Zennon. Fury grew on his face as he stared at the wall and he and his demons ramped up their intensity. They would be through the shield and launch an assault on the Warriors and Simon in seconds.
Tiny clouds of gray dust escaped from the cracks and floated down the face of the wall. The fissures grew wider and razor-thin light poured of out them. No wonder Zennon was furious. Whatever was behind the wall appeared to hold the light of heaven.
Massive sheets of the marble wall pulled loose and fell toward the floor at the far end of the stadium but stopped halfway to the ground as if waiting for the rest of the wall to join them.
Brandon continued to sing, but it wasn't him singing. He was intertwined with the Spirit, and he felt as though the Brandon he'd always been didn't exist anymore—had never existed. His body was gone. His soul and mind were gone as well and all that remained was his spirit.
The rest of the wall had now fallen, and the chunks had all merged with each other into a vast, swirling cloud of whites and grays and now golds and silvers. The cloud morphed into something solid and lay out in front of them like a flat building or a road or . . . What . . . was it? Then it dawned on him. The wall was forming into a massive bridge, so bright Brandon shielded his eyes. A bridge of light, a bridge from heaven, brought into the natural world by a song.
The bridge surged forward and rolled out like a massive wave. Light exploded off of it. Reds. Greens. Blues. Yellows. It slammed down and the noise from the impact was ear shattering. Then a swirling mass of white clouds, miles away at the back of the bridge, streaked toward them. It rolled on like an avalanche, each cloud at the top spilling down the slope of white till it was buried by the next wave above it.
Moments later they were no longer clouds but horses—great thundering beasts—and on the horses were thousands of warriors, dressed in brilliant blues and greens and reds. At the front of the charge rode a being at least twice as large as the rest.
"Oh. My."
Brandon spun at the voice. Dana now stood beside him and took his hand in hers. "Do you see him?"
Laughter came from his right. Reece. Next to him stood Simon, and to his left on the other side of Dana stood Marcus and Miyo. "He comes," she said.
Could it be him? Yes. It was him. Tristan Barrow. On his right and left, Jotham and Orson rode, but they too were changed. So much larger than how he knew them, with a frightening intensity in their eyes. Brandon turned once more to look at Zennon and his army and his heart lurched. They had broken through and were sprinting toward the Warriors.
FIFTY-EIGHT
JUST BEFORE THE DEMONS REACHED BRANDON, DANA, Miyo, and Reece, Simon spun toward the onslaught and raised his arms. "This battle is no longer ours. Sprit of the Living God, take us."
Instantly they vanished and reappeared a moment later in the stands above the stage. Brandon smiled at the small clusters of people who had stayed that dotted the stands around them. Excellent seats for the scene about to unfold.
Brilliant flashes of light exploded from behind Tristan, Jotham, Orson, and the rest of the angel warriors as they pulled silver arrows from the quivers on their backs. Each of them held the arrows up close to their mouths and spoke as if giving the arrows instructions while the whole time they galloped like a tempest toward Zennon and his host of demons.
"What are they doing?" Dana said.
"Don't you see it, Dana?" A look of wonder came over Miyo's face and her eyes brightened. "This is Habakkuk chapter three come to life." She pointed at the angels and her smile lit up her face. " 'His brightness was like the light; He had rays flashing from His hand, and there His power was hidden . . . You rode on Your horses . . . Your bow was made quite ready; oaths were sworn over Your arrows.' Those arrows are carrying the One's power."
The moment the last horse and rider crossed the midpoint of the bridge, Tristan shouted, "Ready!" And as if one, all of the angels nocked their arrows at the same time, pulled them back, and leveled them at the swarm of demons.
Brandon expected their pace to slow as they took dead aim at Zennon's army, but their raised bows seemed to spur the horses to even greater speed and their velocity increased. Foam seeped from the horses' mouths and roars of battle erupted out of the mouths of the angel army.
"Now!" Tristan's voice shook them—a cry full of rage and triumph at the same time. The arrows left every angel's bow in perfect unison, and in less than a second they'd nocked another arrow on their strings, waiting for Tristan's next command to fire.
Most of the first waves of arrows struck the shields of the demon front line and exploded into light, but at least forty got through and slayed those the arrows hit. One of the arrows sank into the chest of a demon that had fought alongside Zennon to break Simon's wall. He stumbled back, but if he felt pain, he didn't show it.
The demon reached up and yanked hard on the arrow to pull it free, but it didn't budge. He pulled with more force with the same result. The arrow grew brighter and then it turned into a golden liquid that puddled over the demon's chest, spread like water over his body to his feet, and up his neck, over his face and head. A puff of sound followed and the demon vanished.
In another blink of the eye, the liquid had reformed as the arrow. A demon to the right stooped and grabbed the arrow, then reared back writhing in pain, his hand no longer attached to his body.
Zennon stood twenty paces behind the front line, his face contorted with rage as Tristan, Jotham, Orson, and the other riders in the front row spilled off the bridge onto the stadium field.
"Again!" Tristan roared.
The second wall of arrows rained down on the demons, but this time they were ready and held their shields more closely together.
"Attack!" The war cry spewed out of Zennon's mouth, and before the sound of it faded, his army, swords at the ready, sprinted toward the coming riders. For the next few minutes, chaos reigned and it was difficult to follow the battle. The clash of swords and fire and smoke filled the field as angel met demon in open battle.
But in less than ten minutes, a scant few of Zennon's army remained alive. He pulled his army back and stood in front of them, watching Tristan. The angel army had suffered losses as well, but far fewer than the demon's.
Zennon pointed to the center of the field and Tristan nodded. They each strode to the middle of the field and stood five yards apart. They spoke to each other but far too faintly for Brandon to hear. Their conversation didn't last more than thirty seconds, and then they returned to their respective armies.
"What was that?" Brandon said.
"My guess is they came to an agreement," Reece said.
"A truce? That doesn't sound like Tristan."
"No," Reece said.
Simon nodded. "Reece is right. Not a truce. But a way to end this, just between the two of them."
Miyo folded her arms. "One-on-one combat to the death."
FIFTY-NINE
AFTER A BRIEF WORD TO HIS ARMY, TRISTAN STRODE BACK to the middle of the field. Zennon was already there. They circled each other, studying, anticipating, preparing to strike.
With a screech, Zennon sprang toward Tristan and launched his sword at the angel's neck, but Tristan ducked under the blow and slashed at Zennon's leg and drew first blood. After that came two or three minutes where they matched each other blow for blow.
As they battled, their bodies grew—one in glory and one in horror—till the brilliance pouring off of Tristan was like a river of blinding light, and the shadows swirling around Zennon were so dark Brandon couldn't make out any of the demon's features. The darkness seemed to suck the light from Tristan into itself as if Zennon were a black hole, but as it was captured more quickly, the brilliance of the light encircling Tristan continued to grow till Brandon had to squint against the light.
Once again their swords clashed against each other. The collision sent an explosion of colors screaming across the sky and the sound shook the earth. The impact threw the two warriors back and they staggered as they regained their balance.
The moment they did, they rushed toward each other again. Both angel and demon moved almost too fast to follow. Their swords rang out again and again. Another massive crash against each other and again they fell apart—both breathing heavily. Both drenched in sweat. Both with blood dripping from their swords.
They engaged once more. An attack, a parry, a slice across arm or leg or chest that drew more blood, neither gaining a sure advantage.
Brandon turned to Simon and Reece. "Will he defeat Zennon?"
Neither man answered, both their faces grim.
Zennon's body continued to grow larger and the darkness that poured from it leapt at Tristan. The blackness wrapped itself around the angel's body like a legion of snakes—so fast the angel had no time to raise his sword. Tristan's face twisted in agony and a scream tore from his lips. The darkness continued to twist its way around him until it covered Tristan entirely and he vanished from sight.
Laughter spewed from Zennon and a rancid smile stayed on his face as he stared up at all of them and shouted, "It is over. He won't be there to rescue you ever again. And I am coming for you."
No. It wasn't possible. Brandon glanced at the shock on the others' faces. Reece looked ill, and Dana and Miyo looked ready to throw up. Simon's was the only face among them that showed no emotion. He turned and looked at Brandon. "It's not finished."
"Why?"
Simon didn't answer and continued to stare down at the field.
"Why, Simon?" Brandon asked again.
"Because darkness cannot ever overcome the light."
Brandon turned back to the field as a shudder coursed through the giant cocoon Zennon had created. Another shudder and then a deep-throated shriek of pain erupted from the demon's mouth. Then another. The globe of darkness he had smothered Tristan with began to glow, and every second it grew brighter as if a star-powered light had been turned on inside. A second later the globe exploded in a kaleidoscope of colors, and Zennan was flung to the ground. Tendrils of fire shot into the sky like a twisted fireworks display, and then a final screech ripped through the air as Tristan stood next to Zennon's writhing body. Tristan took a deep breath, then plunged his sword into Zennon's heart.
The remaining darkness that had enveloped Zennon faded and his features could be seen again. But as soon as they were visible, they changed. Brandon had always assumed the true appearance of a demon would be unspeakably hideous.
Brandon didn't know what he had expected. Maybe a tortured countenance or a demonic face out of a horror movie. Or a visage of evil rampant with scars and grotesquely twisted eyes and ears and mouth. But nothing was there. Not even the hint of a face. Just a dark gray nothingness devoid of feature or form, color or nuance, joy or sorrow.
Reece, Simon, Miyo, Dana, and Brandon stood without speaking. Brandon's gaze swept back and forth over the field of battle. A group of angels, including Jotham and Orson, gathered around Tristan. They grabbed his shoulders and arms, wide grins on their faces. The remnant of Zennon's army that was still alive had vanished. The small crowd still in the stands stood in silence, apparently stunned at what they'd just witnessed.
As Brandon's gaze focused again on Zennon, the demon's remains slowly faded into oblivion. But something remained. A shiny object so small Brandon squinted to see what it was. Could it be . . . ?
"Yes." Simon smiled and held out his hand. In it rested the magician's silver coin. But as Brandon and the others watched, the coin slowly changed from silver to gold. He glanced back to where the shiny object had been on the floor of the stadium. It was gone. It was now in Simon's hand.
"Are you kidding? That's not Zennon's—"
"No, it is not. It's mine. It has always been mine." The smile on Simon's face grew and the magician laughed. "I remember. Zennon stole it long ago." He laughed again. "How could I have forgotten? But what was lost has been found. What was stolen has been returned. Thank you, Abba."
Simon frowned as if trying to recall the rest of the memory. His face cleared and he held up the coin. "A gift from my grandfather many years ago." He looked at Miyo. "Grandfathers give extraordinary gifts, wouldn't you agree?"
Miyo nodded, her eyes full of light. Simon closed his fist tight around the coin and gazed down on the field. Tristan looked up at them, nodded once, then he and his army faded from sight.
"So it ends." Reece adjusted his Stetson.
"No, Reece." Simon took a step forward, his eyes fixed on the star-strewn sky above. "Not for me. For me it is only the first day of a glorious new beginning."
Reece squeezed Simon's shoulder. "May it be so for each of us."
SIXTY
DANA PULLED INTO BRANDON'S DRIVEWAY LATE ON Wednesday afternoon and shut off her engine, but didn't get out of her car. She checked her hair in the rearview mirror, reapplied her coral lipstick, and smoothed her blouse.
_Get out, Dana. It's just Brandon._
But she stayed in her car a few minutes longer. Time enough to remind herself of what he had done for Simon, instead of for himself. What he had done for all of them. The Song had unequivocally died before the appointed time. Died to himself so he might live to Christ. And it had set him free. And melted her heart. But even so, the tiniest part of her was still afraid. The only thing still protecting her might be a papier-mâché fence, but she wasn't quite ready for him to break through it.
When she reached his front door, she fixed her hair for the fiftieth time and rang the bell. He opened the door and smiled, his eyes brighter than she'd seen them in . . . years.
"I brought you a present." She pulled a bag of sunflower seeds out from behind her back.
Brandon laughed, took them, offered thanks, and squinted at her with his head cocked to the side. "I'm not exactly sure how you do it, but you have this amazing ability of getting more beautiful every time I see you."
"Wow. I don't think I've heard a line like that since college."
"Is it still considered a line if it's sincere? And true?" Brandon stepped aside and motioned her inside.
"Yes."
"The really important question is, did it work?"
"The evening is just begining. I'll let you figure out the answer as the night progresses."
"Then let's get started." Brandon bowed and the smile that lit up his face was so free she almost gasped. The bitterness, the frustration, the sorrow he'd carried since his voice disappeared was gone, along with the worthlessness he'd carried since the battle with the religious spirit.
For the first time in ages, she noticed lines etched into his face that squiggled out from the corners of his eyes, and it made him even more handsome. More joyful. More . . . free, as if the trueness of God's love and wild abandon had been chiseled into his face. Aging would be kind to Brandon Scott, she suspected.
He offered his hand to her and she took it and squeezed but didn't hold on. She wasn't ready for that. Yes, she was. No, she wasn't. Yes, she was. _Arrgh!_ Was it possible to be absolutely sure and not sure at all, both at the same time? They walked together down his hallway into the living room. Strange being back in his house after four and a half years away. Dana glanced around the room. It hadn't changed much. A picture of the two of them standing on the edge of Hurricane Ridge caught her attention, the wind whipping her hair back, the sun lighting up their faces.
"Oh my." It was the day he'd asked her to marry him. The day she'd said yes and given him her heart. "When did you put that back up?"
Brandon put his hands on his hips and smiled as he gazed at the picture, then turned to her. "That's my favorite photo of us. Did you know that? I can still remember how nervous I was before I asked."
"Are you going to answer me? When did you put that back up?"
He gazed at the photo for a long time before answering. "I never took it down."
Warmth and joy surged up from inside. Did she really want to be here? Yes, she did.
Brandon turned toward the sliding-glass door that led to his back deck. "I want to show you a project I've been working on."
"What?"
"I did something with the backyard." He reached the door and slid it open. "I think you'll like it."
He led her onto the back deck and stopped at the top of the stairs leading down to his lawn. "What do you think?"
She gazed around the yard but nothing stood out as being different.
"It's been a long time since I've been here, so maybe there's something new and I'm just not seeing it."
"Look up." Brandon smiled like a little boy.
Dana saw it immediately. Thirty, maybe forty feet in the air, nestled between two massive Douglas firs, was a tree house. It appeared to be made out of cedar, and the wood was stained a rich redwood color.
A winding staircase wrapped around one of the firs up to a front door with a stained-glass window made in the shape of a guitar. Of course it would be. Thick six-by-six beams created the foundation for the tree house and the walls shot up from there. The structure seemed to be more windows than wood.
"Am I seeing things, or is it two stories tall?"
"Your eyes are fine." Brandon grinned. "It has a loft up above for sleeping and then a love seat and a few chairs on the first floor for hanging out, reading, singing, whatever. It's wired so there's heat and light."
"No kitchen? No big-screen TV? No hot tub?"
"I know. Shocking. They even refused to put in a racquetball court." He offered his hand again and this time she locked hers around his and held on. She almost stumbled. What was wrong with her? She wasn't some flighty junior high girl. She blew out a quick breath. Funny how a simple touch could send such strong emotions streaming through her.
"Want to see inside?" Brandon led her down the stairs onto the grass and to the base of the tree.
They climbed up the winding staircase, and just before they reached the tree house, Brandon turned. "But my favorite place isn't even inside. It's on the little deck out front."
They settled into the two chairs on the tiny deck and gazed at the view of trees and neighbors' yards and the thick greenbelt that ran from the edge of Brandon's backyard into the distance.
"So when you said you've been working on something, this is what it was?"
"Yep, in all her glory."
"Don't tell me you name tree houses after women like you do with ships."
"You're only allowed to name your tree house after a woman if you call it Dana."
"You didn't." She turned to see if he was serious.
"No, of course not. I chose a Hebrew word." He pointed to the top of the door. She had to squint to see the symbols:
"Which means what when translated into English?"
"Dana."
She couldn't help but smile. "It's stunning, Brandon. You didn't do this yourself, did you?"
"Hardly. I hired Nelson Tree House and Supply right here on the eastside to help me. They're just eight miles from here but build tree houses all over the world. Plus, they have a spread just outside of Preston they call TreeHouse Point with six tree houses they rent out like hotel rooms."
"And you saw what they do and were inspired."
"Very."
"How'd you discover them?"
"About five years ago I went looking for something special to do for the woman I was going to marry. I thought staying there for the weekend after we got back from our honeymoon would be a wonderful way to extend it for a few days."
Dana allowed herself to imagine what that would have been like. Then she went further and allowed the idea to seep into her heart. She took his hand. "I want you to sit up here by yourself on a summer evening when the heat of the day still hangs in the air, and the sun is just dropping below the horizon out over the Olympic Mountains, and do something for me."
"Anything."
"Something you can't do on your own, that you can't make happen or control."
"Then how can I do it for you?"
"I have a feeling you'll get your chance."
"Tell me."
"I want you to listen very closely and hear something very specific."
Brandon ran his finger along the back of her hand. "And that is?"
"I want you to hear my song." She put her other hand around their joined fingers and leaned closer and didn't even try to stop the tears that welled up in her eyes.
"And then what?"
She didn't need to answer. Brandon knew.
"Sing it for you."
"Yes." The word came out in a whisper.
"To be able to do that would be my favorite performance ever."
"Better than the one for Simon?"
"Not even close." Brandon leaned toward her until his lips were next to her ear. "I'm not in love with Simon."
There it was. They'd danced around it since the moment she'd arrived at his home, and now he'd said it. What should she say? That she felt the same and was ready to confess it?
Brandon pulled back and smiled. "So, you want me to be up here and have the Spirit open my ears to hear your song?"
Dana nodded.
"I'm sitting here now."
"You need to be alone."
"I see." Brandon nestled his face into her hair.
"Will you do that for me?" Dana pulled away to look into his eyes. "Will you ask the Spirit?"
"What if he's already answered?"
Dana sat up and leaned back in her chair. "What are you saying?"
He grinned and gave a slight nod. It couldn't be. Had he already heard something? She shook her head. "Are you serious?"
"Last night I was up here with my guitar, thinking of what all of us have gone through over the past three and a half months and how God came through in the end. For Simon, for Miyo, Reece, and Marcus. For you, for the ones who have embraced the message of Warriors Riding, and for me.
"The final hints of light were seeping into the west and the stars looked like they did on my bedroom ceiling when I was a kid. As I sat there, a song lifted off the ground and drifted up into the trees. It sounded like it was played on a piccolo. And then came the vision, clearer than any of the others. I was stunned by what I saw." He leaned back and rubbed her neck, closed his eyes, and dropped into a silence that extended well past a minute.
"What are you doing?" She shoved him. "Tell me!"
He laughed and opened his eyes. "You're sure you want to hear this? You realize the vision was of you, right?"
"Would you like me to push you off this tree house? We have to be at least forty feet up."
"Forty-five." Brandon stood, went into the tree house, and came out with one of his guitars. He played a chord on his guitar and it sounded like falling water in her ears.
"In the vision, you stood on Hurricane Ridge in the exact spot as we did in the picture in my living room, but the wind wasn't blowing this time. You were in profile, and I could tell you were staring at something intently. A soft smile grew on your face and then you walked toward whatever you saw. A moment later the perspective drew back and it was me. You embraced me and didn't let go for a long time. And even though I was watching it from the outside, it almost felt as if your arms were physically holding me. And then a kiss came that was even longer than the hug. The vision shifted and the song poured into me instantly."
She lifted Brandon's guitar out of his hands and placed it gently on the deck.
"Don't you want me to play your song?" he said.
"Yes. Someday soon."
She knew the day. Maybe he did too. If he didn't, he'd have to figure it out on his own. Dana took his face in both her hands, leaned in until the tips of their noses touched, and whispered, "How long did this visionary kiss last?"
"At least thirty seconds."
She leaned in, and just before her lips met his, she said, "Let's make the real one at least double that."
"Triple."
Dana smiled. "Deal."
When they finally pulled apart, she snuggled into his chest and rested her hand on his shoulder. "I'd really like to go on a little trip with you tomorrow."
"Hurricane Ridge."
She pressed deeper into him. "I can't wait."
SIXTY-ONE
THE SMELL OF A BARBECUE DRIFTED THROUGH THE AIR around Brandon as he ambled toward the backyard of Reece's home—as well as great peals of laughter from the members of Warriors Riding who had already arrived. This was an afternoon he would savor. An October sun still warm enough for them to eat outside. The leaves on Reece's massive maple trees on fire with reds and golds. And the chance to celebrate what they had all come through together and dream about what the future might hold.
He turned the corner and smiled. Miyo, Dana, and Marcus sat on the back deck while Reece stood at the barbecue, bathed in a thick smoke that poured out of it. Next to Reece stood Simon, talking with a significant amount of animation.
Brandon clipped up the steps of the deck, walked over to Dana, and gave her a quick kiss.
"Whoa!" Miyo grinned. "Hold the press. Is there something you two would like to share with the rest of us?"
Brandon spun and grinned back at Miyo. "I think we just did."
"Congratulations," she said.
"It's about time," Marcus added.
"Here, here," called Reece.
Brandon offered a mock bow to all of them. "Thank you, thank you."
He settled into the wicker sofa next to Dana as Reece closed the lid of the barbecue and took a seat across from them. "Should be ready to eat in under ten minutes."
When they sat down to eat, they feasted on salmon and chicken, baked potatoes, and asparagus. A Caesar salad rounded out the meal, and Reece produced Moose Tracks and Cookies and Cream ice cream for dessert, served on top of freshly baked brownies.
For the next three hours they spoke of their past year and a half together. What they had learned, how they had grown, their greatest joys and sorrows. How Simon had been part of them long before they existed, and how the circle was greater than they could have imagined, and the way it had come to a close. By the time the shadows grew long, their conversation waned, but that simply made the time together richer. To sit in silence with those he loved more than any others was food for Brandon's soul.
He and Marcus built a fire in Reece's pit that sat a hundred yards behind the house while Reece, Miyo, Simon, and Dana finished cleaning up from dinner. Soon Dana slid into the wooden chair beside him and took his hand, raised it to her lips, and kissed it.
When they'd all settled in and the fire blazed bright, Reece cleared his throat and turned his head slowly around the circle. "We've had an amazing run together."
"You say that like it's past tense," Brandon said.
Reece nodded and let out a soft sigh. "I think it might be. Both of the prophecies have been fulfilled and unless there's another one no one's mentioned . . . Plus, I'm sensing the Spirit saying he has other things in store for each of us now."
Brandon's heart sank a little. But only a little. He'd sensed the same thing, and Dana and he had talked about it. They both felt God was inspiring the two of them to do something together, and it didn't necessarily include the rest of the Warriors.
Reece turned to Marcus. "Any idea what you'll do with your Warriors Riding time?"
"Yes. More time with Kat and the girls, and I feel I need to do a serious revision to my book on alternate realities. I believe there are at least two new books in me that need to be written."
"Simon?" Reece asked.
"The professor and I will be adventuring down similar paths." He glanced at Miyo. "It's not every day you discover you're the author of what a few might call one of the most powerful treatises on the spiritual realms ever written, which you neglected for more than five decades."
Miyo nodded and smiled at Simon. "And I'm thinking that author might need a publisher to work with who believes passionately in the book, so it can reach a few more people than it has so far."
She glanced at all of them and grinned. "And from what this author tells me, apparently the first book only contains two-thirds of what this author knows. I can't wait to learn the rest of his secrets. I think if I help him get published, he might take me on as a student. I cherish the idea that the teacher of my teacher would now teach me."
Simon looked at Miyo. "Are we still on for next Wednesday morning?"
"Without question." Miyo pointed at him and grinned. "We are going to rock the world, friend."
Reece leaned back and pulled up something wrapped in a light-brown cloth from behind the bench he sat on. "If that's the case, then let me make a contribution to the research part of the project. You might find a few things in here worth including in your tome." He pulled off the cloth and tossed the object toward Miyo like a Frisbee. Before it reached her, a smile broke out on her face. She caught it in one hand and lifted it high for all of them to see.
"Reece's journal," Brandon said.
"A treasure," Simon said.
"What about you, Reece?" Brandon asked. "What are your plans?"
"I don't know and I'm allowing myself not to know. I'll continue to run the training school at Well Spring, but I'm going to cut back to only three classes per year." He pointed at each of them and his voice grew stern. "You're still committed to teaching at least twice a year, right? That includes you, Simon."
They all laughed and agreed that they would.
Silence fell over the six. They all let it linger until the wood in the fire pit became a bed of dark-red coals and a sweet sadness seemed to emanate off the remnants of the fire. Finally, when the night sky had finished turning from blue to a star-studded black, Reece spoke once more.
"It's okay, you know." He smiled. "This season might be over, but we'll never be able to get rid of each other. In fact, next month I'd like us all to get together again. I want to go to a place that might even surprise you, Miyo."
She looked up and a smile broke out on her face.
"Where?" Dana asked.
"Let's just say it's not on earth." Reece tilted his head back slightly and grinned. "And once we get there, I promise you'll want to stay forever."
AUTHOR'S NOTE
DEAR READERS,
I hope you've enjoyed reading _Soul's Gate_ , _Memory's Door_ , and _Spirit Bridge_. I hope you were wildly entertained. Most of all, I hope the Well Spring series caused you to think harder, made you feel deeper, and helped your passion grow for the King and Lord of all worlds, Jesus Christ.
I've loved writing this series and will miss Reece, Dana, Marcus, and Brandon. So much of me is in them, and now much of them is in me. I'll miss Simon and Miyo as well. But I think those two might crash one of my story parties before long, and I'll get the chance to catch up on their further adventures.
With _Spirit Bridge_ , I tried to create an epic conclusion to the series because that's what I believe our lives can be: an epic part of the larger story God is weaving in every second of our lives. The small moments that are in truth never small, and the grand moments that will echo throughout eternity.
If you'd like to find out the latest on what's going on with me and my writing, you can sign up for my newsletter at www.jameslrubart.com. And don't hesitate if you feel like shooting me a note. I'd love to hear from you: james@jameslrubart.com.
Press on, dear friends, in the depth and breadth and height of his unquenchable love,
James L. Rubart
September 2013
www.jameslrubart.com
READING GROUP GUIDE
1. What themes did you see in _Spirit Bridge_?
2. Which character did you relate to the most? Why do you think that is?
3. Miyo, a new character to the Well Spring series, was introduced in _Spirit Bridge._ Did you like her? If yes, what did you like about her? Are there qualities she has that you'd like to have? If you didn't like her, why didn't you?
4. Simon was introduced in _Memory's Door_ , but his role was expanded greatly in _Spirit Bridge_. Was he an intriguing character to you? Did you see his full-circle role at the end of the book coming, or was it a surprise?
5. The enemy had blinded Simon's eyes from seeing who he truly was. He'd forgotten his identity. Do you feel like that has ever happened to you?
6. The theme of spiritual warfare runs through the Well Spring series. Do you think this kind of spiritual warfare exists? What is your experience with spiritual warfare?
7. Throughout the Well Spring series, there were ideas that aren't at the forefront of most Christian's minds, such as teleportation, being unseen by others, building armor made out of light . . . What do you think about those kinds of things? Are they possible?
8. The spiritual virus set in motion by Zennon, blinded Brandon and Reece and they reverted back to acting out of their false selves instead of their true selves. Have you had seasons in your life where you've been walking strong, and then felt like you forgot who you were? Where you forgot your true destiny and calling?
9. The biggest themes in the Well Spring series are freedom and restoration. Do you see freedom coming in your life? Do you see restoration coming? In what ways?
10. A number of people have experienced freedom and restoration not _after_ reading one of the Well Spring novels, but _during_ the time of their reading. If that happened to you, are you willing to talk about it? What happened?
ACKNOWLEDGMENTS
THIS NOVEL WAS THE MOST COLLABORATIVE SINCE MY first story, _Rooms_. I had brilliant input from a number of people. Here they are, in no particular order:
• Five of the MMs (Susie Warren, Randy Ingermanson, Tracy Higley, Mary DeMuth, and Thomas Umstattd) who allowed me to sit in the hot seat during our Austin retreat and brainstormed myriad ideas with me to work from.
• My friends Sarah VanDiest and Ruth Voetmann.
• My agent, Lee Hough, who is now exploring the type of glorious worlds I imagined in the Well Spring series.
• My brother from another mother, Allen Arnold.
• My editors, Amanda Bostic and Julee Schwarzburg.
• My best friend and love of my life, Darci.
If you enjoyed _The Spirit Bridge_ , please thank them. If you didn't, blame me. As my friend Bob Lord is fond of saying, it's all in the execution.
And finally to Jesus, for giving me Life, and for gifting my mind to work this way.
ABOUT THE AUTHOR
Christophoto, Bothell, WA
JAMES L. RUBART IS A PROFESSIONAL MARKETER AND speaker. He is the author of the best-selling novel _Rooms_ as well as _Book of Days_ , _The Chair_ , _Soul's Gate,_ and _Memory's Door_. He lives with his wife and sons in the Pacific Northwest.
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Rogation days are days of prayer and fasting in Western Christianity. They are observed with processions and the Litany of the Saints. The so-called major rogation is held on 25 April; the minor rogations are held on Monday to Wednesday preceding Ascension Thursday. The word rogation comes from the Latin verb rogare, meaning "to ask", which reflects the beseeching of God for the appeasement of his anger and for protection from calamities.
Christian beginnings
The Christian major rogation replaced a pagan Roman procession known as Robigalia, at which a dog was sacrificed to propitiate Robigus, the deity of agricultural disease. The practitioners observing Robigalia asked Robigus for protection of their crops from wheat rust.
The minor Rogation days were introduced around AD 470 by Mamertus, bishop of Vienne, and eventually adopted elsewhere. Their observance was ordered by the Council of Orleans in 511, and though the practice was spreading in Gaul during the 7th century, it was not officially adopted into the Roman rite until the reign of Pope Leo III.
The faithful typically observed the Rogation days by fasting and abstinence in preparation to celebrate the Ascension, and farmers often had their crops blessed by a priest at this time. Violet vestments are worn at the rogation litany and its associated Mass, regardless of what colour is worn at the ordinary liturgies of the day.
A common feature of Rogation days in former times was the ceremony of beating the bounds, in which a procession of parishioners, led by the minister, churchwarden, and choirboys, would proceed around the boundary of their parish and pray for its protection in the forthcoming year. This was also known in the northern parts of England as 'Gang-day' or 'gan week', after the old English name for going or walking. This was also a feature of the original Roman festival, when revellers would walk to a grove five miles from the city to perform their rites. Thomas Johnson (1633), speaking of the birch tree, mentions another name : Cross-week : " It serveth well to the decking up of houses and banquetting-rooms, for places of pleasure, and for beautifying of streets in the Crosse or Gang Week, and such like."
In the British Isles
The Rogation Day ceremonies are thought to have arrived in the British Isles in the 7th century.
The oldest known Sarum text regarding Rogation Days is dated from around 1173 to 1220. In it, celebrations in the south of England are described, in which processions were led by members of the congregation carrying banners which represented various biblical characters. At the head of the procession was the dragon, representing Pontius Pilate, which would be followed by a lion, representing Christ. After this there would be images of saints carried by the rest of the congregation. Many torches were present at each procession, weighing between 42 lb (19 kg) and 27 lbs (12 kg), which were bought by the church and parishioners jointly.
Sarum texts from the 13th and 15th centuries show that the dragon was eventually moved to the rear of the procession on the vigil of the Ascension, with the lion taking the place at the front. Illustrations of the procession from the early 16th century show that the arrangements had been changed yet again, this time also showing bearers of reliquaries and incense.
During the reign of King Henry VIII, Rogation processions were used as a way to assist crop yields, with a notable number of the celebrations taking place in 1543 when there were prolonged rains.
During the reign of King Edward VI, the Crown having taken much of the Church's holdings within the country, liturgical ceremonies were not officially condoned or recognized as an official part of worship. However, in the reign of Queen Elizabeth I the celebrations were explicitly mentioned in the royal reformation, allowing them to resume as public processions.
Rogation processions continued in the post-Reformation Church of England much as they had before, and Anglican priests were encouraged to bring their congregations together for inter-parish processions. At specific intervals, clerics were to remind their congregations to be thankful for their harvests. Psalms 103 and 104 were sung, and people were reminded of the curses the Bible ascribed to those who violated agricultural boundaries. The processions were not mandatory, but were at the discretion of the local minister, and were also ascribed more importance when a public right of way needed to be protected from agricultural or other expansion.
The marches would follow prescribed routes, with York and Coventry being unique in their following royal entries. On other routes, altars were erected at certain locations where antiphons were sung.
Any Roman Catholic imagery or icons were banned from the processions. The then Archdeacon of Essex, Grindal of London, besought the church explicitly to label the tradition as a perambulation of the parish boundaries (beating the bounds), further to distance it from the Catholic liturgy. In the book Second Tome of Homelys, a volume containing officially sanctioned homilies of the Elizabethan church, it was made clear that the English Rogation was to remember town and other communal boundaries in a social and historical context, with extra emphasis on the stability gained from lawful boundary lines.
For years after Rogation Days were recognized, the manner in which they were observed in reality was very different from the official decree. Even before religious sensibilities turned towards the puritanical, there were concerns about the lack of piety at such events. While it was officially ordered that the entire congregation attend, bishops began urging their priests to invite only older and more pious men. This, they believed, would stop the drunken revelry. Royal Injunctions concerning the practice were reinterpreted to restrict and regulate participants of the festivities. Robert Herrick penned a piece to capture the mood of the celebrations before their repression:
In London, Rogation Days, just like Easter or Hocktide, were times when begging was "legitimate" for the period of celebration. Though not widely celebrated in the modern Church of England, the holiday is still observed in some areas.
Rogation Sunday in Anglicanism
In the Anglican tradition, Rogation Sunday is celebrated on the 5th Sunday after Easter (also known as the 6th Sunday of Easter).
In the United States
Catholic
The reform of the Liturgical Calendar for Roman Catholics in 1969 delegated the establishment of Rogation Days, along with Ember Days, to the episcopal conferences. Their observance in the Latin Church subsequently declined, but the observance has revived somewhat since Pope John Paul II allowed Rogation days as a permitted, but not mandated, observance. For those Catholics who continue to celebrate Mass according to the General Roman Calendar of 1960 or earlier, the Rogation Days are still kept, unless a higher ranking feast would occur on the day.
Episcopal
The new, Protestant version of the Rogation days became such a fixture in Church life that the tradition was carried over to the Americas by British colonists in Jamaica, Barbados, and South Carolina. Rogation days are an optional observance in the Episcopal Church. Although early associated with rural life, agriculture and fishing, the Book of Common Prayer has been expanded to include propers for commerce and industry and the stewardship of creation, as well as a fruitful season.
See also
Ember days
Triduum
References
Bibliography
Vito Pallabazzer: Lingua e cultura ladina, Belluno 1985, p. 502 (about the rogation days in Ladin tradition)
External links
Rogation Days at liturgies.net
Catholic Encyclopedia article
Eastertide
Latin Church | {
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News International Affairs
Too close to call: Americans waiting to find out who won presidential election
Millions of Americans are currently waiting to see who their president will be, as votes are still being counted following the election on Tuesday.
Donald Trump is up against Joe Biden in a very tight presidential race.
Neither of the two candidates has so far secured the 270 Electoral College votes needed to be named president. So far, Biden has received 238 while Trump has 213.
Ballots are still being counted across the country, but most people are now paying keen attention to Wisconsin, Michigan and Pennsylvania, which are the states they believe will determine who enters the White House.
Mail-in ballots
When counting resumed on Wednesday, Trump questioned the validity of those votes, many of which are mail-in ballots.
"They are finding Biden votes all over the place — in Pennsylvania, Wisconsin, and Michigan. So bad for our Country," he tweeted.
His statement is not so shocking since on Tuesday night he suggested that some of the mail-in ballots should not be counted based on their arrival date.
Trump's comments were disregarded by Biden, who insists that every vote must be counted.
"It's not my place or Donald Trump's place to declare the winner of this election. It's the voters' place," he tweeted on Tuesday night.
Trump slams social media platforms, claims he made them a success
Donald Trump is still talking. This time he's blasting owners of the different social media platforms and claims Facebook CEO Mark Zuckerberg would come to The…
Trump suing Facebook, Twitter and Google
Leave it to former US President Donald Trump to label him being kicked off all major social media platforms as "censorship of the American people". Trump…
J'can born nurse who got first COVID-19 shot honored by President Biden
The Jamaican born nurse who created history by becoming the first person in the US to get the COVID-19 vaccine was on Friday (July 2) honoured by President Joe Biden…
US vaccine donation won't help Jamaica achieve herd immunity but step in right direction – Holness
Prime Minister Andrew Holness has said that the US government's plans to donate six million doses of the COVID-19 vaccine to the Caribbean is a step in the rig…
donald trumpJoe Bidenus presidential election | {
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{"url":"https:\/\/cran.case.edu\/web\/packages\/lnmCluster\/vignettes\/lnm-bicluster.html","text":"# lnmCluster\n\nWelcome to use package lnmCluster. It is a package designed for applying logistic Normal Multinomial Cluster algorithm. Assumptions and model interpretations could be found in paper: XX and YY. The model coding is a little different compare to the paper. Here we use 3 positions to represent the constrains on parameter B, T, and D sequentially and respectively. U stands for unconstrian(same as paper), G stands for group constrain, D stands for diagonal constrain, and C stands for both group and diagonal(i.e.\u00a0CUUU=GUU, CUCC=GUC, CUUC=GUD, CUCU=GUG\u2026..).\n\n# Main functions\n\nFunctions are coded for easy read and easy understand. * lnmbiclust * lnmfa * plnmfa\n\n1 lnmbiclust is the main function that perform our algorithm, which includes default initial values, main estimations as well as model selection. For illustration, we will generate a simulation data from model \u201cGUU\u201d as follows:\n\nset.seed(123)\nn <- 40\nsimp <- rmultinom(n,1,c(0.6,0.4))\nlab <- as.factor(apply(t(simp),1,which.max))\n\n#parameter comes from multinomial\np <- 11\nmu1 <- c(-2.8,-1.3,-1.6,-3.9,-2.6,-2.9,-2.5,-2.7,-3.1,-2.9)\nB1 <- matrix(c(1,0,0,1,0,0,0,0,0,0,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0,0,0,0),nrow = p-1)\nT1 <- diag(c(2.9,0.5,1))\nD1 <- diag(c(0.52, 1.53, 0.56, 0.19, 1.32, 1.77, 0.6, 0.53, 0.37, 0.4))\ncov1 <- B1%*%T1%*%t(B1)+D1\n\nmu2 <- c(1.5,-2.7,-1.1,-0.4,-1.4,-2.6,-3,-3.9,-2.7,-3)\nB2 <- matrix(c(1,0,0,1,0,0,0,0,0,0,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0,0,0,0),nrow = p-1)\nT2 <- diag(c(0.2,0.003,0.15))\nD2 <- diag(c(0.01, 0.62, 0.45, 0.01, 0.37, 0.42, 0.08, 0.16, 0.23, 0.27))\ncov2 <- B2%*%T2%*%t(B2)+D2\n\ndf <- matrix(0,nrow=n,ncol=p-1)\nfor (i in 1:n) {\nif(lab[i]==1){df[i,] <- rmvnorm(1,mu1,sigma = cov1)}\nelse if(lab[i]==2){df[i,] <- rmvnorm(1,mu2,sigma = cov2)}\n}\n\nf_df <- cbind(df,0)\nz <- exp(f_df)\/rowSums(exp(f_df))\n\nW_count <- matrix(0,nrow=n,ncol=p)\nfor (i in 1:n) {\nW_count[i,] <- rmultinom(1,runif(1,10000,20000),z[i,])\n\n}\n\nAfter generated data, we can strat to try to fit one model:\n\nrange_G <- 2 #define the number of components\nrange_Q <- 2 #define the possible number of bicluster.\ncov_str <- \"GUU\" #select the model you want to fit\n#It will fit GUU model with G=2, Q=c(2,2)\nres <- lnmbiclust(W_count=W_count, range_G=range_G, range_Q=range_Q, model=cov_str)\n#where res will be a list contain all parameters. \n\nNotice the default setting is to run all 16 models if parameter model is missing. There are 3 criteria you can choose: AIC, BIC(default) and ICL.\n\nIf you don\u2019t want to fit a model with specific G or Q, the function can do model selection based on criteria you choose. The output will contain two lists in res, one is the paramters of the best model selected by BIC(AIC or ICL), the other one is a dataframe of model names along with AIC, BIC and ICL values for all models that have ran.\n\nrange_G <- c(2:3)\nrange_Q <- c(2:3)\ncov_str <- c(\"UUU\", \"GGC\")\nres <- lnmbiclust(W_count=W_count, range_G=range_G, range_Q=range_Q, model=cov_str, criteria=\"BIC\")\nbest_model=res$best_model it will run G=2, Q_g=c(2,2); G=3, Q_g=c(2,2,2); G=2, Q_g=c(3,3);G=3, Q_g=c(3,3,3). In total 4 models for each UUU and GGC, then select the best one based on BIC. If you want to include permutations in UUU, UUG, UUD or UUC: range_G <- 2 range_Q <- c(2:3) cov_str <- \"UUU\" res <- lnmbiclust(W_count=W_count, range_G=range_G, range_Q=range_Q, model=cov_str, criteria=\"BIC\",permutation=TRUE) res$best_model\n\nit will run G=2, Q_g=c(2,2); G=2, Q_g=c(3,3); G=2, Q_g=c(2,3);G=2, Q_g=c(3,2). In total 4 models for UUU.\n\nSometimes you may want to know more detail about models that ran. For example, if the BIC values are very close between two models, then they may equally good. Only choose the best one with highest BIC is not fair. Here we have output all_fitted_model under lnmbiclust, which gives the output of all models you have ran and model selection criteria.\n\nres$all_fitted_model It will return a dataframe with all combinations of G and Q for all models you have included, decreasing ordered as the criteria you specified, default is ordered by BIC. 2 lnmfa The usage is exactly the same as lnmbiclust. Except it doesn\u2019t have parameter permutation. The only difference would be the model name. Since in this model, the T is fix as identity matrix, the middle position will also fixed as U. So all the 8 models will be: UUU, UUG, UUD, UUC, GUU, GUG, GUD, GUC. range_G <- c(2:3) range_Q <- c(2:3) cov_str <- c(\"UUU\", \"GUC\") res <- lnmfa(W_count=W_count, range_G=range_G, range_Q=range_Q, model=cov_str, criteria=\"BIC\") best_model=res$best_model\nmodel_output=res$all_fitted_model 3 plnmfa The usage is exactly the same as lnmfa, with additional tunning parameters. In here, range_Q need to be specified by a number instead of a range. The range_tuning could be a range of number which is between 0 and 1. And it doesn\u2019t allow model selections between the two model, so you have to specify the model name between UUU and GUU. range_G <- c(2:3) range_tunning=seq(0.5,0.7,length.out=10) range_Q <- 2 cov_str <- \"UUU\" res <- plnmfa(W_count=W_count, range_G=range_G, range_Q=range_Q, model=cov_str, criteria=\"BIC\", range_tuning = range_tuning) best_model=res$best_model\nmodel_output=res\\$all_fitted_model","date":"2023-01-28 01:22:09","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\": 0.35635846853256226, \"perplexity\": 6182.5389707529275}, \"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-2023-06\/segments\/1674764499468.22\/warc\/CC-MAIN-20230127231443-20230128021443-00300.warc.gz\"}"} | null | null |
'use strict';
const glob = require('glob');
const path = require('path');
module.exports = function findPodspecName(folder) {
const podspecs = glob.sync('*.podspec', { cwd: folder });
let podspecFile = null;
if (podspecs.length === 0) {
return null;
}
else if (podspecs.length === 1) {
podspecFile = podspecs[0];
}
else {
const folderParts = folder.split(path.sep);
const currentFolder = folderParts[folderParts.length - 1];
const toSelect = podspecs.indexOf(currentFolder + '.podspec');
if (toSelect === -1) {
podspecFile = podspecs[0];
}
else {
podspecFile = podspecs[toSelect];
}
}
return podspecFile.replace('.podspec', '');
};
| {
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Marián Kello (Gelnica, Eslovaquia, 5 de septiembre de 1982), futbolista eslovaco. Juega de portero y su actualmente juega en el Saint Mirren FC de la Premier League de Escocia.
Selección nacional
Ha sido internacional con la Selección de fútbol de Eslovaquia, ha jugado 1 partido internacional.
Clubes
Referencias
Enlaces externos
Futbolistas de Eslovaquia
Futbolistas del FC VSS Košice
Futbolistas del Football Club Vítkovice
Futbolistas del FBK Kaunas
Futbolistas del Heart of Midlothian Football Club | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 4,661 |
\subsection{Mel-frequency Cepstral Coefficients}
Mel-frequency Cepstrum is a representation of a sound signal, based on the linear cosine transform of a log power spectrum on a nonlinear mel scale of frequency \cite{beigi2011speaker}. The coefficients that collectively comprise the Mel-frequency Cepstrum are called MFCC features. In contrast to the linearly-spaced frequency bands obtained from the cepstrum of a sound signal, in a mel-frequency cepstrum, the frequency bands are uniformly spaced on the mel scale. This frequency warping allows for better representation of sound and voice data.
\subsection{Temporal Derivatives}
In order to extract the dynamic features of speech, auxiliary delta and delta-delta features must be computed as input features for the model, which are calculated as the temporal derivatives of the original MFCC features \cite{krishnan2013sgfiltering}. In order to estimate smooth derivatives $f_{l, n}^{'}$, we often simply compute the local least squares polynomial fit to the data samples, so as to minimize the cost function
\begin{equation*}
C_{l,n}^p = \sum_{m=-M}^M \left( \sum_{k=0}^p a_k m^k - f_{l,n+m} \right)^2
\end{equation*}
with respect to the MFCC coefficients $a_k$ where \textit{f} is the spectrum-based feature vector, \textit{L} being the number of coefficients, \textit{N} being the number of frames, \textit{p} is the order of the polynomial and \textit{M} is the number of samples used to fit the polynomial.
We compute the delta features via the local estimate of the derivative of the input data, computed using Savitsky-Golay filtering \cite{krishnan2013sgfiltering} as we utilize the Librosa \cite{mcfee2015librosa} package to preprocess the dataset.
\section{Introduction}
\input{introduction.tex}
\section{Background Work}
\input{background_works.tex}
\section{Methodology}
\input{methodology.tex}
\section{Results}
\input{results.tex}
\section{Conclusion}
\input{conclusion.tex}
\section*{Acknowledgment}
We would like to thank Far Eastern Memorial Hospital for donating the dataset and the organizers of the 2018 FEMH challenge for providing valuable feedback.
This publication was supported by the Grant or Cooperative Agreement Number, T42OH008672, funded by the Centers for Disease Control and Prevention. Its contents are solely the responsibility of the authors and do not necessarily represent the official views of the Centers for Disease Control and Prevention or the Department of Health and Human Services.
\bibliographystyle{unsrt}
\subsection{Mel-frequency Cepstral Coefficients}
Mel-frequency Cepstrum is a representation of a sound signal, based on the linear cosine transform of a log power spectrum on a nonlinear mel scale of frequency \cite{beigi2011speaker}. The coefficients that collectively comprise the Mel-frequency Cepstrum are called MFCC features. In contrast to the linearly-spaced frequency bands obtained from the cepstrum of a sound signal, in a mel-frequency cepstrum, the frequency bands are uniformly spaced on the mel scale. This frequency warping allows for better representation of sound and voice data.
\subsection{Temporal Derivatives}
In order to extract the dynamic features of speech, auxiliary delta and delta-delta features must be computed as input features for the model, which are calculated as the temporal derivatives of the original MFCC features \cite{krishnan2013sgfiltering}. In order to estimate smooth derivatives $f_{l, n}^{'}$, we often simply compute the local least squares polynomial fit to the data samples, so as to minimize the cost function
\begin{equation*}
C_{l,n}^p = \sum_{m=-M}^M \left( \sum_{k=0}^p a_k m^k - f_{l,n+m} \right)^2
\end{equation*}
with respect to the MFCC coefficients $a_k$ where \textit{f} is the spectrum-based feature vector, \textit{L} being the number of coefficients, \textit{N} being the number of frames, \textit{p} is the order of the polynomial and \textit{M} is the number of samples used to fit the polynomial.
We compute the delta features via the local estimate of the derivative of the input data, computed using Savitsky-Golay filtering \cite{krishnan2013sgfiltering} as we utilize the Librosa \cite{mcfee2015librosa} package to preprocess the dataset.
\section{Introduction}
\input{introduction.tex}
\section{Background Work}
\input{background_works.tex}
\section{Methodology}
\input{methodology.tex}
\section{Results}
\input{results.tex}
\section{Conclusion}
\input{conclusion.tex}
\section*{Acknowledgment}
We would like to thank Far Eastern Memorial Hospital for donating the dataset and the organizers of the 2018 FEMH challenge for providing valuable feedback.
This publication was supported by the Grant or Cooperative Agreement Number, T42OH008672, funded by the Centers for Disease Control and Prevention. Its contents are solely the responsibility of the authors and do not necessarily represent the official views of the Centers for Disease Control and Prevention or the Department of Health and Human Services.
\bibliographystyle{unsrt}
\subsection{Data Processing}
Each audio waveform is processed to derive MFCC features using the Librosa \cite{mcfee2015librosa} library, using a sampling rate of 22050 Hertz. We compute the temporal derivatives (delta) of these MFCC features, of which we compute the mean and maximum across all samples, and concatenate all three vectors into a single vector of size $\mathbb{R}^{3d}$, where \textit{d} is the number of extracted MFCC coefficients. We select the number of MFCC coefficients (\textit{d}) computed to be 15, which we find via grid search over the space of \textit{\{10, 15, 20, 25, 30, 40, 50, 100\}}.
When assessing the performance of any model, we compute a weighted average of the sensitivity and specificity of the model on the binary task of predicting whether the sample is normal or pathological, and the average recall of the model on the multitask objective of classifying the sample as one of four classes. We assign the weights for the above scores as 40\%, 20\%, and 40\% respectively.
\begin{figure*}[t]
\centering
\includegraphics[width=0.75\linewidth]{images/Maryam_FEMH.pdf}
\caption{Proposed model pipeline.}
\label{fig:model_pipeline}
\end{figure*}
\subsection{Hyperparameter Tuning} \label{Hyperparam_tuning}
As the dataset comprises of a mere 200 samples, we perform 5 fold cross validation for every model using the same global seed across all models. We utilize the sequential halving and classification \textit{(SHAC)} algorithm from \textit{Kumar et al.} \cite{kumar2018shac}, as an efficient alternative to exhaustive grid search to sample hyperparameter settings in continuous search spaces. To avoid overfitting the data distribution in the 5 folds used for evaluation of the models, we train and evaluate the \textit{SHAC} algorithm on 5 different folds of the dataset using a different random seed. This preserves the generalization properties of the parameters sampled from the \textit{SHAC} algorithm while also providing robustness to random seed overfitting. For better robustness, we round off all floating point values to the 3rd decimal place, and find that performance is not impacted.
When training the classifiers of the \textit{SHAC} algorithm, we compute a maximum of 10 classifiers, with a batch of 100 hyperparameter samples per classifier and a total budget of 1000 hyperparameter samples evaluated. It is to be noted that once we obtain a sample from the \textit{SHAC} algorithm, we use the same parameters for all 5 folds. Therefore, the sampled parameters are more robust and generalize better, as they must perform well across all 5 folds. We then obtain 100 hyperparameter samples, compute the mean and standard deviation of this batch, and select those candidates which obtain a score greater than the mean plus one standard deviation. We use a publically available implementation of the \textit{SHAC} algorithm \footnote{\href{https://github.com/titu1994/pyshac}{https://github.com/titu1994/pyshac}}.
\subsection{Proposed Model} \label{Proposed_Model}
Our proposed model is comprised of a feature selection stage followed by a multi-class classification stage. We utilize a set of Random Forest models, each trained on the training data of a given fold, to compute the feature importance of the 45 dimension input vector. We then determine a threshold value sampled from the \textit{SHAC} algorithm, which is used to select only those features which are above that threshold. These features are then supplied to a Kernel Support Vector Machine, which utilizes the Gaussian Radial Basis Function as its kernel. We utilize the One-vs-One strategy for multi-class classification, which builds $\frac{N * (N-1)}{2}$ classifiers. Such a strategy is applicable here due to the small amount of data available and relatively fast training, but we observe that One-vs-All strategy is nearly identical in performance. We utilize the excellent Scikit Learn \cite{pedregosa2011scikit} package for all models described in this section. Figure \ref{fig:model_pipeline} details the various stages of the proposed model pipeline.
We construct a search space consisting of the number of trees in the Random Forest \textit{\{10, 20, 50, 100\}}, depth of the tree \textit{\{3, 4, 5, 6, 7, 8, no limit\}}, selection threshold ($U\in(0, 0.5)$), penalty parameter \textit{C} for the SVM ($U\in(0, 25)$), gamma parameter for the RBF kernel ($U\in(-1, 1)$), where we resolve negative values to be \textit{1 / (number of features)}. We then search over this space using the \textit{SHAC} algorithm and sample its best parameters as described in Hyperparameter tuning \ref{Hyperparam_tuning}.
\subsection{Baseline Models}
All baseline models utilize the same input features and 5 fold training as described in the proposed model, to ensure a consistent training methodology. Random Forest based feature selection is performed, but the hyperparameters for the baseline models are searched via \textit{SHAC} to ensure we obtain unbiased hyperparameters. The search space for the Random Forest and the selection threshold remain consistent across all models.
\subsubsection{XGBoost}
We compare against XGBoost \cite{chen2016xgboost}, a powerful Gradient Boosting Tree model which obtains state-of-the-art results on multiple structured and unstructured datasets and is a standard baseline model to compete with.
While XGBoost has a large number of hyperparameters that can be tuned, we find that only three of these parameters significantly impact the final score, and therefore construct a search space only over those three parameters. We search over the number of estimators \textit{\{10, 25, 50, 100, 200\}}, the maximum depth of the tree \textit{\{3, 4, 5, 6, 7, 8\}}, and the learning rate $U\in(0.01, 0.2)$.
\subsubsection{Long Short Term Memory Fully Convolutional Networks}
We also compare this dataset on a hybrid deep neural network, called the Long Short Term Memory Fully Convolutional Network (LSTM-FCN) \cite{karim2018lstm}. It comprises of two branches, one with Convolutional blocks comprised of a Convolutional Layer, followed by Batch Normalization \cite{ioffe2015batch} and then the Relu activation function. Another branch is comprised of a Long Short Term Memory Recurrent layer \cite{hochreiter1997lstm} followed by a dropout \cite{srivastava2014dropout} layer (with a probability of 80\%).
We utilize the same FCN and LSTM branch structure as provided by \textit{Karim et al.} to be consistent, and only modify the number of LSTM cells in the LSTM branch, which we find using grid search \cite{karim2018lstm}. All aspects of initialization and training methodology are kept consistent with the paper to provide the best results.
\subsection{Data Processing}
Each audio waveform is processed to derive MFCC features using the Librosa \cite{mcfee2015librosa} library, using a sampling rate of 22050 Hertz. We compute the temporal derivatives (delta) of these MFCC features, of which we compute the mean and maximum across all samples, and concatenate all three vectors into a single vector of size $\mathbb{R}^{3d}$, where \textit{d} is the number of extracted MFCC coefficients. We select the number of MFCC coefficients (\textit{d}) computed to be 15, which we find via grid search over the space of \textit{\{10, 15, 20, 25, 30, 40, 50, 100\}}.
When assessing the performance of any model, we compute a weighted average of the sensitivity and specificity of the model on the binary task of predicting whether the sample is normal or pathological, and the average recall of the model on the multitask objective of classifying the sample as one of four classes. We assign the weights for the above scores as 40\%, 20\%, and 40\% respectively.
\begin{figure*}[t]
\centering
\includegraphics[width=0.75\linewidth]{images/Maryam_FEMH.pdf}
\caption{Proposed model pipeline.}
\label{fig:model_pipeline}
\end{figure*}
\subsection{Hyperparameter Tuning} \label{Hyperparam_tuning}
As the dataset comprises of a mere 200 samples, we perform 5 fold cross validation for every model using the same global seed across all models. We utilize the sequential halving and classification \textit{(SHAC)} algorithm from \textit{Kumar et al.} \cite{kumar2018shac}, as an efficient alternative to exhaustive grid search to sample hyperparameter settings in continuous search spaces. To avoid overfitting the data distribution in the 5 folds used for evaluation of the models, we train and evaluate the \textit{SHAC} algorithm on 5 different folds of the dataset using a different random seed. This preserves the generalization properties of the parameters sampled from the \textit{SHAC} algorithm while also providing robustness to random seed overfitting. For better robustness, we round off all floating point values to the 3rd decimal place, and find that performance is not impacted.
When training the classifiers of the \textit{SHAC} algorithm, we compute a maximum of 10 classifiers, with a batch of 100 hyperparameter samples per classifier and a total budget of 1000 hyperparameter samples evaluated. It is to be noted that once we obtain a sample from the \textit{SHAC} algorithm, we use the same parameters for all 5 folds. Therefore, the sampled parameters are more robust and generalize better, as they must perform well across all 5 folds. We then obtain 100 hyperparameter samples, compute the mean and standard deviation of this batch, and select those candidates which obtain a score greater than the mean plus one standard deviation. We use a publically available implementation of the \textit{SHAC} algorithm \footnote{\href{https://github.com/titu1994/pyshac}{https://github.com/titu1994/pyshac}}.
\subsection{Proposed Model} \label{Proposed_Model}
Our proposed model is comprised of a feature selection stage followed by a multi-class classification stage. We utilize a set of Random Forest models, each trained on the training data of a given fold, to compute the feature importance of the 45 dimension input vector. We then determine a threshold value sampled from the \textit{SHAC} algorithm, which is used to select only those features which are above that threshold. These features are then supplied to a Kernel Support Vector Machine, which utilizes the Gaussian Radial Basis Function as its kernel. We utilize the One-vs-One strategy for multi-class classification, which builds $\frac{N * (N-1)}{2}$ classifiers. Such a strategy is applicable here due to the small amount of data available and relatively fast training, but we observe that One-vs-All strategy is nearly identical in performance. We utilize the excellent Scikit Learn \cite{pedregosa2011scikit} package for all models described in this section. Figure \ref{fig:model_pipeline} details the various stages of the proposed model pipeline.
We construct a search space consisting of the number of trees in the Random Forest \textit{\{10, 20, 50, 100\}}, depth of the tree \textit{\{3, 4, 5, 6, 7, 8, no limit\}}, selection threshold ($U\in(0, 0.5)$), penalty parameter \textit{C} for the SVM ($U\in(0, 25)$), gamma parameter for the RBF kernel ($U\in(-1, 1)$), where we resolve negative values to be \textit{1 / (number of features)}. We then search over this space using the \textit{SHAC} algorithm and sample its best parameters as described in Hyperparameter tuning \ref{Hyperparam_tuning}.
\subsection{Baseline Models}
All baseline models utilize the same input features and 5 fold training as described in the proposed model, to ensure a consistent training methodology. Random Forest based feature selection is performed, but the hyperparameters for the baseline models are searched via \textit{SHAC} to ensure we obtain unbiased hyperparameters. The search space for the Random Forest and the selection threshold remain consistent across all models.
\subsubsection{XGBoost}
We compare against XGBoost \cite{chen2016xgboost}, a powerful Gradient Boosting Tree model which obtains state-of-the-art results on multiple structured and unstructured datasets and is a standard baseline model to compete with.
While XGBoost has a large number of hyperparameters that can be tuned, we find that only three of these parameters significantly impact the final score, and therefore construct a search space only over those three parameters. We search over the number of estimators \textit{\{10, 25, 50, 100, 200\}}, the maximum depth of the tree \textit{\{3, 4, 5, 6, 7, 8\}}, and the learning rate $U\in(0.01, 0.2)$.
\subsubsection{Long Short Term Memory Fully Convolutional Networks}
We also compare this dataset on a hybrid deep neural network, called the Long Short Term Memory Fully Convolutional Network (LSTM-FCN) \cite{karim2018lstm}. It comprises of two branches, one with Convolutional blocks comprised of a Convolutional Layer, followed by Batch Normalization \cite{ioffe2015batch} and then the Relu activation function. Another branch is comprised of a Long Short Term Memory Recurrent layer \cite{hochreiter1997lstm} followed by a dropout \cite{srivastava2014dropout} layer (with a probability of 80\%).
We utilize the same FCN and LSTM branch structure as provided by \textit{Karim et al.} to be consistent, and only modify the number of LSTM cells in the LSTM branch, which we find using grid search \cite{karim2018lstm}. All aspects of initialization and training methodology are kept consistent with the paper to provide the best results.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 1,453 |
Q: How can I combine hashes in Perl? What is the best way to combine both hashes into %hash1? I always know that %hash2 and %hash1 always have unique keys. I would also prefer a single line of code if possible.
$hash1{'1'} = 'red';
$hash1{'2'} = 'blue';
$hash2{'3'} = 'green';
$hash2{'4'} = 'yellow';
A: For hash references. You should use curly braces like the following:
$hash_ref1 = {%$hash_ref1, %$hash_ref2};
and not the suggested answer above using parenthesis:
$hash_ref1 = ($hash_ref1, $hash_ref2);
A: Check out perlfaq4: How do I merge two hashes. There is a lot of good information already in the Perl documentation and you can have it right away rather than waiting for someone else to answer it. :)
Before you decide to merge two hashes, you have to decide what to do if both hashes contain keys that are the same and if you want to leave the original hashes as they were.
If you want to preserve the original hashes, copy one hash (%hash1) to a new hash (%new_hash), then add the keys from the other hash (%hash2 to the new hash. Checking that the key already exists in %new_hash gives you a chance to decide what to do with the duplicates:
my %new_hash = %hash1; # make a copy; leave %hash1 alone
foreach my $key2 ( keys %hash2 )
{
if( exists $new_hash{$key2} )
{
warn "Key [$key2] is in both hashes!";
# handle the duplicate (perhaps only warning)
...
next;
}
else
{
$new_hash{$key2} = $hash2{$key2};
}
}
If you don't want to create a new hash, you can still use this looping technique; just change the %new_hash to %hash1.
foreach my $key2 ( keys %hash2 )
{
if( exists $hash1{$key2} )
{
warn "Key [$key2] is in both hashes!";
# handle the duplicate (perhaps only warning)
...
next;
}
else
{
$hash1{$key2} = $hash2{$key2};
}
}
If you don't care that one hash overwrites keys and values from the other, you could just use a hash slice to add one hash to another. In this case, values from %hash2 replace values from %hash1 when they have keys in common:
@hash1{ keys %hash2 } = values %hash2;
A: Quick Answer (TL;DR)
%hash1 = (%hash1, %hash2)
## or else ...
@hash1{keys %hash2} = values %hash2;
## or with references ...
$hash_ref1 = { %$hash_ref1, %$hash_ref2 };
Overview
*
*Context: Perl 5.x
*Problem: The user wishes to merge two hashes1 into a single variable
Solution
*
*use the syntax above for simple variables
*use Hash::Merge for complex nested variables
Pitfalls
*
*What do to when both hashes contain one or more duplicate keys
*
*(see e.g., Perl - Merge hash containing duplicate keys)
*(see e.g., Perl hashes: how to deal with duplicate keys and get possible pair)
*Should a key-value pair with an empty value ever overwrite a key-value pair with a non-empty value?
*
*What constitutes an empty vs non-empty value in the first place? (e.g. undef, zero, empty string, false, falsy ...)
See also
*
*PM post on merging hashes
*PM Categorical Q&A hash union
*Perl Cookbook 5.10. Merging Hashes
*websearch://perlfaq "merge two hashes"
*websearch://perl merge hash
*https://metacpan.org/pod/Hash::Merge
Footnotes
1 * (aka associative-array, aka dictionary)
A: This is an old question, but comes out high in my Google search for 'perl merge hashes' - and yet it does not mention the very helpful CPAN module Hash::Merge
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 6,567 |
const createTestServer = require("../test/createTestServer.js");
const client = require("sham-it/client/shamClient");
const fetch = require("node-fetch");
describe("integration: remote client", () => {
let sham;
let isRunning;
beforeAll(async () => {
const port = await createTestServer();
sham = client({ port });
});
afterEach(async () => {
await sham.reset();
});
afterAll(async () => {
await sham.close();
expect(isRunning).toBe(false);
});
describe("Returning the default reply", () => {
test("it should return the default default reply", async () => {
const response = await fetch(`${sham.uri}/some/uri`);
expect(response).toHaveProperty("status", 404);
expect(response.headers.get("content-type")).toBe("text/plain");
expect(await response.text()).toBe("Not Found");
});
});
describe("Using matchers", () => {
test("it should give each matcher an id", async () => {
const matcher = await sham.addMatcher({
when: ({ equals }) => equals("pathname", "/some/uri"),
respond: { body: { yay: true } }
});
expect(matcher).toHaveProperty("id");
});
test("it should return the specified response when a request matching the matcher is made", async () => {
let response = await fetch(`${sham.uri}/test`);
expect(response).toHaveProperty("status", 404);
expect(response.headers.get("content-type")).toBe("text/plain");
expect(await response.text()).toBe("Not Found");
const status = 200;
const contentType = "application/json";
const body = { this: { is: { a: "mock" } } };
await sham.addMatcher({
when: ({ equals }) => equals("pathname", "/test"),
respond: { status, headers: { "Content-Type": contentType }, body }
});
response = await fetch(`${sham.uri}/test`);
expect(response).toHaveProperty("status", status);
expect(response.headers.get("content-type")).toBe(contentType);
expect(await response.json()).toEqual(body);
});
describe("Using complex matchers", () => {
beforeEach(async () => {
await sham.addMatcher({
when: ({
and,
or,
not,
equals,
greaterThan,
greaterThanOrEquals,
lessThan,
lessThanOrEquals,
regex
}) =>
or(
and(equals("method", "PUT"), regex("pathname", /(\/sham){3,5}$/)),
and(
equals("method", "POST"),
greaterThan("body.values.a", 5),
greaterThanOrEquals("body.values.b", 2)
),
and(
equals("method", "GET"),
lessThanOrEquals("query.test", 7),
not(lessThan("query.test", 3))
)
),
respond: {
body: { success: true }
}
});
});
test("example 1", async () => {
expect(
await fetch(`${sham.uri}/sham/sham`, { method: "PUT" })
).toHaveProperty("status", 404);
expect(
await fetch(`${sham.uri}/sham/sham/sham/sham`, { method: "PUT" })
).toHaveProperty("status", 200);
});
test("example 2", async () => {
expect(
await fetch(`${sham.uri}`, {
method: "POST",
headers: { "Content-Type": "application/json" },
body: JSON.stringify({
values: {
a: 5,
b: 2
}
})
})
).toHaveProperty("status", 404);
expect(
await fetch(`${sham.uri}`, {
method: "POST",
headers: { "Content-Type": "application/json" },
body: JSON.stringify({
values: {
a: 6,
b: 1
}
})
})
).toHaveProperty("status", 404);
expect(
await fetch(`${sham.uri}`, {
method: "POST",
headers: { "Content-Type": "application/json" },
body: JSON.stringify({
values: {
a: 6,
b: 5
}
})
})
).toHaveProperty("status", 200);
});
test("example 3", async () => {
expect(await fetch(`${sham.uri}?test=2`)).toHaveProperty("status", 404);
expect(await fetch(`${sham.uri}?test=8`)).toHaveProperty("status", 404);
expect(await fetch(`${sham.uri}?test=6`)).toHaveProperty("status", 200);
});
});
describe("Matcher validation", () => {
test("Must pass an object to addMatcher", async () => {
await expect(sham.addMatcher()).rejects.toEqual(
new Error(
"Error creating matcher: The matcher definition must be an object"
)
);
});
test("Must contain a when property", async () => {
await expect(
sham.addMatcher({
respond: {}
})
).rejects.toEqual(
new Error(
"Error creating matcher: The matcher must contain a valid when property"
)
);
});
test("when property must be an object", async () => {
await expect(
sham.addMatcher({
when: "",
respond: {}
})
).rejects.toEqual(
new Error(
"Error creating matcher: The matcher must contain a valid when property"
)
);
});
test("respond property must be an object", async () => {
await expect(
sham.addMatcher({
when: { op: "==", prop: "pathname", value: "/test" },
respond: ""
})
).rejects.toEqual(
new Error(
"Error creating matcher: The matcher must contain a valid respond property"
)
);
});
//TODO: More validation of when and respond properties, should traverse and check format.
});
test("it should always try match the most recently added matcher first", async () => {
await sham.addMatcher({
when: ({ equals }) => equals("pathname", "/test"),
respond: { body: "test 1" }
});
let response = await fetch(`${sham.uri}/test`);
expect(await response.text()).toBe("test 1");
await sham.addMatcher({
when: ({ equals }) => equals("pathname", "/test"),
respond: { body: "test 2" }
});
response = await fetch(`${sham.uri}/test`);
expect(await response.text()).toBe("test 2");
});
test("it should allow you to list all of the mocks that have been created", async () => {
const matcherA = await sham.addMatcher({
when: ({ equals }) => equals("pathname", "/test"),
respond: { body: "test 1" }
});
const matcherB = await sham.addMatcher({
when: ({ equals }) => equals("pathname", "/test"),
respond: { body: "test 2" }
});
const matchers = await sham.getMatchers();
expect(matchers).toHaveLength(2);
expect(matchers).toContainEqual(matcherA);
expect(matchers).toContainEqual(matcherB);
});
test("it should allow you retrieve a mock by id", async () => {
const created = await sham.addMatcher({
when: ({ equals }) => equals("pathname", "/test"),
respond: { body: "test 1" }
});
const matcher = await sham.getMatcher(created.id);
expect(matcher).toEqual(created);
});
test("it should allow you to delete a mock", async () => {
const matcher = await sham.addMatcher({
when: ({ equals }) => equals("pathname", "/test"),
respond: { body: "test 1" }
});
let response = await fetch(`${sham.uri}/test`);
expect(await response.text()).toBe("test 1");
await sham.deleteMatcher(matcher.id);
response = await fetch(`${sham.uri}/test`);
expect(await response.text()).toBe("Not Found");
});
test("it should allow to set how many times a matcher should match before it expires", async () => {
const { id } = await sham.addMatcher({
when: ({ equals }) => equals("pathname", "/test"),
respond: { body: "test 1" },
times: 2
});
let response = await fetch(`${sham.uri}/test`);
expect(await response.text()).toBe("test 1");
response = await fetch(`${sham.uri}/test`);
expect(await response.text()).toBe("test 1");
response = await fetch(`${sham.uri}/test`);
expect(await response.text()).toBe("Not Found");
const matcher = await sham.getMatcher(id);
expect(matcher).toHaveProperty("times", 0);
});
test("it should reset the list of matchers and requests", async () => {
await sham.addMatcher({
when: ({ equals }) => equals("pathname", "/test"),
respond: { body: "test 1" },
times: 2
});
await fetch(`${sham.uri}/test`);
expect(await sham.getMatchers()).toHaveLength(1);
expect(await sham.getRequests()).toHaveLength(1);
await sham.reset();
expect(await sham.getMatchers()).toHaveLength(0);
expect(await sham.getRequests()).toHaveLength(0);
});
});
describe("Retrieving requests", () => {
test("it should log each request", async () => {
await sham.addMatcher({
when: ({ equals }) => equals("pathname", "/test"),
respond: { body: "test 1" }
});
await fetch(`${sham.uri}/test`);
await fetch(`${sham.uri}/test`);
expect(await sham.getRequests()).toHaveLength(2);
await fetch(`${sham.uri}/test`);
expect(await sham.getRequests()).toHaveLength(3);
});
test("it should log requests which don`t match", async () => {
await fetch(`${sham.uri}/thing1`);
await fetch(`${sham.uri}/thing2`);
expect(await sham.getRequests()).toHaveLength(2);
await fetch(`${sham.uri}/thing3`);
expect(await sham.getRequests()).toHaveLength(3);
});
test("it should record which matcher was matched", async () => {
const matcherA = await sham.addMatcher({
when: ({ equals }) => equals("pathname", "/test1"),
respond: { body: "test 1" }
});
const matcherB = await sham.addMatcher({
when: ({ equals }) => equals("pathname", "/test2"),
respond: { body: "test 2" }
});
const matcherC = await sham.addMatcher({
when: ({ equals }) => equals("pathname", "/test3"),
respond: { body: "test " }
});
await fetch(`${sham.uri}/test1`);
await fetch(`${sham.uri}/test2`);
await fetch(`${sham.uri}/test3`);
await fetch(`${sham.uri}/test4`);
const requests = await sham.getRequests();
expect(requests).toHaveLength(4);
expect(requests[0]).toHaveProperty("matcher", matcherA);
expect(requests[1]).toHaveProperty("matcher", matcherB);
expect(requests[2]).toHaveProperty("matcher", matcherC);
expect(requests[3]).not.toHaveProperty("matcher");
});
});
describe("Asserting that mocks have been called", () => {
describe("sham.hasBeenCalled()", () => {
test("it should return true if there are any requests in the requestStore", async () => {
await fetch(`${sham.uri}/test`);
expect(await sham.hasBeenCalled()).toBe(true);
});
test("it should throw an error if the sham has received no requests", async () => {
await expect(sham.hasBeenCalled()).rejects.toBeDefined();
});
});
describe("sham.not.hasBeenCalled()", () => {
test("it should throw an error if there are any requests in the requestStore", async () => {
await fetch(`${sham.uri}/test`);
await expect(sham.not.hasBeenCalled()).rejects.toBeDefined();
});
test("it should return true if the sham has received no requests", async () => {
expect(await sham.not.hasBeenCalled()).toBe(true);
});
});
describe("sham.hasBeenCalledTimes(number)", () => {
test("it should return true if the number of requests in the requestStore matches the number", async () => {
await fetch(`${sham.uri}/test`);
await fetch(`${sham.uri}/test2`);
expect(await sham.hasBeenCalledTimes(2)).toBe(true);
});
test("it should throw an error if the number of requests in the requestStore does not match the number", async () => {
await fetch(`${sham.uri}/test`);
await expect(sham.hasBeenCalledTimes(2)).rejects.toBeDefined();
});
});
describe("sham.not.hasBeenCalledTimes(number)", () => {
test("it should throw an error if the number of requests in the requestStore matches the number", async () => {
await fetch(`${sham.uri}/test`);
await fetch(`${sham.uri}/test2`);
await expect(sham.not.hasBeenCalledTimes(2)).rejects.toBeDefined();
});
test("it should return true if the number of requests in the requestStore does not match the number", async () => {
await fetch(`${sham.uri}/test`);
expect(await sham.not.hasBeenCalledTimes(2)).toBe(true);
});
});
describe("sham.hasBeenCalledWith(condition)", () => {
test("it should return true if the sham has received a request that matches the condition", async () => {
await fetch(`${sham.uri}/test`);
await fetch(`${sham.uri}/test2`);
expect(
await sham.hasBeenCalledWith(({ and, equals }) =>
and(equals("method", "GET"), equals("pathname", "/test2"))
)
).toBe(true);
});
test("it should throw an error if the sham has not received a request that matches the condition", async () => {
await fetch(`${sham.uri}/test`);
await expect(
sham.hasBeenCalledWith(({ and, equals }) =>
and(equals("method", "GET"), equals("pathname", "/test2"))
)
).rejects.toBeDefined();
});
});
describe("sham.not.hasBeenCalledWith(condition)", () => {
test("it should throw an error if the sham has received a request that matches the condition", async () => {
await fetch(`${sham.uri}/test`);
await fetch(`${sham.uri}/test2`);
await expect(
sham.not.hasBeenCalledWith(({ and, equals }) =>
and(equals("method", "GET"), equals("pathname", "/test2"))
)
).rejects.toBeDefined();
});
test("it should return true if the sham has not received a request that matches the condition", async () => {
await fetch(`${sham.uri}/test`);
expect(
await sham.not.hasBeenCalledWith(({ and, equals }) =>
and(equals("method", "GET"), equals("pathname", "/test2"))
)
).toBe(true);
});
});
describe("sham.hasBeenLastCalledWith(condition)", () => {
test("it should return true if the sham was last called with a request that matches the condition", async () => {
await fetch(`${sham.uri}/test`);
expect(
await sham.hasBeenLastCalledWith(({ and, equals }) =>
and(equals("method", "GET"), equals("pathname", "/test"))
)
).toBe(true);
});
test("it should throw an error if the sham was last called with a request that doesn't match the condition", async () => {
await fetch(`${sham.uri}/test`);
await fetch(`${sham.uri}/test2`);
await expect(
sham.hasBeenLastCalledWith(({ and, equals }) =>
and(equals("method", "GET"), equals("pathname", "/test"))
)
).rejects.toBeDefined();
});
});
describe("sham.not.hasBeenLastCalledWith(condition)", () => {
test("it should throw an error if the sham was last called with a request that matches the condition", async () => {
await fetch(`${sham.uri}/test`);
await expect(
sham.not.hasBeenLastCalledWith(({ and, equals }) =>
and(equals("method", "GET"), equals("pathname", "/test"))
)
).rejects.toBeDefined();
});
test("it should return true if the sham was last called with a request that doesn't match the condition", async () => {
await fetch(`${sham.uri}/test`);
await fetch(`${sham.uri}/test2`);
expect(
await sham.not.hasBeenLastCalledWith(({ and, equals }) =>
and(equals("method", "GET"), equals("pathname", "/test"))
)
).toBe(true);
});
});
describe("matcher.hasBeenCalled()", () => {
test("it should return true if there are any requests in the requestStore that matched the matcher", () => {});
test("it should throw an error if the sham has received no requests that matched the matcher", () => {});
});
describe("matcher.not.hasBeenCalled()", () => {
test("it should throw an error if there are any requests in the requestStore that matched the matcher", () => {});
test("it should return true if the sham has received no requests that matched the matcher", () => {});
});
describe("matcher.hasBeenCalledTimes(x)", () => {
test("it should return true if there are x requests in the requestStore that matched the matcher", () => {});
test("it should throw an error if there are x requests in the requestStore that matched the matcher", () => {});
});
describe("matcher.not.hasBeenCalledTimes(x)", () => {
test("it should throw an error if there are x requests in the requestStore that matched the matcher", () => {});
test("it should return true if there are x requests in the requestStore that matched the matcher", () => {});
});
describe("matcher.hasBeenCalledWith(condition)", () => {
test("it should return true if the sham has received a request that matches the condition and matched the matcher", () => {});
test("it should throw an error if the sham has not received a request that matches the condition and matched the matcher", () => {});
});
describe("matcher.not.hasBeenCalledWith(condition)", () => {
test("it should throw an error if the sham has received a request that matches the condition and matched the matcher", () => {});
test("it should return true if the sham has not received a request that matches the condition and matched the matcher", () => {});
});
describe("matcher.hasBeenLastCalledWith(condition)", () => {
test("it should return true if the last call that matched the matcher also matches the condition", () => {});
test("it should throw an error if the last call that matched the matcher also matches the condition", () => {});
});
describe("matcher.not.hasBeenLastCalledWith(condition)", () => {
test("it should throw an error if the last call that matched the matcher also matches the condition", () => {});
test("it should return true if the last call that matched the matcher also matches the condition", () => {});
});
});
});
| {
"redpajama_set_name": "RedPajamaGithub"
} | 7,640 |
Features Business Operations Commercial
Last call to nominate outstanding women in aviation
March 8, 2012 By administrator
March 8, 2012, Toronto – The nomination deadline for the fourth annual Elsie MacGill Northern Lights (EMNL) awards is fast approaching.
March 8, 2012, Toronto – The nomination deadline for the fourth annual
Elsie MacGill Northern Lights (EMNL) awards is fast approaching. Named
after Elsie MacGill, the first Canadian female aircraft designer, the
award's mission is to recognize excellence and to inspire women to enter
the aviation and aerospace industries in Canada. The EMNL awards honour
outstanding women in aviation and aerospace who have demonstrated
determination, perseverance, leadership and courage throughout their
MacGill graduated from the University of Toronto's engineering program
in 1927, becoming the first Canadian woman to earn a degree in
electrical engineering, and eventually became the first woman in North
America with an advanced degree in aeronautics. Dubbed the "Queen of the
Hurricanes," she was pivotal in the design and production of the Hawker
Hurricane in Canada during the Second World War.
The EMNL award has experienced overwhelming success in its first three
years, and the upcoming year of 2012 marks an important milestone: the
award has expanded and will now honour women in four separate
categories: Flight Operations/Maintenance, Business, Government, and
Rising Star. Honorees will be presented with their awards at the 2012
gala ceremony and dinner in September 2012.
Past winners of this prestigious award include Heather Sifton, former
president and CEO of the Buttonville Municipal Airport; Kathy Fox,
retired vice-president operations for Nav Canada and currently an
appointed member of the Transportation Safety Board; and Roberta Taylor,
an aviation trailblazer and social activist who now teaches at the
University of Victoria.
For more information about the award, sponsorship opportunities, and to
nominate a woman in aviation and aerospace for the Award, please visit www.northernlightsaward.ca. The nomination deadline is March 31, 2012.
Eagle Copters Ltd.
Erickson Incorporated
MacKay praises women for military contributions
DART announces approval for access-steps | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 6,647 |
Q: Displaying GeoJSON data on mapboxgl in reactjs I have created this GeoJSON document for waterStations
var waterStation = {
type: 'FeatureCollection',
features: [
{
type: 'Feature',
properties: {
title: 'Water Refill Station',
description: 'Description to be added...'
},
geometry: {
type: 'Point',
coordinates: [-120.4295379, 37.3634714]
}
}]};
Then I have followed the mapboxgl tutorials to create data points on a map with popups. However now I have built a csv to GeoJson converter and would like to change the variable waterStation in the following code to geoJson, which is the name of my new variable.
waterStation.features.forEach(function(marker) {
console.log(geoJson.features[1]);
console.log(marker);
var refill = document.createElement('div');
refill.className = 'water-station';
refill.appendChild(document.createElement('i'));
new mapboxgl.Marker(refill).setLngLat(marker.geometry.coordinates).setPopup(new mapboxgl.Popup({offset: 25}).setHTML('<h3>' + marker.properties.title + '</h3><p>' + marker.properties.description + '</p>')).addTo(map);
});}
My issue is that the forEach function will not output either of those console.log() executions when I make the change from waterStation to geoJson. A copy of how I am doing my csv to geojson is listed below.
import axios from 'axios';
import Papa from 'papaparse';
var results = {};
var geoJson = {
type: 'FeatureCollection',
features: []
};
axios.get(`path to my csv file`).then(res => {
var csvString = res.data;
results = Papa.parse(csvString, {
delimiter: ",",
header: true,
dynamicTyping: true
});
for (var i = 0; i < results.data.length; i++) {
geoJson.features.push({
'type': 'Feature',
'geometry': {
'type': 'Point',
'coordinates': [
results.data[i].longitude,
results.data[i].latitude
]
},
'properties': {
'title': results.data[i].title,
'description': results.data[i].description
}
});
}
});
A: I have found a quick and short answer to this. Because of the way axios works the .push() does not load at the same time as outside the call. To fix this I just dropped the popup forEach loop inside the .then() and it will display all the data at the same time.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 9,902 |
"Corvetto" is an Italian literary fairy tale written by Giambattista Basile in his 1634 work, the "Pentamerone".
It is Aarne-Thompson type 531. Other tales of this type include "The Firebird and Princess Vasilisa", "Ferdinand the Faithful and Ferdinand the Unfaithful", "King Fortunatus's Golden Wig", and "The Mermaid and the Boy". Another, literary variant is Madame d'Aulnoy's "La Belle aux cheveux d'or", or "The Story of Pretty Goldilocks".
Synopsis
Corvetto served a king loyally and was favored by him. Envious fellow servants tried to slander him, but failed. An ogre lived nearby, with a magnificent horse, and finally the servants said that the king should send Corvetto to steal it. Corvetto went, and jumped on the horse. It shouted to its master, who chased after with wild animals (one of them being a Werewolf), but Corvetto rode it off. The king was even more pleased, and the other servants told him to send Corvetto after the ogre's tapestry. Corvetto went, hid under the ogres' bed, and in the night stole both the tapestries and the counterpane from the bed (causing the ogre and ogress to argue about who hogged them). He dropped them from a window and fled back to the king.
The servants then persuaded him to send Corvetto for the entire palace. He went and talked with the ogress, offering to help her. She asked him to split wood for her. He used the axe on her neck. Then he dug a deep pit in the doorway and covered it. He lured the ogre and his friends into it, stoned them to death, and gave the king the palace.
See also
Boots and the Troll
Dapplegrim
Esben and the Witch
The Gifts of the Magician
Thirteenth
References
Italian fairy tales
Fictional servants
ATU 500-559 | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 1,076 |
#ifndef GrColor_DEFINED
#define GrColor_DEFINED
#include "GrTypes.h"
#include "SkColor.h"
#include "SkColorPriv.h"
#include "SkUnPreMultiply.h"
/**
* GrColor is 4 bytes for R, G, B, A, in a specific order defined below. The components are stored
* premultiplied.
*/
typedef uint32_t GrColor;
// shift amount to assign a component to a GrColor int
// These shift values are chosen for compatibility with GL attrib arrays
// ES doesn't allow BGRA vertex attrib order so if they were not in this order
// we'd have to swizzle in shaders.
#ifdef SK_CPU_BENDIAN
#define GrColor_SHIFT_R 24
#define GrColor_SHIFT_G 16
#define GrColor_SHIFT_B 8
#define GrColor_SHIFT_A 0
#else
#define GrColor_SHIFT_R 0
#define GrColor_SHIFT_G 8
#define GrColor_SHIFT_B 16
#define GrColor_SHIFT_A 24
#endif
/**
* Pack 4 components (RGBA) into a GrColor int
*/
static inline GrColor GrColorPackRGBA(unsigned r, unsigned g, unsigned b, unsigned a) {
SkASSERT((uint8_t)r == r);
SkASSERT((uint8_t)g == g);
SkASSERT((uint8_t)b == b);
SkASSERT((uint8_t)a == a);
return (r << GrColor_SHIFT_R) |
(g << GrColor_SHIFT_G) |
(b << GrColor_SHIFT_B) |
(a << GrColor_SHIFT_A);
}
/**
* Packs a color with an alpha channel replicated across all four channels.
*/
static inline GrColor GrColorPackA4(unsigned a) {
SkASSERT((uint8_t)a == a);
return (a << GrColor_SHIFT_R) |
(a << GrColor_SHIFT_G) |
(a << GrColor_SHIFT_B) |
(a << GrColor_SHIFT_A);
}
// extract a component (byte) from a GrColor int
#define GrColorUnpackR(color) (((color) >> GrColor_SHIFT_R) & 0xFF)
#define GrColorUnpackG(color) (((color) >> GrColor_SHIFT_G) & 0xFF)
#define GrColorUnpackB(color) (((color) >> GrColor_SHIFT_B) & 0xFF)
#define GrColorUnpackA(color) (((color) >> GrColor_SHIFT_A) & 0xFF)
/**
* Since premultiplied means that alpha >= color, we construct a color with
* each component==255 and alpha == 0 to be "illegal"
*/
#define GrColor_ILLEGAL (~(0xFF << GrColor_SHIFT_A))
#define GrColor_WHITE 0xFFFFFFFF
#define GrColor_TRANSPARENT_BLACK 0x0
/**
* Assert in debug builds that a GrColor is premultiplied.
*/
static inline void GrColorIsPMAssert(GrColor SkDEBUGCODE(c)) {
#ifdef SK_DEBUG
unsigned a = GrColorUnpackA(c);
unsigned r = GrColorUnpackR(c);
unsigned g = GrColorUnpackG(c);
unsigned b = GrColorUnpackB(c);
SkASSERT(r <= a);
SkASSERT(g <= a);
SkASSERT(b <= a);
#endif
}
/** Inverts each color channel. */
static inline GrColor GrInvertColor(GrColor c) {
U8CPU a = GrColorUnpackA(c);
U8CPU r = GrColorUnpackR(c);
U8CPU g = GrColorUnpackG(c);
U8CPU b = GrColorUnpackB(c);
return GrColorPackRGBA(0xff - r, 0xff - g, 0xff - b, 0xff - a);
}
static inline GrColor GrColorMul(GrColor c0, GrColor c1) {
U8CPU r = SkMulDiv255Round(GrColorUnpackR(c0), GrColorUnpackR(c1));
U8CPU g = SkMulDiv255Round(GrColorUnpackG(c0), GrColorUnpackG(c1));
U8CPU b = SkMulDiv255Round(GrColorUnpackB(c0), GrColorUnpackB(c1));
U8CPU a = SkMulDiv255Round(GrColorUnpackA(c0), GrColorUnpackA(c1));
return GrColorPackRGBA(r, g, b, a);
}
static inline GrColor GrColorSatAdd(GrColor c0, GrColor c1) {
unsigned r = SkTMin<unsigned>(GrColorUnpackR(c0) + GrColorUnpackR(c1), 0xff);
unsigned g = SkTMin<unsigned>(GrColorUnpackG(c0) + GrColorUnpackG(c1), 0xff);
unsigned b = SkTMin<unsigned>(GrColorUnpackB(c0) + GrColorUnpackB(c1), 0xff);
unsigned a = SkTMin<unsigned>(GrColorUnpackA(c0) + GrColorUnpackA(c1), 0xff);
return GrColorPackRGBA(r, g, b, a);
}
/** Converts a GrColor to an rgba array of GrGLfloat */
static inline void GrColorToRGBAFloat(GrColor color, float rgba[4]) {
static const float ONE_OVER_255 = 1.f / 255.f;
rgba[0] = GrColorUnpackR(color) * ONE_OVER_255;
rgba[1] = GrColorUnpackG(color) * ONE_OVER_255;
rgba[2] = GrColorUnpackB(color) * ONE_OVER_255;
rgba[3] = GrColorUnpackA(color) * ONE_OVER_255;
}
/** Normalizes and coverts an uint8_t to a float. [0, 255] -> [0.0, 1.0] */
static inline float GrNormalizeByteToFloat(uint8_t value) {
static const float ONE_OVER_255 = 1.f / 255.f;
return value * ONE_OVER_255;
}
/** Determines whether the color is opaque or not. */
static inline bool GrColorIsOpaque(GrColor color) {
return (color & (0xFFU << GrColor_SHIFT_A)) == (0xFFU << GrColor_SHIFT_A);
}
static inline GrColor GrPremulColor(GrColor color) {
unsigned r = GrColorUnpackR(color);
unsigned g = GrColorUnpackG(color);
unsigned b = GrColorUnpackB(color);
unsigned a = GrColorUnpackA(color);
return GrColorPackRGBA(SkMulDiv255Round(r, a),
SkMulDiv255Round(g, a),
SkMulDiv255Round(b, a),
a);
}
/** Returns an unpremuled version of the GrColor. */
static inline GrColor GrUnpremulColor(GrColor color) {
GrColorIsPMAssert(color);
unsigned r = GrColorUnpackR(color);
unsigned g = GrColorUnpackG(color);
unsigned b = GrColorUnpackB(color);
unsigned a = GrColorUnpackA(color);
SkPMColor colorPM = SkPackARGB32(a, r, g, b);
SkColor colorUPM = SkUnPreMultiply::PMColorToColor(colorPM);
r = SkColorGetR(colorUPM);
g = SkColorGetG(colorUPM);
b = SkColorGetB(colorUPM);
a = SkColorGetA(colorUPM);
return GrColorPackRGBA(r, g, b, a);
}
/**
* Flags used for bitfields of color components. They are defined so that the bit order reflects the
* GrColor shift order.
*/
enum GrColorComponentFlags {
kR_GrColorComponentFlag = 1 << (GrColor_SHIFT_R / 8),
kG_GrColorComponentFlag = 1 << (GrColor_SHIFT_G / 8),
kB_GrColorComponentFlag = 1 << (GrColor_SHIFT_B / 8),
kA_GrColorComponentFlag = 1 << (GrColor_SHIFT_A / 8),
kNone_GrColorComponentFlags = 0,
kRGB_GrColorComponentFlags = (kR_GrColorComponentFlag | kG_GrColorComponentFlag |
kB_GrColorComponentFlag),
kRGBA_GrColorComponentFlags = (kR_GrColorComponentFlag | kG_GrColorComponentFlag |
kB_GrColorComponentFlag | kA_GrColorComponentFlag)
};
GR_MAKE_BITFIELD_OPS(GrColorComponentFlags)
static inline char GrColorComponentFlagToChar(GrColorComponentFlags component) {
SkASSERT(SkIsPow2(component));
switch (component) {
case kR_GrColorComponentFlag:
return 'r';
case kG_GrColorComponentFlag:
return 'g';
case kB_GrColorComponentFlag:
return 'b';
case kA_GrColorComponentFlag:
return 'a';
default:
SkFAIL("Invalid color component flag.");
return '\0';
}
}
static inline uint32_t GrPixelConfigComponentMask(GrPixelConfig config) {
SkASSERT(config >= 0 && config < kGrPixelConfigCnt);
static const uint32_t kFlags[] = {
0, // kUnknown_GrPixelConfig
kA_GrColorComponentFlag, // kAlpha_8_GrPixelConfig
kRGBA_GrColorComponentFlags, // kIndex_8_GrPixelConfig
kRGB_GrColorComponentFlags, // kRGB_565_GrPixelConfig
kRGBA_GrColorComponentFlags, // kRGBA_4444_GrPixelConfig
kRGBA_GrColorComponentFlags, // kRGBA_8888_GrPixelConfig
kRGBA_GrColorComponentFlags, // kBGRA_8888_GrPixelConfig
kRGBA_GrColorComponentFlags, // kSRGBA_8888_GrPixelConfig
kRGB_GrColorComponentFlags, // kETC1_GrPixelConfig
kA_GrColorComponentFlag, // kLATC_GrPixelConfig
kA_GrColorComponentFlag, // kR11_EAC_GrPixelConfig
kRGBA_GrColorComponentFlags, // kASTC_12x12_GrPixelConfig
kRGBA_GrColorComponentFlags, // kRGBA_float_GrPixelConfig
kA_GrColorComponentFlag, // kAlpha_16_GrPixelConfig
kRGBA_GrColorComponentFlags, // kRGBA_half_GrPixelConfig
};
return kFlags[config];
GR_STATIC_ASSERT(0 == kUnknown_GrPixelConfig);
GR_STATIC_ASSERT(1 == kAlpha_8_GrPixelConfig);
GR_STATIC_ASSERT(2 == kIndex_8_GrPixelConfig);
GR_STATIC_ASSERT(3 == kRGB_565_GrPixelConfig);
GR_STATIC_ASSERT(4 == kRGBA_4444_GrPixelConfig);
GR_STATIC_ASSERT(5 == kRGBA_8888_GrPixelConfig);
GR_STATIC_ASSERT(6 == kBGRA_8888_GrPixelConfig);
GR_STATIC_ASSERT(7 == kSRGBA_8888_GrPixelConfig);
GR_STATIC_ASSERT(8 == kETC1_GrPixelConfig);
GR_STATIC_ASSERT(9 == kLATC_GrPixelConfig);
GR_STATIC_ASSERT(10 == kR11_EAC_GrPixelConfig);
GR_STATIC_ASSERT(11 == kASTC_12x12_GrPixelConfig);
GR_STATIC_ASSERT(12 == kRGBA_float_GrPixelConfig);
GR_STATIC_ASSERT(13 == kAlpha_half_GrPixelConfig);
GR_STATIC_ASSERT(14 == kRGBA_half_GrPixelConfig);
GR_STATIC_ASSERT(SK_ARRAY_COUNT(kFlags) == kGrPixelConfigCnt);
}
#endif
| {
"redpajama_set_name": "RedPajamaGithub"
} | 2,168 |
using Microsoft.IdentityModel.Clients.ActiveDirectory;
using System;
using System.Windows.Forms;
using System.Security;
using System.Net.Http.Headers;
using RESTfulOutlook.Utils;
using System.Globalization;
using System.Runtime.InteropServices;
using System.Threading.Tasks;
using Microsoft.Graph;
namespace RESTfulOutlook
{
public partial class frmMain : Form
{
// clientId is used by the application to uniquely identify itself to Azure AD.
// redirectUri is the URI where Azure AD will return OAuth responses.
// authority is the sign-in URL of the tenant.
// graphApiEndpoint is the resource url for the unified graph api
private static string clientId;
Uri redirectUri;
private static string authority;
private static string graphApiEndpoint;
// ADAL and Graph SDK objects
private AuthenticationContext authContext = null;
private AuthenticationResult authResult = null;
public GraphServiceClient graphClient;
// Basic authentication objects
private SecureString passwordEntered = new SecureString();
private string userNameEntered = string.Empty;
public string userName = null;
// token cache, logging and config objects
private FileCache fc;
public LoggedOnUserHelper user;
ClassLogger applogger = null;
ClassLogger sdklogger = null;
ConfigHelper config = null;
public frmMain()
{
InitializeComponent();
// init config helper
config = new ConfigHelper();
config.clientId = Properties.Settings.Default.ClientId;
config.graphEndpoint = Properties.Settings.Default.GraphEndpoint;
config.redirectUri = Properties.Settings.Default.RedirectUri;
// init config values
redirectUri = new Uri(config.redirectUri);
authority = String.Format(CultureInfo.InvariantCulture, config.aadInstance, "common");
clientId = config.clientId;
graphApiEndpoint = config.graphEndpoint;
// create log and token cache objects
applogger = new ClassLogger("restfuloutlook-app.log");
sdklogger = new ClassLogger("restfuloutlook-graphsdk.log");
user = new LoggedOnUserHelper();
fc = new FileCache(Environment.CurrentDirectory);
// init button state
btnMailAPI.Enabled = false;
btnGraphAPI.Enabled = false;
btnContactsAPI.Enabled = false;
btnCalendarAPI.Enabled = false;
btnReportingService.Enabled = false;
btnUserPhotoAPI.Enabled = false;
}
public void ToggleButtons()
{
if (rdoBasic.Checked)
{
btnReportingService.Enabled = !btnReportingService.Enabled;
}
if (rdoGraphAPI.Checked)
{
btnMailAPI.Enabled = !btnMailAPI.Enabled;
btnContactsAPI.Enabled = !btnContactsAPI.Enabled;
btnCalendarAPI.Enabled = !btnCalendarAPI.Enabled;
btnGraphAPI.Enabled = !btnGraphAPI.Enabled;
}
}
public void ToggleRdoButtons()
{
rdoGraphAPI.Enabled = !rdoGraphAPI.Enabled;
rdoBasic.Enabled = !rdoBasic.Enabled;
}
public void Logout()
{
try
{
if (rdoGraphAPI.Checked)
{
// clear the token cache
authContext.TokenCache.Clear();
// check for cache type
if (Properties.Settings.Default.TokenCache == "File")
{
fc.Clear();
}
else
{
// clear cookies from browser control
ClearCookies();
}
// clear the user info
user.Clear();
}
else
{
// reset basic auth controls
passwordEntered = null;
userNameEntered = null;
tbUsername.Enabled = true;
mskPassword.Enabled = true;
ToggleButtons();
ToggleRdoButtons();
}
}
catch (Exception ex)
{
applogger.Log(ex.Message);
}
finally
{
// reset UI text
ToggleRdoButtons();
ToggleButtons();
lblUsername.Text = "No User Logged In";
btnLoginLogout.Text = "Login";
}
}
private async Task GetGraphSDKClient()
{
bool userCancel = false;
try
{
// setup the context based on app settings
if (Properties.Settings.Default.TokenCache == "Adal")
{
authContext = new AuthenticationContext(authority);
}
else
{
authContext = new AuthenticationContext(authority, fc);
}
// get access token
switch (Properties.Settings.Default.AuthPromptBehavior)
{
case "Auto":
authResult = await authContext.AcquireTokenAsync(graphApiEndpoint, clientId, redirectUri, new PlatformParameters(PromptBehavior.Auto, null));
break;
case "Never":
authResult = await authContext.AcquireTokenAsync(graphApiEndpoint, clientId, redirectUri, new PlatformParameters(PromptBehavior.Never, null));
break;
case "RefreshSession":
authResult = await authContext.AcquireTokenAsync(graphApiEndpoint, clientId, redirectUri, new PlatformParameters(PromptBehavior.RefreshSession, null));
break;
default:
authResult = await authContext.AcquireTokenAsync(graphApiEndpoint, clientId, redirectUri, new PlatformParameters(PromptBehavior.Always, null));
break;
}
// create the graph client
graphClient = new GraphServiceClient(
new DelegateAuthenticationProvider(
(requestMessage) =>
{
requestMessage.Headers.Authorization = new AuthenticationHeaderValue(authResult.AccessTokenType, authResult.AccessToken);
return Task.FromResult(0);
}));
}
catch (AdalException ae)
{
if (ae.ErrorCode != "user_interaction_required")
{
applogger.Log(ae.Message);
userCancel = true;
}
}
catch (Exception ex)
{
applogger.Log(ex.Message);
}
finally
{
if (userCancel == false)
{
GetUserInfo();
userName = authResult.UserInfo.DisplayableId;
lblUsername.Text = userName;
btnLoginLogout.Text = "Logout";
ToggleRdoButtons();
ToggleButtons();
}
else
{
lblUsername.Text = "No User Logged In";
btnLoginLogout.Text = "Login";
}
}
}
public void GetUserInfo()
{
// populate user info
user.DisplayableId = authResult.UserInfo.DisplayableId;
user.GivenName = authResult.UserInfo.GivenName;
user.FamilyName = authResult.UserInfo.FamilyName;
user.AccessToken = authResult.AccessToken;
user.IdToken = authResult.IdToken;
user.ExpiresOn = authResult.ExpiresOn;
user.AccessTokenType = authResult.AccessTokenType;
}
public async void Login()
{
try
{
if (rdoGraphAPI.Checked)
{
// get the graph client
await GetGraphSDKClient();
}
else
{
// store the basic auth creds
passwordEntered = converToSecureString(mskPassword.Text);
userNameEntered = tbUsername.Text;
tbUsername.Text = string.Empty;
mskPassword.Text = string.Empty;
lblUsername.Text = userNameEntered;
tbUsername.Enabled = false;
mskPassword.Enabled = false;
ToggleButtons();
ToggleRdoButtons();
btnLoginLogout.Text = "Logout";
}
}
catch (Exception ex)
{
applogger.Log(ex.Message);
}
}
public SecureString converToSecureString(string pass)
{
var secureString = new SecureString();
if (pass.Length > 0)
{
foreach (var c in pass.ToCharArray())
{
secureString.AppendChar(c);
}
}
return secureString;
}
#region Form Button Clicks
private void btnLoginLogout_Click(object sender, EventArgs e)
{
try
{
if (rdoBasic.Checked && (tbUsername.Text == string.Empty || mskPassword.Text == string.Empty) && btnLoginLogout.Text == "Login")
{
MessageBox.Show("Authenticate using basic credentials", "Warning", MessageBoxButtons.OK, MessageBoxIcon.Warning);
return;
}
else if (rdoBasic.Checked && btnLoginLogout.Text == "Logout")
{
btnReportingService.Enabled = false;
ToggleRdoButtons();
Logout();
}
else if (btnLoginLogout.Text == "Login")
{
Login();
}
else
{
Logout();
}
}
catch(Exception ex)
{
applogger.Log(ex.Message);
}
}
private void btnContactsAPI_Click(object sender, EventArgs e)
{
Forms.ContactsAPI mContactsAPI = new Forms.ContactsAPI(ref graphClient, ref applogger, ref sdklogger);
mContactsAPI.Owner = this;
mContactsAPI.ShowDialog(this);
}
private void btnReportingService_Click(object sender, EventArgs e)
{
Forms.ReportingService mReportingService = new Forms.ReportingService(userNameEntered, passwordEntered);
mReportingService.Owner = this;
mReportingService.ShowDialog(this);
}
private void btnCalendarAPI_Click(object sender, EventArgs e)
{
Forms.CalendarAPI mCalendarAPI = new Forms.CalendarAPI(ref graphClient, ref applogger, ref sdklogger);
mCalendarAPI.Owner = this;
mCalendarAPI.ShowDialog(this);
}
private void btnMailAPI_Click(object sender, EventArgs e)
{
Forms.MailAPI mMailAPI = new Forms.MailAPI(ref graphClient, ref applogger, ref sdklogger);
mMailAPI.Owner = this;
mMailAPI.ShowDialog(this);
}
private void btnGraphAPI_Click(object sender, EventArgs e)
{
Forms.GraphAPI mGraph = new Forms.GraphAPI(authResult, user.DisplayableId);
mGraph.Owner = this;
mGraph.ShowDialog(this);
}
private void btnSettings_Click(object sender, EventArgs e)
{
Forms.Settings mSettings = new Forms.Settings();
mSettings.Owner = this;
mSettings.ShowDialog();
try
{
// update the config values
clientId = Properties.Settings.Default.ClientId;
redirectUri = new Uri(Properties.Settings.Default.RedirectUri);
config.clientId = clientId;
config.redirectUri = Properties.Settings.Default.RedirectUri;
}
catch (Exception ex)
{
// if we fail on a bad config setting, clear property
applogger.Log("Settings failed to update: " + ex.Message);
Properties.Settings.Default.ClientId = "";
Properties.Settings.Default.RedirectUri = "";
Properties.Settings.Default.Save();
}
}
private void btnUserInfo_Click(object sender, EventArgs e)
{
Forms.UserInfoForm mUserInfo = new Forms.UserInfoForm(user);
mUserInfo.Owner = this;
mUserInfo.ShowDialog(this);
}
private void btnScopes_Click(object sender, EventArgs e)
{
string bodyText = "View users' basic profile\r\n" + "View users' email address\r\n"
+ "Read user contacts\r\n" + "Read user calendars\r\n" + "Read user mail\r\n"
+ "Access directory as the signed on user\r\n" + "Sign in and read user profile"
+ "Sign in and read user profile\r\n" + "Read items in all site collections\r\n"
+ "Read threat intelligence data for your organization\r\n" + "Read activity data for your organization\r\n"
+ "Read service health information for your organization\r\n" + "Read activity reports for your organization";
MessageBox.Show(bodyText, "Office365 Graph Scopes", MessageBoxButtons.OK, MessageBoxIcon.Information);
}
#endregion
#region Cookie Management
// This function clears cookies from the browser control used by ADAL.
private void ClearCookies()
{
const int INTERNET_OPTION_END_BROWSER_SESSION = 42;
InternetSetOption(IntPtr.Zero, INTERNET_OPTION_END_BROWSER_SESSION, IntPtr.Zero, 0);
}
[DllImport("wininet.dll", SetLastError = true)]
private static extern bool InternetSetOption(IntPtr hInternet, int dwOption, IntPtr lpBuffer, int lpdwBufferLength);
#endregion
private void rdoGraphAPI_CheckedChanged(object sender, EventArgs e)
{
if (rdoGraphAPI.Checked == true)
{
mskPassword.Text = "";
tbUsername.Text = "";
tbUsername.Enabled = false;
mskPassword.Enabled = false;
}
}
private void rdoBasic_CheckedChanged(object sender, EventArgs e)
{
if (rdoBasic.Checked == true)
{
tbUsername.Enabled = true;
mskPassword.Enabled = true;
}
}
private void frmMain_FormClosing(object sender, FormClosingEventArgs e)
{
// cleanup resources on exit
applogger.Dispose();
sdklogger.Dispose();
}
}
} | {
"redpajama_set_name": "RedPajamaGithub"
} | 1,835 |
package org.apache.camel.processor;
import org.apache.camel.ContextTestSupport;
import org.apache.camel.Exchange;
import org.apache.camel.Route;
import org.apache.camel.builder.RouteBuilder;
import org.apache.camel.component.mock.MockEndpoint;
import org.apache.camel.impl.JndiRegistry;
import org.apache.camel.support.RoutePolicySupport;
import org.junit.Test;
public class RoutePoliciesRefTest extends ContextTestSupport {
private final MyCustomRoutePolicy policyA = new MyCustomRoutePolicy("A");
private final MyCustomRoutePolicy policyB = new MyCustomRoutePolicy("B");
@Override
protected JndiRegistry createRegistry() throws Exception {
JndiRegistry jndi = super.createRegistry();
jndi.bind("policy-a", policyA);
jndi.bind("policy-b", policyB);
return jndi;
}
private static final class MyCustomRoutePolicy extends RoutePolicySupport {
private final String name;
private MyCustomRoutePolicy(String name) {
this.name = name;
}
@Override
public void onExchangeBegin(Route route, Exchange exchange) {
exchange.getIn().setHeader(name, name);
}
}
@Test
public void testCustomPolicies() throws Exception {
MockEndpoint mock = getMockEndpoint("mock:result");
mock.expectedBodiesReceived("Hello World");
mock.expectedHeaderReceived("A", "A");
mock.expectedHeaderReceived("B", "B");
template.sendBody("direct:start", "Hello World");
assertMockEndpointsSatisfied();
}
@Override
protected RouteBuilder createRouteBuilder() throws Exception {
return new RouteBuilder() {
@Override
public void configure() throws Exception {
from("direct:start")
.routePolicyRef("policy-a, policy-b")
.to("mock:result");
}
};
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 2,210 |
Guangzhou Auto Rolls Out Concept Cars; Prepares to Launch Own Brand
The state-owned company, which is partnered in joint-venture plants with Honda and Toyota, says the show cars are the first step in introducing the auto maker's own brand.
Peter Homola | Nov 29, 2007
Guangzhou Automobile Industry Group Co. Ltd. introduced three concept cars at the recent 5th annual Guangzhou International Automobile Exhibition in China that will be produced under a yet-to-be-announced brand name.
Meanwhile, the Ford Verve and Mazda2 sedan were among the most important global auto makers' premieres at the show, also known as Auto Guangzhou 2007.
State-owned Guangzhou Auto, which is partnered in vehicle-plant joint ventures with Honda Motor Co. Ltd. and Toyota Motor Corp., says the concepts are the first step in introducing the auto maker's own brand.
The show cars include what the company calls a 4-door coupe, along with a battery powered sedan dubbed the AEV and a futuristic hybrid minivan named AHEV that was designed by Italy's Torino Design SpA.
The Chinese auto maker uses the abbreviations GAC or GAIE on the concept cars, but it is not clear what the final brand name will be, although a new vehicle badge is introduced at the show.
Construction of a research and design center and vehicle plant site already is under way in Guangzhou's Payu district. The Chinese auto maker will invest some $916 million, including $404 million on the R&D center and $512 million on production facilities in order to launch its own brand of passenger cars by 2010.
Plans call for an annual capacity of 100,000 cars and 100,000 engines in the first stage. The second phase will see capacity expanded to 200,000 vehicles and 250,000 engines annually.
Guangzhou Auto says in a statement that it plans to build several models. The first will be a sedan, "between the intermediate and limousine level" that is expected to reach the market in 2010.
Among other Chinese auto makers at the show, BYD Auto Co. Ltd. unveiled its new BYD F1 small car for the first time. The car, which has a similar design to the Toyota Aygo minicar built in Czech Republic, will be available in Chinese dealerships next April.
As with Guangzhou Auto, BYD also introduced a new vehicle logo. The old logo was similar to BMW AG's badge, and the German auto maker has objected to applications to register the BYD logo in other countries.
Changan Auto Co. Ltd. showed a sporty version of its Benben small car, called the Benben Sport. The Changan Benben, or Benni for export markets, which was designed by IDEA Institute SpA, first was introduced under its codename CV6 in September. The Benben Sport has a modified front facia.
FAW Tianjin Xiali Automobile Co. Ltd., a subsidiary of China's largest vehicle maker FAW Group, exhibited restyled versions of the Xiali N3, now dubbed the Xiali N3+, and its Vela cars.
Among global auto makers, the Ford Verve 4-door notchback is a concept car, but the Mazda2 sedan will be built by Changan Ford Mazda Automobile Co. Ltd. at its Nanjing plant. The car will go on sale in first-half 2008 through Changan Mazda Motor Sales Co. Ltd.'s distribution network.
Guangzhou Honda Automobile Co. Ltd. unwrapped its next-generation Honda Accord at the show, with Job One set for early 2008, while the highlight of the Nissan Motor Co. Ltd. exhibit was its new Qashqai cross/utility vehicle.
Nissan used the show to announce the Qashqai will be built locally by its Dongfeng Motor Group Co. Ltd. JV, joining the U.K. and Japan as production sites. Nissan also unveiled facelifted versions of the Nissan Tiida hatchback and sedan.
Nearby, Toyota displayed its Yaris subcompact car, which is slated to begin production at the Guangzhou Toyota Motor Co. Ltd. JV plant in mid-2008. Also on Toyota's stand was the redesigned Vios, which is manufactured at Tianjin FAW Toyota Motor Co. Ltd. in China.
Beijing Hyundai Motor Co. Ltd. unveiled the Hyundai Elantra HDC, a new-generation Elantra that is expected to reach Chinese dealerships next April. The abbreviation HDC stands for HD China. The model's design is somewhat modified from the new Korean-made Elantra, which was unveiled last year.
Additionally, Dongfeng Yueda Kia Motors Co. Ltd. showed a modified version of the Kia Cerato, with sales starting in China next month.
TAGS: Vehicles
Ford Reveals Second Verve Concept | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 8,455 |
I strive to provide high-quality medical care with a strong emphasis on disease prevention. I believe that maintaining a strong personal relationship with the patient is an important factor in producing the best healthcare.
When I go to Dr. Zebaida, I am always confident that I am getting high quality care. He keeps me current on my vaccinations and reviews my medication list for optimal health maintenance. I would highly recommend this Dr. He has cared for my husband and guided him through difficult times.
×Post a ResponseAre you Dr. Oren Zebaida, MD?
I will recommend Dr Zebaida to all my friends. Dr. Zebaida is caring, thorough, compassionate, patient and knowledgeable. Try him, you will not disappointed.
How was your experience with Dr. Zebaida?
Check the quality of care at hospitals where Dr. Zebaida treats patients. | {
"redpajama_set_name": "RedPajamaC4"
} | 304 |
Georg Wilhelm Richard Knetsch (* 9. Februar 1904 in Wiesbaden; † 28. Juni 1997 in Würzburg) war ein deutscher Geologe. Er war Professor an der Universität Würzburg und dort Vorstand des Geologischen Instituts und 1960/61 Rektor.
Leben
Knetsch studierte 1923 bis 1925 an der Universität Marburg und 1925 bis 1927 an der Universität München, unter anderem bei Emanuel Kayser, Hans Cloos, Ferdinand Broili. 1927 war er Assistent an der Universität München und 1928 bis 1936 als praktischer Geologe in Südafrika, Südwestafrika (Namibia), Ghana (Goldküste), Sierra Leone. 1937 war er an der Reichsanstalt für das Deutsche Bäderwesen und 1938 als Privatdozent an der Universität Bonn. 1939 bis 1945 war er Wehrgeologe unter anderem in Libyen. 1949 wurde er außerplanmäßiger Professor an der Universität Bonn. 1951 bis 1953 war er Direktor der Abteilung Geologie der Universität Kairo und Berater der ägyptischen Regierung in Bergbau- und Wasserfragen. Ab 1955 war er ordentlicher Professor in Würzburg.
Er befasste sich in den 1930er und 1940er Jahren auch mit der Geologie von Trockengebieten in Südwestafrika (zum Beispiel Diamantlagerstätten an der Oranje-Mündung) und in Libyen (Marmara-Senke) Er verfasste ein Buch über die Geologie Deutschlands.
1961 erhielt er die Hans-Stille-Medaille. 1974 wurde er Ehrenmitglied der Geologischen Vereinigung. 1962 wurde er Mitglied der Leopoldina. Zudem ist er seit Namensgeber für den Knetschberg in der Antarktis.
Schriften
Über Wickelstrukturen aus dem fränkischen Röt. In: Abh. dtsch. Akad. Wiss. Berlin, Kl. III, 1960 (1), Berlin 1960, S. 375–377
Geologie von Deutschland und einigen Randgebieten, Enke Verlag 1963
mit Josef Frechen, Michael Hopmann Die vulkanische Eifel, Bonn, Wilhelm Stollfuss 1960
mit Werner Beetz, Fritz Behrend, Fritz-Erdmann Klingner Der geologische Bau, die nutzbaren Lagerstätten und die Bergwirtschaft Afrikas, Teil 1 bis 3, Erich Obst (Herausgeber) Handbuch der praktischen Kolonialwissenschaften, Band III, Walter de Gruyter 1942–1943
Literatur
Egon T. Degens (Herausgeber) Ein Nord-Süd-Profil: Zentraleuropa, Mittelmeerraum, Afrika; Festband Georg Knetsch (zur Vollendung seines 80. Lebensjahres), Geologisch-Paläontologisches Institut, Universität Hamburg, 1984
Weblinks
Nachlass an der Universität Freiburg
Einzelnachweise
Geologe (20. Jahrhundert)
Rektor der Julius-Maximilians-Universität Würzburg
Hochschullehrer (Julius-Maximilians-Universität Würzburg)
Mitglied der Leopoldina (20. Jahrhundert)
Absolvent der Ludwig-Maximilians-Universität München
Deutscher
Geboren 1904
Gestorben 1997
Mann | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 3,465 |
Q: objective-c - argument of parent function passed into child block is not changed inside I'm new to ios and objective-c programming and currently I'm a bit confused with this behavior -
I have function which calls handler with block inside. This function receives different arguments but inside block handler it's not changed, it stays as it was declared on first call:
- (void)searchBarSearchButtonClicked:(UISearchBar *)searchBar
{
// called with different strings - "foo", "bar"
[self startSearchText:searchBar.text];
}
- (void)startSearchText:(NSString *)text
{
__block CGFloat page = 1;
__weak LSAllFavoritesViewController *weakSelf = self;
// initial search request
[weakSelf makeSearchWithText:text byPage:page success:^{
page += 1;
}];
// infinite scrolling
[weakSelf.searchDisplayController.searchResultsTableView addInfiniteScrollingWithActionHandler:^
{
// text will remain "foo" for all next requests
[weakSelf makeSearchWithText:text byPage:page success:^{
page += 1;
[weakSelf.searchDisplayController.searchResultsTableView.infiniteScrollingView stopAnimating];
}];
}];
}
A: From the source code, it is obvious that addInfiniteScrollingWithActionHandler: does nothing except the first time it got called. You should store text into a private variable instead, so you can always get latest value from inside the block.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 5,552 |
Biografia
Frequentò le scuole della Fondazione Eumenio Ancoechea a Trives. Studiò Insegnamento a Ourense e si unì all'Associazione dei lavoratori della scuola di Orense (ATEO). Era un insegnante alla scuola di Medos tra il 1934 e il 1936. Era un membro del Partito socialista radicale, fu arrestato nel 1936 e assassinato a San Cosmede de Cusanca nell'agosto del 1937.
Collegamenti esterni
Páxina web sobre Antonio Caneda
Ficha en Nomes e Voces
Tríptico homenaxe Antonio Caneda 2007 | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 8,480 |
James and Mike play Snow Bros. for NES!
I'm glad you guys are playing this one. Merry Christmas from Oklahoma!
Please do Demon's Crest for SNES!
There's a sister game, actually. It's "The Great Giana Sisters" which is a clear spin-off of "Super Mario Bros" (Giana should have been "Gianna", an actual Italian name).
Yep the Giana Sisters, which I bought on Wiiu, the remake. Interesting concept, but full of problems. They never bothered patching the bugs, what a bunch of morons.
Lots of fond memories of this one. Fun two player game. The blinking number was your continues when you run down the 3 lives you have from each continue.
Snow Bros. was an arcade game in the wake of Bubble Bobble.
The Great Giana Sisters was a spoof of Super Mario Bros. on Commodore 64 and Amiga.
Hey while we're on the subject, go play Turrican on Amiga or C64. Only you'll need a joystick where autofire and regular fire are two separate buttons.
Reminds me of my favorite NES puzzler: Kickle Cubicle.
-The potions are power ups, there are three different kinds (range, power, speed). The one that "made you sick" is actually a screen-clearing super power.
-There is a famous game with sisters, "The great Giana sisters", it's a Super Mario Bros knockoff for the C64 but it's actually really good in its own way.
Giana Sisters originally released on Commodore 64, and an updated re-release for Xbox1. | {
"redpajama_set_name": "RedPajamaC4"
} | 1,741 |
\section{Introduction}
Quantum tori have been considered in various contexts;
\begin{enumerate}
\item\label{e1}
Generalizing the definition of
algebraic tori one obtains the notion of {\it quantum $n$-torus} over an abstract field $\F$ as
the $\F$-algebra ${\cal O}_q((\F^{\times})^n)$ with generators
$x_1^{\pm}, \cdots, x_n^{\pm}$ and the relation
$$x_i x_j = q x_j x_i.$$
See
\cite{BG}.
\item \label{e2} More often one is interested in a generalization of tori in the context of real structure
on complex manifolds. Then the appropriate generalization to non-commutative setting is based on
the notion of a $C^*$-algebra. Namely, in the above example we would assume
that $\F=\C$ and ${\cal O}_q((\F^{\times})^n)$ is a $C^*$-algebra (that is a normed algebra with
an involution $x\mapsto x^*,$ where $x^*$ is read as an operator adjoint to
$x$), and the $x_i$ are unitary, that is $x^*=x^{-1}$.
See \cite{C}
\item Many more beautiful and important examples can be seen as generalizations of the above,
including quantum groups.
\end{enumerate}
Classically, in non-commutative geometry one studies representation theory of the algebras in question.
In case \ref{e1}, finite-dimensional representations in $\F$-vector spaces, and in case \ref{e2},
representations in Hilbert spaces. One of the main suppositions of non-commutative geometry is that
unlike commutative case there is no geometric object corresponding to the quantum algebra, and the best
we can have in place of the Gel'fand-Naimark duality (co-ordinate algebra -- geometric space) is the correspondence
between the algebra and its category of representations.
In this paper, however, we
construct geometric objects, which can be seen as representing the information coded in the algebra of
a quantum $2$-torus. This is similar to what has been done by the second author in \cite{Z3} in the case
when $q$ is a root of unity. In that case the appropriate geometric object is a Noetherian Zariski geometry,
and when the algebra in question is commutative the Zariski geometry is just an affine algebraic variety,
as in the classical duality.
The object $T_q^2(\F)$ constructed in this paper over an algebraically closed field $\F$ hopefully can be
classified as an analytic Zariski geometry in the sense of \cite{Z2}, but we don't prove this fact here.
Our main result, apart from construction as such, is that a
simple $L_{\omega_1,\omega}$-sentence characterizing $T_q^2(\F)$ is categorical in uncountable cardinals.
\medskip
Let $\Gamma$ denote an infinite cyclic group generated by an element $q\in \F^{\times}$.
We denote ${\cal A}_q$ the non-commutative algebra ${\cal O}_q((\F^{\times})^2)$ with generators written as
$U,U^{-1}, V, V^{-1}$ satisfying
$$
VU = qUV.
$$
Our objective is to construct a structure $T_q^2(\F)$ which interprets $U$, $U^{-1}$, $V$, $V^{-1}$ as
operators acting on it and thus represents
the algebra ${\cal A}_q.$
In section 2,
we first construct non-commutative geometric objects
called $\Gamma$-bundles and line-bundles.
Then we construct the {\it quantum} 2-torus $T_q^2(\F)$
associated with the algebra ${\cal A}_q$ over
the algebraically closed field $\F$
having two quantum line-bundles with a pairing function.
After constructing $T_q^2(\F)$, in section 3
we study its properties from model theoretic point of view.
Three main theorems proved in this paper are;
\begin{enumerate}
\item
$T_q^2(\F)$ is axiomatisable by an $L_{\omega_1, \omega}$-sentence which is categorical in uncountable cardinals.
(Theorem \ref{Lomega1})
\item
The first-order theory of line-bundles, which is a reduct of $T_q^2(\F)$, is superstable.
(Theorem \ref{main1})
\item The first-order theory of $T_q^2(\F),$ for $q$ not a root of unity, interprets the ring of integers.
Hence the theory of the quantum 2-torus is undecidable and unstable.
(Theorem \ref{main2})
\end{enumerate}
Prerequisites in model theory is minimal and all found in standard
text books such as \cite{M} or \cite{TZ}.
Let $\C, \R, \Z, \N$ denote the set of complex numbers, the set of real numbers,
the set of integers, and the set of natural numbers, respectively.
All the fields considered in this paper are of characteristic zero.
\subsection{Further works}
In a forthcoming work we would like to classify $T_q^2(\F)$ as an analytic Zariski structure,
just like \cite{Z3} classifies a quantum torus at root of unity as Noetherian Zariski structure.
This requires a quantifier elimination statement and a detailed analysis of definability,
this time including $\L_{\omega_1, \omega}$-formulae.
A very important model theoretic next step in the study of quantum tori would be the study of
definable bijections between $T_q^2(\F)$ and $T_{q'}^2(\F)$, analogue of regular isomorphisms
between algebraic varieties in algebraic geometry. Here "definable" assumes definability in
an ambient larger structure over a field $\F$, where the $T_q^2(\F)$ are definable for each
choice of $q$. Such a definable bijection (isomorphisms of tori) at the level of coordinate
algebra ${\cal O}_q((\F^{\times})^n)$ must correspond to a Morita equivalence between algebras.
\section{The quantum 2-torus $T_q^2(\F)$}
Let $\F$ be a field, and $q \in \F^*,$ not a root of unity.
Consider a $\F$-algebra ${\cal A}_q$ generated by operators
$U, U^{-1}, V, V^{-1}$ satisfying
$$
VU = q UV, \quad UU^{-1} = U^{-1}U = VV^{-1} = V^{-1}V = I.
$$
Let $\Gamma_q = q^\Z = \{ q^n : n \in \Z \}$ be
a cyclic multiplicative subgroup of $\F^{*}$.
From now on in this section we work in an uncountable
$\F$-module ${\cal M}$ such that $\dim {\cal M} \geq |\F|$.
Also we drop the subscript $q$ from $\Gamma_q$ when it is clear
from the context.
\subsection{$\Gamma$-sets, $\Gamma$-bundles, line-bundles}
For each pair $(u, v) \in \F^* \times \F^*$,
we will construct two ${\cal A}_q$-modules $M_{|u,v \rangle}$ and $M_{\langle v, u|}$
so that
both $M_{|u,v \rangle}$ and $M_{\langle v, u|}$
are sub-modules of ${\cal M}$.
Before starting the construction of $M_{|u,v \rangle}$ and $M_{\langle v, u|}$
for general $q$, it is important to keep in mind
the case when $q$ is actually a root of unity.
In such case we can also define $M_{|u,v \rangle}$ and $M_{\langle v, u|}$
in the same manner described in this paper, however $M_{|u,v \rangle}$ and $M_{\langle v, u|}$
will be inter-definable uniformly on the pair $(u, v)$.
We now start the construction with $q$ not a root of unity.
The module $M_{|u, v \rangle}$ is generated by linearly independent
elements labelled
$\{ \u(\gamma u, v) \in {\cal M}: \gamma \in \Gamma \}$ satisfying
\begin{equation}\label{UVu}
\begin{array}{ccl}
U & : & \u(\gamma u, v) \mapsto \gamma u \u( \gamma u, v), \\
V & : & \u(\gamma u, v) \mapsto v \u( q^{-1} \gamma u, v), \\
\end{array}
\end{equation}
and also
\begin{equation}\label{UVinvu}
\begin{array}{ccl}
U^{-1} & : & \u(\gamma u, v) \mapsto \gamma^{-1} u^{-1} \u( \gamma u, v), \\
V^{-1} & : & \u(\gamma u, v) \mapsto v^{-1} \u( q \gamma u, v).\\
\end{array}
\end{equation}
Next let $\phi : \F^{*} / \Gamma \rightarrow \F^*$ such that $\phi(x\Gamma) \in x\Gamma$
for each $x\Gamma \in \F^*/\Gamma$.
Put $\Phi$ = $\ran (\phi)$.
We call $\phi$ a {\it choice function} and $\Phi$ the system of representatives.
Set for $\langle u, v \rangle \in \Phi^2$
\begin{equation}
\begin{array}{lcl}
\Gamma \cdot \u(u, v) & := & \{ \gamma \u(u, v) : \gamma \in \Gamma \}, \\
\U_{\langle u, v \rangle} & := & \bigcup_{\gamma \in \Gamma} \Gamma \cdot \u(\gamma u, v) =
\{ \gamma_1 \cdot \u( \gamma_2 u, v) : \gamma_1, \gamma_2 \in \Gamma \}.
\end{array}
\end{equation}
And set
\begin{equation}\label{FU}
\begin{array}{lcl}
\U_\phi & := & \bigcup_{\langle u, v \rangle \in \Phi^2} \U_{\langle u, v \rangle} \\
& = &
\{ \gamma_1 \cdot \u( \gamma_2 u, v) :
\langle u, v \rangle \in \Phi^2, \gamma_1. \gamma_2 \in \Gamma \}, \\
\F^* \U_\phi & := &
\{ x \cdot \u(\gamma u, v) : \langle u, v \rangle \in \Phi^2,
x \in \F^*, \gamma \in \Gamma \}. \\
\end{array}
\end{equation}
Note: The notation like $x \cdot \u(\gamma u, v)$ above should be read as
a 4-tuple $(x, \gamma, u, v)$.
We call $\Gamma \cdot \u(u,v)$ a $\Gamma$-{\bf set} over the pair $(u, v)$,
$\U_\phi$ a $\Gamma$-bundle over $\F^*\times \F^*/\Gamma$,
and $\F^* \U_\phi$ a {\bf line-bundle} over $\F^*$.
Notice that $\U_\phi$ can also be seen as a bundle inside
$
\bigcup_{\langle u, v \rangle} M_{|u, v \rangle}.
$
Furthermore the line bundle $\F^*\U_\phi$ is closed under the action of
the operators $U$ and $V$ satisfying the relations (\ref{UVu}) and (\ref{UVinvu}).
We define the module $M_{\langle v, u |}$ generated by
linearly independent elements labelled
$\{ \v(\gamma v, u) \in {\cal M} : \gamma \in \Gamma \}$ satisfying
\begin{equation}\label{UVv}
\begin{array}{ccl}
U & : & \v(\gamma v, u) \mapsto u \v( q\gamma v, u), \\
V & : & \v(\gamma v, u) \mapsto \gamma v \v( \gamma v, u), \\
\end{array}
\end{equation}
and
\begin{equation}\label{UVinvv}
\begin{array}{ccl}
U^{-1} & : & \v(\gamma v, u) \mapsto u^{-1} \v( q^{-1} \gamma v, u), \\
V^{-1} & : & \v(\gamma v, u) \mapsto \gamma^{-1} v^{-1} \v( \gamma v, u). \\
\end{array}
\end{equation}
Similarly a $\Gamma$-set
$\Gamma \cdot \v(v, u)$ over the pair $(v, u)$,
a $\Gamma$-bundle $\V_\phi$ over $\F^*/\Gamma\times \F^*$ ,
and $\F^* \V_\phi$ a {\bf line-bundle} over $\F^*$ are defined.
As before the $\Gamma$-bundle $\V_\phi$ can also be seen as a bundle inside
$
\bigcup_{\langle v, u \rangle} M_{\langle v, u |}.
$
In the next section we treat $\F^* \U_\phi$ as an object definable
in the structure $(\U_\phi, \V_\phi, \F)$.
For this we introduce an equivalence relation $E$
identifying $\gamma \in \Gamma$ as an element of $\F^*$.
Thus
$\F^* \U_\phi \simeq
(\F^* \times \U_\phi)/E$ where
for $(x, \gamma_1 \cdot \u( \gamma_3u, v)),
(x', \gamma_2 \cdot \u( \gamma_3u, v)) \in \F^* \times \U_\phi$
define
$$
\begin{array}{cc}\label{equiv}
(x, \gamma_1 \cdot \u( \gamma_3u, v)) \sim_E (x', \gamma_2 \cdot \u( \gamma_3u, v)) &
\Longleftrightarrow \\
\exists \gamma \in \Gamma \, ( x' = x \gamma^{-1}
\wedge \gamma_2 = \gamma \gamma_1 ) &
\end{array}
$$
We will then
consider that the two operators $U$ and $V$ are acting on this definable
classes $\F^* \U_\phi$ in the next section.
Similarly for $\F^* \V_\phi$ and the actions of $U, V$.
\begin{remark}
Relations (\ref{UVu}) mean that elements $\u(\gamma u, v)$ are
{\rm eigenvectors}
and $\gamma u$ are
{\rm eigenvalues} of the operator U.
\end{remark}
Having defined the line bundles $\F^*\U_{\phi}$ and $\F^*\V_{\phi}$, we realize
that any particular properties of the element $q$ or the choice function
$\phi$ are not used.
This means the following:
\begin{prop}\label{iso1}
Let $\F$, $\F'$ be fields
and $q \in \F$, $q' \in \F'$ such that
there is an field isomorphism $i$ from $\F$ to $\F'$ sending $q$ to $q'$.
Then $i$ can be extended to an isomorphism from
the $\Gamma$-bundle $\U_{\phi}$ to the $\Gamma'$-bundle $\U_{\phi'}$
and also from the line-bundle $\F^*\U_{\phi}$ to the line-bundle $(\F^*)'\U_{\phi'}$.
The same is true for the line-bundles $\F^*\V_{\phi}$ and $(\F')^*\V_{\phi'}$.
In particular the isomorphism type of $\Gamma$-bundles and line-bundles does
not depend on the choice function.
\end{prop}
\proof
Let $i$ be an isomorphism from $\F$ to $\F'$ sending $q$ to $q'$.
Set $i (x \cdot \u (\gamma u, v)) = i(x) \cdot \u ( i(\gamma u), i(v))$.
Then this defines an isomorphism from $\F^* \U_\phi$ to $(\F')^* \U_{\phi'}$.
\qed
\subsection{Pairing function and quantum 2-torus}
It is clear from the construction that there is no interactions between
$\Gamma$-bundles $\U_{\phi}$ and $\V_{\phi}$.
We now introduce the notion of {\it pairing function}
$\langle \cdot \, | \, \cdot \rangle$
which plays the r\^{o}le of an {\it inner product}
of two $\Gamma$-bundles $\U_\phi$ and $\V_\phi$:
\begin{equation}\label{pairing}
\langle \cdot \, | \, \cdot \rangle : \Big( \V_\phi \times \U_\phi \Big)
\cup \Big( \U_\phi \times \V_\phi \Big)
\rightarrow \Gamma.
\end{equation}
We would like two operators $U, V$ to behave like {\it unitary operators}
on Hilbert space.
This requirement forces us to postulate the following:
\begin{enumerate}
\item $\langle \u(u,v) | \v(v, u) \rangle = 1$,
\item for each $r, s \in \Z$,
$\langle U^rV^s \u(u, v) | U^rV^s \v(v, u) \rangle = 1$,
\item for $\gamma_1, \gamma_2, \gamma_3, \gamma_4 \in \Gamma$,
$$\langle \gamma_1 \u(\gamma_2u, v) | \gamma_3 \v(\gamma_4v,u) \rangle =
\langle \gamma_3 \v(\gamma_4v, u) | \gamma_1 \u(\gamma_2u,v) \rangle^{-1},$$
\item $\langle \gamma_1 \u(\gamma_2u, v) | \gamma_3 \v(\gamma_4v,u) \rangle =
\gamma_1^{-1} \gamma_3 \langle \u(\gamma_2u, v) | \v(\gamma_4v,u) \rangle$, and
\item for $v' \not\in \Gamma \cdot v$ or $u' \not\in \Gamma \cdot u$,
$
\langle q^s \v(v',u) | q^r \u(u',v) \rangle
$
is not defined.
\end{enumerate}
\begin{prop}
The {\bf pairing} function (\ref{pairing}) defined above satisfies
the following:
for any $m, k, r, s \in \N$ we have
\begin{equation}\label{pairing1}
\langle q^s \v(q^mv,u) | q^r \u(q^ku,v) \rangle =
q^{r-s-km}
\end{equation}
and
\begin{equation}\label{pairing2}
\langle q^r \u(q^ku,v) | q^s \v(q^mv,u) \rangle =
q^{km+s-r} =
\langle q^s \v(q^mv,u) | q^r \u(q^ku,v) \rangle^{-1}.
\end{equation}
\end{prop}
\proof
We only prove (\ref{pairing1}). For this, it is enough to notice that
for each $r, s \in \Z$,
$\langle U^rV^s \u(u, v) | U^rV^s \v(v, u) \rangle = 1$ implies that
$$\langle \u(q^ru, v) | \v(q^sv, u) \rangle = q^{rs}.$$
\qed
Finally we are ready to define the notion of quantum 2-torus:
\begin{defn}\label{q-torus}
We call the multi-sorted structure
$(\U_\phi, \V_\phi, \langle \cdot \, | \, \cdot \rangle, \F )$ with actions
$U$, $V$ with $U$ satisfying (\ref{UVu}),
$V$ satisfying (\ref{UVv})
and $\langle \cdot \, | \, \cdot \rangle$
a pairing function defined as above a {\bf quantum 2-torus} $T_q^2(\F)$ over the
field $\F$.
\end{defn}
From Proposition \ref{iso1} we know that the structure of the line-bundles does
not depend on the choice function. The next proposition tells us that
the structure of the quantum 2-torus $T_q^2(\F)$ depends only on $\F$, $q$
and not on the choice function.
\begin{prop}[cf. Proposition 4.4, \cite{Z1}]
Given $q\in \F^*$ not a root of unity,
any two structures of the form $T_q^2(\F)$ are isomorphic
over $\F$. In other words, the isomorphism type of $T_q^2(\F)$ does not
depend on the system of representatives $\Phi$.
\end{prop}
\proof
Let $\phi, \psi$ be two choice functions
of $\F^*/\Gamma$. Consider two structures
$(\U, \V)_\phi = (\U_\phi, \V_\phi)$ and
$(\U, \V)_\psi = (\U_\psi, \V_\psi)$.
We show that these two structures are isomorphic over $\F$.
Suppose $\phi$ picks $\langle u_g, v_g \rangle$ from $\F^*/\Gamma$ and
$\psi$ picks $\langle u_0, v_0 \rangle$ from the same coset of $\langle u_g, v_g \rangle$.
Consider the bases
$\{ \u(q^ku_g, v_g) : k \in \Z \}$ of $U_{\langle u_g, v_g \rangle}$ and
$\{ \v(q^kv_g, u_g) : k \in \Z \}$ of $V_{\langle u_g, v_g \rangle}$ in the
structure $(\U_\phi, \V_\phi)$.
Since $\langle u_0, v_0 \rangle$ and $\langle u_g, v_g \rangle$ are in the same coset
of $\F^*/\Gamma$ there are $s, t \in \Z$ such that $u_0 = q^su_g, v_0 = q^tv_g$.
We now want to transfer the structure of $\U_{\langle u_g, v_g \rangle}$ and
$\V_{\langle u_g, v_g \rangle}$
to $\U_{\langle u_0, v_0 \rangle}$ and $\V_{\langle u_0, v_ \rangle}$
respectively as follows. Set
\begin{itemize}
\item $\u(u_0, v_0) := q^{st}\u(q^su_g, v_g)$,
\item $\u(q^ku_0, v_0) := v_0^kV^{-k}\u(u_0, v_0)$,
\item $\v(v_0, u_0) := \v(q^tv_g, u_g)$,
\item $\v(q^kv_0, u_0) := u_0^{-k} U^k \v(v_0, u_0)$,
\end{itemize}
where $k \in \Z$.
First notice that we have
$$
\begin{array}{lcl}
\u(q^ku_0,v_0) & = & v_0^k V^{-k} \u (u_0, v_0) \\
& = & (q^t v_g)^k V^{-k} (q^{st} \u (q^s u_g, v_g)) \\
& = & q^{kt} v_g^k q^{st} v_g^{-k} \u(q^{s+k}u_g, v_g) \\
& = & q^{kt + st} \u(q^{k+s}u_g, v_g),
\end{array}
$$
and
$$
\begin{array}{lcl}
\v(q^kv_0,u_0) & = & u_0^{-k} U^k \v(v_0, u_0) \\
& = & q^{-ks}u_g^{-k} U^k \v( g^tv_g, u_g) \\
& = & q^{-ks}u_g^{-k} u_g^k \v( g^{t+k}v_g, u_g) \\
& = & q^{-sk}\v(q^{k+t}v_g, u_g). \\
\end{array}
$$
From these relations we see that
the operators $U$ and $V$ act on the set
$\{ \u(q^ku_0, v_0) : k \in \Z \}$ according to the definition of
$\U_{\phi}$, that is
$$\begin{array}{lcl}
U(\u(u_0, v_0)) & = & U(q^{st}\u(q^su_g, v_g)) \\
& = & q^{st} U(\u(q^su_g, v_g)) \\
& = & q^{st}q^su_g\u(q^su_g,v_g) \\
& = & u_0 q^{st}\u(q^su_g,v_g) \\
& = & u_0 \u(u_0,v_0), \\
V(\u(u_0, v_0)) & = & V(q^{st}\u(q^su_g, v_g)) \\
& = & v_0 \u(q^{-1}u_0,v_0), \\
U(\u(q^ku_0,v_0)) & = & U(v_0^kV^{-k}\u(u_0,v_0)) \\
& = & q^ku_0 \u(q^ku_0, v_0), \\
V(\u(q^ku_0,v_0)) & = & V( q^{kt + st} \u(q^{k+s}u_g, v_g)) \\
& = & v_0 \u(q^{k-1}u_0, v_0). \\
\end{array}$$
By similar calculations we see that the operators $U$ and $V$ act on the set
$\{ \v(q^kv_0, u_0) : k \in \Z \}$ according to the definition of $\V_\phi$.
Finally from the following relations we see that we can properly transfer
the pairing function from $(\U_{\langle u_g, v_g \rangle}, \V_{\langle v_g, u_g \rangle})$
to $(\U_{\langle u_0, v_0 \rangle}, \V_{\langle v_0, u_0 \rangle})$:
$$\langle \v(v_0,u_0)|\u(u_0,v_0)\rangle =
\langle \v(q^tv_g, u_g)|q^{st}\u(q^su_g, v_g) \rangle = q^{st-st}=1$$
and
$$\begin{array}{lcl}
\langle \v(q^mv_0,u_0)|\u(q^ku_0,v_0) \rangle & = &
\langle q^{-sm}\v(q^{m+t}v_g,u_g)|q^{st+kt}\u(q^{k+s}u_g,v_g) \rangle \\
& = & q^{st+kt-(-sm)-(m+t)(k+s)} \\
& = & q^{-mk}.
\end{array}$$
We have now shown that the two structures
$(\U_{\langle u_g, v_g \rangle}, \V_{\langle v_g, u_g \rangle})$
and $(\U_{\langle u_0, v_0 \rangle}, \V_{\langle v_0, u_0 \rangle})$ are isomorphic.
Therefore so are the two structures $(\U, \V)_\phi$ and $(\U, \V)_\psi$.
\qed
From the above proposition we have as a corollary to Proposition \ref{iso1}
the following:
\begin{cor}\label{isomorph}
Let $\F$, $\F'$ be fields
and $q \in \F$, $q' \in \F'$ such that
there is a field isomorphism $i$ from $\F$ to $\F'$ sending $q$ to $q'$.
Then $i$ can be extended to an isomorphism
from the quantum 2-torus
$T_q^2(\F)$ to the quantum 2-torus $T_{q'}^2(\F')$.
In particular the isomorphism type of quantum 2-torus does
not depend on the choice function.
\end{cor}
From now on we drop the subscript $\phi$ from line-bundles $\U_\phi$,
$\V_\phi$ and write simply as
$T_q^2(\F) = (\U, \V, \langle \cdot \, | \, \cdot \rangle, \F)$.
\section{The model theory of quantum 2-torus over algebraically closed field}
We now study the model theory of quantum 2-tori $T_q^2(\F)$ under the assumption
that $\F$ is algebraically closed.
After introducing an appropriate language, we shall prove three theorems in this
section;
\begin{enumerate}
\item
$T_q^2(\F)$ is axiomatisable by an $L_{\omega_1, \omega}$-sentence $\Psi$ which is categorical
in uncountable cardinals.
(Theorem \ref{Lomega1})
\item
The first-order theory of line-bundles, which is a reduct of $T_q^2(\F)$, is superstable.
(Theorem \ref{main1})
\item The first-order theory of $T_q^2(\F),$ for $q$ not a root of unity,
interprets the ring of integers.
Hence the theory of the quantum 2-torus is undecidable and unstable.
(Theorem \ref{main2})
\end{enumerate}
\subsection{The language for quantum 2-tori}
To define the sentence $\Psi$ we introduce a language $\L_q$ which is the
language for multi-sorted structure
$(\U, \V, \langle \cdot \, | \, \cdot \rangle, \F)$ ; \\
$$\L_q = \{ +, \cdot, \U, \V, U, V, \langle \cdot \, | \, \cdot \rangle, \F, \Gamma, \pi \}$$
where $+, \cdot$ defined
on $\F$ and $\Gamma \subset \F$. Furthermore $U, V$ are operators acting
on $\U$ and $\V$. Each $\gamma \in \Gamma$ acts on $\U$ and $\V$.
Also $\pi$ is a function symbol which will be interpreted as a surjection
from $\U$ onto $\F^* \times \F^*/\Gamma$ and from $\V$ onto $\F^* \times \F^*/\Gamma$.
\subsection{$T_q^2(\F)$ is $L_{\omega_1, \omega}$-categorical
in uncountable cardinals}
Here we define the $\L_{\omega_1, \omega}$-sentence $\Psi$ in $\L_q$
describing the quantum 2-torus $T_q^2(\F) = (\U, \V, \langle \cdot \, | \, \cdot \rangle, \F)$.
Then we show that the sentence $\Psi$ is categorical in uncountable cardinals.
Recall how we treat $\F^* \U$ as an object definable in the structure
$(\U, \V, \langle \cdot \, | \, \cdot \rangle, \F)$.
Similarly for $\F^* \V$.
We extend that the two operators $U$ and $V$ are acting on
these definable sets $\F^* \U$ and $\F^* \V$.
Let $\Psi$ be the $L_{\omega_1, \omega}$-sentence stating that
\begin{enumerate}
\item $\F$ is an algebraically closed field of characteristic zero,
\item $q \in \F$ and not a root of unity,
\item $\Gamma$ is a multiplicative subgroup of $\F$ generated by $q$, i.e., $\Gamma \simeq q^{\Z}$,
\item $\pi$ is surjective from $\U$ onto $\F^* \times \F^*/\Gamma$,
\item for each $\gamma \in \Gamma, (u, v) \in \F^* \times \F^*/\Gamma$,
$\pi^{-1}(\gamma u,v) \subset \U$ is generated by an element and
\begin{itemize}
\item for each $\u \in \pi^{-1}(\gamma u,v)$ and $\gamma' \in \Gamma, \gamma' \u \in \pi^{-1}(\gamma u,v)$,
\item for each $\u \in \pi^{-1}(\gamma u,v)$ and $x \in \F^*, x\u \in \F^* \pi^{-1}(\gamma u,v)$,
\end{itemize}
\item $\F^* \U$, $\F^*V$ are $\F$-modules,
\item operators $U, V$ act on $\F^*\U$ and $\F^*\V$ according to (\ref{UVu}) and (\ref{UVv}),
more precisely,
\begin{itemize}
\item for each $\u \in \pi^{-1}(\gamma u,v), x \in \F^*$ we have
$U(x, \u) \in \F^*U$, $\gamma u \u \in \pi^{-1}(\gamma u,v)$ and
$U(x, \u) = \gamma u \u$,
\item for each $\u \in \pi^{-1}(\gamma u,v), x \in \F^*$ we have
$V(x, \u) \in \F^*\V$, there exists
$\u' \in \pi^{-1}(q^{-1}\gamma u, v)$ and $V(x, \u) = xv\u'$,
\end{itemize}
\item the properties of the pairing function, more precisely,
\begin{itemize}
\item for any $\u \in \pi^{-1}(u,v), \v \in \pi^{-1}(v,u)$,
\begin{itemize}
\item $\langle \u,\v \rangle = 1$,
\item for any $r, s \in \Z$,
$\langle U^rV^s(\u), U^rV^s(\v) \rangle = 1$, \\
where $1$ is the multiplicative identity element of $\F$.
\end{itemize}
\item for any $\gamma_1, \gamma_2, \gamma_3, \gamma_4 \in \Gamma$ and
$\u \in \pi^{-1}(\gamma_2, v), \v \in \pi^{-1}(\gamma_4 v, u)$,
\begin{itemize}
\item $\langle \gamma_1 \u, \gamma_3 \v \rangle =
\langle \gamma_3 \v, \gamma_1 \u \rangle^{-1}$ and,
\item $\langle \gamma_1 \u, \gamma_3 \v \rangle = \gamma_1^{-1} \gamma_3
\langle \u, \v \rangle$.
\end{itemize}
\end{itemize}
\end{enumerate}
\begin{lemma}
Let $M = (\U, \V, \langle \cdot \, | \, \cdot \rangle, \F)$ be an infinite
$\L_q$-structure satisfying $\Psi$.
Then $M$ is a quantum 2-torus over $\F$.
\end{lemma}
\proof
Let $\F$ be an infinite algebraically closed field of characteristic zero,
$q \in \F$ and $\Gamma = q^\Z \subset \F$ given by $\Psi$.
Then $\U$ and $\V$ are the $\Gamma$-bundles defined over $\F$ and $q$ where
operators $U, V$ satisfy relations (\ref{UVu}), (\ref{UVinvu}), (\ref{UVv}) and (\ref{UVinvv}).
We then construct line-bundles $\F^*\U$ and $\F^*\V$. Since the sentence $\Psi$ describes the
properties of the pairing function, from Proposition \ref{iso1} we
see that $M$ is a quantum 2-torus over $\F$.
\qed
Thus Corollary \ref{isomorph} gives us
\begin{thm}\label{Lomega1}
The $L_{\omega_1, \omega}$-sentence $\Psi$ is categorical in uncountable cardinals.
\end{thm}
\proof
Notice that any uncountable model of $\Psi$ is a quantum 2-torus $T_q^2(\F)$
over an uncountable algebraically closed field $\F$ of characteristic zero.
Since all such uncountable fields $\F$ are isomorphic once we fix the cardinality,
so are the quantum 2-tori $T_q^2(\F)$ over such fields $\F$.
Hence $\Psi$ is categorical in uncountable cardinals.
\qed
\subsection{Superstability of $\Th(\F, +, \cdot, 0, 1, \Gamma)$}
From now on we study the first-order theoretic properties of quantum 2-tori.
In this subsection we show that the first-order
theory of $(\F, +, \cdot, 0, 1, \Gamma)$ is axiomatizable and superstable.
Key idea is that the predicate
$\Gamma(x)$ describes the property of the set $q^\Z$ as a multiplicative
subgroup with the following Lang-type property.
\begin{defn}[Definition 2.3 \cite{P}]\label{LTD}
Let $K$ be an algebraically closed field, and $A$ a commutative algebraic
group over $K$ and $\Gamma$ a subgroup of $A$.
We say that $(K, A, \Gamma)$ is of {\rm Lang-type} if
for every $n < \omega$ and every subvariety $X$ (over $K$)
of $A^n = A \times \cdots \times A$ ($n$ times),
$X \cap \Gamma^n$ is a finite union of cosets of
subgroups of $\Gamma^n$.
\end{defn}
The Lang-type property gives us
\begin{prop}[Proposition 2.6 \cite{P}]\label{LTP}
Let $K$ be an algebraically closed field, $A$ a commutative algebraic group
over $K$, and $\Gamma$ a subgroup of $A$.
Then $(K, A, \Gamma)$ is of Lang-type if and only if
$\Th(K, +, \cdot, \Gamma, a)_{a \in K}$ is stable and $\Gamma(x)$ is
one-based.
\end{prop}
Here $\Gamma(x)$ is {\it one based} means that for every $n$ and
every definable subset $X \subset \Gamma^n$, $X$ is a finite
boolean combination of cosets of definable subgroups of
$\Gamma^n$.
With the above Definition \ref{LTD} and Proposition \ref{LTP} in mind, we axiomatize
the properties of $(\F, +, \cdot, \Gamma )$ as follows;
\bigskip
\noindent
{\bf Axioms for $(\F, +, \cdot, \Gamma )$}
\begin{itemize}
\item[A. 1]
$\Gamma$ satisfies the first order theory of a cyclic group with generator $q,$
\item[A. 2] (Lang-type) for every $n$ and every variety $X$ of $(\F^*)^n$,
$X \cap \Gamma^n$ is a finite union of cosets of definable subgroups
of $\Gamma^n$.
\end{itemize}
Let $T_{\F, \Gamma}$ denote the set of all logical consequences of the
axioms for $\Gamma$ and ${\rm ACF}_0$ axioms for the algebraically closed
fields of characteristic zero.
\begin{lemma}\label{Lang}
The {\rm Lang-type} property of $(\F, +, \cdot, \Gamma)$ is witnessed by its
first-order theory.
\end{lemma}
\proof
We may suppose $X$ is irreducible.
Each such variety $X \subset (\F^*)^n$
is definable by an irreducible polynomial $f(x_1, \cdots, x_n)$
over $\F^*$. Definable cosets of $\Gamma^n$ are of the form
$\overline{\gamma} \Gamma^n =
\gamma_1 \Gamma \times \cdots \times \gamma_n \Gamma$
where $\gamma_1, \cdots, \gamma_n \in \Gamma(\F)$.
Hence the sentence "$X \cap \Gamma^n$ {\it is a finite union of cosets of
definable subgroups}" is expressed as
$$
\begin{array}{ll}
(f(x_1, \cdots, x_n) = 0) \wedge \Gamma(x_1) \wedge \cdots \wedge
\Gamma(x_n) & \longleftrightarrow \\
\bigvee_{i=1}^{N_f} \varphi_i(x_1, \cdots, x_n). & \\
\end{array}
$$
Where each $\varphi_i(x_1, \cdots, x_n)$ defines a coset.
Crucial point here is that the number $N_f$ of the bound of cosets is
computable for each polynomial $f$.
For this note first that for any $k \in \N$
the number of cosets of $q^{k\Z}$ in $q^\Z$ is $k$.
Suppose
$$
f(x_1, \cdots, x_n) = \sum_{i=0}^{\deg(f)} \overline{a}_i
\overline{x}_i^{m_1} ,
$$
where each $m_i$ is a multi index. Let $M_i$ be the sum of
multi index $m_i$. Then the bound $N_f$ of number of cosets
is $\deg(f) \cdot \sum_{i=0}^{\deg(f)} M_i$.
Therefore the Lang-type property is first-order.
\qed
\begin{prop}\label{CompFGamma}
$T_{\F, \Gamma}$ is complete. Hence $T_{\F, \Gamma} =
\Th(\F, +, \cdot, \Gamma)$.
\end{prop}
\proof
Consider a saturated model $(\F, +, \cdot, \Gamma, q)$
of $T_{\F, \Gamma}$.
Set $\Gamma(\F) = \{ x \in \F : \F \models \Gamma(x) \}$.
Let $q$ be an element of $\F$ interpreting the constant.
By the axioms
for $\Gamma$, $q^\Z \subset \Gamma(\F) \subset \F$ .
Consider a complete type $t_0(x)$ generated by the following set of formulas,
$$
t(x) = \{ \Gamma(x), \, \exists y (x = qy), \, \exists y ( x = q^2y), \, \cdots \}.
$$
By saturation there exists $\gamma_0 \in \Gamma(\F)$ realizing $t_0(x)$.
Clearly, $\gamma_0 \notin q^\Z$.
Suppose elements $\gamma_0, \cdots , \gamma_i \in \Gamma(\F)$
have been defined.
Let $t_{i+1}(x)$ be a complete type generated by the type $t(x)$ and the set
$$
\{ x \neq \gamma_0^{n_0} , \cdots, x \neq \gamma_i^{n_i}
\, : \, n_0, \cdots, n_i \in \Z \}.
$$
From saturation, we have $\gamma_{i+1} \in \Gamma(\F)$ such that
$$
\gamma_{i+1} \notin \bigcup_{l = 0}^{i} \gamma_l^\Z.
$$
In this way by saturation as before
we see that there exist
$\gamma_0, \gamma_1, \cdots, \gamma_i , $
$\cdots \in \Gamma(\F)$ $(i < |\F|)$
such that
$$\Gamma(\F) = q^\Z \cup \bigcup_{i < |\F|} \gamma_i^\Z.$$
Now take two saturated models $(\F, +, \cdot, \Gamma, q)$ and $(\F', +, \cdot, \Gamma', q')$
of $T_{\F, \Gamma}$ of the same cardinality. There is an isomorphism $i$ from $\F$ to $\F'$
sending $q$ to $q'$.
By the above formula for $\Gamma(\F)$ and the back-and-forth argument
we can extend $i$ to have that $\Gamma(\F) \simeq \Gamma'(\F')$. Hence
$(\F, +, \cdot, \Gamma, q)$ and $(\F', +, \cdot, \Gamma', q')$
are isomorphic as saturated models of $T_{\F, \Gamma}$. This completes the
proof of the completeness of the theory $T_{\F, \Gamma}$.
\qed
\begin{thm}\label{main}
$T_{\F, \Gamma}$ is superstable.
\end{thm}
\proof
Notice first that the multiplication of $\F$ is an algebraic group and
$(\F, \cdot, \Gamma)$ is of the Lang-type by A. 2 above.
Thus by Proposition 2.6 of \cite{P}, we see that $T_{\F, \Gamma}$ is
at least stable. $T_{\F, \Gamma}$ is in fact superstable since
\begin{enumerate}
\item
the stability spectrum of $T_{\F, \Gamma}$ is the same as
that of $T_{\Gamma(\F)}$, the theory of restriction of $(\F, +, \cdot, \Gamma)$ to $\Gamma(\F)$.
Let $C \subset \F$. Observe first that there is only one complete 1-type over $C$ in $T_{\F, \Gamma}$,
which is realized by elements in $\F - \acl_{\rm F}(\Gamma(\F) \cup C)$ where $\acl_{\rm F}$
is the field-theoretic algebraic closure.
Hence the cardinality of complete 1-types in $T_{\F, \Gamma}$ is bounded by the
cardinality of the complete 1-types in $T_{\Gamma(\F)}$. Thus they have the same stability spectrum.
\item $T_{\Gamma(\F)}$ is superstable.
For $q$ transcendental, this is Theorem 1 in Section 5 of \cite{Z7}.
Combined with Proposition \ref{LTP}, it is easy to extend it to arbitrary $q$.
\end{enumerate}
\qed
\subsection{Superstability of the line-bundle}
In this subsection we show that the first-order theory of the line-bundle $(\U, \F)$ is superstable.
Recall the $\L_{\omega_1, \omega}$-sentence $\Psi$ describing the properties of
the quantum 2-torus $T_q^2(\F)$. We now investigate the sentence $\Psi$ from
the first-order theoretic point of view.
Let $\L_q' = \L_q - \{ \langle \cdot \, | \, \cdot \rangle \}$.
Let $\Th(\U, \F)$ denote the first-order $\L_q'$-theory of the line bundle $(\U, \F)$.
Unlike $\L_{\omega_1, \omega}$-sentence $\Psi$, in $\Th(\U, \F)$ we can only say
that $\Gamma$ satisfies the first-order theory of a cyclic group with generator $q$.
Let $M$ be a model of $\Th(\U, \F)$, then we have;
for each $\gamma \in \Gamma$ and $(u, v) \in \F^* \times \F^*/\Gamma$,
$\pi^{-1}(\gamma u, v)$, which is denoted as $\U_{(\gamma u,v)}$, is a subset of
the $\Gamma$-bundle $\U$ that is generated by an element.
We also have $\U_{(\gamma u,v)} \subsetneq \F^* \U_{(\gamma u,v)}$
wher $\F^* \U_{(\gamma u,v)}$ is a subset of the line-bundle $\F^* \U$.
Furthermore we have
$$
\U = \bigcup_{\gamma, (u,v)} \U_{(\gamma u,v)}, \quad
\F^* \U = \bigcup_{\gamma, (u,v)} \F^* \U_{(\gamma u,v)}.
$$
\begin{prop} \label{TUF_is_superstable}
The first-order theory of line-bundle $(\U, \F)$ is superstable.
\end{prop}
\proof
We show that the first-order theory of line-bundle $(\U, \F)$
is superstable in two steps;
1) show that the theory $\Th(\U, \F)$ of line-bundle
$(\U, \F)$ is {\it prime} over the theory $T_{\F, \Gamma}$;
i.e., any isomorphism between two models of
$T_{\F, \Gamma}$ can be extended to an
isomorphism between two models of $\Th(\U, \F)$,
2) since the theory $T_{\F, \Gamma}$ is superstable
(Theorem \ref{main})
the theory $\Th(\U, \F)$ of line-bundle
$(\U, \F)$ is superstable as well.
{\bf Proof} of 1): Since the theory $T_{\F, \Gamma}$ is complete
(Proposition \ref{CompFGamma}),
we may assume that
$(\F_1, \Gamma) = (\F_2, \Gamma)$.
We show that two saturated models $M_1$ and $M_2$ of $\Th(\U, \F)$
with the same cardinality are isomorphic as line-bundles over
$\F^* \times \F^*/\Gamma$.
Let $\U_1$ and $\U_2$ denote the $\Gamma$-bundles over
$\F^* \times \F^*/\Gamma$ in $M_1$ and $M_2$ respectively.
Similarly, let $\F^* \U_1$ and
$\F^* \U_2$ denote the line-bundles over $\F^* \times \F^*/\Gamma$ in
$M_1$ and $M_2$ respectively.
Take $(u, v), (u', v') \in \F^* \times \F^*/\Gamma$.
Consider vectors $\u(u, v) \in M_1$ and $\u(u', v') \in M_2$ respectively.
The $\Gamma$-sets $\Gamma \cdot \u(u,v)$ in $M_1$ and $\Gamma \cdot \u(u', v')$ in $M_2$ are
isomorphic. Therefore those 1-dimensional submodules generated by
$\Gamma \cdot \u(u, v)$ and $\Gamma \cdot \u(u', v')$ are isomorphic as well.
Hence we see that
$\F^* \U_{(u,v)}$ in $M_1$ and $\F^* \U_{(u', v')}$ in $M_2$ are isomorphic.
Now by applying the operator $V$ to $\u(u, v)$ in $M_1$ and $\u(u', v')$ in $M_2$
we move to other $\Gamma$-sets $\Gamma \cdot V(\u(u, v))$ in
$M_1$ and $\Gamma \cdot V(\u(u', v'))$ in $M_2$ respectively.
Then two 1-dimensional submodules generated by
$\Gamma \cdot V(\u(u, v))$ and $\Gamma \cdot V(\u(u', v'))$ are isomorphic as well.
In this way we see that the $\Gamma$-bundle in $M_1$
and the $\Gamma$-bundle in $M_2$ are isomorphic.
Then we extend this isomorphism to an isomorphism between
the line-bundles $M_1$ and $M_2$. This completes the proof of primeness.
{\bf Proof} of 2): By the primeness shown in 1)
we see that any realization of a type in $\Th(\U, \F)$ is
fixed by automorphisms of models of $T_{\F, \Gamma}$, hence
the cardinality of types in
$\Th(\U, \F)$ is bounded by the cardinality of
the types in $T_{\F, \Gamma}$. Therefore by Theorem \ref{main},
the theory $\Th(\U, \F)$ of line-bundle $(\U, \F)$ is superstable.
\qed
It follows immediately that we have the following second main theorem;
\begin{thm}\label{main1}
\begin{enumerate}
\item The first-order theory of line-bundle $(\V, \F)$ is superstable,
\item The first-order theory of line-bundles $(\U, \V, \F)$ is superstable.
\end{enumerate}
\end{thm}
\subsection{Arithmetic in the theory of quantum 2-torus}
In this subsection we show that with the pairing function the ring of integers
can be defined in $\Gamma$. In this regard it is similar to the theory of pseudo-exponentiation,
the model theory of which can successfully be investigated ``modulo arithmetic'' as in \cite{Z5} or \cite{KZ}.
First we may identify $(\Gamma, \cdot)$ with $(\Z, +)$ via the correspondence
$$q^r \mapsto r.$$
This gives us immediately a definable addition $+$ on $\Z$ by the exponential law.
A definable multiplication $\times$ on $\Gamma$ is defined as follows with the pairing function.
Fix $u, v \in \F$, $\u(u, v) \in \U$, and $\v(v, u) \in \V$ which satisfy
$$
\langle \u(u, v) | \v(v, u) \rangle = 1.
$$
Then given $\alpha, \beta, \gamma \in \Z$, set by (\ref{pairing2})
$$
\alpha \times \beta = \gamma \quad \text{if and only if} \quad
\langle q^\alpha \u(u, v) | q^\beta \v(v, u) \rangle = q^{\gamma}.
$$
Let $\oplus$ and $\otimes$ be the pull-backs of $+$ and $\times$ in $(\Gamma, \cdot, 1)$ respectively
via the above correspondence. We then have
\begin{prop}
The two operations $\oplus$ and $\otimes$ defined above are commutative,
i.e., for $\gamma_1, \gamma_2 \in \Gamma$ we have
\begin{enumerate}
\item $\gamma_1 \oplus \gamma_2 = \gamma_2 \oplus \gamma_1$,
\item $\gamma_1 \otimes \gamma_2 = \gamma_2 \otimes \gamma_1$.
\end{enumerate}
\end{prop}
\begin{thm}\label{main2} (i) With the pairing function,
within $(\Gamma, \cdot, 1, q)$ we can define $(\Gamma, \oplus, \otimes, 1, q)$
and $(\Gamma, \oplus, \otimes, 1, q) \simeq (\Z, +, \cdot, 0, 1)$.
Hence the theory of the quantum 2-torus
$(\U, \V, \langle \cdot \, | \, \cdot \rangle, \F, \Gamma)$
is undecidable and unstable.
(ii) The non-elementary theory of the quantum 2-torus
$(\U, \V, \langle \cdot \, | \, \cdot \rangle, \F, \Gamma)$
over fixed $\Gamma=q^{\Z}$ is categorical in uncountable cardinalities.
\end{thm}
\proof (i) This is essentially the Proposition above.
\noindent
(ii) This is a direct corollary of the two statements
\claim 1. The non-elementary theory of $(\F,\Gamma),$ the field with a distinguished fixed subgroup,
is categorical in uncountable cardinalities.
\claim 2. The quantum 2-torus $(\U, \V, \F, \Gamma)$
with the pairing function is prime over $(\F,\Gamma).$
For Claim 1, note first that the first-order theory of $\F$ is uncountable categorical
since $\F$ is algebraically closed. For $\Gamma \simeq q^\Z$, what we cannot
state in the first-order theory is
$x \in \Gamma \longleftrightarrow \exists n \in \Z \, (x = q^n)$. This is expressible
in the non-elementary theory. Thus the non-elementary theory of $(\F, \Gamma)$
is categorical in uncountable cardinalities.
Claim 2 is in fact part of the proof of Proposition~\ref{TUF_is_superstable}.
\qed
| {
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} | 2,664 |
Alys Williams (Fountain Valley (California), Estados Unidos, 28 de mayo de 1994) es una waterpolista olímpica de Estados Unidos campeona olímpica en Tokio 2020, triple campeona mundial (2015,2017 y 2019), y campeona en los Juegos Panamericanos de 2019.
Palmarés internacional
Referencias
Medallistas olímpicos
Medallistas olímpicos de oro de Tokio 2020
Medallistas olímpicos de oro de Estados Unidos | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 2,638 |
{"url":"https:\/\/socratic.org\/questions\/an-object-with-a-mass-of-5-kg-is-pushed-along-a-linear-path-with-a-kinetic-frict-4","text":"An object with a mass of 5 kg is pushed along a linear path with a kinetic friction coefficient of u_k(x)= 6x-1 . How much work would it take to move the object over #x in [2, 3], where x is in meters?\n\nJan 19, 2016\n\nSee details in Explanation section\n\nExplanation:\n\nThe question is similar to another question solved as bellow. The difference is in the value of coefficient of friction. Choose appropriate value and solve.\nIn case of difficulty, use comment section below.\nCheers\n\n-=-=-=-=-=-=-=-=-=-=-\n\nForce of kinetic friction which needs to be overcome to move the object\n\n${F}_{k} =$Coefficient of kinetic friction ${\\mu}_{k} \\times$normal force $\\eta$\nwhere $\\eta = m g$\nInserting given quantities and taking the value of $g = 9.8 m \/ {s}^{2}$\n${F}_{k} = \\left(x + 3\\right) \\times 5 \\times 9.8 N$\n${F}_{k} = 49 \\left(x + 3\\right) N$\n\nWhen this force moves through a small distance $\\mathrm{dx}$, the work done is given as\n${F}_{k} \\mathrm{dx} = 49 \\left(x + 3\\right) \\mathrm{dx}$\nWhen the force moves through a distance from $x \\in \\left[2 , 3\\right]$, total work done is integral of RHS over the given interval.\n\nTotal work done$= {\\int}_{2}^{3} 49 \\left(x + 3\\right) \\mathrm{dx}$\n$\\implies$Total work done$= 49 {\\int}_{2}^{3} \\left(x + 3\\right) \\mathrm{dx}$\n\n$= 49 \\left({x}^{2} \/ 2 + 3 x + C\\right) {|}_{2}^{3}$, where C is constant of integration.\n$= 49 \\left[\\left({3}^{2} \/ 2 + 3 \\times 3 + C\\right) - \\left({2}^{2} \/ 2 + 3 \\times 2 + C\\right)\\right]$\n$= 49 \\left[\\frac{9}{2} + 9 - 2 - 6\\right]$\n$= 49 \\left[4.5 + 1\\right]$","date":"2019-04-26 09:48:34","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 17, \"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\": 0.7558890581130981, \"perplexity\": 708.0403097455885}, \"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-2019-18\/segments\/1555578765115.93\/warc\/CC-MAIN-20190426093516-20190426115516-00533.warc.gz\"}"} | null | null |
{"url":"https:\/\/math.stackexchange.com\/questions\/3166400\/unique-line-in-mathbbp4-intersecting-three-pairwise-non-intersecting-lines","text":"# Unique line in $\\mathbb{P}^4$ intersecting three pairwise non-intersecting lines not in a hyperplane.\n\nI need to show that there is a unique line (in $$\\mathbb{P}^4$$ I assume, or could they also mean in $$\\mathbb{R}^5$$?) that intersects three lines $$L,M,N$$ which are pairwise non-intersecting and not in the same hyperplane.\n\nIn a previous exercise I worked out that $$\\dim(\\langle L, M\\rangle \\cap N)=0$$, so a single point in $$\\mathbb{P}^4$$.\n\nI think I have to use this dimension, but I'm not sure what it means. It says $$\\langle L, M\\rangle$$ is the union of all lines through $$L$$ and $$M$$. So is $$\\langle L, M\\rangle \\cap N$$ then the set of all lines through all three lines?\n\nOther things I tried:\n\nI know that $$\\langle L, M, N \\rangle = 4$$, since these lines are not in the same hyperplane.\n\nLet $$P$$ be a point on $$L$$. Let $$\\Pi$$ be the plane containing $$M$$ and $$P$$. In the same way we can construct a plane $$\\Pi'$$ through $$N$$ and $$P$$. But I don't know if I'm going in the good direction, I simply don't know how to visualize this stuff in higher dimensions..\n\nThe key here is that $$\\langle L,M\\rangle$$ here is a hyperplane, three-dimensional in $$\\mathbb{P}^4$$. There is, as you have noted, a single point $$x$$ where $$N$$ meets this hyperplane.\n\nNow, the union of all lines through $$x$$ that intersect $$L$$ is a 2-d plane in $$\\langle L,M\\rangle$$. Similarly, the union of lines through $$x$$ intersecting $$M$$ is another 2-d plane in $$\\langle L,M\\rangle$$. The intersection of these planes will be a line; it can't be a plane because then $$L$$ and $$M$$ would intersect, and a dimension argument says it's at least a line. That line passes through $$x$$, so it's one of the lines that defines each of the planes, and thus it's the line we seek.\n\nNow, seeing how this fits together, an explicit construction:\n\nDefine the lines $$L$$, $$M$$, $$N$$ as follows: $$L=\\{ax_1+bx_2\\mid a,b\\in \\mathbb{R}\\}$$, $$M=\\{cy_1+dy_2\\mid c,d\\in \\mathbb{R}\\}$$, $$N=\\{ez_1+fz_2\\mid e,f\\in \\mathbb{R}\\}$$ where $$x_1,x_2,y_1,y_2,z_1,z_2$$ are pairs of points on each line, with coordinates in $$\\mathbb{R}^5\\setminus \\{0\\}$$. All of these use the description of $$\\mathbb{P}^4$$ as the quotient of $$\\mathbb{R}^5$$ minus the origin by $$\\mathbb{R}^*$$.\n\nNow, the six 5-tuples $$x_1,x_2,y_1,y_2,z_1,z_2$$ in $$\\mathbb{R}^5$$ must have a nontrivial linear dependence relation; there are constants $$A,B,C,D,E,F$$ not all zero so that $$Ax_1+Bx_2+Cy_1+Dy_2+Ez_1+Fz_2 = 0$$. These constants can be found by Gaussian elimination on the matrix with rows $$x_1,x_2,y_1,y_2,z_1,z_2$$ augmented with a $$6\\times 6$$ identity.\n\nSince the lines don't lie in a hyperplane, our six points must span $$\\mathbb{R}^5$$, and the constants $$A,B,C,D,E,F$$ are unique up to constant multiples. Also, since $$L$$ and $$M$$ don't intersect, there's no nontrivial linear combination of $$x_1,x_2,y_1,y_2$$ that's zero - which means that at least one of $$E$$ and $$F$$ is nonzero. Similarly, at least one of $$A$$ and $$B$$ is nonzero, and at least one of $$C$$ and $$D$$ is nonzero.\n\nThe line we seek is the set of linear combinations $$\\{\\alpha(Ax_1+Bx_2)+\\beta(Cy_1+Dy_2)+\\gamma(Ez_1+Fz_2)\\mid (\\alpha,\\beta,\\gamma)\\in \\mathbb{R}^3\\}$$ Since the three vectors $$Ax_1+Bx_2$$, $$Cy_1+Dy_2$$, $$Ez_1+Fz_2$$ are linearly dependent, that's a $$2$$-dimensional subset of $$\\mathbb{R}^5$$, which projects to a line. It intersects $$L$$ at $$Ax_1+Bx_2$$ for $$\\alpha=1,\\beta=0,\\gamma=0$$ and similarly for the other two lines. We could also eliminate the redundancy by restricting to $$\\alpha+\\beta+\\gamma=0$$.\n\n\u2022 How do you see all lines from $L$ through $x$ lie in $\\langle L, M \\rangle$? Wouldn't that mean that all these lines also go through $M$, since $\\langle L, M \\rangle$ is the set of all lines going through $L$ and $M$? Wouldn't that then mean that there are infinitely many lines through $L, M$ and $N$? \u2013\u00a0The Coding Wombat Mar 28 at 22:03\n\u2022 $\\langle L, M\\rangle$ isn't a set of lines. It's a set of points - each point in it lies in some line intersecting both $L$ and $M$. That set of points is a 3-d hyperplane. If we take some random line composed of points in it, that probably won't be one of the lines we used to define it, so there's no reason to expect it will intersect either $L$ or $M$. \u2013\u00a0jmerry Mar 28 at 22:13\n\u2022 How do we know the line is unique? Couldn't there be a line through L,M and N, not going through $x$? \u2013\u00a0The Coding Wombat Mar 28 at 22:19\n\u2022 No. $x$ is the only point on $N$ that lies on any line intersecting $L$ and $M$. That's what your previous exercise result is telling you. We have to work a bit constructing the line and showing that it's the only line that works, but that any such line goes through $x$? We know that from the start. (In my explicit construction, $x$ is the point $Ez_1+Fz_2$.) \u2013\u00a0jmerry Mar 28 at 22:48","date":"2019-07-22 08:39:48","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\": 69, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.7580471634864807, \"perplexity\": 102.52697017607849}, \"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-2019-30\/segments\/1563195527828.69\/warc\/CC-MAIN-20190722072309-20190722094309-00163.warc.gz\"}"} | null | null |
{"url":"http:\/\/mathonline.wikidot.com\/the-spectrum-of-an-element-in-a-normed-or-banach-algebra-ove","text":"The Spectrum of an Element in a Normed or Banach Algebra over C\n\n# The Spectrum of an Element in a Normed or Banach Algebra over C\n\nSo far we have only discussed properties of the spectrum of a point $x$ is an algebra $\\mathfrak{A}$ over $\\mathbb{C}$ with unit. When $\\mathfrak{A}$ is a normed algebra (not necessarily with a unit), more can be said.\n\n Theorem 1: Let $\\mathfrak{A}$ be an normed algebra over $\\mathbb{C}$ and let $x \\in \\mathfrak{A}$. Then there exists a point $\\lambda \\in \\mathrm{Sp}(\\mathfrak{A}, x)$ such that $|\\lambda| \\geq r(x)$.\n\nWhen $\\mathfrak{A}$ is a Banach algebra, we obtain the following theorem.\n\n Theorem 2: Let $\\mathfrak{A}$ be a Banach algebra over $\\mathbb{C}$ and let $x \\in \\mathfrak{A}$. Then $\\mathrm{Sp}(\\mathfrak{A}, x)$ is a nonempty compact subset of $\\mathbb{C}$ and moreover, $r(x) = \\max \\{ |\\lambda| : \\lambda \\in \\mathrm{Sp}(\\mathfrak{A}, x) \\}$.\n\nRecall that a subset of $\\mathbb{C}$ is compact if and only if it is closed and bounded.\n\nIn the proof below, we assume that $\\mathfrak{A}$ has a unit. The Theorem is true regardless of this assumption.\n\n\u2022 Proof: Suppose that $\\lambda \\in \\mathbb{C}$ is such that $|\\lambda| > r(x) > 0$ so that $|\\lambda^{-1}| < r(x)^{-1}$. Then $r(\\lambda^{-1}x) < 1$.\n\u2022 Therefore $1 - \\frac{1}{\\lambda} x \\in \\mathrm{Inv}(\\mathfrak{A})$ by the theorem on the Invertibility of 1 - a When r(a) < 1 in a Banach Algebra with Unit page, and thus $\\lambda - x \\in \\mathrm{Inv}(\\mathfrak{A})$. So $\\lambda \\not \\in \\mathrm{Sp}(\\mathfrak{A}, x)$. Thus if $\\lambda \\in \\mathrm{Sp}(\\mathfrak{A}, x)$ then $\\lambda \\leq r(x)$.\n\u2022 But by Theorem 1 there exists a $\\lambda \\in \\mathbb{C}$ such that $|\\lambda| \\geq r(x)$. Therefore, there exists a $\\lambda \\in \\mathbb{C}$ such that $r(x) = |\\lambda|$ and:\n(1)\n\\begin{align} \\quad r(x) = \\max \\{ |\\lambda| : \\lambda \\in \\mathrm{Sp}(\\mathfrak{A}, x) \\} \\end{align}\n\u2022 Observe that as a result, $\\mathrm{Sp}(\\mathfrak{A}, x)$ is a bounded subset of $\\mathbb{C}$. Consider the map $F : \\mathbb{C} \\to \\mathfrak{A}$ defined for all $z \\in \\mathbb{C}$ by $F(z) = z - x$. Note that $F(z) \\in \\mathrm{Inv}(\\mathfrak{A})$ if and only if $z \\in \\mathbb{C} \\setminus \\mathrm{Sp}(\\mathfrak{A}, x)$. So:\n(2)\n\\begin{align} \\quad F^{-1}(\\mathrm{Inv}(\\mathfrak{A})) = \\mathbb{C} \\setminus \\mathrm{Sp}(\\mathfrak{A}, x) \\end{align}\n\u2022 Clearly $F : \\mathbb{C} \\to \\mathfrak{A}$ is a continuous mapping. We know that $\\mathrm{Inv}(\\mathfrak{A})$ is an open set in $X$ from Inv(A) is an Open Subset of A in a Banach Algebra with Unit page. Thus by continuity of $F$ and the equality above, $\\mathbb{C} \\setminus \\mathrm{Sp}(\\mathfrak{A}, x)$ is open in $\\mathfrak{A}$, i.e., $\\mathrm{Sp}(\\mathfrak{A}, x)$ is closed in $\\mathfrak{A}$.\n\u2022 Since closed and boundedness implies compactness in $\\mathbb{C}$, we see that $\\mathrm{Sp}(\\mathfrak{A}, x)$ is compact in $\\mathbb{C}$. $\\blacksquare$","date":"2019-03-22 04:19:35","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\": 0, \"wp-katex-eq\": 0, \"align\": 2, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.994010329246521, \"perplexity\": 77.25024105478234}, \"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-2019-13\/segments\/1552912202628.42\/warc\/CC-MAIN-20190322034516-20190322060516-00425.warc.gz\"}"} | null | null |
Killing clover in St. Augustine grass involves several different methods. Although the proper herbicide will remove clover and other broadleaf weeds from your lawn, you can also implement certain strategies that reduce the likelihood of the clover showing up again, or even spreading in the first place. It is important to use the right type and amount of herbicide in a St. Augustine lawn; mistakes will tend to kill the grass as well as the clover. Killing and otherwise preventing the growth of clover requires proper lawn care and proper mechanical maintenance in addition to the use of herbicide.
Obtain an herbicide from your garden or lawn supply store suitable for use with southern grasses. The herbicide should mention somewhere on the packaging that it is effective against clover specifically or broadleaf weeds in general. If you are trying to kill the clover before it grows, select a pre-emergence herbicide. This type is especially useful when you are working with a thin or younger lawn. Otherwise, choose a post-emergence herbicide.
Apply the herbicide in the precise amounts directed by the packaging. Overuse of the herbicide may damage or kill your lawn.
Fertilize your lawn every month during the growing season. If your soil is sandy, use no more than 1 lb. of fertilizer per 1,000 square feet of lawn. If your soil is thicker, use slightly less. Keeping the lawn healthy and growing vigorously will enable the St. Augustine grass to compete with the clover, preventing it from gaining a foothold in your lawn. Consult with a garden center in order to determine the best type of fertilizer for use with the soil in your area.
Mow your lawn regularly. Mowing will prevent clover plants from going to seed, which will make clover germination in the next year much less likely. Mow every five days if you are keeping your lawn below 2 inches in height, weekly or almost weekly for a mowing height of 2 1/2 inches, and every two weeks for any greater height. If you keep your grass shorter, you will be able to more effectively keep the clover under control. Mowing frequency can be reduced during the winter and late fall. | {
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expiratory reserve volume in copd
Deborah Leader RN, PHN, is a registered nurse and medical writer who focuses on COPD. The pathophysiological mechanisms of COPD are largely expiratory and obstructive. NIH MedlinePlus. Environmental perturbations: Obesity. Pulmonary function tests. Shore SA. So if you breathe out normally as you would, then try and breathe out even more until you physically cannot breathe out any more air, then this is the expiratory reserve volume. You can tap into this reserve volume when you exercise and your tidal volume increases. Verywell Health uses only high-quality sources, including peer-reviewed studies, to support the facts within our articles. Read our, Medically reviewed by Benjamin F. Asher, MD, Using an Incentive Spirometer to Strengthen Lungs. Symptoms Multidisciplinary Respiratory Medicine. So that all of your breathing takes place through your mouth, a technician will put a clip on your nose to keep it gently closed. The average expiratory and inspiratory flow-volume curves for healthy and COPD subjects are presented in Figure 1. There also are a handful of people for whom PFTs are contraindicated, including those who've recently had a heart attack or stroke or abdominal, chest, or eye surgery; people who have a collapsed lung (pneumothorax) or an aneurysm in any part of the body; and anyone who has tuberculosis or a respiratory infection. 1978;44(2):156–165. Volume effect and exertional dyspnoea after bronchodilator in patients with COPD with and without expiratory flow limitation at rest. Once you've mastered the technique, you'll be asked to breathe in as deeply and fully as possible, and then to exhale as hard and fast as you can in order to completely empty your lungs.. Ulster Med J. However, their consequences are inspiratory and elastic. You'll be given a small hand-held device with a sterile mouthpiece that connects to a spirometer, a machine that's about the size and shape of a printer that will both register the force of your breath and print out the results. Results: With increasing BMI in the group as a whole, functional residual capacity, residual volume, expiratory reserve volume, and specific airway resistance (sRaw) decreased exponentially (all P < .001); total lung capacity (TLC) decreased linearly (P < .001); and inspiratory capacity (IC) and IC/TLC increased linearly (P < .001). Sign up for our Health Tip of the Day newsletter, and receive daily tips that will help you live your healthiest life. 29. blood volume the plasma volume added to the red cell volume ; see also blood volume . Dynamic hyperinflation (DH) is a prognostically relevant factor in chronic obstructive pulmonary disease (COPD) (Aalstad et al., 2018; Casanova et al., 2005). Pol J Radiol. This is measurement is obtained during lung volume testing through spirometry, a type of pulmonary function test, or PFT.. An update on contraindications for lung function testing.Thorax. Work from several groups has established that the reduced expiratory airflow in COPD leads to incomplete lung emptying, particularly with the rapid respiratory rates and large tidal volumes seen during exercise. Shown are resting lung volumes in patients with chronic obstructive pulmonary disease (COPD) and in age-matched healthy normal individuals. Expiratory reserve volume is an important measurement of lung function testing that, when combined with results from other PFTs, is primarily used to diagnose and distinguish between lung diseases such as chronic obstructive pulmonary disease (COPD), asthma, and pulmonary fibrosis.2 Because imaging of the lungs, such as X-rays or computerized tomography (CT) scans, often cannot make these distinctions, PF… IRV decreased to make room for increased tidal volume along with ERV. Am Fam Physician. Group A was composed of patients taking less than 2 L oxygen/min, while group B was taking equal to or greater than 2 L oxygen/min. Pulmonary function tests. xation volume, the patient affected by EFL needs longer expiratory time as the expiratory flow is lower. If you continue browsing the site, you agree to the use of cookies on this website. Expiratory reserve volume is an important measurement of lung function testing that, when combined with results from other PFTs, is primarily used to diagnose and distinguish between lung diseases such as chronic obstructive pulmonary disease (COPD), asthma, and pulmonary fibrosis., Because imaging of the lungs, such as X-rays or computerized tomography (CT) scans, often cannot make these distinctions, PFTs are highly useful., The results of pulmonary function testing, including ERV measurements, can also contribute information used to:, Pulmonary function tests such as spirometry are very safe procedures, but some people do experience shortness of breath, lightheadedness, or coughing. ERV can be useful in a variety of ways, from diagnosing lung disease to evaluating a person's lungs prior to surgery. For example, if the ERV to vital capacity ratio is high, it suggests that the lungs are stiff and unable to expand and contract properly; lung fibrosis might be the culprit. Sanja Jelic, MD, is board-certified in sleep medicine, critical care medicine, pulmonary disease, and internal medicine. In later stages there is decreased expiratory flow at all lung volumes ( see Figure 49-1 ). Once you're situated, the practitioner will give you specific instructions about how to hold the mouthpiece and breathe into it. Maximum amount of air that can be exhaled over normal tidal volume (from the resting expiratory level) when person expires forcefully ERV= 1100ml Expiratory Reserve Volume (ERV) IRV TV ERV RV IC FRC VC TLC RV 2011;66:714-723. 2012;77(1):28-36. doi:10.12659/pjr.882578. The amount of air present in the lungs at the end of a normal expiration is the functional residual capacity (FRC) that includes expiratory reserve volume (ERV) and residual volume (RV, the volume of air remaining in the lungs after a deep expiration), which is a result of the force displayed by expiratory muscles in the healthy young people to overcome chest wall elasticity, while in the elderly it … Role of computed tomography in quantitative assessment of emphysema. Therefore, the inspiration starts at an end-expiratory lung volume (EELV) greater than the relaxation volume leading to dy-namic lung hyperinflation (dLH) [21]. American Lung Association. The Understanding Potential Long-term Impacts on Function with Tiotropium (UPLIFT®) trial included IC measurements. The wife of a patient who was admitted 3 days ago with an exacerbation of chronic obstructive pulmonary disease (COPD) states that she is worried about her husband because he appears to be breathing "really hard." In chronic obstructive pulmonary disease (COPD), worsening expiratory flow limitation together with alteration in the elastic properties of the lung are associated with progressive lung hyperinflation and gradual decline in the resting inspiratory capacity over time. expiratory reserve volume: [ vol´ūm ] the space occupied by a substance or a three-dimensional region; the capacity of such a region or of a container. In other words, if you were breathing in and out normally, but then forcefully pushed out as much additional air as possible after an exhale, the extra air would represent your expiratory reserve volume. Ranu H, Wilde M, Madden B. 2016;234:79–84. Chronic obstructive pulmonary disease (copd) power point, No public clipboards found for this slide. Mar 13, 2018. In: Exploring Human Biology in the Laboratory. ment in COPD by reducing the expiratory flow reserve in the tidal volume range including lung senescence and breathing at low-lung volume (near residual volume) as is frequently observed in comorbidities such as morbid obesity, chronic congestive heart failure and restrictive diseases of the thoracic cage21. Looks like you've clipped this slide to already. Now customize the name of a clipboard to store your clips. Analysis of the configuration of maximum expiratory flow-volume curves. During exercise, your respiratory rate increases, which is facilitated by the intercostal muscles. Mead J. Cooper BG. The average ERV volume is about 1200 mL in men and 700 mL in women.. This will, in turn, help inform an effective treatment plan. Mar 16, 2019. What Is an FEV1/FVC Ratio and What Does It Mean? Choromańska A, Macura KJ. Maximum expiratory flow vol-ume curves in the two groups of patients with COPD. Ⓒ 2021 About, Inc. (Dotdash) — All rights reserved. Comparing tidal-to-maximum flow-volume (F-V) loops is a simple and widely available method to assess EFL in patients with COPD. In later stages there is decreased expiratory flow at all lung volumes (see Figure 49-1). MIFR were comparable (p . Changes in each parameter are exponential (solid curved line), with the greatest change in the transition between overweight (> 25 kg/m 2 ) and obese (> 30 kg/m 2 ). In chronic obstructive pulmonary disease (COPD), this phenomenon is exaggerated as the connective tissue in the lung parenchyma is destructed in addition to the airway narrowing. INTRODUCTION. FRC refers to the volume of air left in the lungs after a normal, passive exhalation and used to evaluate the elasticity of the lungs and chest wall. Pulmonary function tests. We then subdivided the COPD patients into 2 groups, A and B. Pressure–volume (P–V) curves of the respiratory system are shown with tidal P–V curves during rest (filled area) and exercise (open area). Or, if that ratio is very low, it could mean resistance in the lungs is resulting from asthma. However, their consequences are inspiratory and elastic. Morton Publishing Company; 2016:234. Functional residual capacity (FRC) and expiratory reserve volume (ERV) % predicted plotted versus body mass index (BMI) in 373 patients. Expiratory Reserve Volume The amount of extra air exhaled (above tidal volume) during a forceful breathe out. National Heart, Lung, and Blood Institute. Barreiro TJ, Perillo I. IC analysis from UPLIFT® (N = 5992) was performed at 1 and 6 months, and every 6 months through 4 years. 2017. Plethysmography Tests the Volume of Your Lungs, Pulmonary Function Tests Can Evaluate Your Lung Function, FRC Tests are Among Several Pulmonary Function Tests, Obstructive and Restrictive Lung Disease Differences and Treatment, Getting a Forced Vital Capacity (FVC) Test, Role of computed tomography in quantitative assessment of emphysema, An update on contraindications for lung function testing, The Physiological Basis and Clinical Significance of Lung Volume Measurements, Determine if existing lung disease is improving or getting worse, Check to see how well treatment for lung disease is working, Monitor for toxic side effects of certain medications, Screen for lung problems in smokers or people whose jobs put them at risk for lung disease (through exposure to toxic chemicals, for example). If you continue browsing the site, you agree to the use of cookies on this website. Increased expiratory resistences cause, in turn, a reduction in expiratory flow. Functional residual capacity (FRC) refers to the volume of air left in the lungs after a normal, passive exhalation. Because it requires taking a series of very deep breaths, it's advisable to eat lightly beforehand, avoid alcohol and smoking, and dress in non-restrictive clothing. Thus, when EFL arises in COPD patients [22], they breath with progres- An Approach to Interpreting Spirometry. Traditionally, both the severity of COPD and the efficacy of treatment interventions have been assessed using resting lung function measures, particularly forced expiratory volume in 1 s (FEV1). When respiratory rate rises, the time for exhalation is progressively constrained. It is used to evaluate the elasticity of the lungs and chest wall in persons with respiratory illnesses like chronic obstructive pulmonary disease (COPD). Women who are pregnant and people experiencing stomach bloating, extreme fatigue, or muscle weakness may not get accurate results from PFTs.. In COPD, expiratory flow limitation (EFL) occurs because of the combined effects of increased airway resistance and reduced lung recoil: alveolar emptying is therefore critically dependent on expiratory time, which, if insufficiently long, results in … 28. 1. Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. Ponce MC, Sharma S. Pulmonary Function Tests. Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. The changes in inspiratory capacity (IC) over time in chronic obstructive pulmonary disease (COPD) patients are unknown. Remember that ERV is just one measurement performed in a pulmonary function test that can help your doctor narrow down a diagnosis of whether your condition is obstructive or restrictive in nature. Early in the course of COPD, the expiratory flow-volume curve shows a scooped-out lower part of the expiratory limb as a result of abnormal flow at low lung volume. A S T H M A. Pulmonary Function Tests: Overview. Clipping is a handy way to collect important slides you want to go back to later. 15. Dynamic hyperinflation (DH) refers to the variable increase in end-expiratory lung volume (EELV) above the relaxation volume … Remains the same. Lung volume testing is done to determine expiratory residual volume can be done in the office of a pulmonologist (lung doctor) or at a hospital as an outpatient procedure. 2004;69(5):1107-1115. What are the names of Santa's 12 reindeers? ERV testing is very safe, noninvasive, and can provide information about your breathing status and lung function in a way that X-rays and CT scans can't. Lung function is physiologically divided into four volumes: expiratory reserve volume, inspiratory reserve volume, residual volume, and tidal volume. Douglas MM, Douglas JM. See our Privacy Policy and User Agreement for details. 2011;80(2):84-90. Expiratory reserve volume (ERV) decreased with statistical significance (p < 0.05) while inspiratory capacity (IC) substantially increased as immersion progressed. Lung Procedures & Tests. It is a noninvasive technique and preparation is minimal. You may also have decreased ERV if you are shorter or live in a location with a lower altitude. 2011;1(1):263-82. doi:10.1002/cphy.c100017. Pulmonary functions (1) In other words, expiratory flow limitation and the resulting air trapping/lung hyperinflation tend to increase operating lung volumes, thus reducing inspiratory reserve volume … The pathophysiological mechanisms of COPD are largely expiratory and obstructive. Pulmonary function testing in COPD. Lung Volumes IRV TV ERV 4 Volumes 4 Capacities – Sum of 2 or more lung volumes RV IC FRC VC TLC RV 17. These confirm the 750 JAYAMANNE, EPSTEIN, GOLDRING 7 6 5 4 VOLUME Liters FIGURE 1. Boni E(1), Corda L, Franchini D, Chiroli P, Damiani GP, Pini L, Grassi V, Tantucci C. Author information: (1)Cattedra di Medicina I, Università di Brescia, Italy. Updated March 23, 2020. ERV is generally reduced with obesity, abdominal swelling (ascites), or after upper abdominal surgery. You'll likely be asked to do this at least three times. 12:3. BACKGROUND: Expiratory flow limitation (EFL) is a key physiological abnormality in COPD. An expiratory reserve volume (ERV) is the amount of air that can be breathed out after a normal exhalation. Relation of concavity in the expiratory flow-volume loop to dynamic hyperinflation during exercise in COPD. Nonuniform ventilation of the lungs is seen even in the earlier stages of COPD and this leads to low ventilation/perfusion ratios. presence of airway obstruction of varying severity. See our User Agreement and Privacy Policy. Instead, Xrs would relate to estimates of communicating volume, namely, expiratory reserve volume (ERV) and single-breath alveolar volume (VaSB). National Center for Biotechnology Information. J Appl Physiol Respir Environ Exerc Physiol. Values of MEFR and MIFR at different lung volumes are shown in the Table 1. For the actual test, you will be seated in a chair. Early in the course of COPD, the expiratory flow-volume curve shows a scooped-out lower part of the expiratory limb as a result of abnormal flow at low lung volume. ERV is added to another measurement, residual volume (RV), which refers to the volume of air left in the airways after maximal exhalation, to determine FRC. Expiratory reserve volume: the maximal volume of air that can be exhaled from the end-expiratory position: IRV: Inspiratory reserve volume: the maximal volume that can be inhaled from the end-inspiratory level: IC: Inspiratory capacity: the sum of IRV and TV: IVC: Inspiratory vital capacity: the maximum volume of air inhaled from the point of maximum expiration: VC: Vital capacity: the volume … Lutfi M. The Physiological Basis and Clinical Significance of Lung Volume Measurements. MEFR at all lung volumes were significantly lower in the COPD group (p , 0.001). How Can Inspiratory Capacity Help Manage My Lung Disease? 1 In other words, expiratory flow limitation and the resulting air trapping/lung hyperinflation tend to increase operating lung volumes, thus reducing inspiratory reserve volume (IRV). Johns Hopkins Medicine. Bowen University, Iwo, Osun State, Nigeria. In COPD, because of resting and dynamic hyperinflation (a further increase in end-expiratory lung volume), exercise tidal … Varga J, Casaburi R, Ma S, et al. Expiratory Flow Rates The maximum expiratory flow rates of both groups are shown in Table 2. These complex relationships remain incompletely understood. The analysis of flow-volume loops shows that, as the disease progresses, the flow generated during expiration of a tidal volume becomes very close to the flow generated during forced maximal expiration. The heart rate increases during exercise. Respir Physiol Neurobiol. We hypothesized that in COPD the presence of noncommunicating lung would disrupt the expected Xrs-volume relationship compared with plethysmographic functional residual capacity (FRCpleth). Compr Physiol. What Is an Expiratory Reserve Volume (ERV) Test? To sum up: Your expiratory reserve volume is the amount of extra air — above a normal breath — … The inspiratory reserve volume is relatively constant but the expiratory reserve volume tends to reduce. There's a very small risk of an asthma attack for those who have asthma.. Often, various ratios are calculated using these measurements. limitation contributes to dynamic hyperinflation during exercise, whereby the end-expiratory lung volume progressively increases and inspiratory capacity (IC) and inspiratory reserve volume are reduced, and which is associated with dyspnea and exercise intolerance in COPD (O'Donnell et al., 2004). You can change your ad preferences anytime. Again, ERV is not a separate test but rather one of several measurements of lung function obtained from spirometry. Thank you, {{form.email}}, for signing up. Expiratory reserve volume is also often measured along with vital capacity (the total amount of air that can be exhaled, including the ERV) and inspiratory reserve volume, which—as you might imagine—measures the amount of extra air you can intentionally draw into your lungs after you've breathed in normally.. We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. If you use a short-acting inhaler, it may be necessary to cease using it for six to eight hours prior to undergoing pulmonary function testing.. It is determined after a key measurement of lung volume—functional reserve capacity (FRC)—has been measured. For healthy and COPD subjects are presented in Figure 1 within our articles about, (... Asked to do this at least three times an FEV1/FVC ratio and what Does it?... Lung disease for increased tidal volume volume measurements tidal-to-maximum flow-volume ( F-V loops... 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\section{Introduction}
We consider the Lie group analysis of the class of radiant plasma energy equations of form
\begin{equation}\label{EqGAW}
u_t=\left[G(x)A(u)u_x\right]_x+W(t);\quad t\in(0,t_1),\quad x\in [0,x_1].
\end{equation}
As usual, $x$ and $t$ are respectively space and time coordinates.
$G$, $A$ and $W$ are arbitrary sufficiently smooth (analytic) functions of their variables.
Dependent variable $u$ represents energy density for which the main contribution is radiant energy,
often approximated by the equilibrium expression $\frac{4}{c}\epsilon\sigma T^4$, where $T$ is the absolute temperature,
$\sigma$ is the Stefan--Boltzmann constant, $\epsilon$ is the emissivity and c is the speed of light (e.g. \cite{Drake}).
$G(x)$ is mass density and $G(x)A(u)$ is the energy diffusivity. In general, $A$ may depend on temperature, and therefore on $u$,
so a linear model is inappropriate when the temperature is highly variable, due to laser heating.
In the setting of a plasma laboratory \cite{Lindl1998}, $W$ is the power of a laser used to heat the plasma.
For convenience, it will be assumed hereafter that a unit of length has been chosen so that $x_1=1$.
\medskip
In general, in realistic simulations the energy transport equation must be solved numerically.
However, some insight may be gained from special cases of (\ref{EqGAW}) that may be reduced to ordinary differential equations,
to algebraic equations or even to exact solutions. Therefore it is advantageous to have a full classification of models that allow symmetry reductions.
A classical Lie point symmetry classification has been done in \cite{Broadbridge&Lavrentiev&Williams1999} for the case of uniform density $G$.
However, it is a key feature of inertial confinement experiments that the laser blast causes some local compression.
Therefore we allow density to vary in space.
After completing the classical point symmetry classification, we consider local conservation laws and associated potential symmetries,
as well as some nonclassical symmetries. Finally, we construct some exact solutions.
We exclude some details of the cases $A=\mathop{\rm const}\nolimits$ (linear equations) and $W(t)=\mathop{\rm const}\nolimits$ (a complete classification of this case can be found
in the series of articles~\cite{Vaneeva&Johnpillai&Popovych&Sophocleous}).
\section{On group classification}
We start our investigation of symmetry properties of class~\eqref{EqGAW} by finding its group of usual equivalence transformations
and classification of Lie point symmetries.
Let us note that Lie symmetries of different subclasses of class~\eqref{EqGAW} have been investigated by many authors.
Thus, e.g., linear equations have been classified by Lie~\cite{Lie1881}
in his classification of linear second-order PDEs with two independent variables.
(See also a modern treatment of this subject in~\cite{Ovsiannikov1982}.)
Classification of nonlinear equations with $G(x)=1$ and $W(t)=0$ can be found in~\cite{Ovsiannikov1959}.
In~\cite{Popovych&Ivanova2004NVCDCEs} one can find, in particular, the group classification of~\eqref{EqGAW} with $W(t)=0$.
The series~\cite{Vaneeva&Johnpillai&Popovych&Sophocleous} contains as a particular case
the complete group classification of the subclass $W(t)=1$.
Symmetries of time-dependent equations~\eqref{EqGAW} with $G(x)=1$ have been found in~\cite{Broadbridge&Lavrentiev&Williams1999}.
First of all we look for the (point) equivalence group of class~\eqref{EqGAW}, i.e., transformations of dependent and independent
variables that move any equation from class~\eqref{EqGAW} to an equation of the same class.
Following the results of~\cite{Kingston&Sophocleous1998,Popovych&Ivanova2004NVCDCEs} for equivalence transformations of parabolic equations,
without loss of generality we search for equivalence transformations of the form
\[
\tilde t=\tilde t(t), \quad \tilde x=\tilde x(t,x), \quad \tilde u=m(t,x)u+n(t,x).
\]
Substituting the above change of variables to~\eqref{EqGAW}, requiring the transformed equation to be
$\tilde u_{\tilde t}=(\tilde G(\tilde x)\tilde A(\tilde u)\tilde u_{\tilde x})_{\tilde x}+\tilde W(\tilde t)$,
we get an equation that is polynomial with respect to the derivatives of~$u$. Setting to zero its coefficients with respect to unconstrained variables
we get a system of overdetermined partial differential equations, general solution of which leads to the following theorem.
\begin{theorem}
Point equivalence group~$G^\sim$ of class~\eqref{EqGAW} consists of scaling and translation transformations of dependent and independent variables
\begin{gather}\nonumber
\tilde t=\varepsilon_4t+\varepsilon_1 ,\quad
\tilde x=\varepsilon_5x+\varepsilon_2 ,\quad
\tilde u=\varepsilon_6u+\varepsilon_3 ,\\
\tilde A=\varepsilon_7 A ,\quad
\tilde G=\varepsilon_4^{-1}\varepsilon_5^2\varepsilon_7^{-1}G ,\quad
\tilde W=\varepsilon_4^{-1}\varepsilon_6W , \label{EquivTransf}
\end{gather}
where $\varepsilon_i=\mathop{\rm const}\nolimits$, $\varepsilon_4\ldots\varepsilon_7\ne0$.
\end{theorem}
Below we perform the group classification of class~\eqref{EqGAW} up to the transformations~\eqref{EquivTransf}.
In the framework of the classical Lie--Ovsiannikov approach we search for an infinitesimal operator of Lie point symmetry of form
\[
X=\tau(t,x,u)\partial_t+\xi(t,x,u)\partial_x+\eta(t,x,u)\partial_u.
\]
Splitting with respect to unconstrained variables the equation obtained from the infinitesimal invariance condition
(application of the second prolongation of~$X$ to~\eqref{EqGAW} on the manifold of~\eqref{EqGAW} is zero)
we get the following system for coefficients of the symmetry operator~$X$:
\begin{gather*}
\tau_x=\tau_u=\xi_u=\eta_{uu}=0,\\
GA(2\xi_x-\tau_t)- G_xA\xi- GA_u\eta=0,\\
\eta_t- W_t\tau-GA\eta_{xx}-G_xA\eta_x+W(\eta_u-\tau_t)=0,\\
GA_u(2\xi_x-\eta_u-\tau_t)-GA\eta_{uu}- GA_{uu}\eta- G_xA_u\xi=0,\\
GA(\xi_{xx}+\xi_x-2\eta_{xu})-G_xA\tau_t-\xi_t-G_xA_u\eta -G_{xx}A\xi -2 GA_u\eta_x=0.
\end{gather*}
An immediate consequence of these equations is $\eta_{uu}=0$. Then, from the rest of the equations we obtain
that either $\eta=0$, or, up to the equivalence group~\eqref{EquivTransf}, $A=u^m$ or $A=e^u$.
Solving the rest of the system of classifying equations separately in these three cases we get the following result.
\begin{theorem}
Allowing for point equivalence transformations~\eqref{EquivTransf},
equivalence classes of~\eqref{EqGAW} (with additional condition $W_tA_u\ne0$) that admit non-trivial Lie symmetry algebras,
are represented by the canonical forms in Tables~\ref{TableLieSymCaseAForAll}--\ref{TableLieSymCaseAum}.
\end{theorem}
In the tables, the universal quantifier denotes an arbitrary function.
\begin{center}
\footnotesize\setcounter{tbn}{0}\renewcommand{\arraystretch}{1.1}
Table \refstepcounter{tabu}\label{TableLieSymCaseAForAll}\thetabu. Case $\forall A$ \\[1ex]
\begin{tabular}{|l|c|c|l|c|}
\hline
N\raisebox{0ex}[2.5ex][0ex]{\null} & $G(x)$ & $W(t)$ & \hfill $A^{\rm max}\hfill$ \\[0.5ex]
\hline
\refstepcounter{tbn}\label{caseAforallGxaWt-1}\arabic{nomer}.\raisebox{0ex}[2.5ex][0ex]{\null} & $x^a$ & $1/t$
& $\langle (a-2)t\partial_t-x\partial_x \rangle$ \\[0.5ex]
\refstepcounter{tbn}\label{caseAforallGexWt-1}\arabic{nomer}.\raisebox{0ex}[2.5ex][0ex]{\null} & $e^{x}$ & $1/t$
& $\langle t\partial_t-\partial_x \rangle$ \\[0.5ex]
\refstepcounter{tbn}\label{caseAforallGx2W}\arabic{nomer}.\raisebox{0ex}[2.5ex][0ex]{\null} & $x^2$ & $\forall$
& $\langle x\partial_x \rangle$ \\[0.5ex]
\refstepcounter{tbn}\label{caseAforallG1W}\arabic{nomer}.\raisebox{0ex}[2.5ex][0ex]{\null} & $1$ & $\forall$
& $\langle \partial_x \rangle$ \\[0.5ex]
\refstepcounter{tbn}\label{caseAforallG1Wt-1}\arabic{nomer}.\raisebox{0ex}[2.5ex][0ex]{\null} & $1$ & $1/t$
& $\langle \partial_x, 2t\partial_t+x\partial_x \rangle$ \\[0.5ex]
\hline
\end{tabular}
\end{center}
Additionally to this there exist extra symmetries in the following cases
\begin{center}
\footnotesize\setcounter{tbn}{0}\renewcommand{\arraystretch}{1.1}
Table \refstepcounter{tabu}\label{TableLieSymCaseAexp}\thetabu. Case $A=e^{u}$ \\[1ex]
\begin{tabular}{|l|c|c|l|c|}
\hline
N\raisebox{0ex}[2.5ex][0ex]{\null} & $G(x)$ & $W(t)$ & \hfill $A^{\rm max}\hfill$ \\[0.5ex]
\hline
\refstepcounter{tbn}\label{caseAexpGW}\arabic{nomer}.\raisebox{0ex}[2.5ex][0ex]{\null} & $\forall$ & $\forall$
& $\langle e^{-\int Wdt}(\partial_t+W\partial_u),\,$ \\[0.5ex]
&&& $ e^{-\int Wdt}\Big(\int e^{\int Wdt}dt \partial_t+(W\int e^{\int Wdt}dt-e^{-\int Wdt})\partial_u\Big) \rangle$ \\[0.5ex]
\refstepcounter{tbn}\label{caseAexpGg1W}\arabic{nomer}.\raisebox{0ex}[2.5ex][0ex]{\null} & $\frac1{Z''}$ & $\forall$
& $\mathcal{A}_1$ \\[0.5ex]
\refstepcounter{tbn}\label{caseAexpGgW}\arabic{nomer}.\raisebox{0ex}[2.5ex][0ex]{\null} & $1$ & $\forall$
& $\langle e^{-\int Wdt}(\partial_t+W\partial_u),\,\partial_x,\, x\partial_x+2\partial_u,\,$ \\[0.5ex]
&&& $ e^{-\int Wdt}\Big(\int e^{\int Wdt}dt \partial_t+(W\int e^{\int Wdt}dt-e^{-\int Wdt})\partial_u\Big) \rangle$ \\[0.5ex]
\hline
\end{tabular}
\end{center}
{\footnotesize
Here $Z=Z(x)$ is an arbitrary solution of ordinary differential equation
\[
-\frac{Z'''}{Z''}=\frac{3(mZ''+n)-a}{mZ+nx+p},
\]
$m$, $n$, $p$, $a$ are arbitrary constants, $\mathcal{A}_1$ is three-dimensional Lie algebra whose operators look like
$X=\tau\partial_t+\xi\partial_x+\eta\partial_u$ with
$\xi=mZ+nx+p$, $\eta=-mZ_x-n+A-\tau_t$ and $\tau$ being a solution of equation
$\tau''+W\tau'+W'\tau=0$, that is
$$\tau=e^{-\int Wdt} \left[\int^t e^{\int^{t_1} ~W(t_2)dt_2}~dt_1+c_2\right].$$
}
\begin{center}
\footnotesize\setcounter{tbn}{0}\renewcommand{\arraystretch}{1.1}
Table \refstepcounter{tabu}\label{TableLieSymCaseAum}\thetabu. Case $A=u^m$ \\[1ex]
\begin{tabular}{|l|c|l|c|}
\hline
N\raisebox{0ex}[2.5ex][0ex]{\null} & $G(x)$ & $W(t)$ & \hfill $A^{\rm max}\hfill$\\[0.5ex]
\hline
\refstepcounter{tbn}\label{caseAumGWt-(m+1)m}\arabic{nomer}.\raisebox{0ex}[2.5ex][0ex]{\null} & $\forall$ & $t^{-(m+1)/m}$
& $\langle mt\partial_t-u\partial_u \rangle$ \\[0.5ex]
\refstepcounter{tbn}\label{caseAumGxkWtn}\arabic{nomer}.\raisebox{0ex}[2.5ex][0ex]{\null} & $gx^k$ & $t^n$
& $\langle (k-2)t\partial_t-(mn+m+1)x\partial_x+(k-2)(n+1)u\partial_u \rangle$ \\[0.5ex]
\refstepcounter{tbn}\label{caseAumGxkWexpt}\arabic{nomer}.\raisebox{0ex}[2.5ex][0ex]{\null} & $gx^k$ & $we^{t}$
& $\langle (k-2)\partial_t-mx\partial_x+(k-2)u\partial_u \rangle$ \\[0.5ex]
\refstepcounter{tbn}\label{caseAumGexpxWtn}\arabic{nomer}.\raisebox{0ex}[2.5ex][0ex]{\null} & $ge^{x}$ & $t^n$
& $\langle t\partial_t-(mn+m+1)\partial_x+(n+1)u\partial_u \rangle$ \\[0.5ex]
\refstepcounter{tbn}\label{caseAumGexpxWexpt}\arabic{nomer}.\raisebox{0ex}[2.5ex][0ex]{\null} & $ge^{x}$ & $we^{t}$
& $\langle \partial_t-m\partial_x+u\partial_u \rangle$ \\[0.5ex]
\refstepcounter{tbn}\label{caseAumGx2Wt-(m+1)m}\arabic{nomer}.\raisebox{0ex}[2.5ex][0ex]{\null} & $gx^2$ & $t^{-(m+1)/m}$
& $\langle x\partial_x,\, mt\partial_t-u\partial_u \rangle$ \\[0.5ex]
\refstepcounter{tbn}\label{caseAumG1Wtn}\arabic{nomer}.\raisebox{0ex}[2.5ex][0ex]{\null} & $g$ & $t^{n}$
& $\langle \partial_x,\, 2t\partial_t+(mn+m+1)x\partial_x+2(n+1)u\partial_u \rangle$ \\[0.5ex]
\refstepcounter{tbn}\label{caseAumG1Wexpt}\arabic{nomer}.\raisebox{0ex}[2.5ex][0ex]{\null} & $g$ & $we^{t}$
& $\langle \partial_x,\,2\partial_t+mx\partial_x+2u\partial_u \rangle$ \\[0.5ex]
\hline
\end{tabular}
\end{center}
{\footnotesize
Here $g=\pm1$, $w=\pm1$.
In Cases~1 and~6 we require $m\ne-1$, to avoid case $W=\mathop{\rm const}\nolimits$.
}
\section{Reductions to ordinary differential equations}
Lie symmetry analysis is one of very few available systematic tools used to construct solutions of (systems of) nonlinear partial differential equations.
Although, in contrast to the case of ordinary differential equations, it does not provide us with the general solution of a system,
in many cases it allows to construct wide classes of solutions being invariant with respect to symmetry transformations.
Roughly speaking, the main theorem on invariant solutions of differential equations~\cite{Ovsiannikov1982,Olver1986} states
that all solutions invariant with respect to an $r$-parametric solvable group of symmetries of the given $n$-dimensional system
of partial differential equations
(with some additional restrictions on the Lie algebras of infinitesimal invariance transformations)
can be obtained by solving a system of differential equations with $n-r$ independent variables.
In particular, if $r=n-1$, invariant solutions can be constructed via solving a system of ordinary differential equations.
Note, that reductions with respect to $n$-dimensional subgroups lead to algebraic equations.
In this paper we consider the case of a single equation with two independent variables.
Thus, to construct its solutions being invariant with respect to $1$-dimensional Lie algebra
spanned by infinitesimal symmetry generator of form $v=\tau\partial_t+\xi\partial_x+\eta\partial_u$,
we need to solve the following equation (sometimes called the invariant surface condition)
\[
\tau u_t+\xi u_x=\eta.
\]
Solution of this equation (its first integral)
gives an expression (Ansatz) for the invariants that can be used to define one new independent variable and the new dependent variable.
Substituting this in the initial equation we reduce it to an ordinary differential equation.
Any solution of the reduced equation yields an invariant solution of the initial equation.
This reduction procedure works only if the symmetry algebra satisfies the property of transversality.
For more details see~\cite{Ovsiannikov1982,Olver1986}.
Otherwise (in case of \emph{systems of} partial differential equations) one may try to look for so-called \emph{partially invariant solutions}.
As we discussed above, in general any subgroup of a (not necessarily point) Lie symmetry group corresponds to a class of invariant solutions
of (a system of) differential equations.
In most cases there exists an infinite number of such subgroups.
This makes it practically impossible to construct directly all invariant solutions of the system even if its complete symmetry group is known.
An effective systematic way to classify such solutions
is to find a so-called ``optimal system'' of invariant solutions,
from which one can reconstruct all possible invariant solutions
by application of symmetry transformations to the solutions from the optimal system.
The background for construction of optimal systems of solutions of differential equations is given by the following statement~\cite{Ovsiannikov1982}:
Any two conjugate subgroups of a Lie symmetry group of a system of differential equations correspond to systems of reduced equations
that are related by a conjugacy transformation in the Lie symmetry group of the system
acting on the solutions invariant with respect to each subgroup.
Thus, all invariant solutions for a given system
can be constructed by selecting a subgroup in each conjugacy class of all symmetry subgroups.
Such a selection is called an optimal set (or optimal system) of subgroups of a Lie symmetry group.
Then we construct solutions being invariant with respect to the listed subgroups of symmetry transformations.
Action of the complete symmetry group on the above solutions give us all possible invariant solutions of the initial system.
A set of subalgebras of the Lie symmetry algebra corresponding to the optimal system of subgroups (called also ``optimal system of subalgebras'') consists of
subalgebras being inequivalent up to the actions of adjoint representation of the Lie symmetry group on its Lie algebra.
Ovsiannikov~\cite{Ovsiannikov1982} proposed an effective algorithm of construction of such optimal systems
(see also a nice simpler explanation and examples for optimal systems of one-dimensional subalgebras in~\cite{Olver1986}).
It is useful to note that optimal systems of subalgebras of low-dimensional Lie algebras (dimension less than or equal to 4)
are classified in~\cite{Patera&Winternitz1977}.
Using these results we can easily write down all inequivalent subalgebras of Lie symmetry algebras of
equations from class~\eqref{EqGAW} with power nonlinearity.
All equations presented in Table~3 possess 1-dimensional (Cases 1--5) or 2-dimensional (Cases 6--8) Lie symmetry algebras.
In Case~6 the invariance algebra is Abelian and its optimal system of subalgebras is
$\langle x\partial_x \rangle$, $\langle mt\partial_t-u\partial_u+\varepsilon x\partial_x\rangle$ ($\varepsilon=0,\pm1$), $\langle x\partial_x,\, mt\partial_t-u\partial_u\rangle$.
Symmetry algebras in Cases 7--8 are non-Abelian with optimal systems of subalgebras
$\langle e_1 \rangle$, $\langle e_2 \rangle$, $\langle e_1, e_2\rangle$, where $e_1$, $e_2$ are the basis generators
of the corresponding algebras.
Even though the symmetry algebras in Cases 7--8 are non-Abelian, they are solvable so they still lead to successive
reductions.
In Table~4 we list all essential Lie reductions of equations from Table~3
(in each case the value of parameter functions for equations~\eqref{EqGAW} coincide with those from Table~3).
More precisely, we perform reductions of the corresponding equations with respect to the subalgebras from the adduced optimal systems.\\
The non-stationary reductions of equations from Cases 7 and 8 are partial cases of reductions of Cases 2 and 3 correspondingly.\\
Reductions with respect to subalgebras containing $x\partial_x$ trivially lead to the $x$-independent solutions.
\pagebreak
\begin{center}
\renewcommand{\arraystretch}{1.2}
Table~4. Reduced ODEs for~\eqref{EqGAW}. \\
\footnotesize
\begin{tabular}{|l|c|c|l|}
\hline \raisebox{0ex}[2.5ex][0ex]{\null}
N & Ansatz $\tilde u=$& $\omega$ &\hfill {Reduced ODE\hfill} \\
\hline
1& $\varphi(\omega)t^{-1/m}$ & $x$ & $m(G\varphi^m\varphi')'+\varphi+m=0$\\
2& $\varphi(\omega)t^{n+1}$ & $xt^{\frac{mn+m+1}{k-2}}$ & $g(\omega^k\varphi^m\varphi')'+1-(n+1)\varphi-\frac{mn+m+1}{k-2}\omega\varphi'=0$\\
3& $\varphi(\omega)e^t$ & $xe^{mt/(k-2)}$ & $\varphi+\frac{m}{k-2}\omega\varphi'=g(\omega^k\varphi^m\varphi')'+w$\\
4& $\varphi(\omega)t^{n+1}$ & $x+(mn+m+1)\ln t$ & $(n+1)\varphi+(mn+m+1)\varphi'=g(e^{\omega}\varphi^m\varphi')'+1$\\
5& $\varphi(\omega)e^t$ & $x+mt$ & $m\varphi'+\varphi=g(e^{\omega}\varphi^m\varphi')'+w$\\
6& $\varphi(\omega)t^{-1/m}$ & $xt^{-\varepsilon/m}$ & $g(\omega^2\varphi^m\varphi')'+1+\frac1m\varphi+\frac{\varepsilon}{m}\omega\varphi'=0$\\
\hline
\end{tabular}
\end{center}
\section{Conservation laws and potential symmetries}
Roughly speaking~\cite{Olver1986} a {\em conservation law} of a system of
partial differential equations $\mathcal{L}(x,u_{(r)})=0$ can be understood as a divergence expression
${\rm div}\,F=0$ which vanishes for all solutions of this system.
Here $x=(x_1,\ldots,x_n),$ $u=(u^1,\ldots,u^m).$
$F=(F^1,\ldots,F^n),$ where $F^i=F^i(x,u_{(r)}),$ is a conserved vector of this conservation law,
$u_{(r)}$ is the set of all partial derivatives of function $u$ with respect to $x$
of order not greater than~$r$, function $u$ itself is considered as the derivative of zero order.
The {\em order} of the conserved vector $F$ is the maximal order of derivatives that explicitly appear in $F$.
A conserved vector $F$ is called {\em trivial} if
$F^i=\hat F^i+\check F^i$, $i=\overline{1,n}$,
where $\hat F^i$ and $\check F^i$ are, likewise~$F^i$, functions of $x$ and derivatives of $u$,
$\hat F^i\equiv0|_{\mathcal L}$,
and the $n$-tuple $\check F=(\check F^1,\ldots,\check F^n)$
is a null divergence (i.e. its divergence vanishes identically).
A conservation law is called trivial, if its conserved vector is trivial.
Two conservation laws are equivalent, if their difference is a trivial conservation law.
Conservation laws are called linearly dependent if there exists a linear combination of them which is a trivial conservation law.
The above explanation is useful for the first intuitive illustration of notion of conservation laws.
However, to obtain complete understanding and to be able to describe correctly all possible conservation laws of (a system of) differential equations,
we should introduce a more rigorous definition of conservation laws
(see, e.g.,~\cite{Popovych&Ivanova2004ConsLawsLanl} for more details and examples).
Namely, for any system~$\mathcal{L}$ of differential equations the set~$\mathop{\rm CV}\nolimits(\mathcal{L})$ of its conserved vectors is a linear space,
and the subset~$\mathop{\rm CV}\nolimits_0(\mathcal{L})$ of trivial conserved vectors is a linear subspace in~$\mathop{\rm CV}\nolimits(\mathcal{L})$.
The factor space~$\mathop{\rm CL}\nolimits(\mathcal{L})=\mathop{\rm CV}\nolimits(\mathcal{L})/\mathop{\rm CV}\nolimits_0(\mathcal{L})$
coincides with the set of equivalence classes of~$\mathop{\rm CV}\nolimits(\mathcal{L})$ with respect to the equivalence relation of conserved vectors.
\begin{definition}\label{DefinitionOfConsLaws}
The elements of the factor space~$\mathop{\rm CL}\nolimits(\mathcal{L})$ are called {\em conservation laws} of the system~$\mathcal{L}$,
and~$\mathop{\rm CL}\nolimits(\mathcal{L})$ is called {\em the space of conservation laws} of~$\mathcal{L}$.
\end{definition}
Thus, description of the conservation laws of a system~$\mathcal{L}$
is reduced to finding~$\mathop{\rm CL}\nolimits(\mathcal{L})$
(more precisely, to construction of its basis if $\dim \mathop{\rm CL}\nolimits(\mathcal{L})<\infty$ or a system of
generatrices if $\dim \mathop{\rm CL}\nolimits(\mathcal{L})=\infty$).
The elements of~$\mathop{\rm CV}\nolimits(\mathcal{L})$ from the same equivalence class define
conserved vectors of the same conservation law.
This allows us to identify the elements from~$\mathop{\rm CL}\nolimits(\mathcal{L})$ with their representatives in~$\mathop{\rm CV}\nolimits(\mathcal{L})$.
The {\em order of the conservation law} is called the minimum of the orders of the conserved vectors corresponding to this conservation law.
Linear (in)dependence of conservation laws is understood as linear (in)dependence of them as elements of~$\mathop{\rm CL}\nolimits(\mathcal{L})$.
Thus, conservation laws of a system~$\mathcal{L}$ are called {\em linearly dependent} if there exists a linear combination of their representatives,
which is a trivial conserved vector.
\begin{note*}
If a (local) transformation of variables connects two systems of differential equations, then, by the action of this transformation, a conservation law of
the first of these systems is transformed into a conservation law of the second system,
i.e. the equivalence transformation establishes a one-to-one correspondence between conservation laws of these systems.
So, similarly to the problem of symmetry group classification,
we can consider a problem of classification of conservation laws of a class of (systems of) differential equations with respect to its equivalence group.
(See~\cite{Popovych&Ivanova2004ConsLawsLanl} for more details, rigorous definitions and proofs.)
\end{note*}
Since equation~\eqref{EqGAW} is second-order evolutionary $(1+1)$-dimensional, then without loss of generality~\cite{Popovych&Ivanova2004ConsLawsLanl}
we can search for its conservation laws in form
\begin{equation}\label{EqConsLawGen}
D_tT(t,x,u)+D_xX(t,x,u,u_x)=0.
\end{equation}
Now, we expand the total derivatives in the above expression on the solution manifold of~\eqref{EqGAW}, take into account its differential consequences and
decompose the obtained expression with respect to the derivatives of~$u$. Solution of the resulting system of partial differential equations
gives the following theorem.
\begin{theorem}\label{TheoremLocalCL}
Any (nonlinear) equation from class~\eqref{EqGAW} admits exactly two linearly independent conservation laws
with densities and fluxes of form
\begin{gather}\textstyle
T= u-\int Wdt,\qquad X=-GAu_x ,\\ \textstyle
T=(u-\int Wdt)\cdot\int\frac{dx}G ,\qquad X=-GAu_x\cdot\int\frac{dx}G +\int Adu .
\end{gather}
\end{theorem}
\begin{note}
It follows from existence of two linearly independent local conservation laws, that equation~\eqref{EqGAW} is equivalent
up to contact transformations to an equation of form $u_t=(F(t,x,u,u_x))_{xx}$
(see results of~\cite{Popovych&Samoilenko2008} for the second order $(1+1)$-dimensional evolution equations).
\end{note}
In the framework of group analysis of differential equations,
one of the natural applications of conservation laws is construction of non-local (potential) symmetries.
A system of differential equations may admit such symmetries when at least one of its equations
(or a differential consequence) can be written in a conserved form or, in other words,
the system possesses a non-trivial conservation law.
After introducing potentials from the conservation law as additional dependent variables,
we obtain a new (potential) system of differential equations.
Any local symmetry transformation of the obtained system induces a symmetry of the initial system.
If transformations of some of the ``non-potential'' local variables
explicitly depend on non-local potentials, this symmetry
is called a non-local (potential) symmetry of the initial system,
otherwise it projects into point symmetries of the initial system.
For more details about potential symmetries and their applications we refer the reader to~\cite{Bluman&Kumei1989}.
It follows from Theorem~\ref{TheoremLocalCL} that for equations from class~\eqref{EqGAW} there exist exactly two potential systems constructed
with the found conservation laws:
\begin{gather}\label{SysPotSys1}\textstyle
v_x=u-\int Wdt,\qquad v_t=GAu_x,\\ \textstyle
z_x=(u-\int Wdt)\cdot\int\frac{dx}G,\qquad z_t=GAu_x\cdot \int\frac{dx}G-\int Adu.
\label{SysPotSys2}
\end{gather}
(Here $v=v(t,x)$ and $z=z(t,x)$ are potential variables.)
It is known~\cite{Popovych&Ivanova2004ConsLawsLanl} that the equivalence group for a class of
systems of equations or the symmetry group for a single system can be naturally prolonged to potential variables.
One can use these prolonged equivalence groups for classification of potential symmetries of the given system.
In view of this statement we classify potential symmetries of class~\eqref{EqGAW}
up to the (trivial natural) prolongation of group~\eqref{EquivTransf} to the potential variables.
In the present work we reduce ourselves to classification of the potential symmetries of class~\eqref{EqGAW}
that arise from potential system~\eqref{SysPotSys1}.
Finding all Lie symmetries of the potential system~\eqref{SysPotSys1} we prove the following result.
\begin{theorem}
All inequivalent equations from class~\eqref{EqGAW} ($W(t)\ne0$) having potential symmetries that arise from system~\eqref{SysPotSys1}
are exhausted by the following ones:
\begin{itemize}
\item
$A(u)=u^{-2}$, $G(x)=1$, $W(t)=S'(t)$, $S(t)$ is a solution of the differential equation $S''(S^2+a_2)=a_1(S')^2$ ($a_2=0,\pm1$):\\
$A_{\rm pot}=\langle \partial_x, \partial_v, a_1\frac{S'}{S''}\partial_t+(v-\frac{a_1}2x)\partial_x+[-u^2+(a_1+2S)u+a_1\frac{(S')^2}{S''}-a_1S-a_2-S^2]\partial_u
+(a_2x-\frac{a_1}2v)\partial_v\rangle$.
\item
$A(u)=u^{-2}$, $G(x)=1$, $W(t)=w$: $A_{\rm pot}=\langle \partial_x, \partial_v, \partial_t-wx\partial_v, 2t\partial_t-x\partial_x+2u\partial_u+v\partial_v, wt^2\partial_t+v\partial_x-(u-2wt)u\partial_u\rangle$.
\end{itemize}
(Together with the values of the arbitrary elements $A$, $G$ and $W$ for each case we adduce the potential symmetry algebras.)
\end{theorem}
We comment that the above second-order differential equation for $S(t)$, can be integrated twice to achieve a transcendental equation.
\begin{note}
As (to the best of our knowledge) there exists no systematic investigation of the potential symmetries of equations of form~\eqref{EqGAW}
with $W(t)\ne0$, in the above theorem for completeness we adduced also the constant-coefficient case.
\end{note}
Classification of the potential conservation laws and potential symmetries corresponding to other potential systems is a subject of a sequel paper.
\section{Exact solutions}
\subsection{The case with no restriction except $A=e^u$}
From Table 2, this case has two independent additional symmetries. For an equation with this level of generality
(two free functions $G$ and $W$) to have an extra symmetry, it must be transformable to a simpler equation for which the symmetry is very simple.
Let $\mu=\exp(u)$.
\begin{equation}
\mu_t=\mu[G(x)\mu_x]_x+W(t)\mu~.
\end{equation}
Let $\mu(x,t)=\Theta (x,t) exp(\int^t W(s)ds).$ Then
\[
e^{-\int W(t)dt}\Theta_t=[G(x)\Theta_x]_x,
\]
or more simply,
\begin{equation}
\label{simply}
\Theta_\tau=\Theta[G(x)\Theta_x]_x~,
\end{equation}
where
\[\tau=\int^t e^{\int^t W(s)ds}dt\,.
\]
Unlike the case of general energy diffusivity $A(u)$,
this equation is invariant under $\tau$-translation and therefore has a pseudo-steady state solution $\Theta=\Theta(x)$ satisfying
\[
G(x)\Theta_x=c,
\]
with $c$ an arbitrary constant.
From ~\eqref{EqGAW}, the heat flux is $-G(x)\mu_x$ which in the case of this solution, equates to a time dependent flux that is uniform in space,
taking the value $-c\,\exp(\int W(t)dt)$. The solution for $\mu(x,t)$ takes the form of multiplicative separation of variables,
\begin{equation}
\mu=e^{\int W(t)dt}\left[c \int \frac{dx}{G(x)}+c_2\right],
\end{equation}
with $c_2$ arbitrary. That is equivalent to a solution for $u(x,t)$ in the form of an additive separation of variables,
\begin{equation}
u=\int W(t)dt+\log\left(\int \frac{dx}{G(x)}~+c_4\right)+c_3,
\end{equation}
with $c_4$ and $c_3$ arbitrary constants.
\medskip
Equation \ref{simply} also has a scaling symmetry $\Theta\partial /\partial \Theta -\tau \partial /\partial \tau$.
Under this symmetry, invariant solutions have the form
$\Theta \tau=F(x)$, which is equivalent to
\[
u=-\log \tau + \log F(x)+\int^tW(s)ds,
\]
again an additive separated solution.
\subsection{A case with quadratic mass density}
Consider Table 3, Case 6. $A(u)=u^m, ~G(x)=x^2, ~W(t)=t^{-1-1/m}$.
\medskip
The two-dimensional symmetry algebra is generated by
$ax\partial_x+bmt\partial_t-bu\partial_u~;~~(a,b\in\Re).$
With $b\ne 0$, invariant solutions are of the form
\[
u=t^{-1/m}f(\phi)\,;\quad \phi=xt^{-a/(bm)},
\]
where
\begin{equation}
\label{reduction3.6} \frac{-1}{m}f(\phi)+\frac{-a}{bm}\phi f'(\phi)=[\phi^2f^mf'(\phi)]'+1.
\end{equation}
When $b=a$, this can be directly integrated to first order,
\[
f'(\phi)=\frac{-1}{m}\phi^{-1}f^{1-m}-\phi^{-1}f^{-m}-c_4\phi^{-2}f^{-m},
\]
with $c_4$ arbitrary.
This is an exactly solvable Bernoulli equation (as well as being a Riccati equation), only in the case $m=-1$.
This represents a heat diffusion coefficient that decreases with temperature. Then $g=1/f$ satisfies a first-order linear equation.
The two-parameter focussing solution is
\begin{equation}
u=t\,f(xt);\quad f(\phi)=\frac{c_5}{-\phi+c_6\phi e^{c_5/\phi}}.
\end{equation}
This equivalence class of equations may also represent an increasing diffusion coefficient $A=(u_\infty-u)^{-1}$.
Here, $u_{\infty}$ is an upper bound to the energy density.
Then define $v=u_\infty-u$ that satisfies
\[v_t=\left(G(x)v^{-1}v_x\right)_x-1.
\]
This has the same symmetry reduction as above except that the constant source term 1 in (\ref{reduction3.6}) must be replaced by $-1$.
If $g=1/f$, then $g$ satisfies a linear first-order equation, leading to the two-parameter focussing solution
\begin{equation}
u=u_{\infty}-t\,f(xt);\quad f(\phi)=\frac{1}{-1+(c_6/\phi) e^{-c_6/\phi}E_i(c_6/\phi)+(c_5/\phi)e^{-c_6/\phi}}.
\end{equation}
\subsection{Spatially uniform solution}
The $x$-independent solution $u=Y(t)$ is available in the general case of ~\eqref{EqGAW}, not just in the special cases uncovered by classical Lie symmetry analysis. This is because equations of form~\eqref{EqGAW}
are $Q$-conditionally (nonclassically) invariant with respect to the operator $\partial_x$.
In many practical cases of heated radiant plasma in a container with boundaries at $x=-1,1$,
the initial condition will be symmetric and $u_x$ will remain zero at $x=0$.
In an ideal thermodynamically closed system, the container is perfectly insulated and hence there will be zero heat flux at $x=1$, implying that the Neumann boundary condition $u_x=0$ will apply also at that boundary. The total energy content is
\begin{gather*}
\nonumber
\int_0^1 u(x,t)dx=\bar u(t), \mbox{ and}\\
\frac{d\bar u}{dt}=\int_0^1 u_t(x,t)dx
=\int_0^1 \partial_x [G(x)A(u)u_x]+W(t)dx=W(t)
\end{gather*}
implying for any solution $u(x,t)$,
\[
\bar u(t)=\bar u(0)+\int_0^t W(s)ds=Y(t).
\]
Hence, in a closed system for which zero-flux Neumann boundary conditions must be applied, the spatially uniform solution is the time dependent
mean value of any spatially variable solution.
In the circumstance of a closed system, the diffusion process is expected to evolve any solution asymptotically towards
the spatially uniform mean value $u=Y(t)$. This solution is stable, as can be seen from linear stability analysis.
Assume $u=Y(t)+v(x,t)$ is a solution of ~\eqref{EqGAW}, $v$ being a small perturbation with
\[
v^2+v_x^2=O(\varepsilon^2).
\]
Then to order $\varepsilon$,
\begin{gather*}
\nonumber
v_t=\partial_x[G(x)A(Y(t))v_x]\\
\implies v_\tau=\partial_x[G(x)v_x],
\end{gather*}
where $\tau=\int_0^tA(Y(s))ds$.
The equation for $v(x,\tau)$ is non-denerate provided $G$ has a minimum value $G_{min}>0$, in which case it is a dissipative parabolic equation.
Since both $u$ and $Y$ satisfy Neumann boundary conditions, so must $v_x=0$ at $x=0,1.$
The mean value of $u$ is fully accounted for in $Y(t)$, so the mean value of $v$ must be zero.
Since it has zero gradient at the boundaries, the solution for $v$ dissipates to a function with zero gradient and zero mean value, that is $v\to 0$.
\subsection{An integrable model}
The second equivalence class given in Theorem 4, represented by
\[
u_t=\partial_x\left[u^{-2}u_x\right]+1
\]
is in fact an integrable case. Some other members of this equivalence class were used in~\cite{Broadbridge&Rogers1999}.
In the case of energy transport in a plasma, the minor modification $u=v-b$ gives a model that has diffusivity increasing with energy density
\[
v_t=\partial_x\left[\frac{1}{(b-v)^2}v_x\right]+1.
\]
However the energy density $v$ must then be restricted to be less than $b$.
Let $u=\phi_x$ for some potential $\phi$. Then it is sufficient that
\[
\phi_t=\frac{1}{\phi_x^2}\phi_{xx}+x.
\]
Using the identity $\phi_t t_x x_\phi=-1$, the hodograph transformation results in Burgers' equation
\[
x_t=x_{\phi\phi}-xx_{\phi}.
\]
This gives the possibility of constructing some relevant solutions for plasma energy.
If we also allow a small amount of energy leakage at $x=1$, then we impose a constant-flux $J=R$ boundary condition at $x=1$.
With a constant sink, rather than a constant source term and with the boundary labels $x=0,1$ interchanged,
this problem has already been transformed in~\cite{Broadbridge&Rogers1999} to a linear boundary value problem.
An identical treatment applies with a constant source.
In principle, but with some difficulty, arbitrary initial conditions with $v(x,t)<b$ may be treated in this way.
\section{Conclusion}
When the mass density is allowed to be non-uniform, the equation for radiant energy transport in a laser-heated plasma, has a richer Lie point symmetry algebra, an additional non-obvious local conservation law and associated potential symmetries. These have been used to effect variable reductions and to construct some special solutions in closed form. When the nonlinear energy diffusivity depends exponentially on energy density, there is a special symmetry allowing reduction by separation of variables, independent of the form of variable density and laser intensity. When the density is a squared linear function of coordinate $x$ and the energy diffusivity and the laser intensity are particular powers of energy density and time respectively, the nonlinear partial differential equation has a symmetry reduction to an ordinary differential equation that may, in some cases, be solved in terms of elementary functions and exponential integrals. These solutions may be indicative of energy distributions when in the future, the mass density can be better predicted and controlled.
The potential symmetry classification shows that any model with a genuine potential symmetry is equivalent to a spatially homogeneous model but with three possible types of time-dependent laser intensity. The special case of constant laser intensity and inverse-square nonlinear diffusivity, not only allows a second potential symmetry, but is in fact an integrable nonlinear model that may be transformed to Burgers' equation. A nonclassical, rather than classical symmetry classification is required to pick up the trivial spatially uniform but time-dependent solution that applies to the general form of Equation (\ref{EqGAW}). In a thermodynamically closed system, this simple solution is stable and it is in fact simply the spatial arithmetic mean of the more general spatially dependent solution.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 4,067 |
OTHER BOOKS BY DAVID HINTON
_Writing_
FOSSIL SKY
HUNGER MOUNTAIN: A FIELD GUIDE TO MIND AND LANDSCAPE
_Translation_
I CHING
THE LATE POEMS OF WANG AN-SHIH
CLASSICAL CHINESE POETRY: AN ANTHOLOGY
THE SELECTED POEMS OF WANG WEI
THE MOUNTAIN POEMS OF MENG HAO-JAN
MOUNTAIN HOME: THE WILDERNESS POETRY OF ANCIENT CHINA
THE MOUNTAIN POEMS OF HSIEH LING-YÜN
TAO TE CHING
THE SELECTED POEMS OF PO CHÜ-I
THE FOUR CHINESE CLASSICS
ANALECTS
CHUANG TZU: THE INNER CHAPTERS
THE LATE POEMS OF MENG CHIAO
THE SELECTED POEMS OF LI PO
THE SELECTED POEMS OF T'AO CH'IEN
THE SELECTED POEMS OF TU FU
Translation, introduction, and annotation copyright © 2015 by David Hinton
All rights reserved under International and Pan-American Copyright Conventions. No part of this book may be used or reproduced in any manner whatsoever without written permission from the publisher, except in the case of brief quotations embodied in critical articles and reviews.
Library of Congress Cataloging-in-Publication data is available.
Cover art: _Auspicious Grain._ Anonymous (late 12th c.). Courtesy of The National Palace Museum, Taipei, Taiwan, Republic of China.
Cover design by Gopa & Ted2, Inc.
Interior design by David Bullen
COUNTERPOINT
2560 Ninth Street, Suite 318
Berkeley, CA 94710
www.counterpointpress.com
Distributed by Publishers Group West
10 9 8 7 6 5 4 3 2 1
e-book ISBN 978-1-61902-683-4
CONTENTS
_Introduction_
I. Emperor Hui of Liang Book One
II. Emperor Hui of Liang Book Two
III. Kung-Sun Ch'ou Book One
IV. Kung-Sun Ch'ou Book Two
V. Duke Wen of T'eng Book One
VI. Duke Wen of T'eng Book Two
VII. Li Lou Book One
VIII. Li Lou Book Two
IX. Wan Chang Book One
X. Wan Chang Book Two
XI. Master Kao Book One
XII. Master Kao Book Two
XIII. To Fathom the Mind Book One
XIV. To Fathom the Mind Book Two
_Notes_
_Historical Table_
_Key Terms: An Outline of Mencius' Thought_
_Further Reading_
ILLUSTRATION
_Auspicious Grain._ Anonymous (late 12th century). Courtesy of The National Palace Museum, Taipei, Taiwan, Republic of China.
Image representing the people's prosperity under a ruler who is fulfilling the Mandate of Heaven. See Introduction p. 20.
Introduction
In a culture that makes no distinction between those realms we call the heart and the mind, Mencius was the great thinker of the heart. He was the second originary sage in the Confucian tradition, which has shaped Chinese culture for over two thousand years, and it was he who added the profound inner dimensions of human being to the Confucian vision.
In the ruins of a magisterial monotheism, a situation not entirely unlike our own, Confucius (551–479 B.C.E.) recognized society as a structure of human relationships, and spoke of those relationships as a system of "ritual" that people enact in their daily lives, thus infusing the secular with sacred dimensions. There is little sense of the inner self in Confucius' thought: identity is determined by a person's ritual roles in the social fabric, and this selflessness contributes deeply to the sense of human community as a sacred rite. The explicit realm of Confucius' teachings is occupied with the practical issues of how society works as a selfless weave of caring relationships; and in the implicit realm, that ritual weave is woven into the vast primal ecology of a self-generating and harmonious cosmos.
The Confucian social vision represents the end of a devastating, millennium-long transformation from a spiritualist to a humanist culture, and Mencius (4th C. B.C.E.) invested that humanist vision with its inner dimension by recognizing that the individual too is a part of the primal ecology. He saw all the spiritual depths of that cosmology inside us, and this led to a mystical faith in the inherent nobility of human beings. In his chaotic and war-ravaged times, he was therefore passionate in his defense of the people. Indeed, he advocated a virtual democracy in which a government's legitimacy depended upon the assent of the people. Such is the enduring magic of the Mencian heart — full of compassionate and practical concern for the human condition, and yet so empty that it contains the ten thousand transformations of the entire cosmos.
The tangible beginnings of Chinese civilization lie in the archaic Shang Dynasty (c. 1766–1040 B.C.E.), which bridged the transition from Neolithic to Bronze Age culture. (For an outline of the early dynasties and rulers that figure prominently in Mencius' writings, see Historical Table.) The Shang was preceded by the Neolithic Hsia Dynasty, about which very little is known. It appears that in the Paleolithic cultures that preceded the Hsia, nature deities were worshiped as tribal ancestors: hence a tribe may have traced its lineage back to an originary "High Ancestor River," for instance. This practice apparently continued through the Hsia into the Shang, where evidence of it appears in oracle-bone inscriptions. Eventually, although these nature deities continued to be worshiped in their own right, religious life focused on the worship of human ancestors. By forging this religious system into a powerful form of theocratic government, the Shang was able to dominate China for no less than seven hundred years.
The Shang emperors ruled by virtue of their lineage, which was sanctified by Shang Ti ("Celestial Lord"), a supreme deity who functioned as the source of creation, order, ethics, etc. ( _Shang_ here represents two entirely different words in Chinese.) The Shang lineage may even have led to Shang Ti as its originary ancestor. In any case, Shang Ti provided the Shang rulers with a transcendental source of legitimacy and power: he protected and advanced their interests, and through their spirit-ancestors, they could decisively influence Shang Ti's shaping of events. All aspects of people's lives were thus controlled by the emperor: weather, harvest, politics, economics, religion, etc. Indeed, people didn't experience themselves as substantially different from spirits, for the human realm was simply an extension of the spirit realm.
Such was the imperial ideology, so convenient to the uses of power as it accorded little ethical value to the masses, who were not of select lineages. (Not surprisingly, the rise of Shang Ti seems to coincide with the rise of the Shang Dynasty, and later myth speaks of him as the creator of Shang civilization.) In the cruelest of ironies, it was overwhelming human suffering that brought the Chinese people into their earthly lives, beginning the transformation of this spiritualistic culture to a humanistic one. In the cultural legend, the early Shang rulers were paradigms of nobility and benevolence. But by the end of the Shang, the rulers had become cruel and tyrannical, and as there was no ethical system separate from the religious system, there was nothing to shield the people from their depredations. Meanwhile, a small nation was being pushed to the borders of the Shang realm by western tribes. This state of semi-barbarian people known as the Chou gradually adopted the cultural traits of the Shang. Eventually, under the leadership of the legendary sage-emperors Wen ("cultured") and Wu ("martial"), the Chou overthrew the tyrannical Shang ruler, thus founding the Chou Dynasty (1040–223 B.C.E.), which was welcomed wholeheartedly by the Shang people.
The Chou conquerors were faced with an obvious problem: if the Shang lineage had an absolute claim to rule the world, how could the Chou justify replacing it with their own, and how could they legitimize their rule in the eyes of the Shang people? Their solution was to redefine Shang Ti as _Heaven,_ thus ending the Shang's claim to legitimacy by lineage, and then proclaim that the right to rule depended upon the Mandate of Heaven: once a ruler becomes unworthy, Heaven withdraws its mandate and bestows it on another. This was a major event in Chinese philosophy: the first investment of power with an ethical imperative. And happily, the early centuries of the Chou appear to have fulfilled that imperative admirably.
But eventually the Chou foundered because of its increasing inhumanity and its lack of the Shang's transcendent source of legitimacy: if the Mandate could be transferred to the Chou, it could obviously be transferred again. The rulers of the empire's component states ( _chu hou:_ "august lords") grew increasingly powerful, claiming more and more sovereignty over their lands, until finally they had established virtually independent nations. Eventually these rulers (properly called "dukes") even began assuming the title of emperor, thus equating themselves with the Chou emperor, who was by now a mere figurehead. The rulers of these autonomous states could at least claim descent from those who were first given the territories by the early Chou rulers. But this last semblance of legitimacy was also crumbling because these rulers were frequently at war with one another, which hardly inspired confidence in the claim that they were familial members of the ruling kinship hierarchy that was sanctioned by Heaven. More importantly, power was being usurped by a second tier of "august lords" whenever they had the strength to take it, and even by a third tier of high government officials. This history, beginning with the Chou's overthrow of the Shang, represents a geologic split in China's social structure: political power was breaking free of its family/religious context and becoming a separate entity.
The final result of the Chou's "metaphysical" breakdown was, not surprisingly, all too physical: war. In addition to constant pressure from barbarians in the north (the first devastating blow to Chou power was a barbarian invasion in 770 B.C.E.) and the Ch'u realm that dominated south China, there was relentless fighting between the empire's component states and frequent rebellion within them. This internal situation, so devastating to the people, continued to deteriorate after Confucius' time, until it finally gave an entire age its name: the Warring States Period (403–221 B.C.E.). Meanwhile, rulers caught up in this ruthless competition began looking for the most able men to help them rule their states, and this precipitated the rise of an independent intellectual class — a monumental event, for this class constituted the first open space in the cultural framework from which the imperial ideology could be challenged.
The old social order had now collapsed entirely, and these intellectuals began struggling to create a new one. Although this was one of the most virulent and chaotic periods in Chinese history, it was the golden age of Chinese philosophy, for there were a "Hundred Schools of Thought" trying to envision what this new social order should be like. These schools were founded by thinkers who wandered the country with their disciples, teaching and trying to convince the various rulers to put their ideas into practice, for the desperate times had given them an urgent sense of political mission.
The first great figure of this intellectual class was Confucius, whose thought survives in a collection of aphoristic sayings entitled the _Analects._ Confucius' social philosophy derives from a rational empiricism, a methodology which Mencius shared and which represents a total break with Shang spiritualism. Blatant power-politics had made it impossible to believe in Heaven (let alone Shang Ti) as a transcendental source of order and legitimacy, so Confucius tried to rescue the fragmented Chou culture by putting it on a more viable rational and secular basis. He began from the empirical observation that human society is a structure, a weave of relationships between individuals who each occupy a certain locus in that structure: parent and child, ruler and subject, friend and friend, merchant and customer, and so forth. Confucius invested this anthropological observation with a philosophical dimension by recognizing that a vital community depends upon its members' fulfilling their communal responsibilities with an attitude of human caring. Always looking to the past as his source of wisdom, Confucius saw that societies flourished when their citizens (most especially their rulers) honored this moral principle, and inevitably crumbled when they ignored it: even the powerful transcendental glue of the Shang theocracy couldn't withstand the corrosive influence of the Shang emperors' depredations.
But Confucius' social philosophy goes well beyond this moral dimension, for he described the web of social responsibilities as a system of "Ritual" ( _li:_ see Key Terms). _Ritual_ had been a religious concept associated with the worship of spirits, but Confucius extended its use to include all the caring acts by which we fulfill our responsibilities to others in the community. Hence, the entire weave of everyday social life takes on the numinous aspect of the sacred. There is little sense of the inner self in the _Analects:_ the Ritual social fabric is paramount, and individual identity is defined entirely in terms of a person's social roles. All of the Confucian moral virtues (see Key Terms) apply only in the social context: one cannot speak of a person being virtuous in isolation. And there is indeed a kind of spiritual clarity in the selflessness of this Ritual weave, a clarity which became a defining aspect in the structure of Chinese political and spiritual consciousness throughout the ages.
Confucius located his human society within a cosmology that the Taoists described eloquently, but which he himself referred to only through silence:
_Adept Kung said: "When the Master talks about civility and cultivation, you can hear what he says. But when he talks about the nature of things and the Way of Heaven, you can't hear a word."_
(V.12)
A major component in that cosmology is the evolving concept of "Heaven." The most primitive meaning of _Heaven (t'ien)_ is "sky." By extension, it also comes to mean "transcendence," for our most primal sense of transcendence may be the simple act of looking up into the sky. So it's hardly surprising that when the Chou wanted to reinvent Shang Ti in a more impersonal form, they would choose Heaven. By association with the idea of transcendence and that which is beyond us, it is natural that _Heaven_ also comes to mean "fate" or "destiny." And this is precisely what we find in Confucius, where "destiny" has evolved out of the early Chou sense of an impersonal deity. But rather than destiny in the sense of a transcendental force deciding human fate, this is destiny as the inevitable evolution of things according to the principles inherent in them. Although Confucius focuses on its manifestations in human history, there is little real difference between this Confucian Heaven and that of the Taoists, who identified it with natural process proceeding according to the principle of _tzu-jan. Tzu-jan_ 's literal meaning is "self-so" or "the of-itself" or "being such of itself," hence "spontaneous" or "natural." But a more descriptive translation might be "occurrence appearing of itself," for it is meant to describe the ten thousand things unfolding spontaneously, each according to its own nature. The Taoist ideal is to dwell as an organic part of the _tzu-jan_ process. For Confucius, the mechanism of Heaven's process would be _tzu-jan_ 's Confucian counterpart: _li_ (Ritual). The Ritual structure of society is part of a much larger weave, the Ritual structure of natural process, and the Confucian ideal is for human community to dwell as an organic part of the cosmological weave of _li._
The Confucian and Taoist Ways are traditionally described as the two poles of Chinese thought, but their shared cosmology affords them a fundamental unity, and that unity is no doubt why Chinese culture could eventually adopt both of these Ways simultaneously: the Confucian Way has defined the societal realm for Chinese intellectuals throughout the millennia, and the Way of philosophical Taoism has defined the private spiritual realm. The spiritual ecology of this shared cosmology might be seen as a return to the original spirituality of paleolithic China, for the sense of belonging to natural process is a secular version of the worship of nature deities as ancestral spirits. And it represents a complete secularization of the spiritualist regime that had dominated China since the rise of the Shang. Although ancestors continued to be attended assiduously, it was now a Confucian ritual of love and respect rather than an appeal to otherworldly powers. And although Confucius and Mencius recognized sacrifices to gods and spirits, they didn't necessarily believe any of the religious claims associated with such worship. For them, the value of such practices lay in the function they served in the Ritual structure of society. Mencius goes so far as to say that if gods and spirits don't fulfill human needs, they should be replaced (XIV.14). At the more fundamental level of the shared cosmology itself, it would appear to represent the resurgence of an ancient cosmology, a return to the culture's most primal roots – the Paleolithic and beyond. "Heaven" had become the current way of referring to its physical processes, and it was by recognizing the vast reach of Heaven within us that Mencius endowed the human with profound inner dimensions:
_The ten thousand things are all there in me. And there's no joy greater than looking within and finding myself faithful to them._
(XIII.4)
This inner dimension also takes on ethical and political dimensions in Mencius' thought. Rather than privileged kinship relations as a basis of ethical value, Mencius proposes human belonging to the primal cosmology. Hence, citizens are all of equal value in and of themselves simply because they are all endowed with that vast reach of Heaven.
As with most intellectual figures in ancient China, very little is known of Mencius' life. He was born in Tsou, which was a dependency of Lu, the homeland of Confucius where the Chou cultural tradition was especially strong. His Chinese name was Meng K'o, and he is known as Meng Tzu, meaning "Master Meng," from which the latinized _Mencius_ derives. According to tradition, he received his education first under the tutelage of a sagely mother and then under a disciple of Master Szu, who was Confucius' grandson and the reputed author of _The Doctrine of the Mean (Chung Yung),_ a book which came to be associated with the book of Mencius' writings, the _Mencius._ Sharing with most other philosophers of the time a faith in the political mission of the intellectual, he traveled with his disciples to the various states advising their rulers, hoping his ideas would be adopted and so lead to a more humane society. A number of rulers welcomed him, some even becoming benefactors, but his ideas were too radical and threatening. Few, if any, showed much inclination to put them into practice.
The book which bears Mencius' name probably represents the teachings of his mature thought. Unlike the _Analects,_ which is largely made up of short aphoristic fragments without any supporting context, the _Mencius_ is composed of longer and more developed passages, which makes it a fuller exposition of Confucian thought. It is entirely possible that Mencius wrote part or all of the book himself, though it is perhaps more likely that it was composed by his disciples. But if this is the case, it appears to be a compilation of carefully taken notes that represent pretty exactly the master's actual words. So, unlike the _Analects,_ much of which is clearly not written by the historical Confucius, the _Mencius_ seems almost entirely authentic. Indeed, it is considered a paragon of literary eloquence and style. The book contains fourteen chapters, arranged in seven pairs. Each pair shares the same title, which is taken from whatever personage happens to appear in the first sentence, a seemingly arbitrary method devised by a later editor. The only exception to this is the final pair: "To Fathom the Mind." This title, also drawn from the first sentence, is expressive of the unique character of these final chapters, for they seem to be an especially late and eloquent distillation of Mencius' ideas, containing many of his most striking and radical statements. An uncanny fact about Mencius is that his most distinctive and fundamental departures are found in only a handful of statements, which suggests that Mencius would appear an even more radical thinker if only more of his teachings had survived.
The inner dimension of human being was a central topic for the early Taoist masters, and they shared Mencius' cosmological view of the inner self; but for Mencius this was part of a political vision, and that is what makes him so important. As the human heart-mind is part of the fabric of Heaven, it is therefore inherently good and moral. Given this central belief in the inherent goodness of human nature, Mencius found the key to a flourishing society in a government that allows our inborn nobility to flourish of itself (here the similarity to Taoist thought is again unmistakable). And spiritual self-cultivation is the key both to that inner flourishing and to a benevolent government. The importance of self-cultivation among intellectuals was paramount in Confucius, who advocated government by a class of highly educated professionals. But in Mencius' cosmological context it takes on a decidedly spiritual dimension, reflecting the unity of self and cosmos:
_To fathom the mind is to understand your nature. And when you understand your nature, you understand Heaven._
(XIII.1)
This idea of spiritual self-cultivation as a political act proved very appealing to the Neo-Confucianists of the Sung Dynasty. Although he was certainly influential, Mencius was not considered a preeminent figure until the rise of Neo-Confucianism, about 1,500 years after his death. Hoping to inspire people in the reconstruction of a beleaguered society, the Neo-Confucianists felt a need to give Confucian philosophy something of the spiritual depth that had made Buddhism (especially Ch'an or Zen Buddhism) so compelling in their culture. To do this they redefined the Confucian tradition by supplementing the _Analects_ with three lesser-known texts which added a spiritual depth to Confucius' teachings, thus forming the canonical "Four Books": _The Analects, Mencius, The Great Learning,_ and _The Doctrine of the Mean._ The Neo-Confucianists expanded Confucian self-cultivation to emphasize Ch'an meditation and the practice of the arts. Indeed, the monumental landscape painting that arose during the Sung was conceived in these Neo-Confucian terms: to look deeply into the ten thousand things is to look deeply into oneself. And, following Mencius, to look deeply into oneself is to look deeply into Heaven.
Given Mencius' faith in the inherent nobility of human beings, it is no surprise that he focuses so resolutely on the responsibility of rulers and intellectuals to create a society in which that nobility can flourish. For Mencius, the Mandate of Heaven is revealed through the will of the people:
_Heaven sees through the eyes of the people. Heaven hears through the ears of the people._
(IX.5)
Indeed, the Mencian polity is a virtual democracy, for the emperor only has authority to rule so long as he has the people's approval. Once he loses their approval, he loses the Mandate of Heaven. Then, if they must, the people have every right to overthrow him.
The Mandate of Heaven remained the standard against which rulers were measured throughout the ages, though it was of course a standard they rarely met. Two millennia after Mencius, rulers of dubious repute felt compelled to commission paintings like _Auspicious Grain_ (see cover illustration and interior illustration), as if they could mask reality by associating themselves with a monumental totemic image representing the people's prosperity under a ruler who is fulfilling the Mandate of Heaven. However rare the society it depicts may be, it is indeed a beautiful image: a sacred human community flourishing in the shimmering weave of Heaven's natural process.
I
Emperor Hui of Liang Book One
1 Mencius went to see Emperor Hui of Liang, and the emperor said: "Even a thousand miles wasn't too great a journey for you. You must come bringing something of great profit to my nation."
"Don't talk about profit," said Mencius. "It's Humanity and Duty that matter. Emperors say _How can I profit my nation?_ Lords say _How can I profit my house?_ And everyone else says _How can I profit myself?_ Then everyone high and low is scrambling for profit, pitching the nation into grave danger.
"If the ruler in a nation of ten thousand war-chariots is killed, the assassin is no doubt lord to a house of a thousand war-chariots. And if the ruler in a nation of a thousand war-chariots is killed, the assassin is no doubt lord to a house of a hundred war-chariots. A thousand in ten thousand or a hundred in a thousand – this is no small amount. But when people betray Duty and crave profit, they aren't content until they've got it all. If they aren't Humane, they'll abandon their kindred, and if they aren't Dutiful, they'll betray their ruler.
"Just talk about Humanity and Duty, and leave it at that. Don't talk about profit."
2 Mencius went to see Emperor Hui of Liang and found him standing beside a pool. Gazing at the deer and wild geese, the emperor said: "And do the wise also enjoy such things?"
"Only the wise can enjoy them," replied Mencius. "If they aren't wise, even people who have such things can't enjoy them. _The Book of Songs_ says:
_He planned the sacred tower and began._
_He planned it well and managed it well,_
_and the people worked with devotion,_
_so it was finished in less than a day._
_He planned and began without haste,_
_and the people were children coming._
_With the emperor in the sacred gardens_
_there, the deer lay in pairs at ease,_
_paired deer all sleek and glistening,_
_white birds all bright and shimmering,_
_and with the emperor at the sacred pool_
_there, the fish leapt so strong and sure._
Emperor Wen used the people's labor to build his tower and his pool, and yet the people delighted in them. They called the tower _Sacred Tower_ and the pool _Sacred Pool,_ and they were delighted that he had deer and fish and turtles. The ancients knew joy because they shared their joy with the people.
"In _The Declaration of T'ang,_ the tyrant Chieh's people say: _When will you founder, o sun? We'll die with you gladly._ The people so hated him that they thought dying with him was better than living with him. He had towers and ponds, birds and animals – but how could he enjoy them alone?"
3 Emperor Hui of Liang said: "I've devoted myself entirely to the care of my nation. If there's famine north of the river, I move people east of the river and grain north of the river. And if there's famine east of the river, I do the opposite. I've never seen such devotion in the governments of neighboring countries, but their populations are growing by leaps and bounds while mine hardly grows at all. How can this be?"
"You're fond of war," began Mencius, "so perhaps I could borrow an analogy from war. War drums rumble, armies meet, and just as swords clash, soldiers throw down their armor and flee, dragging their weapons behind them. Some run a hundred feet and stop. Some run fifty feet and stop. Are those who run fifty feet justified in laughing at those who run a hundred feet?"
"No, of course not," replied the emperor. "It's true they didn't run the full hundred feet, but they still ran."
"If you understood this, you wouldn't long to have more people than neighboring countries. Look – when growing seasons aren't ignored, people have more grain than they can eat. When ponds aren't plundered with fine-weave nets, people have more fish and turtles than they can eat. When mountain forests are cut according to their seasons, people have more timber than they can use. When there's more grain and fish than they can eat, and more timber than they can use, people nurture life and mourn death in contentment. People nurturing life and mourning death in contentment – that's where the Way of emperors begins.
"When every five-acre farm has mulberry trees around the farmhouse, people wear silk at fifty. And when the proper seasons of chickens and pigs and dogs are not neglected, people eat meat at seventy. When hundred-acre farms never violate their proper seasons, even large families don't go hungry. Pay close attention to the teaching in village schools, and extend it to the child's family responsibilities – then, when their silver hair glistens, people won't be out on roads and paths hauling heavy loads. Our black-haired people free of hunger and cold, wearing silk and eating meat at seventy – there have never been such times without a true emperor.
"But you don't think about tomorrow when people are feeding surplus grain to pigs and dogs. So when people are starving to death in the streets, you don't think about emptying storehouses to feed them. People die, and you say _It's not my fault, it's the harvest._ How is this any different from stabbing someone to death and saying _It's not me, it's the sword_? Stop blaming harvests, and people everywhere under Heaven will come flocking to you."
4 Emperor Hui of Liang said: "I'm ready to be taught without resenting it."
"Is there any difference between killing someone with a stick or killing them with a sword?" began Mencius.
"No, there's no difference."
"And killing with a sword or a government – any difference?"
"No difference."
"There's plenty of juicy meat in your kitchen and plenty of well-fed horses in your stable," continued Mencius, "but the people here look hungry, and in the countryside they're starving to death. You're feeding humans to animals. Everyone hates to see animals eat each other, and an emperor is the people's father and mother – but if his government feeds humans to animals, how can he claim to be the people's father and mother?
"When Confucius said _Whoever invented burial figures deserved no descendants,_ he was condemning the way people make human figures only to bury them with the dead. But that's nothing compared to the way you're pitching your people into starvation."
5 Emperor Hui of Liang said: "As you know, this country was once the strongest anywhere under Heaven. But here I am: defeated by Ch'i in the east, my eldest son dead in the battle; seven hundred square miles lost to Ch'in in the west; and humiliated by Ch'u in the south. Now, out of respect for the dead, I long to wash all this shame away. How can I do that?"
"To be a true emperor, even a hundred square miles can be land enough," replied Mencius. "If an emperor's rule is Humane – punishment and taxation are light, people plow deep and hoe often, and strong men use their leisure time to cultivate themselves as sons and brothers, loyal subjects and trustworthy friends. They serve father and brother when home, and when away they serve elders and superiors. So even with nothing but sticks for weapons, they can overcome the fierce swords and armor of nations like Ch'in or Ch'u.
"In such countries, emperors violate the proper seasons of their people. They don't let them plow or weed or tend to their parents. Parents are cold and hungry, brothers and wives and children are scattered far apart. Those emperors are dragging their people down into ruin. So if a true emperor invaded their countries, who would oppose him? Therefore it is said: _No one can oppose the Humane._ If only you would believe this."
6 Mencius went to see Emperor Hsiang of Liang. Talking with someone after he'd left, he said: "At first sight, he didn't seem like much of a sovereign, and after meeting him I saw nothing to command respect. But suddenly he began asking questions.
_"What could bring stability to all beneath Heaven?_ he asked.
_"In unity is stability,_ I replied.
_"Who can unify all beneath Heaven?_
_"One who has no lust for killing._
_"But who would give it all to him?_
_"Is there anyone who wouldn't give it to him? Don't you know about rice shoots? If there's a drought in the sixth or seventh month, rice shoots wither. But if the Heavens then fill with clouds, and rain falls in sheets, the shoots burst into life again. When this happens, who can resist it? Today, all of the world's great shepherds share a lust for killing. If there were someone free of that lust, people everywhere under Heaven would crane their necks watching for him to come. And if such a man really appeared, the people going home to him would be like a flood of water pouring down. Who could resist it?"_
7 Emperor Hsüan of Ch'i said: "I'd like to hear about Duke Huan of Ch'i and Duke Wen of Chin."
"The disciples of Confucius never spoke of Huan or Wen," replied Mencius, "so their histories weren't passed down through the generations, and I've heard nothing of them. You won't learn much about the true emperor from them."
"Tell me then – this Integrity that makes a true emperor, what is it?" asked Emperor Hsüan.
"If you watch over the people, you're a true emperor and nothing can resist you."
"Can someone like me watch over the people?"
"Yes."
"How do you know this?"
"I heard a story about you from Hu He: _Sitting in the palace one day, the emperor saw some people leading an ox past outside._
_"'Where's that ox being taken?_ ' he asked.
_"'We're going to consecrate the new bell with its blood.'_
_"'Let it go. I can't bear to see it shivering with fear like an innocent person being hauled off to the executioner.'_
_"'Then shall we leave the bell unconsecrated?'_
_"'No, no – that would never do. Use a sheep instead.'_ Did that really happen?"
"Yes," replied the emperor.
"You have the heart of a true emperor. The people all thought you were being miserly. But I know you just couldn't bear the suffering."
"Are the people really like that? Ch'i may be a small country, but how could I begrudge a single ox? I just couldn't bear to see it shivering with fear like an innocent person being hauled off to the executioner. So I told them to use a sheep instead."
"It isn't so strange that the people thought you miserly," said Mencius. "You wanted to use a small animal instead of a large one, so how were they to know? If you were so grieved by something innocent going to the executioner, then what's the difference between an ox and a sheep?"
The emperor laughed and said: "What was going on in this heart of mine? I certainly didn't begrudge the expense of an ox, but I wanted to use a sheep instead. No wonder the people called me a miser."
"No harm done," said Mencius. "That's how Humanity works. You'd seen the ox, but not the sheep. And when noble-minded people see birds and animals alive, they can't bear to see them die. Hearing them cry out, they can't bear to eat their meat. That's why the noble-minded stay clear of their kitchens."
After a moment, the emperor spoke: "The _Songs_ say
_It's another person's heart,_
_but mine has fathomed it._
This describes you perfectly. It was I who did these things, but when I turned inward in search of motives, I couldn't fathom my own heart. It was you who explained it, and only then did I come to this realization. So how can this heart of mine be that of a true emperor?"
"What if someone said this to you: _I'm strong enough to lift a thousand pounds, but I can't lift a feather?_ Or: _My sight's so good I can see the tip of an autumn hair, but I can't see a cartload of firewood_? Would you believe it?"
"No, of course not."
"You have compassion enough for birds and animals, but you do nothing for your people. And why is that? When feathers can't be lifted, someone isn't using their strength. When a cartload of firewood can't be seen, someone isn't using their sight. And when the people aren't watched over, someone isn't using their compassion. So if you aren't a true emperor, it's only because you're unwilling, not because you're incapable."
"The unwilling and the incapable – is there any difference in form?" asked the emperor.
"You can say that you're incapable of bounding over the North Sea with T'ai Mountain tucked under your arm, and in fact you are incapable. You can also say that you're incapable of breaking up a little kindling for an old woman, but in fact you're unwilling, not incapable. Your failure to be a true emperor isn't like failing to bound over the North Sea with T'ai Mountain tucked under your arm. It's like failing to break up a little kindling for an old woman.
"Honor your own elders as befits elders, and extend this honor to all elders. Honor your own children as befits children, and extend this honor to all children. Then you can turn all beneath Heaven in the palm of your hand.
"The _Songs_ say:
_Setting an example for his wife_
_and extending it to his brothers,_
_he ruled both home and country,_
which describes how this heart here can be applied elsewhere. Just do that and your compassion will be expansive enough to watch over all within the four seas. If your compassion isn't expansive, you can't even watch over your own wife and child. This is precisely why the ancients so completely surpassed the rest of us: they made whatever they did expansive. That's all. You have compassion enough for birds and animals, but you do nothing for your people. And why is that?
"To know whether something is light or heavy, you must weigh it. To know whether something is long or short, you must measure it. It's like this for all things, and especially for the heart. If only you would measure yours.
"Or perhaps you want to keep sending out your armies with their armor and swords, endangering your subjects and stirring up hatred among the other rulers. Is that what fills your heart with delight?"
"No," replied the emperor. "How could I delight in that? I only do it for the sake of a great dream."
"And this great dream – may I hear what it is?"
The emperor just smiled and said nothing.
"Is your grand cuisine not enough for your tongue? Are your summer and winter robes not enough for your body? Perhaps all the beautiful sights here aren't enough for your eyes, and the beautiful music isn't enough for your ears? Or is it that your attendants aren't fine enough to serve you? But you have many assistants and advisors: whatever you find wanting, they can supply. So this can't be the kind of dream you harbor."
"No," replied the emperor, "it isn't."
"Then it isn't hard to guess what your great dream is. You dream of more land. You dream of Ch'in and Ch'u paying court to you, of ruling over the entire Middle Kingdom and pacifying the barbarian nations on all four borders. Doing the kinds of things you do in search of such a dream – that's like climbing a tree in search of a fish."
"Is it really so bad?" asked the emperor.
"Yes, and it's much more dangerous," replied Mencius. "Climb a tree in search of a fish, and though you won't find a fish, you also won't find disaster. But do the kinds of things you do in search of your dream, and though you wear body and mind ragged, you'll find disaster for sure."
"Please – can you tell me more about this?"
"If Chou and Ch'u went to war, who do you think would win?"
"Ch'u would win."
"So the small is clearly no match for the large," continued Mencius, "the few is clearly no match for the many, and the weak is clearly no match for the strong. Here within the vast seas, there are nine regions, each spreading a thousand square miles, and your Ch'i is but one of them. To conquer eight with one, how is that any different from Chou declaring war on Ch'u?
"You must return to fundamentals. If you were renowned for Humane government, every scholar under Heaven would long to stand in your court, every farmer would long to plow in your countryside, every merchant would long to trade in your markets, every traveler would long to travel your roads, and everyone beneath Heaven who despised their rulers would long to rush here and confide in you. If you made this happen, who could resist it?"
"I'm not all that bright," said the emperor. "I still can't see my way through this. But I'm determined and want your help. If you'll explain clearly, perhaps I can learn, and even though I'm not terribly clever, I'll try to act on your counsel."
"To keep the mind constant without a constant livelihood – only the wisest among us can do that. Unless they have a constant livelihood, the common people will never have constant minds. And without constant minds, they'll wander loose and wild. They'll stop at nothing, and soon cross the law. Then, if you punish them accordingly, you've done nothing but snare the people in your own trap. And if they're Humane, how can those in high position snare their people in traps? Therefore, in securing the people's livelihood, an enlightened ruler ensures that they have enough to serve their parents and nurture their wives and children, that everyone has plenty to eat in good years and no one starves in bad years. If you do that, you'll be leading the people toward virtue and benevolence, so it will be easy for them to follow you.
"But now, with you securing their livelihood, the people never have enough to serve their parents or nurture their wives and children. In good years they live miserable lives, and in bad years they starve to death. All they can do is struggle to stay free of death and worry about failing. Where could they ever find the leisure for Ritual and Duty?
"If you want to put my words into practice, why not return to fundamentals? When every five-acre farm has mulberry trees around the farmhouse, people wear silk at fifty. And when the proper seasons of chickens and pigs and dogs are not neglected, people eat meat at seventy. When hundred-acre farms never violate their proper seasons, even large families don't go hungry. Pay close attention to the teaching in village schools, and extend it to the child's family responsibilities – then, when their silver hair glistens, people won't be out on roads and paths hauling heavy loads. Our black-haired people free of hunger and cold, wearing silk and eating meat in old age – there have never been such times without a true emperor."
II
Emperor Hui of Liang Book Two
1 Chuang Pao went to see Mencius and said: "I went to see the emperor, and he told me that he loves music. I didn't know what to say. _Loving music_ – what do you think of that?"
"If the emperor truly loves music," replied Mencius, "there may be hope for Ch'i."
Some days later, Mencius went to see the emperor and asked: "Is it true you told Chuang that you love music?"
The emperor blushed and said: "I cannot claim to love the music of ancient emperors, only our own trifling music."
"If you truly love music," said Mencius, "there may be hope for Ch'i. And it makes no difference if it's today's music or the music of ancient times."
"Please – can you tell me more about this?" asked the emperor.
"To enjoy music alone or to enjoy it with others," began Mencius, "which is the greater pleasure?"
"With others, of course," replied the emperor.
"And to enjoy music with a few or to enjoy it with many – which is the greater pleasure?"
"With many, of course."
"Can I tell you about enjoyment? Suppose there was a performance of beautiful music here. Suppose the people heard the sound of their emperor's bells and drums, pipes and flutes, and turning faces furrowed with worry toward each other, they said: _Why does our emperor let his love of music make our lives so desperate – father and son, brother and brother, mother and child all separated and scattered apart?_ Suppose there was a hunt ranging through the fields here. Suppose the people heard the sound of your carriages and horses, saw the beauty of your banners and streamers, and turning faces furrowed with worry toward each other, they said: _Why does our emperor let his love of hunting make our livesso desperate – father and son, brother and brother, mother and child all separated and scattered apart?_
"There could be only one explanation for all this: never sharing pleasure with the people.
"But suppose there was a performance of beautiful music here. Suppose the people heard the sound of their emperor's bells and drums, pipes and flutes, and turning happy faces full of delight toward each other, they said: _Listen – they're making music, so our emperor must be feeling fine!_ And suppose there was a hunt ranging through the fields here. Suppose the people heard the sound of your carriages and horses, saw the beauty of your banners and streamers, and turning happy faces full of delight toward each other, they said: _Look – they're out hunting, so our emperor must be feeling fine!_
"There could be only one explanation for all this: sharing pleasure with the people. Sharing pleasure with the people – that's what makes an emperor an emperor."
2 Emperor Hsüan of Ch'i asked: "Is it true that Emperor Wen's park covered seventy square miles?"
"The _Chronicles_ say it did," replied Mencius.
"Was it really so vast?"
"To the people it seemed small."
"My park covers only forty square miles, and yet the people consider it huge," said the emperor. "How can this be?"
"Emperor Wen's park may have covered seventy square miles, but it was open to the people: they gathered dry grasses for their fires there, they hunted pheasants and rabbits there. He shared it with the people, so is it any wonder the people considered it small?
"When I first came to the borders of your nation, I asked about the great prohibitions of this land. Only then did I dare enter. I was told that there is a park covering forty square miles, and that anyone who kills a deer there is punished as if they'd killed a person. So this park is a forty-square-mile trap set in the middle of the country. Is it any wonder the people consider it huge?"
3 Emperor Hsüan of Ch'i asked: "Is there a Way to foster good relations with neighboring countries?"
"There is," replied Mencius. "Only a person of great Humanity can use the large to serve the small. So it is that Emperor T'ang served Ko and Emperor Wen served the K'un tribes. Only a person of great wisdom can use the small to serve the large. So it is that Emperor T'ai served the Hsün-yü tribes and Kou Chien served the nation of Wu.
"Whoever uses the large to serve the small delights in Heaven. Whoever uses the small to serve the large fears Heaven. If you delight in Heaven, you nurture all beneath Heaven. If you fear Heaven, you nurture your own nation. The _Songs_ say:
_Fearing august Heaven's majesty,_
_we nurture our nation forever."_
"Your words are great indeed," said the emperor. "But I have a weakness: I love valor."
"Then let it not be small valor that you love. That is to clutch your sword and glare angrily, shouting _How dare he oppose me?_ It's such coarse valor – at best useful only against a lone opponent. Let it be great valor that you love.
"The _Songs_ say:
_Majestic in his fury and wrath,_
_the emperor marshalled his forces._
_He met the invaders in Chü_
_and secured Chou's prosperity,_
_fulfilling all beneath Heaven._
Such is the valor of Emperor Wen. In a single act of wrath, he brought peace to the people throughout all beneath Heaven.
"The _Book of History_ says: _Heaven sent down people. It created a sovereign for them and made him their teacher, saying 'You must help the Celestial Lord show his love for them. To every corner of the land, I will judge those who offend and those who do not. In all beneath Heaven, who will dare cast their ambition against my purpose?'_
"There was only one man causing trouble in all beneath Heaven, but Emperor Wu took it as a personal disgrace. Such is the valor of Emperor Wu. In a single act of wrath, he too brought peace to the people throughout all beneath Heaven.
"Now if you too, in a single act of wrath, bring peace to the people throughout all beneath Heaven, the people's only fear will be that your love of valor may end."
4 Emperor Hsüan of Ch'i received Mencius in the Snow Palace and said: "Does the sage also enjoy such pleasures?"
"Yes," replied Mencius. "Denied such pleasures, there are those who would malign their sovereign. To malign a sovereign because you're denied such pleasures is wrong. But when a sovereign fails to share such pleasures with his people – that too is wrong. If you delight in the people's pleasure, the people will delight in your pleasure. If you worry over the people's troubles, the people will worry over your troubles. Make all beneath Heaven your delight and all beneath Heaven your worry – then how can you fail to be a true emperor?
"Long ago, Duke Ching of Ch'i asked his prime minister, Lord Yen: _I long to visit Chuan-fu Mountain and Ch'ao-wu Mountain, then travel along the coastline south to Lang-yeh Mountain. What can I do to make my travels rival those of the ancient emperors?_
" _What a fine question,_ replied Lord Yen. _When the Son of Heaven visited the august lords, it was called an Inspection Tour because he was inspecting the territories under their care. And when the august lords went to the Son ofHeaven's court, it was called a Duty Report because they reported on how they had carried out their duties. These things were not done without a purpose. In spring, it was to inspect the planting and provide whatever the farmers lacked. And in autumn, it was to inspect the harvest and help whoever didn't_
_bring in enough. In the Hsia Dynasty there was a saying:_
_If our emperor doesn't journey_
_where will we find rest?_
_If our emperor doesn't tour,_
_where will we find help?_
_Each journey, each tour,_
_he's a model for august lords._
_"It's not like that anymore. Now_
_marching armies demand supplies,_
_so there's no food for the hungry_
_and no rest for the work-weary._
_Looking away, voices full of hate,_
_the people turn to shadowy crime._
_Defying the mandate, rulers abuse us._
_They drift, awash in food and drink._
_Adrift, unbridled, wild, wanton:_
_among lords this means trouble._
_To follow the drift downstream, all thought of return gone: that is called adrift. To follow the drift upstream, all thought of return gone: that is called unbridled. To follow animals, all moderation gone: that is called wild. To wallow in wine, all moderation gone: that is called wanton. The early emperors never indulged in pleasures adrift and unbridled, or actions wild and wanton._
_"It is for you to choose your path._
"Duke Ching was overjoyed. He issued great proclamations throughout the land, then he went to live in a hut outside the city. He opened the granaries to those in need, and summoned his Grand Music-master, saying: _Compose for me the joyous harmony of sovereign and subject._ Hence the _Chih Shao_ and _Chüeh Shao,_ with lyrics saying: _How can guiding the sovereign be a crime?_ To guide the sovereign is to love the sovereign."
5 Emperor Hsüan of Ch'i said: "Since I never use it, people all tell me I should tear down the Palace of Light. Should I tear it down or not?"
"It's the Palace of Light because it's the palace of an emperor," replied Mencius. "If you want to govern as a true emperor, don't tear it down."
"To _govern as a true emperor_ – could you explain this for me?"
"In ancient times, when Emperor Wen ruled Ch'i – farmers were taxed one part in nine, descendants of worthy officials were insured a livelihood, there were inspections at border crossings and markets but no taxes, fish traps were not regulated, criminals were punished but not their families.
"Old men without wives we call widowers. Old women without husbands we call widows. Old people without children we call loners. Children without fathers we call orphans. These four kinds of people – they are the forsaken ones of this world. They have no one to turn to. When Emperor Wen's rule spread Humanity throughout the land, he put these four kinds of people above all else. The _Songs_ say:
_While the rich manage in fine fashion,_
_the forsaken nurture no hope, no hope._
"Your words are fine indeed," said the emperor.
"You call them fine, but in practice you ignore them. Why is that?"
"I have a weakness," replied the emperor. "I love the bounty of wealth."
"In ancient times, Emperor Kung Liu loved the bounty of wealth," said Mencius. "But the _Songs_ say:
_He filled granaries with stores,_
_bundled supplies and provisions_
_into sacks and well-stocked bags._
_His splendor spreading repose,_
_he kept archers in plain sight,_
_flourished spear, shield, and ax._
_Only then did his march begin._
Hence, those who stayed had granaries full of stores, and those who went had bags well stocked. Only then could he begin his march to settle a homeland. If you love the bounty of wealth, let it be the people's love too – then how will it keep you from being a true emperor?"
"I have another weakness," said the emperor. "I love beauty and passion."
"In ancient times," replied Mencius, "Emperor T'ai also loved beauty and passion. He adored the palace courtesans. But the _Songs_ say:
_Our true old father T'ai_
_came early on his horse,_
_skirting a western river_
_to reach Ch'i Mountain,_
_and with Lady Chiang_
_founded our homeland._
At that time, women never languished without husbands, nor men without wives. If you love beauty and passion – let it be the people's love too, then how will it keep you from being a true emperor?"
6 Mencius said to Emperor Hsüan of Ch'i: "Suppose one of your ministers entrusts his family to the care of a friend and then leaves on a journey to Ch'u. When he returns, he finds that the friend abandoned his family to hunger and cold. What should be done?"
"End the friendship," replied the emperor.
"And if a chief judge can't govern his court – what should be done?"
"Turn him out," pronounced the emperor.
"And if someone can't govern this land stretching out to the four borderlands – what then?"
The emperor suddenly turned to his attendants and spoke of other things.
7 Mencius went to see Emperor Hsüan of Ch'i and said: "If a nation is called ancient, it isn't because the trees there are tall. It's because the ministers there are descended from generations of high officials. But there's no sense of old family bonds between you and your ministers. Those you promote one day are gone the next, and you hardly notice."
"But how can I recognize mediocrity and avoid it?" asked the emperor.
"To advance only the wise," replied Mencius, "a sovereign often promotes the common above the august, the distant above the familial. In deciding who is worthy, always remain cautious. When your attendants all say someone is wise, that doesn't make him worthy. When your high ministers all say someone is wise, that doesn't make him worthy. When everyone in the country says someone is wise, investigate thoroughly. If you find that he is indeed wise and worthy, take him into your government.
"When your attendants all say someone is unworthy, don't listen. When your high ministers all say someone is unworthy, don't listen. When everyone in the country says someone is unworthy, investigate thoroughly. If you find that he is indeed unworthy, turn him out.
"When your attendants all say someone deserves death, don't listen. When your high ministers all say someone deserves death, don't listen. When everyone in the country says someone deserves death, investigate thoroughly. If you find that he does indeed deserve death, put him to death. Then it will be said _The entire country put him to death._
"If it's like this in your country, you've truly become mother and father to the people."
8 Emperor Hsüan of Ch'i asked: "Is it true that Emperor T'ang banished the tyrant Chieh, and Emperor Wu overthrew the tyrant Chou?"
"Yes, according to the histories," replied Mencius.
"So is the murder of a sovereign acceptable?"
"A thief of Humanity is called a thief," replied Mencius. "A thief of Duty is called a felon. Someone who's both a thief and a felon is called a commoner. I've heard of the commoner Chou's punishment, but I've never heard of a sovereign's murder."
9 Talking with Emperor Hsüan of Ch'i, Mencius said: "To build a grand home, you must send the master carpenter in search of huge trees. If he finds them, you'll be pleased and consider him truly capable. But if the workers then cut them into small pieces, you'll be angry and consider them truly inept.
"When grown, we're anxious to put our youthful learning to use. But what if an emperor says _Put aside what you've learned and obey me?_ If you have a piece of jade, even if it's worth ten thousand _yi_ in gold, you need to trust a jade-carver to cut and polish it for you. And in governing the nation – if you say _Put aside what you've learned and obey me,_ how is that any different from trying to teach the jade-carver how to cut jade?"
10 After Ch'i invaded the nation of Yen and conquered it, Emperor Hsüan said: "Some say I shouldn't annex Yen, and some say I should. For a nation of ten thousand war-chariots to conquer a nation of ten thousand war-chariots in only fifty days – human strength alone cannot perform such feats. If I don't annex Yen, Heaven will surely be offended and send down calamities. But if I do – what then?"
"If annexation will please the Yen people," replied Mencius, "then do it. There are examples of this among the ancients: Emperor Wu, for instance. And if annexation won't please the Yen people, then don't do it. There are also examples of this among the ancients: Emperor Wen, for instance.
"If a nation of ten thousand war-chariots invades another nation of ten thousand war-chariots, and the invader is welcomed with baskets of food and jars of wine, there can be only one reason: the people are fleeing fire and flood. But if the flood just gets deeper and the fire hotter, they'll no doubt turn again."
11 When Ch'i invaded Yen and annexed it, the other emperors began plotting Yen's rescue.
Emperor Hsüan said: "The other emperors are planning to invade. What shall I do?"
"I've heard of having seventy square miles and ruling all beneath Heaven," replied Mencius. "Emperor T'ang is an example. But I've never heard of ruling a thousand square miles and cowering in fear of others.
"The _Book of History_ says: _Emperor T'ang's expeditions began in Ko._ There he gained the trust of all beneath Heaven – so when he marched east, the western tribes complained. And when he marched south, the northern tribes complained: _Why does he leave us for last?_ People watched for him the way they watched for rain in the midst of a great drought. When he came, they went to market unhindered again and tended their fields without interference. He punished the rulers and comforted the people, like rain falling in its season. And so, a great joy rose among the people. The _Book of History_ also says: _We're waiting for our lord: his coming will bring us back to life._
"Now the Yen emperor tyrannized his people, so you attacked him. The people thought they were being rescued from fire and flood, so they welcomed you with baskets of food and jars of wine. How can you justify killing elders and taking the young captive, tearing down temples and stealing sacred vessels? The power of Ch'i was already feared throughout all beneath Heaven, and now you've doubled your territory without making your government Humane. No wonder all beneath Heaven is up in arms.
"Hurry! Send out orders to release old and young, to leave the sacred vessels where they are. Consult the people of Yen, appoint a new ruler, and then leave. There's still time to prevent this invasion."
12 There was a battle on the border between Chou and Lu.
"I lost thirty-three officials," complained Duke Mu of Chou, "but not one of my people died. There are too many to punish. But if I don't punish them, I'll be condoning what they did: watching their leaders die without lifting a finger to help. What can I do?"
"In years of calamity and failed harvests," replied Mencius, "how many thousands of your people suffered – young and old alike abandoned to gutters and ditches, the strong scattered to every corner of the land? Meanwhile, your granaries were full and your storehouses well stocked. Your officers kept all this from you, thus disparaging their lord and ravaging their people.
"Master Tseng said: _Beware! Beware! Whatever you give out is given back._ It was only now that the people had a chance to give back what you'd given them. You mustn't blame them. If you governed with Humanity, the people would love your officers and die willingly to protect them."
13 Duke Wen of T'eng said: "T'eng is a small nation wedged in between two powerful neighbors. Should I pay court to Ch'i or Ch'u?"
"This kind of thing is beyond me," replied Mencius. "But if you need an answer, I have one suggestion: make your moats deeper and your city walls stronger, then stand beside your people to defend your land. If they would rather die than desert you, your country will be safe."
14 Duke Wen of T'eng said: "The Ch'i army is fortifying Hsüeh. I'm terribly worried. What shall I do?"
"In ancient times," replied Mencius, "Emperor T'ai lived in Pin. But the Ti tribes kept attacking, so he went to settle below Ch'i Mountain. It wasn't something he wanted: he had no choice. If your actions are noble, true emperors will rise again among the children and grandchildren of future generations. Your own success depends upon Heaven alone, but whatever you make and hand down – that will continue.
"What can you possibly do about Ch'i? Just devote yourself to noble actions, and let come what will."
15 Duke Wen of T'eng said: "T'eng is a small nation. We'll run ourselves into the ground paying these great neighbors homage, and still never escape them. What shall I do?"
"In ancient times," replied Mencius, "Emperor T'ai lived in Pin. But the Ti tribes kept attacking. He paid them homage with furs and silks but didn't escape them. He paid them homage with horses and hounds but didn't escape them. He paid them homage with pearls and jade but still didn't escape them. Finally, he called the elders together and said: _What the Ti want is my land. I have heard that the noble-minded will not use what nurtures the people to harm the people. Living without a ruler seems innocuous enough, my friends, so I've decided to leave you._ Setting out from Pin, he crossed the Liang Mountains, founded a new capital below Ch'i Mountain, and there he settled.
_"What Humanity!_ cried out the people of Pin. _We can't lose him!_
"Some people followed him like crowds flocking to market. Others said: _This is the land our ancestors watched over. It isn't a question of what we want. We may die defending it, but we can't abandon this land._
"Choose between these two ways, and you will choose well."
16 Duke P'ing of Lu was about to leave the palace when a trusted advisor named Tsang Ts'ang said: "When you leave you always tell your officials where you're going, my Lord. But now your horses are harnessed and your carriage ready, and you haven't told anyone where you're going. May I ask?"
"I'm going to see Mencius."
"Incredible!" exclaimed Tsang. "How could you debase yourself by going to visit such a commoner, my Lord? Is it because you think he's a sage? A sage is the source of Ritual and Duty. But this Mencius gave his mother a more lavish funeral than his father. You mustn't go see him."
"Yes, perhaps you're right."
Later, Adept Yüeh Cheng entered and said: "Why haven't you gone to see Mencius, my Lord?"
"Because someone told me that Mencius gave his mother a more lavish funeral than his father," replied the duke.
"Incredible! Why do you say it was more lavish? Is it because he mourned his father as a scholar should and mourned his mother as a state minister should? Is it because he made offerings in three vessels for his father and in five for his mother?"
"No, I was thinking about the beauty of his mother's coffin and shroud."
"But it isn't that one was more lavish than the other," said Yüeh Cheng. "He just had more money when his mother died."
Later, Yüeh Cheng went to see Mencius and said: "I told Duke P'ing about you, and he was going to come see you. But the duke has a trusted advisor named Tsang Ts'ang, and he talked him out of it."
"If we go, it's because something urges us on," commented Mencius. "And if we stay, it's because something holds us back. Going and staying – even these are matters beyond our control. It was Heaven that kept me from meeting the duke. This child of the Tsang family – how could he have done such a thing?"
III
Kung-Sun Ch'ou Book One
1 Kung-sun Ch'ou said: "If you took charge in Ch'i, could you re-create the successes of Kuan Chung and Lord Yen?"
"You certainly are a man of Ch'i," replied Mencius. "You think of no one but Kuan Chung and Lord Yen.
"Someone once asked Tseng Hsi: _Who is the wiser, you or Adept Lu?_
"Tseng Hsi shifted around uneasily and replied: _My father was Master Tseng, and even he was in awe of Lu._
_"Well then, who is the wiser, you or Kuan Chung?_
"Tseng's face flushed with anger, and he said: _How could you compare me with Kuan Chung? His sovereign trusted him so utterly, and he ran the government for so long – but his achievements were still utterly meager. How could you compare me with him?_
"If even Tseng Hsi bridled at the idea of being another Kuan Chung, how could you suggest that I would want such a thing?"
"But Kuan Chung made his sovereign the finest of august lords," said Kung-sun, "and Lord Yen led his to such splendor. Are such achievements not worthy of your aspirations?"
"To be a true emperor in Ch'i," replied Mencius, "that would be a simple matter – no harder than turning your hand over."
"Then I'm more confused than ever," said Kung-sun. "Emperor Wen's Integrity was unsurpassed, and he lived to be a hundred, but he still couldn't spread his tranquil rule to all beneath Heaven. His practices were carried on by Emperor Wu and Duke Chou, and only then did great success come. You act like becoming a true emperor is a simple matter – so is Emperor Wen not a worthy exemplar?"
"How could anyone compare to Emperor Wen?" said Mencius. "In the Shang Dynasty, there were six or seven sage emperors between T'ang and Wu Ting, so all beneath Heaven lived content for a long time. And it's hard to change something that's gone on for so long.
"The august lords all paid court to Wu Ting, and so he commanded all beneath Heaven as if he were turning it in the palm of his hand. Chou was a tyrant, but his rule didn't come that much later than Wu Ting's. The traditions of ancient families had been handed down, the ways of good government had been preserved, and he had counselors of great wisdom: Lord Wei, Wei Chung, Prince Pi Kan, Lord Chi, Chiao Ko. That's why he lasted so long before losing everything to Wen. There wasn't a foot of land that wasn't his territory, or a single person who wasn't his subject. Emperor Wen had such difficulty because he began with only a hundred square miles. The Ch'i people have a saying:
_Though you may have deep wisdom,_
_seizing an opportunity works better._
_Though you may have a fine hoe,_
_awaiting the season works better._
"So in our time, to be a true emperor in Ch'i would be a simple matter. The Hsia, Shang, and Chou never controlled more than a thousand square miles, even at their height – so Ch'i has enough territory. You can hear roosters crowing and dogs barking all the way out to the four borderlands – so Ch'i has enough people. It isn't a question of land or people: to be a true emperor here in Ch'i, all you need is Humane government. Then no one could oppose you.
"But the failures of the emperor have never been greater than they are today, and the sufferings of people under tyranny have never been worse than they are today. It's so easy giving food to the hungry, so easy giving water to the thirsty.
"Confucius said: _Integrity spreads through the land faster than a proclamation sent racing down the line of postal stations._ If a nation of ten thousand war-chariots embraced Humane government today, the people would rejoice as if they'd escaped hanging by their heels. In times like these, you can do half as much as the ancients and get twice the results."
2 Kung-sun Ch'ou said: "Suppose you became prime minister in Ch'i and put the Way into practice, making the Ch'i sovereign an emperor without peer – would you feel moved, or not?"
"My mind has been utterly still since I was forty," replied Mencius.
"Then you must be way beyond Meng Pin."
"That wouldn't be hard. Now Master Kao – he'd stilled his mind even before me."
"Is there a Way to follow in stilling the mind?"
"There is," replied Mencius. "To cultivate great valor, Po-kung Yu never bowed down and never broke off a stare. He knew that the least intimidation was as bad as being slapped in the marketplace. An affront was the same to him whether it came from a peasant or a sovereign who commanded a nation of ten thousand war-chariots, and he'd run his sword through the august lord as easily as the peasant. He knew every insult had to be returned in kind.
"Of cultivating valor, Meng Shih-she said: _I consider defeat victory. To gauge an enemy before attacking, to calculate your chances of success before fighting – that is to live in fear of great armies. How can I ever be certain of victory? All I can do is live without fear._
"Meng Shih-she was like Master Tseng, and Po-kung Yu was like Adept Hsia. It's impossible to say which of the two had the most profound valor, but Meng Shih-she nurtured his _ch'i_.
"Long ago, Master Tseng said to Adept Hsiang: _Do you love valor? I once heard about great valor from Confucius. If you look within and find yourself less than honorable, you'll fear even a peasant as an enemy. But if you look within and find yourself honorable, you'll face even an army of ten million men._
"Meng Shih-she nurtured _ch'i,_ but that's still nothing like Master Tseng nurturing essentials."
"May I ask about the stillness of your mind, and the stillness of Master Kao's mind?" asked Kung-sun Ch'ou.
"Master Kao says _Don't search the mind for what you can't find in words, and don't search_ ch'i _for what you can't find in the mind,"_ replied Mencius. "Not searching _ch'i_ for what you can't find in the mind – that's fine. But not searching the mind for what you can't find in words – that isn't.
"The will guides _ch'i,_ and _ch'i_ fills the body. So for us the will comes first, and ch'i second. That's why I say: _Keep a firm grasp on your will, but never tyrannize your ch'i_."
At this, Kung-sun Ch'ou said: "If you say _For us the will comes first, and ch'i second,_ how can you also say _Keep a firm grasp on your will, but never tyrannize your ch'i?_ "
"When the will is whole, it moves _ch'i,_ and when _ch'i_ is whole, it moves the will. When we stumble and hurry, _ch'i_ is affected, but that in turn moves the mind."
"May I ask what makes you excel and flourish so?"
"I understand words, and I nurture the _ch'i_ -flood."
"May I ask what you mean by _ch'i_ -flood?"
"That's hard to explain," replied Mencius. "It's _ch'i_ at its limits: vast and relentless. Nourish it with fidelity and allow it no injury – then it fills the space between Heaven and earth. It is the _ch'i_ that unifies Duty and the Way. Without it, we starve. And it's born from a lifetime of Duty: a few token acts aren't enough. When the things we do don't satisfy the mind, we starve.
"That's why I say: _Master Kao still doesn't understand Duty. He thinks it's something outside of us._ You must devote yourself to this ch'i-flood without forcing it. Don't let it out of your mind, but don't try to help it grow and flourish either.
"If you do, you'll be acting like that man from Sung who worried that his rice shoots weren't growing fast enough, and so went around pulling at them. At the end of the day, he returned home exhausted and said to his family: _I'm worn out. I've been helping the rice grow._ His son ran out to look and found the fields all withered and dying.
"In all beneath Heaven, there are few who can resist helping the rice shoots grow. Some think nothing they do will help, so they ignore them. They are the ones who don't even bother to weed. Some try to help them grow: they are the ones who pull at them. It isn't just that they aren't making things better – they're actually making them worse!"
"What do you mean by _understanding words_?" asked Kung-sun Ch'ou.
"I understand what lies hidden beneath beguiling words. I understand the trap beneath extravagant words. I understand the deceit beneath depraved words. And I understand the weariness beneath evasive words.
"Born of the mind, such things cripple government. And then what is born of government cripples all our endeavors. If ever great sages arise again, they will confirm what I've said.
"Tsai Yü and Adept Kung were masters of eloquence," said Kung-sun Ch'ou. "Jan Po-niu, Min Tzu-ch'ien, and Yen Hui were masters of Integrity's principles. Confucius had mastered both, and still he said: _I'm not much good at eloquence._ So you must already be a great sage, Master."
"What a thing to say!" responded Mencius. "Long ago, Adept Kung asked Confucius: _And are you a great sage, Master?_
_"I couldn't make such a claim,_ replied Confucius. _I learn relentlessly and teach relentlessly, that's all._
"At this, Adept Kung said: _To learn relentlessly is wisdom, and to teach relentlessly is Humanity. To master wisdom and Humanity – isn't that to be a sage?_
"So even Confucius couldn't claim to be a sage. What a thing to say!"
"Of those times," said Kung-sun, "I have heard that Adept Hsia, Adept Yu, and Adept Chang each embodied one aspect of the sage completely. And that Jan Po-niu, Min Tzu-ch'ien, and Yen Hui each embodied all aspects of the sage, but only partially. Which of these is preferable?"
"Let's skip that for now."
"What do you think of Po Yi and Yi Yin?"
"Their Ways were different," replied Mencius. "Po Yi refused to serve a sovereign he disdained or govern a people he disdained. So he took office in times of wise rule and renounced office in times of chaos. Yi Yin, on the other hand, thought any sovereign he served was that much more worthy, and any people he served was that much more worthy. So he took office in times of wise rule, and he took office in times of chaos.
"But Confucius was different. If it was wise to take office, he took office; and if it was wise to stay somewhere, he stayed. If it was wise to linger, he lingered; and if it was wise to hurry away, he hurried away.
"All three were great sages of long ago. I cannot compare to any of them. But Confucius is the one I take for a teacher."
"Did Po Yi and Yi Yin so nearly equal Confucius?"
"No. In all the time since people first came into being, there's never been another like Confucius."
"But were they alike in any way?"
"Yes," replied Mencius. "Given a hundred square miles of territory to rule, they could have inspired the august lords to pay them homage and so made all beneath Heaven their own. But if making all beneath Heaven their own meant violating their Duty even once or killing even a single innocent person, they all would have refused. In this they were alike."
"May I ask how they differed?"
"Tsai Yü, Adept Kung, and Master Yu were all wise enough to understand a sage. And they would never defile themselves by giving someone they admired undue praise. Still, Tsai Yü said: _In my view, the Master was a far greater sage than Yao or Shun._
"Adept Kung said: _Seeing a state's Ritual, he understood its government. And hearing a state's music, he understood its ruler's Integrity. Looking back, he could gauge all the emperors of a hundred generations. And no one ever proved him wrong. In all the time since people first came into being, there's never been another like him._
"And Master Yu said: _And why only people? Unicorns are like other animals, phoenixes like other birds, T'ai Mountain like common hills, rivers andseas like flowing ditches. And the sage is like other people, though he's also different from them: he stands above them. In all the time since people first came into being, there's never been another with the abounding excellence of Confucius."_
3 Mencius said: "To pretend force is Humanity – that's the mark of a tyrant, and a tyrant needs a large country. To practice Humanity through Integrity – that's the mark of a true emperor, and a true emperor doesn't need a large country. T'ang began with only seventy square miles, and Emperor Wen began with only a hundred square miles. If you use force to gain the people's submission, it isn't a submission of the heart. It's only a submission of the weak to the strong. But if you use Integrity to gain the people's submission, it's a submission of the sincere and delighted heart. It's like the submission of seventy disciples to Confucius.
"The _Songs_ say:
_From west and from east,_
_from south and from north –_
_every thought in submission._
That says it exactly."
4 Mencius said: "From Humanity comes honor. From Inhumanity comes disgrace. To despise disgrace and yet practice Inhumanity – that's like despising water and living in bottomlands. If you despise disgrace, there's nothing like treasuring Integrity and honoring noble officials. When those of great wisdom are ministers and those of great ability are officials, the nation is untroubled. And if the ruler uses such times of peace to clarify his policies, then even the largest countries will stand in awe of him.
"The _Songs_ say:
_Before the Heavens darkened with rain,_
_I gathered up mulberry roots,_
_wove tight window and door._
_Now those people down below –_
_how could they disparage me?_
_Whoever wrote this poem certainly understood the Way,_ commented Confucius. _If a ruler can govern his nation well, how could anyone disparage him?_
"These days, rulers use times of peace to indulge in the pleasures of music and idle amusement. They're bringing ruin down upon themselves. We bring it all upon ourselves: prosperity and ruin alike. The _Songs_ say:
_Always worthy of Heaven's Mandate,_
_he found great prosperity in himself._
And the "T'ai Chia" says:
_Ruin from Heaven_
_we can weather._
_Ruin from ourselves_
_we never survive._
That says it exactly."
5 Mencius said: "Honor the wise, employ the able, and you'll have great worthies for ministers – then every noble official throughout all beneath Heaven will rejoice and long to stand in your court. Collect rent in the markets but no tax, or enforce laws but collect no rent – then every merchant throughout all beneath Heaven will rejoice and long to trade in your markets. Conduct inspections at the border but collect no tax – then every traveler throughout all beneath Heaven will rejoice and long to travel your roads. Have farmers help with public fields but collect no tax – then every farmer in all beneath Heaven will rejoice and long to work your land. Don't demand tributes in cloth from families and villages – then people throughout all beneath Heaven will rejoice and long to become your subjects.
"If you can do these five things with sincerity, the people in neighboring countries will all revere you as their parent. And not since people first came into being has anyone ever managed to lead children against their own parents. So if you do this, you won't have an enemy anywhere in all beneath Heaven. When you haven't an enemy anywhere in all beneath Heaven, you'll be Heaven's minister. And no one has become that without becoming a true emperor."
6 Mencius said: "Everyone has a heart that can't bear to see others suffer. The ancient emperors had hearts that couldn't bear to see others suffer, and so had governments that couldn't bear to see others suffer. If you lead a government that can't bear to see others suffer, ruling all beneath Heaven is like turning it in the palm of your hand.
"Suddenly seeing a baby about to fall into a well, anyone would be heart-stricken with pity: heart-stricken not because they wanted to curry favor with the baby's parents, not because they wanted the praise of neighbors and friends, and not because they hated the baby's cries. This is why I say everyone has a heart that can't bear to see others suffer.
"And from this we can see that without a heart of compassion we aren't human, without a heart of conscience we aren't human, without a heart of courtesy we aren't human, and without a heart of right and wrong we aren't human. A heart of compassion is the seed of Humanity. A heart of conscience is the seed of Duty. A heart of courtesy is the seed of Ritual. And a heart of right and wrong is the seed of wisdom.
"These four seeds are as much a part of us as our four limbs. To possess them and yet deny their potential – that is to wound yourself. And to deny the sovereign's potential – that is to wound the sovereign. We all possess these four seeds, and if we all understand how to nurture them, it will be like fire blazing forth or springs flooding free. Nurtured, they're enough to watch over all within the four seas. Unnurtured, they aren't enough to serve even our own parents."
7 Mencius said: "How can the arrow-maker be any less Humane than the armor-maker? It's just that the arrow-maker hopes to wound people and the armor-maker hopes to protect them. It's like this for shaman-healers and coffin-makers too. So you can't be too careful in choosing your trade.
"Confucius said: _Of villages, Humanity is the most beautiful. If you choose to dwell anywhere else – how can you be called wise?_ Humanity is the noble honor Heaven affirms and the tranquil place humans dwell. Failing to practice Humanity when there's nothing stopping you – that is a failure of wisdom. Without Humanity and wisdom, Ritual and Duty, we're nothing but slaves. A slave ashamed of being a slave – that's like a bow-maker ashamed of making bows or an arrow-maker ashamed of making arrows. If you feel shame, there's nothing like practicing Humanity.
"The Humane are like archers. They square up their stance before shooting. And if they fail to hit the mark, they don't resent the victor who does. Instead, they always look within themselves to find the reason for their failure."
8 Mencius said: "Whenever someone told Adept Lu he'd made a mistake, he was delighted. Whenever Emperor Yü heard someone say something honorable, he bowed. But the great Shun – he went way beyond that. Thinking the honorable was something everyone shared, he gave up his own ways and followed the people. He was always happy to adopt what the people considered honorable. From his life as a farmer, potter, and fisherman to his life as emperor, there was nothing he didn't learn by adopting it from the people. And to adopt what the people consider honorable is to help them live honorably. So for the noble-minded, nothing is more important than helping the people live honorably."
9 Mencius said: "Po Yi never served a sovereign he disdained, nor did he remain friends with a friend he disdained. He never served in a foul man's court, or even talked with such a man. Serving such a man or even talking with him – for Po Yi, that was like donning fine court robes to sit in mud and ash. He pushed his hatred of the foul impossibly far: if he met a neighbor whose hat wasn't on straight, he would hurry away without looking back, as if it would tarnish him. That's why he refused all offers from august lords, however honorable the offers were. He refused because it was demeaning to attend them.
"Liu-hsia Hui, on the other hand, wasn't shamed by defiled rulers, nor did he consider common positions below him. When in office, he never hid his wisdom and always depended on the Way. When dismissed, he bore no resentment. And suffering adversity, he remained untroubled. He said: _You are who you are, and I am who I am. Even if you stripped naked and stood beside me, how could you ever tarnish me?_ Hence he was completely at ease no matter who he was with, and never insisted on leaving. If he was asked to stay, he stayed – for he never felt demeaned and forced to leave.
"Po Yi was too pinched and Liu-hsia Hui too undignified," commented Mencius. "Pinched and undignified: the noble-minded avoid both."
IV
Kung-Sun Ch'ou Book Two
1 Mencius said: "The seasons of Heaven cannot rival the industry of earth. And the industry of earth cannot rival an accord of the people.
"Suppose there were a city with a three-mile inner wall and a seven-mile outer wall. An army surrounds the city and attacks, but fails to conquer it. To surround the city in the first place, this army must have been blessed by the seasons of Heaven. But it failed to conquer the city because the seasons of Heaven cannot rival the industry of earth.
"Now suppose a city's walls are high, its moat deep, its weapons strong and sharp, its supplies plentiful. But this time, the people abandon it and flee. The city falls because the industry of earth cannot rival an accord of the people.
"And so it is said: _Borders and frontiers can't corral the people. Ranges of mountains can't secure a nation. And sharp weapons can't keep all beneath Heaven in awe._
"Master the Way and your supporters are countless. Lose the Way and your supporters are few. When your supporters are few, even your own family will turn against you. When you supporters are countless, all beneath Heaven will follow you. Hence, the noble-minded ruler never goes to war, or if he does, victory is a simple matter – for he is followed by all beneath Heaven while his enemy's own family is turning against him."
2 Just as Mencius was about to leave for court, a courier arrived with a message from the emperor: "I wanted to come visit you today, but I have a cold and must avoid the wind. I'll hold court again tomorrow, and wonder if I'll have a chance to see you then?"
To this, Mencius replied: "Unfortunately, I too am sick and so cannot attend court."
The next morning, Mencius went to offer the Tung-kuo family his condolences, whereupon Kung-sun Ch'ou said: "Yesterday you declined the emperor's summons, saying you were sick. But today you're out visiting, offering condolences. Should you really be doing this?"
"Yesterday I was sick," replied Mencius, "but today I am well again. So why shouldn't I go out to offer my condolences?"
The emperor sent someone to see how Mencius was feeling, and a doctor came too. Adept Meng Chung told them: "Yesterday, when the emperor's message arrived, Mencius was sick and could not attend court. Today he's feeling a little better, so he hurried off to court. But I don't know if he'll be able to get there or not."
Meng then sent some people to find Mencius and tell him: "You mustn't return home. Go to the emperor's court at once."
But Mencius still didn't go. Instead, he spent the night at Ching Ch'ou's house. There, Lord Ching said: "Inside the home, there is father and son. Outside, there is sovereign and subject. These are the great bonds of human community. Between father and son, affection rules. Between sovereign and subject, reverence rules. I've seen the emperor's reverence for you, but I have yet to see any sign of your reverence for the emperor."
"What a thing to say!" responded Mencius. "In all of Ch'i, there's no one who talks to the emperor about Humanity and Duty. Is that because they don't consider Humanity and Duty to be beautiful things? Or is it because they say to themselves: _Talking to a person like that about Humanity and Duty – what good would it do?_ Is anything more irreverent that that? I've never dared offer the emperor anything less than the Way of Yao and Shun. So is there anyone in all of Ch'i with more reverence for the emperor than I?"
"No," said Lord Ching, "that isn't what I meant. The _Book of Ritual_ says: _When your father calls, don't pause to answer. When your sovereign summons, don't wait for a carriage._ You were leaving for the emperor's court, but when his summons arrived you refused to go. Isn't this a violation of Ritual?"
"So that's what you meant?" replied Mencius. "Master Tseng said: _Nothing can rival the wealth of Chin and Ch'u. Still – they may have wealth, but I have Humanity; and they may have nobility, but I have Duty. So why should I envy them?_ If Master Tseng said this, how could it be wrong? It must be part of the one Way.
"There are three things known throughout all beneath Heaven as exalted: nobility, age, and Integrity. At court, nothing rivals nobility. In the village, nothing rivals age. But for nurturing the people, nothing rivals Integrity. How can you ignore two of these because you possess one of them? If a sovereign is doing great things, he must have advisors he cannot summon. If he wants counsel, he goes to them. If he does not honor Integrity and delight in the Way like this, he is not worthy of their help.
"T'ang first took Yi Yin as a teacher, then as a counselor – and so he became a true emperor with ease. Duke Huan first took Kuan Chung as a teacher, then as a counselor – and so he became the finest of august lords with ease.
"Now all beneath Heaven is full of countries equal in territory and Integrity. None can overcome another for one simple reason: their rulers all want advisors they can teach, rather than advisors they can learn from. T'ang never presumed to summon Yi Yin; Duke Huan never presumed to summon Kuan Chung. And Kuan Chung is scarcely worthy of anyone's aspirations. If he was not to be summoned, am I?"
3 Adept Ch'en said: "The Ch'i emperor once offered you a hundred _yi_ in the purest gold, and you refused. But now in Sung you've accepted seventy, and in Hsüeh fifty. If your refusal then was right, your acceptance now is wrong. And if your acceptance now is right, your refusal then was wrong. You can only have it one way."
"Both were right," replied Mencius. "In Sung I was leaving on a long journey, and farewell gifts are always given to departing travelers. So when the emperor said _Please accept this farewell gift,_ why should I refuse? In Hsüeh I was worried about my safety. The emperor said _I've heard about your worries. This is to help you buy weapons._ So why should I refuse?
"But in Ch'i there was no reason for the gift. A gift for no reason is a bribe. And when have the noble-minded ever taken bribes?"
4 Mencius went to P'ing Lu and said to the governor there: "If you had a spearman who abandoned his post three times in a single day, would you discharge him or not?"
"I wouldn't wait for three times," replied Governor K'ung Chü-hsin.
"But you have abandoned your own post many times," countered Mencius. "In years of calamity and failed harvests, how many thousands of your people suffered – young and old alike abandoned to gutters and ditches, the strong scattered to every corner of the land?"
"But there was nothing I could do."
"Suppose someone entrusted their cattle and sheep to your care. Surely you would try to find grass and hay for them. And if you couldn't find any, would you return them to their owner or just stand by and watch them die?"
"So, I myself am to blame."
Some time later, Mencius went to see the emperor and said: "I know five provincial governors in your country. The only one who understands how he himself is to blame is K'ung Chü-hsin. Shall I tell you what happened?"
"I myself am to blame," replied the emperor.
5 Mencius said to Ch'ih Wa: "When you resigned as governor of Ling Ch'iu and asked to be appointed chief judge, it seemed a wise choice because a chief judge advises the emperor. It's been several months since you were appointed – how is it you still haven't counseled the emperor?"
Soon thereafter, Ch'ih Wa offered his counsel to the emperor. When his counsel was ignored, he resigned and went away.
At this, the Ch'i people said: "What Mencius urged Ch'ih Wa to do was fine indeed. As for what Mencius himself does – things aren't so clear."
When Adept Kung-tu told him about this, Mencius said: "I've heard that officials resign if they cannot fulfill their duties, and that counselors resign if they cannot offer their advice. But I'm neither an official nor a counselor, so when it comes to engagement and withdrawal, why shouldn't I just do as I please?"
6 When Mencius was a minister in Ch'i, he went to T'eng on a mission of condolence. The emperor sent as his deputy Wang Huan, the governor of Ko. But even though Mencius saw Wang Huan morning and night on their travels to and from T'eng, he never discussed the purpose of their journey.
"The position of minister in Ch'i is no small thing," commented Kung-sun Ch'ou, "and the road between Ch'i and T'eng is hardly short. How is it you traveled all that way and never discussed the purpose of your journey with him?"
"There were others appointed to arrange things," replied Mencius. "What was there for us to discuss?"
7 Mencius traveled from Ch'i to Lu for the burial of his mother. On his way back to Ch'i, he stopped at Ying. There, Ch'ung Yü said: "You didn't think me unworthy of directing the work of the coffin-makers. The work was urgent, so there was no time for questions. But now there's one I'd like to ask, if you don't mind: _Wasn't that awfully beautiful wood?_ "
"In the most ancient times, there weren't rules about how coffins were to be built," replied Mencius. "Later on, there were rules requiring inner and outer coffins to be seven inches thick, whether they were for the Son of Heaven or a common peasant. It isn't a question of beauty, but of expressing all that's in our hearts. If we can't find beautiful wood, we feel uneasy. And if we can't afford it, we feel uneasy. So if they could find it, and they could afford to buy it, the ancients always used the most beautiful wood. How could all this be any different for me?
"And to keep soil from the body of a loved one caught in the midst of such a change – is that not a great joy? I've heard that the noble-minded never scrimp when it comes to parents – not for all beneath Heaven."
8 Acting on his own, Shen T'ung asked: "Is an attack against Yen acceptable?"
"Yes," replied Mencius. "Emperor K'uai had no right to abdicate in favor of Lord Chih. And Lord Chih had no right to accept.
"Suppose there was an official that you especially liked, and you gave him your salary and position without telling the emperor. Suppose that he took it without securing the emperor's approval. Would that be acceptable? And how is that any different from what's happened in Yen?"
Soon Ch'i attacked Yen, and someone asked: "Is it true that you encouraged Ch'i to attack Yen?"
"I did not!" bristled Mencius. "When Shen T'ung asked if an attack against Yen would be acceptable, I said _Yes_. And soon Ch'i attacked. But if he'd asked _For whom is an attack against Yen acceptable?_ I would have said: _An attack by someone Heaven appointed is acceptable._
"Suppose one person killed another, and someone asked: _Is the killing of a person acceptable?_ I would answer: Yes. But if the question was: _For whom is the killing of a person acceptable?_ I would say: _The killing of a person by a chief judge is acceptable._ Now to attack Yen with another Yen – how could I ever encourage such a thing?"
9 The Yen people had turned to rebellion. The Ch'i emperor said: "I'm too ashamed to face Mencius."
"I wouldn't worry too much," said Ch'en Chia. "Who do you consider the most Humane and wise – you or Duke Chou?"
"What a thing to ask!" said the emperor.
"Duke Chou put Kuan Shu in charge of Shang, and then Kuan Shu used Shang to launch his rebellion. If Chou sent Kuan Shu knowing what would happen, he wasn't Humane. And if he sent Kuan Shu without knowing what would happen, he wasn't wise. So Chou's Humanity and wisdom weren't perfect, and how could yours be anything like his? Shall I go explain this to Mencius?"
Ch'en Chia went to see Mencius and asked: "What kind of man was Duke Chou?"
"An ancient sage," replied Mencius.
"Is it true that he put Kuan Shu in charge of Shang, and then Kuan Shu used Shang to launch his rebellion?"
"It is."
"Did he send Kuan Shu to Shang knowing he would launch a rebellion?"
"No, he didn't know what Kuan Shu was going to do."
"So even a sage makes mistakes?"
"Duke Chou was the younger brother, and Kuan Shu the elder," replied Mencius. "So it's hardly surprising Chou would make such a mistake. But in ancient times, when the noble-minded made mistakes, they knew how to change. These days, when the noble-minded make mistakes, they persevere to the bitter end. In ancient times, mistakes of the noble-minded were like eclipses of sun and moon: there for all the people to see. And when a mistake was made right, the people all looked up in awe. But these days, the noble-minded just persevere to the bitter end, and then they invent all kinds of explanations."
10 Mencius resigned his office and returned home. The emperor went to see him and said: "I wanted to come see you the other day, but could not. When we served together in the same court, I was overjoyed. But now you've left me and returned to your home. I wonder if I can still come here to see you?"
"I wouldn't have dared ask," replied Mencius, "but that is my deepest wish."
Another day, the emperor said to Lord Shih: "I want to give Mencius a house in the center of the capital and ten thousand measures of rice to support his disciples. Then my ministers and people will always have a noble example there before them. Would you talk to him for me?"
Lord Shih passed this message to Mencius through his disciple, Adept Ch'en. When Ch'en gave Shih's message to him, Mencius said: "I see. Yes, how would Lord Shih know such a thing cannot be done? Perhaps he thinks I'm after wealth. But if I were after wealth, why would I give up a hundred thousand so I could have ten thousand?
"Chi Sun once said: _Adept Shu Yi was strange indeed. He arranged an appointment for himself, and when his counsel was ignored, he resigned. But then he used this to arrange lofty appointments for his sons and brothers. People all want wealth and renown, of course. But there in the midst of it, he certainly found his high ground._
"In the ancient markets, people simply traded what they had for what they had not. The government supervised, nothing more. But then came an uncivil old man who always searched out high ground and climbed up on top. Surveying the situation carefully, he found all the profits to be had, then snared every one. The people all thought him uncivil, so they taxed him. And so it was that the taxing of merchants began."
11 Mencius left Ch'i and spent the night in Chou. There, on behalf of the Chou emperor, a man wanted to convince Mencius to stay. He sat down and began talking to Mencius, but Mencius said nothing. Instead, he fell asleep with his head on the table. Quite unhappy, the man said: "I fasted a full day and night before daring to speak with you. But instead of listening, you sleep. I won't disturb you again."
"Please sit," said Mencius. "I'll try to explain this clearly. Long ago, if Duke Mu of Lu didn't have someone always by Master Szu's side, Szu soon lost interest in him. On the other hand – if Hsieh Liu and Shen Hsiang didn't have someone always by Duke Mu's side, Mu soon lost interest in them.
"Now you've gone to all this trouble, but I'm certainly not being treated the way Master Szu was. So am I ignoring you, or are you ignoring me?"
12 Talking with some people after Mencius left Ch'i, Yin Shih said: "If he didn't know the emperor would never be another T'ang or Wu, he isn't very bright. If he knew this and came anyway, he was just trying to get ahead. He came a thousand miles to see the emperor, failed, and left disappointed – but then it took him three days to leave Chou. What made him linger there? It all seems rather suspect to me."
When Adept Kao told him about this, Mencius said: "What does Yin Shih know about me? When I came a thousand miles to see the emperor, that was what I wanted. But to fail and leave disappointed – how could that be what I wanted? It was something I couldn't avoid.
"I waited three days to leave Chou, it's true, but even that felt too soon. The emperor was on the verge of a transformation, and if that had happened he would have called me back. Only when I left Chou and the emperor still didn't send after me – only then did the longing for home well up. But had I abandoned the emperor even then?
"The emperor is capable of noble things. If he'd listened to me, it would have meant peace not just for the people of Ch'i, but for the people throughout all beneath Heaven. The emperor was on the verge of a transformation, and every day I hoped for that. So am I like the little man whose face clouds over with anger and resentment when the sovereign ignores his counsel, who leaves and travels hard all day before stopping?"
When Yin Shih heard this, he said: "It is I who am the little man."
13 Mencius left Ch'i. As they traveled away, Ch'ung Yü said: "You look so unhappy, Master. But just the other day I heard you say: _The noble-minded never resent Heaven and never blame people_."
"That was then," replied Mencius. "This is now. A true emperor should arise every five hundred years, and there should also arise others worthy of renown in their time. It's been over seven hundred years since the Chou began: enough time and more. And surely the world is ready. But it seems Heaven still doesn't want to bring peace and order to all beneath Heaven. If it did, who could it choose in our time besides me? So why should I be unhappy?"
14 Mencius had left Ch'i and was staying in Hsiu. There, Kung-sun Ch'ou asked: "To serve in office but refuse a salary – is that the ancient Way?"
"No," replied Mencius. "I was ready to leave after seeing the Ch'i emperor once. And I wasn't about to change my mind – that's why I refused a salary. But then war broke out, so I couldn't very well ask to leave. I had no intention of staying so long."
V
Duke Wen of T'eng Book One
1 When he was heir apparent, Duke Wen of T'eng went on a journey to Ch'u. He went by way of Sung, and there stopped to see Mencius. Mencius told him that people are inherently good, and that he must strive to equal Yao and Shun.
When he returned from Ch'u, the duke again stopped to see Mencius, and Mencius said: "Do you doubt what I told you? There is one and only one Way. Ch'eng Chien said to Duke Ching of Ch'i: _Those sage-emperors were men, and I am a man. Why should I be in awe of them?_ Yen Hui said: _What kind of man was Shun, and what kind of man am I? If we're devoted, we can be like him._ And Kung-ming Yi said: _Emperor Wen is my teacher. And how could he ever deceive me?_
"Now if you evened out the borders, T'eng would measure fifty square miles: big enough to do great things. The _Book of History_ says: _If herbs don't make your head swim, they won't cure your illness_."
2 Wen was heir apparent when Duke Ting of T'eng passed away, so he said to Jan Yu: "Mencius once counseled me in Sung, and I've never forgotten a word of what he said. The death of a father is a time of great sorrow and responsibility. Before I do anything, I want you to go see Mencius and ask his advice.
Jan Yu went to see Mencius in Chou, and Mencius said: "This is a good thing. Mourning a parent's death – that is when you face yourself utterly. Master Tseng said: _In life, serve parents according to Ritual. In death, bury them according to Ritual. And then make offerings to them according to Ritual. Do this, and you can be called a worthy child._
"I've never studied the rituals of august lords. Still, I have heard something about such matters. The practice has been the same for three dynasties, and for everyone from the Son of Heaven to simple peasants: a mourning period of three years, clothes of plain cloth cut straight, meals of common porridge."
When Jan Yu returned and reported what Mencius had said, Wen decided to observe a three-year mourning period. But the elders and the hundred officials protested: "This is not the way of the ancestral rulers in Lu, our homeland, nor is it the way of our own ancestral rulers. And to violate their practice – that is not for you to do. The _Annals_ say: _In mourning and sacrifice, follow the ways of your ancestors."_
"My way has also been handed down from the ancients," said Wen.
Later, he said to Jan Yu: "In the past, I spent my time with horses and swords rather than books and teachers. And now the elders and the hundred officials all consider me lacking, so I'm afraid they won't devote themselves to the great issues of our nation. Go for me, and seek the counsel of Mencius."
So Jan Yu returned to Chou and inquired of Mencius.
"I see," replied Mencius. "Why does he look to others for his answers? Confucius said:
When the sovereign dies – trust government to the prime minister, drink broth, wear a charcoal face dark as ink. Take your place and mourn, then none of the hundred officials will dare be without grief. Show others the way, for the commitments of leaders become the passions of followers. The noble-minded have the Integrity of wind, and little people the Integrity of grass. When the wind sweeps over grass, it bends.
So these things depend upon Wen alone."
When Jan Yu returned and reported what Mencius had said, Wen said: "I see. Yes, these things do depend upon me and me alone."
For five months he stayed in his mourning hut, issuing no proclamations or precepts. Soon both the hundred officials and the family could both say: "How wise!" And when it came time for the burial, people traveled from every corner of the land to watch. The sorrow in his face, the grief in his sobs: it was a great comfort to the other mourners.
3 Duke Wen of T'eng asked about governing his country, and Mencius said: "Never neglect the endeavors of the people. The _Songs_ say:
_We gather thatch-reeds by day,_
_and braid rope into the night._
_We hurry to build field huts,_
_then begin planting the hundred grains._
This is how the people live: it's their Way.
"With a constant livelihood, people's minds are constant. Without a constant livelihood, people's minds are never constant. And without constant minds, they wander loose and wild. They stop at nothing, and soon cross the law. Then, if you punish them accordingly, you've done nothing but snare the people in your own trap. And if they're Humane, how can those in high position snare their people in traps?
"Therefore, the wise ruler practices humility, economy, and reverence toward his subjects. And he takes from the people only what is due him. Yang Hu said: _If you cultivate wealth, you give up Humanity. If you cultivate Humanity, you give up wealth._
"In the Hsia Dynasty, each family had fifty acres and paid a personal tax. In the Shang, each family had seventy acres and paid a mutual tax. And in the Chou, each family had a hundred acres and paid a communal tax. But in fact, the people always paid one part in ten. _Communal_ means _everyone_ together, and _mutual_ means _mutual assistance._
"Master Lung said: _In administering the land, nothing is better than the mutual system, and nothing worse than the personal._ The personal tax is based on harvest averages over a number of years. In good years, when there's a wild abundance of rice and a heavy tax would hardly be noticed, little is taken. But in bad years, when the harvest isn't worth the manure it grew from, the tax is exorbitant. When the people's father and mother wears them out with worry, letting them work desperately all year long and then go into debt just to care for their parents, when he abandons young and old alike to gutters and ditches – how can he be called the people's father and mother?
"As for ensuring a livelihood for descendants of worthy officials, that is already the practice in T'eng. But the _Songs_ say:
_When rain falls on our public land,_
_it also falls on our private land._
Only in the mutual system is there public land. These lines are about the Chou, so there's no doubt that it too used the mutual system.
" _Hsiang, hsü, hsüeh,_ and _hsiao_ were established for the education of the people. _Hsiang_ for nurturing, _hsiao_ for educating, and _hsü_ for archery: these are the names used for village schools. In the Hsia Dynasty they were called _hsiao,_ in the Shang _hsü,_ and in the Chou _hsiang._ For schools of advanced studies, all three dynasties used the name _hsüeh._ But the purpose of all alike was to illuminate the bonds of human community for the people. And when leaders themselves illuminate those bonds, the common people are full of tender affection. If a true emperor arose, he would have to come learn these things from you, and then you would be the teacher of emperors.
"The _Songs_ say:
_Chou may be an ancient country,_
_but its mandate is renewed again._
It was Emperor Wen who renewed it. If you devoted yourself, there's no doubt you could renew your own nation in the same way.
Duke Wen sent Pi Chan to ask about the well-field system, and Mencius said: "Your sovereign is anxious to practice Humane government. He chose carefully when he sent you, so you must spare no effort.
"Humane government begins in settled boundaries. Unless settled boundaries are properly fixed, the well-fields won't be divided equally, nor will the yield given for official salaries be fair. This is why tyrants and corrupt officials always avoid settled boundaries. But once settled boundaries are properly fixed, land shares and salary amounts are easily established.
"T'eng has very little territory. Still, you need both noble-minded leaders and peasants in the countryside. Without noble-minded leaders, who will foster order among the peasants? And without peasants, who will nurture the noble-minded leaders?
"In the countryside, tax people one ninth of their produce, according to the well-field system. In the capital, tax people one tenth of their income. From ministers down, officials should all have fifty acres for sacrificial offerings. And among the peasants, each extra man in a family should be given an additional twenty-five acres. People should never leave their village – not when they move their house and not when they die. If villagers sharing well-fields are friends in all things, help each other keep watch, and care for each other in illness – then the people will live in affection and harmony.
"Each square mile of land contains a well-field, and each well-field contains nine hundred acres. The central plot is public land. The eight families each own a hundred acres of private land, and together they cultivate the public land. Once the public land has been tended, they can turn to their own. This is what distinguishes peasants from officials.
"Such are the broad outlines. As for the details of making all this work well, the refinements and elaborations – that's up to you and your sovereign."
4 There was a man named Hsü Hsing who claimed to follow the Way of Shen Nung. He left Ch'u and journeyed to T'eng, where he went to the palace gate and said to Duke Wen: "I lived in a land far away, and there heard that you practice Humane government. I want to live under your rule, so I've come to ask for a piece of land." The Duke granted Hsü Hsing's request, and Hsü soon had dozens of disciples, all of whom wore sackcloth and earned their living by making sandals and weaving mats.
Ch'en Hsiang and his brother were disciples of Ch'en Liang. Leaving Sung with plows on their backs, they journeyed to T'eng and said: "We have heard that yours is the government of a sage, and we want to live under the rule of a sage."
Ch'en Hsiang went to see Hsü Hsing one day, and was overjoyed. He abandoned his old teacher and took Hsü Hsing as his teacher. He later went to see Mencius and told him what Hsü Hsing had said: "The T'eng sovereign is truly wise and worthy, but he's never learned of the Way. A wise and worthy sovereign earns his living by cultivating the land with his people. It's during breakfast and dinner that he rules. But here, with all his granaries and treasuries, the duke wounds the people while pampering himself. So how can he be wise and worthy?"
"Does Master Hsü eat only the grain he himself has grown?" asked Mencius.
"Yes," replied Ch'en Hsiang.
"And does Master Hsü wear only cloth he himself has woven?"
"No, but he wears only sackcloth."
"Does Master Hsü wear a hat?"
"Yes."
"What kind?"
"Raw silk."
"Did he weave it himself?"
"No, he traded grain for it."
"How is it Master Hsü doesn't weave his own hat?"
"It would interfere with his farm work."
"Does Master Hsü use metal and stoneware for cooking? And for plowing, does he use iron?"
"He does."
"And does he make all these things himself?"
"No, he trades grain for them."
"To trade grain for tools and implements doesn't hurt potters and smithies," said Mencius. "They trade their tools and implements for grain, and does that hurt farmers? Why doesn't Master Hsü become a potter and smithy as well, so he himself can make everything his home needs? The markets of those who practice the hundred crafts are pure bedlam: why does he join in the confusion of barter and trade? How can he bear it?"
"You can't practice a craft and be a farmer too."
"Then how could someone govern all beneath Heaven and also be a farmer? There are the endeavors of great men, and the endeavors of small men. And whatever they need, the hundred crafts provide. If we all had to make things before we could use them, we'd all spend our lives running back and forth on the roads.
"And so it is said:
Some use their minds to work, and some use their muscles. Those who use their minds govern, and those who use their muscles are governed. Those who are governed provide for those who govern, and those who govern are provided for by those who are governed.
People throughout all beneath Heaven know this to be sound practice.
"In the time of Emperor Yao, things were still wild and unsettled in all beneath Heaven. Rivers burst their banks and floods raged across the world. Grasses and trees grew thick with abandon. Birds and animals roamed everywhere in herds and flocks. The five grains never grew tall. Birds and animals crowded people in: even the Middle Kingdom was a tangle of animal trails and bird tracks.
"It was Yao who worried about how to change all this. He fostered Shun so he could bring order to things. Shun assigned Yi to manage fire, and Yi set fire to the mountains and marshes, sending the birds and animals into hiding. Yü carved out the nine rivers. He cleared the Chi and T'a, and sent them flowing into the sea. He opened up the Ju and Han, banked up the Huai and Szu – and sent them all flowing into the Yangtze. Only then were the people of the Middle Kingdom able to grow food. To do this work, Yü spent eight years away from home and passed by his gate three times without entering. Even if he'd wanted to tend fields, how could he have done it?
"Hou Chi taught the ways of agriculture to the people, taught them how to plant the five grains. And when the five grains ripened, the people were well fed. But once people have plenty of food and warm clothes, they lead idle lives. This is their Way. Then, unless they're taught, they're hardly different from the birds and animals. The sage-emperor worried about this. He made Hsieh minister of education so the people would be taught about the bonds of human community: affection between father and son, Duty between sovereign and subject, responsibility between husband and wife, proper station between young and old, sincerity between friend and friend.
"Yao said:
_Encourage them and reward them._
_Help them and perfect them._
_Support them and give them wings,_
_and reveal them to themselves._
_Then you will bring Integrity alive in them._
If a sage ruler worries about his people like this, how could he have time for farming? Yao's great worry was that he might not find a Shun. And Shun's great worry was that he might not find a Yü or Kao Yao. If your great worry is tending your own hundred acres, you're simply a farmer.
"To share your wealth is called generosity. To teach people about living nobly is called loyalty. To be worthy of all beneath Heaven is called Humanity – and so it's easy to give all beneath Heaven away, but to be worthy of it is difficult indeed.
"Confucius said:
Great indeed was the rule of Yao! Heaven alone is truly majestic, and only Yao could equal it. He was boundless, so vast and boundless the people couldn't even name him. And how majestic, how exalted and majestic a ruler Shun was: possessing all beneath Heaven as if it were nothing to him!
Ruling all beneath Heaven, didn't Yao and Shun have enough to worry about? How could they worry about farm work too? I've heard of our ways converting barbarians into Chinese, but I've never heard of Chinese reverting into barbarians.
"Ch'en Liang is a product of Ch'u. But he admired the Way of Duke Chou and Confucius, so he came north to study in the Middle Kingdom. Among scholars from the north, none could better him. He could only be called a truly great scholar. You and your brother studied under him for dozens of years. Then he dies and you suddenly turn against him.
"After Confucius died and their three years of mourning were over, his disciples packed their things and prepared to return home. They went in and bowed to Adept Kung. They faced each other and wept until they'd all lost their voices. Only then did they leave for home. Adept Kung returned to the burial grounds, built a hut, and lived alone there for another three years before he finally set out for home.
"Eventually, Adept Hsia, Adept Chang and Adept Yu came to think Master Yu was as wise as the sage, and so wanted to study under him as they had under Confucius. They tried to convince Master Tseng to join them, but Tseng said: _I could never do that. Rinsed clean by the Yangtze and Han rivers, bleached by the autumn sun – something shimmering so perfectly white is beyond compare._
"Now some tribesman with a twittering shrike's tongue comes from the south condemning the Way of the ancient emperors, and you turn against your teacher and go to study with him. You're nothing like Master Tseng. I've heard of leaving dark ravines to live in high trees, but I've never heard of leaving high trees to live in dark ravines.
"In the _Songs,_ among the 'Hymns of Lu,' there's a poem that speaks of
_fighting down the wild tribes_
_and punishing Ch'u and Shu._
Duke Chou fought these people to rescue the Middle Kingdom, and now you want to study under them. Yours was a poor conversion indeed.
"In Master Hsü's Way, market prices should all be the same. He claims that would end deceit, that even if children were sent to market, no one would cheat them. Cloth of the same length would bring the same price, whether it was cotton or silk. Bundled fiber of the same weight would bring the same price, whether it was hemp or silk. The five grains would bring the same price for the same measure, and shoes would all bring the same price for the same size.
"But inequality is the very nature of things. One thing may be two or five times as valuable as another, or perhaps ten or a hundred times, or even a thousand or ten thousand times. If you tried to make everything equal in value, confusion would reign in all beneath Heaven. If elegant shoes and workaday shoes brought the same price, who would bother to make elegant shoes? If we follow the Way of Master Hsü, we'll lead each other into utter deceit. How could a nation be governed this way?"
5 A follower of Mo Tzu named Yi Chih wanted to go see Mencius, so he asked Hsü Pi to arrange a visit. Mencius said: "I would like very much to see him, but I'm quite ill. When I'm feeling better, I'll go see him. He needn't come here."
Later, Yi Chih again tried to arrange a visit with Mencius, and Mencius said: "Now I can see him. But first I must straighten him out a little – for if he isn't thinking straight, how can he see the Way?
"I have heard Adept Yi is a follower of Mo Tzu. In funerals, Mo Tzu's school follows the Way of simplicity. And Adept Yi apparently thinks such simplicity can transform all beneath Heaven. So how can he himself denounce it instead of treasure it? He gave his parents lavish burials, but the principle of simplicity condemns that as a tawdry way of serving them."
When Master Hsü told Adept Yi what Mencius had said, Adept Yi replied: "According to the Confucian Way, the ancients ruled _as if watching over newborn children._ What can such words mean if not that our love should be the same for everyone, even if it always begins with loving our parents?"
When Master Hsü told Mencius what Adept Yi had said, Mencius replied: "Does Adept Yi really believe we can love a neighbor's newborn child the way we love our own brother's child? The only time that's true is when the newborn is crawling around a well and about to fall in, for the child doesn't know any better. Heaven gives birth to all things: they have a single source. But Adept Yi insists they have two, that's why he believes such things.
"Imagine people long ago who didn't bury their parents. When their parents die, they toss them into gullies. Then one day they pass by and see them there: bodies eaten away by foxes and sucked dry by flies. They break into a sweat and can't bear to look. That sweat on their faces isn't a show for their neighbors: it's a reflection of their deepest feelings. So when they go home and return with baskets and shovels to bury their parents, it's because burying parents truly is the right thing, the Way for all worthy children and Humane people."
When Master Hsü told Adept Yi what Mencius had said, Adept Yi grew pensive. Eventually he said: "I have now been taught."
VI
Duke Wen of T'eng Book Two
1 Ch'en Tai said: "It seems small of you – refusing to go see the august lords. If you did, you could make whoever you met a true emperor – or at the very least, the finest of august lords. The _Annals_ say: _Bend a foot to straighten ten._ It seems worth doing, doesn't it?"
Mencius replied: "Once when he was out hunting, Duke Ching of Ch'i summoned his gamekeeper with a plume-crested flag. The gamekeeper didn't come, so the duke wanted to have him executed, but Confucius said: _A man of great resolve never forgets that he could be abandoned to ditches and gutters, and a man of great valor never forgets that he could lose his head._ What was it Confucius admired in the gamekeeper? The man wasn't entitled to such a lofty summons, so he didn't answer it. And how would it be if people came without waiting for a summons?
"And besides, _bend a foot to straighten ten_ is talking about profits. When it's a matter of turning a profit, don't people think it's fine even if they bend ten feet to straighten one?
"Once, because Hsi was a favorite of his, Lord Chien of Chao assigned Wang Liang to drive for him. Hsi didn't catch a single bird all day, so he returned to Lord Chien saying: _He's the worst driver in all beneath Heaven._
"When someone told him what Hsi had said, Wang Liang said: _Let me try again._ It took no small amount of persuasion, but Hsi finally agreed. This time Hsi caught ten birds in a single morning, and on returning exclaimed: _He's the finest driver in all beneath Heaven!_
" _Then I'll let him drive for you all the time,_ said Lord Chien.
"But when he told Wang Liang, Wang Liang refused: _I drove hard for him according to the precepts, and we didn't catch a single bird all day. Then I drove shamelessly for him, and in a single morning we caught ten birds. The_ Songs _say:_
_They drove with flawless skill,_
_shot arrows with fierce precision._
_I'm not accustomed to driving for little people. I'll go now, if you please._
"Even though he was a mere driver, Wang was ashamed to compromise for an archer. They could have piled birds and animals up like mountains, but he still wouldn't do it. What kind of person would bend the Way to please others? You've got it all wrong: if you bend yourself, you'll never straighten anyone else."
2 Ching Ch'un said: "How could Kung-sun Yen and Chang Yi be anything less than truly great men? If their anger flashed, the august lords cowered. And if they were content, all beneath Heaven was tranquil."
"Does that make them great men?" replied Mencius. "Haven't you studied Ritual? When a boy comes of age, he receives his father's mandate. When a girl marries, she receives her mother's mandate. Saying farewell at the gate, she cautions her: _Now that you're going to your new home, you must be reverent and cautious, and never disobey your husband._ To make deference the norm – that is the Way of married women.
"As for the man who can be called great: He dwells in the most boundless dwelling-place of all beneath Heaven, places himself at the center of all beneath Heaven, and practices the great Way of all beneath Heaven. If he succeeds in these ambitions, he and the people enjoy the rewards together. If he fails, he follows the Way alone. Wealth and renown never mean much to him, poverty and obscurity never sway him, and imposing force never awes him."
3 Chou Hsiao asked: "In ancient times, did the noble-minded take office?"
"They did," replied Mencius. "The _Chronicles_ say: _When Confuciuswent three months without a position, he got anxious and restless. And when he left one nation for another, he always carried his token of credentials with him._
"And Kung-ming Yi said: _When the ancients went three months without a position, people began offering condolences._
"Offering condolences after three months!" responded Chou Hsiao. "Is it really all that urgent?"
"When a man loses his office," replied Mencius, "it's like an august lord losing his nation. The _Book of Ritual_ says:
_An august lord helps plow and plant to provide sacrificial grains. His wife helps spin silk to make sacrificial clothes. If the animals are not fat, the grains not clean, the garments not ready, he dare not perform the sacrifice._
_And if an official holds no land, he performs no sacrifice. If the sacrificial animals, ritual vessels, and sacrificial garments are not all ready, he dare not perform the sacrifice or offer a banquet._
Isn't that reason enough for condolences?"
"Why is it Confucius always carried his token of credentials with him when he left one nation for another?" asked Chou Hsiao.
"An official serving in office is like a farmer working the land. If a farmer left one nation for another, would he leave his plow behind?"
"People serve government here in Chin, too," said Chou Hsiao, "but I've never heard of such urgency. If taking office is such an urgent thing, why is it such a difficult question for the noble-minded?"
"When a son is born, parents hope he will one day have a home and family. When a daughter is born, they hope she will one day find a husband. Parents all feel this way. But if children don't wait for their parents' blessings or the arrangements of a matchmaker, if they drill holes in the wall to peer at each other or climb over it for secret meetings, their parents and everyone else think it's appalling.
"Worthy ancients all wanted to serve in office, but never if it meant violating the Way. To secure a position by violating the Way – is that any different from drilling a hole in a wall?"
4 P'eng Keng said: "Traveling around, preaching to august lords for your rice, scores of carriages and hundreds of followers trailed out behind you – isn't that awfully indulgent?"
"If what you do for someone violates the Way," replied Mencius, "accepting even a basketful of rice from them is too much. But abiding in the Way, Shun accepted all beneath Heaven from Yao and didn't think it indulgent. But perhaps you would call it indulgent?"
"No," replied P'eng Keng. "But still, it's shameful when a man doesn't work to earn his rice."
"If someone like you won't trade what you have for what you need, farmers will be left with useless grain and women with useless cloth. But if you will, carpenters and carriage-makers can earn their rice from you. Now here's a man who is a worthy child at home and humble when away, who learned the Way of ancient emperors, preserving it for future students – and you don't think he's even worth feeding. How can you honor carpenters and carriage-makers, but not a master of Humanity and Duty?"
"When carpenters and carriage-makers work, their motive is rice," replied P'eng Keng. "But when the noble-minded practice the Way – is their motive nothing more than rice?"
"Why are you talking about motives?" countered Mencius. "When someone works for you, he deserves to be fed and should be. And besides, do you feed people for their motives or their work?"
"For their motives."
"So if there's a man flinging mortar around and smashing tiles, and his motive is rice, do you feed him?"
"No."
"Then you don't feed people for their motives; you feed them for their work."
5 Wan Chang said: "Sung is a small nation. If its government became that of a true emperor and it were therefore invaded by Ch'i and Ch'u, what could be done?"
"When T'ang lived in Po," replied Mencius, "Po bordered on Ko, which had a ruler who was dissolute and neglected the sacrifices. When T'ang sent someone to ask why the sacrifices were being neglected, Ko's ruler said: _We don't have enough animals._ T'ang sent him cattle and sheep, but instead of using them for sacrifices, he used them for food.
"Again T'ang sent someone to ask why the sacrifices were being neglected, and the Ko ruler said: _We don't have enough millet._ So T'ang sent Po people to help plow and plant, he sent gifts of food for the old and young. But the Ko ruler ambushed them: he led his people out to steal their wine and food, millet and rice. Anyone who resisted was killed: even a boy bringing millet and meat was killed and his gifts stolen.
"The _Book of History_ speaks of this: _For the ruler of Ko, the bearers of gifts were enemies._ And when T'ang sent an army to avenge the murder of this boy, everyone within the four seas said: _It isn't lust for all beneath Heaven: it's revenge for the abuse of common men and women._
_"Emperor T'ang began his expeditions in Ko,_ says the _Book of History._ After eleven expeditions, he hadn't an enemy left anywhere in all beneath Heaven. When he marched east, the western tribes complained. And when he marched south, the northern tribes complained: _Why does he leave us for last?_ People watched for him the way they watched for rain in the midst of a great drought. When he came, they went to market unhindered again and weeded their fields without interference. He punished the rulers and comforted the people, like rain falling in its season. And so a great joy rose among the people. The _Book of History_ says: _We're waiting for our lord: his coming will end our suffering._
"It also says:
_When Yu refused to submit, Emperor Wu marched east and soothed its men and women. They filled baskets with azure-Heaven silk and yellow-earth silk. They went to Wu saying: 'Let us rest here before you. We will cleave to the state of Chou and serve it alone.'_
The noble-minded of Yu offered baskets of Heaven-and-earth silk to welcome the noble-minded of Chou. The peasants of Yu offered baskets of food and jars of wine to welcome the peasants of Chou. Emperor Wu rescued the people from fire and flood, seizing only their cruel rulers.
"In "The Great Declaration," Wu says:
_Let us brandish weapons and strength._
_Let us strike deep into their homelands,_
_and seizing the tyrants ruling there,_
_put them to death for everyone to see._
_Then our splendor will outshine T'ang's._
If Sung doesn't have the government of a true emperor, it could fall like that. But if it does have the government of a true emperor, everyone within the four seas will raise their heads and watch for him, wanting him for their sovereign. Then, even though Ch'i and Ch'u are large and powerful nations, what would he have to fear from them?"
6 Mencius said to Tai Pu-sheng: "You wish your emperor were noble and worthy? I'll try to explain this clearly. Suppose a high minister of Ch'u wanted his son to learn the language of Ch'i. Should he get someone from Ch'i to teach his son, or someone from Ch'u?"
"Someone from Ch'i."
"With only a single teacher from Ch'i and everyone else around the boy yammering in Ch'u, the father could cane him every day and he'd still never speak Ch'i. But if he took his son to some district in Ch'i for a few years, then he could cane the boy every day and he'd never speak Ch'u.
"Now, because you consider Hsüeh Chü-chou a noble and worthy man, you've appointed him to serve among the emperor's closest advisors. If among these advisors old and young, stately and humble, there were only men like Hsüeh Chü-chou – who could help the emperor commit ignoble acts? And if among these advisors old and young, stately and humble, there were none like Hsüeh Chü-chou – who would help him act nobly? One Hsüeh Chü-chou, alone – what can he do for the Sung emperor?"
7 Kung-sun Ch'ou asked: "Never trying to see august lords and advise them: is that a form of Duty?"
"In ancient times, if you didn't hold office you didn't see the sovereign," replied Mencius. "Tuan-kan Mu fled over a wall to avoid his sovereign, and Hsieh Liu bolted the door so his couldn't get in. But they were fanatics. When rulers show such determination, it's all right to see them.
"Yang Hu wanted to see Confucius, and yet wasn't willing to compromise Ritual propriety. But the custom is: if a scholar is not at home to receive a high minister's gift, he goes to the minister's gate and bows in thanks. So Yang Hu waited for Confucius to go out, then sent him a steamed piglet. Confucius likewise waited for Yang Hu to go out, then went to his house and bowed before the gate. If Yang Hu had simply asked to see him, how could Confucius have refused?
"Master Tseng said: _Shrugging shoulders and forcing smiles – it's more grueling than hot summer fieldwork._
"Adept Lu replied: _To say you agree when you don't, and pretend blushing keeps you honest – I can't understand that at all._
"From this it's easy to understand what the noble-minded cultivate in themselves."
8 Tai Ying-chih said: "To levy only a ten percent tax on income, to abolish all other taxes, including those at the borders and in the markets – that isn't something we can do this year. What if we reduce these taxes now, and give them up completely next year?"
"Suppose someone stole one of his neighbor's chickens every day," replied Mencius. "Suppose someone said to him _This is not the noble-minded Way,_ and he replied _What if I only steal one a month for now, and give it up completely next year?_
"If you recognize something is wrong, you want to see it end quickly. So how can you wait until next year?"
9 Adept Kung-tu said: "Everyone but your own disciples thinks you love to argue, Master. Is it true?"
"It isn't that I love to argue," replied Mencius. "I just can't see how to avoid it. All beneath Heaven has endured for ages and ages – sometimes in peace, sometimes in confusion. In the time of Emperor Yao, floods raged across the Middle Kingdom. Snakes and dragons filled the land, leaving nowhere for the people to settle. Lowland people built nests in the treetops; highland people camped in caves.
"The _Book of History_ says: _The flood was a warning to us._ And the flood was nothing less than a vast deluge, so Yao appointed Yü to bring the waters under control. Yü dug furrows in the land and sent the waters flowing into the sea. He drove the snakes and dragons into marshes. Where the water rushed toward the sea, it carved out rivers: the Yangtze and Huai, the Yellow and Han. Obstacles and dangers were rinsed away, and ravaging birds and animals disappeared. Only then could people level farmland and settle down.
"But once Yao and Shun died, the Way of sages began to unravel. One savage ruler followed another. They leveled houses to build their pleasure lakes, leaving the people without a place to rest. They let the fields go wild, turning them into parks and preserves, leaving the people without silk and rice. Twisty words and savage acts became official policy. And with the spread of parks and preserves, ponds and lakes, swarms of birds and animals soon returned. By the time of Tyrant Chou, all beneath Heaven was pure chaos. Duke Chou helped Emperor Wu put an end to Tyrant Chou. He conquered Yen after a three-year war and executed its ruler. He drove Fei Lien to the edge of the sea and there put him to death. He conquered fifty nations, drove away all the tigers and leopards, rhinos and elephants. And so, a great joy rose throughout all beneath Heaven. The _Book of History_ says:
_How vast the splendor of Emperor Wen's plans_
_and the glory of Emperor Wu fulfilling them:_
_preserving and inspiring us who come later,_
_they were perfectly true and without flaw._
"But after them, things began to unravel again, and the Way grew weak. Twisty words and savage acts again became official policy. There were ministers killing emperors, and sons killing fathers. Confucius was heartsick, so he wrote _The Spring and Autumn Annals._ It talks about issues the Son of Heaven faces, which is why Confucius said: _If people understand me, it's because of_ The Spring and Autumn Annals; _and if they condemn me, it's also because of_ The Spring and Autumn Annals.
"But there've been no sage emperors since then, only these august lords indulging themselves with such abandon. Pundits go around talking nonsense, filling all beneath Heaven with the claims of Yang Chu and Mo Tzu: if there's a doctrine that can't be traced back to Yang, it can surely be traced back to Mo. Yang's school preaches _everyone for themselves,_ and so denies the sovereign. Mo's school preaches _lovingeveryone equally,_ and so denies the father. No father and no sovereign – that's the realm of birds and animals.
"Kung-ming Yi said: _There's plenty of juicy meat in your kitchen and plenty of well-fed horses in your stable – but the people here look hungry, and in the countryside they're starving to death. You're feeding humans to animals._ Unless the Way of Yang and Mo withers and the Way of Confucius flourishes, twisty words will keep deluding the people and blocking the path of Humanity and Duty. When Humanity and Duty are blocked up, humans are fed to animals. And pretty soon humans will be feeding on humans. I'm heartsick over it all, and so guard the Way of ancient sages. If we resist Yang and Mo, driving their reckless ideas away, those pundits will stop spreading their twisty words. Born of the mind, such things cripple our endeavors, and then our endeavors cripple government. If ever great sages arise again, they won't question what I've said.
"In ancient times, Yü controlled the floodwaters and brought peace to all beneath Heaven. Duke Chou subjugated the wild tribes of the east and north, drove the fierce animals away, and brought peace of mind to the people. When Confucius finished _The Spring and Autumn Annals,_ rebellious ministers and thieving sons were filled with fear.
"The _Book of Songs_ says:
_fighting down the wild tribes_
_and punishing Ch'u and Shu._
_And so no one dares resist us._
No father and no sovereign – this is what Duke Chou fought against. And so, continuing the work of the three sages, I want to rectify people's minds and put an end to twisty words, resist dangerous conduct and drive reckless ideas away. It isn't that I love to argue. I just can't see how to avoid it, for only those who speak out against Yang and Mo are true followers of the sages."
10 K'uang Chang said: "Isn't Master Chung a man of utterly pure principles? A recluse in the wilds of Wu Ling, he once had nothing to eat for three days, which robbed him of hearing and sight. There was a plum tree standing beside his well, dung worms eating at its fruit. He crawled over to it and began eating too. He took three bites, and suddenly he could hear and see again."
"Surely Master Chung is the finest man in the nation of Ch'i," replied Mencius. "But still, how can he be called a man of pure principles? To master his discipline completely, you'd have to be an earthworm – eating leaf rot up above and drinking from the Yellow Springs of graveland down below.
"Was Chung's house built by the great recluse Po Yi or the great bandit Chih? And was his millet grown by Po Yi, or Chih the bandit? How could he know?"
"What difference does it make?" countered K'uang Chang. "He wove sandals with hemp spun by his wife, and they bartered them for the things they needed."
"Master Chung comes from an old and noble family of Ch'i," said Mencius. "His brother's lofty position earned him ten thousand measures of grain. But Chung thought his brother only earned that grain by ignoring Duty, so he refused to eat it. And he thought his brother only paid for his house by ignoring Duty, so he refused to stay in it. Instead, he lived in Wu Ling, far from his brother and mother.
"One day he returned home and found that his brother had been given a live goose by someone wanting favors. He frowned and said: _What good is this cackling creature to you?_ A few days later, his mother killed the goose and served it to Chung for dinner. Having been away, his brother returned just then and said: _Isn't this the meat of that cackling goose?_ Chung thereupon ran outside and threw it up.
"He never again ate his mother's food, but he ate his wife's. He never again lived in his brother's house, but he lived in his Wu Ling house. So did he perfect that way of life completely? Only an earthworm could master Chung's discipline completely."
VII
Li Lou Book One
1 Mencius said: "Even with the sharp eyes of Li Lou and the skill of Master Kung-shu, you need a compass and square to render circles and squares true. Even with the penetrating ear of Maestro K'uang, you need the six pitch-pipes to tune the five notes true. And even with the Way of emperors Yao and Shun mastered, you need Humane government to govern all beneath Heaven in justice.
"There may be rulers today renowned for their Humanity, but they're neither blessings to the people nor beacons to future generations, for they aren't furthering the Way of ancient emperors. Hence it is said:
_Virtue alone isn't enough for government,_
_and law cannot alone put itself into action._
And the _Songs_ say:
_Never transgress and never forget:_
_always abide in the ancient rules._
Has anyone ever erred by honoring the laws of ancient emperors?
"Having reached the limits of sight trying to render round and square, level and straight, the sage turns to compass and square. You can depend on them always. Having reached the limits of hearing trying to tune the five notes true, the sage turns to the six pitch-pipes. You can depend on them always. And having reached the limits of mind trying to let Humanity shelter all beneath Heaven, the sage turns to government that never oppresses the people. Hence it is said:
_If you want to go high, begin atop hills and mounds._
_If you want to go deep, begin among rivers and marshes._
So if you want to govern and don't begin with the Way of ancient emperors, how can you be called wise?
"That's why only the Humane are fit for high position: if the Inhumane hold high position, evil is sown among the people. When the Way isn't in a leader's thoughts, officials stop fostering the law. When the court doesn't trust the Way, workers don't trust principles. And when a ruler ignores Duty, the people ignore regulations. In such times, a nation survives on luck alone.
"Hence it is said:
_If city walls are unfinished and weapons scarce, it doesn't spell disaster for the nation. If people aren't plowing new fields or piling up wealth, it doesn't spell ruin for the nation. But if a leader ignores Ritual and officials ignore learning, the people turn to banditry and rebellion, and the nation crumbles in less than a day._
And the _Songs_ say:
_Heaven is dark with menace –_
_stop this idle drift and chatter._
_Idle drift and chatter_ means _chitchat doing nothing._ To ignore Duty in serving the ruler, to ignore Ritual in taking office and renouncing office, to deny the Way of ancient emperors in your speech – that is chitchat doing nothing.
"Hence it is said:
_To expect impossible achievements from a ruler – that is called honoring him. To open up his virtue and seal up his depravity – that is called revering him. But to excuse him as incapable of something – that is called plundering him."_
2 Mencius said: "The final perfection of circle and square is the compass and square. And the final perfection of human community is the sage. If you want to be a ruler, you must enact the Way of a ruler fully. If you want to be a minister, you must enact the Way of a minister fully. In either case, simply take Yao and Shun as your standard and you'll succeed. Unless a minister serves his sovereign the way Shun served Yao, he'll fail to revere his sovereign. And unless a ruler governs his people the way Yao governed his people, he'll do nothing more than plunder them.
"Confucius said:
_There are two Ways: Humanity and Inhumanity. It's that simple. If a ruler tyrannizes his people ruthlessly, he will be killed and his nation destroyed. If he's less than ruthless in his tyranny, his life will be in danger and his nation pared away. Such rulers are given names like The Dark and The Cruel. And such curses are never changed, not even by a hundred generations of the most devoted sons and caring grandsons._
"This is what the _Songs_ are talking about when they say:
_A warning to the Shang isn't far off:_
_it's the last Hsia tyrant's overthrow."_
3 Mencius said: "When the Three Dynasties practiced Humanity, they possessed all beneath Heaven. When they practiced Inhumanity, they lost all beneath Heaven. And when the nations of our time rise and fall, persist and perish – it's no different.
"When the Son of Heaven practices Inhumanity, he cannot preserve all within the four seas. When the august lords practice Inhumanity, they cannot preserve the gods of soil and grain. When high counselors and ministers practice Inhumanity, they cannot preserve the ancestral temples. When officials and common people practice Inhumanity, they cannot preserve their own four limbs.
"To dread death and yet love Inhumanity – that is like dreading drunkenness and yet insisting on wine."
4 Mencius said: "If you try to love people but they keep distant, turn back to your Humanity. If you try to govern people but they resist, turn back to your wisdom. If you try to honor people but they don't reciprocate, turn back to your reverence.
"When you attempt something and fail, always turn back to yourself for the reason. Rectify yourself, and all beneath Heaven will return home to you. The _Songs_ say:
_Always worthy of Heaven's Mandate,_
_he found great prosperity in himself."_
5 Mencius said: "There is a saying the people keep repeating:
_All beneath Heaven: nation: family._
All beneath Heaven is rooted in nation. Nation is rooted in family. And family is rooted in self."
6 Mencius said: "To govern isn't difficult: Just don't offend the great families. Whoever the great families admire, the nation will admire. Whoever the nation admires, all beneath Heaven will admire. And so your Integrity and teaching will flood all within the four seas."
7 Mencius said: "When all beneath Heaven abides in the Way, small Integrity serves great Integrity, and small wisdom serves great wisdom. When all beneath Heaven ignores the Way, small serves large, and weak serves strong. Either way, Heaven issues it forth – and those who abide by Heaven endure, while those who defy Heaven perish.
"Duke Ching of Ch'i said: _We cannot give commands and we refuse to accept them – that is to be cut off from others and doomed._ And so in tears he gave his daughter to Wu as a bride.
"Now, even though small countries take large countries as their teachers in ruthlessness, they're too proud to submit to them. This is like disciples refusing to submit to their teachers. If you're proud, there's nothing like taking Emperor Wen as your teacher. Whoever takes Wen as his teacher will soon govern all beneath Heaven: if he begins with a large country, it will take only five years; and if he begins with a small country, it will take only seven.
"The _Songs_ say:
_The sons and grandsons of Shang_
_numbered over a hundred thousand._
_But the Celestial Lord mandated it,_
_so they succumbed to Emperor Wen,_
_to Emperor Wen they succumbed._
_Heaven's mandate is not forever:_
_Shang officials sure and bright_
_now pour libations in our temples._
And of this, Confucius said:
_There's no outnumbering Humanity. If the ruler of a nation loves Humanity, no enemy in all beneath Heaven can stand against him._
Now, even though they want no enemy in all beneath Heaven to stand against them, rulers refuse to practice Humanity. This is like clutching hot metal without dousing it in water.
_And who can clutch hot metal_
_without dousing it in water?_
say the _Songs_."
8 Mencius said: "You can't talk sense to the Inhumane. They find repose in risk, profit in disaster, and joy in what will destroy them. If you could talk sense to them, would there be ruined countries and ravaged houses?
"A child once sang:
_When the Ts'ang-lang flows clear_
_I rinse my hat strings clean._
_When the Ts'ang-lang flows muddy_
_I rinse my feet clean._
And of this, Confucius said:
_Listen well, my little ones. When clear it rinses hat strings clean, and when muddy it rinses feet clean. The choice is its own._
And so, only after a person has demeaned himself will others demean him. Only after a great family has destroyed itself will others destroy it. And only after a country has torn itself down will others tear it down. The "T'ai Chia" says:
_Ruin from Heaven_
_we can weather._
_Ruin from ourselves_
_we never survive._
That says it exactly."
9 Mencius said: "The tyrants Chieh and Chou lost the people – that's why they lost all beneath Heaven. And it was in losing the people's hearts that they lost the people.
"The way to win over all beneath Heaven is to win over the people. The way to win over the people is to win over the people's hearts. And the way to win over the people's hearts is to surround them with what they want and keep them clear of what they hate.
"The people return to Humanity like water flowing downhill or animals heading into the wilds. Driving fish into them, otters serve deep waters; driving sparrows into them, kestrels serve thickets. And driving the people to them, the tyrants Chieh and Chou likewise served T'ang and Wu. If there were today a single ruler in all beneath Heaven who loved Humanity, the august lords would all serve him by driving the people to him. He may not want to be emperor, but how could he avoid it?
"Those who want to be emperor are like people who start searching for three-year-old moxa, hoping to cure a seven-year-old illness. If they haven't stored it away in advance, they'll have to suffer without it. It's like that with Humanity – if you haven't devoted yourself to it, you'll be hounded by worry and shame until you're finally caught in death's snare. The _Songs_ say:
_You'll never save this world,_
_just sink into ruin together._
That says it exactly."
10 Mencius said: "You can't talk sense to the reckless, and you can't help the suicidal. To refuse Ritual and Duty when you speak – that is called reckless. To believe you cannot dwell in Humanity or abide in Duty – that is called suicidal. Humanity is our tranquil home, and Duty our sure path. And how could anyone leave a tranquil home empty or a sure path untraveled?"
11 Mencius said: "The Way is close at hand but sought far off. Essentials are easy but sought in the difficult.
"If people all treated family as family and elders as elders, all beneath Heaven would be at peace."
12 Mencius said: "If a common official cannot inspire a sovereign's trust, he'll never win over the people and govern them. But there's a Way to inspire a sovereign's trust. If you can't inspire trust in your friends, you'll never inspire trust in your sovereign. But there's a Way to inspire trust in your friends. If in serving your family you can't bring them joy, you'll never inspire trust in your friends. There's a Way to bring joy to your family. If you look within and find you aren't faithful to yourself, you'll never please your family. But there's a Way to be faithful to yourself. If you cannot render benevolence clear in the world, you'll never be faithful to yourself.
"Hence, the Way of Heaven is in faithful things, and the Way of humankind is in faithful thought. If you're faithful to yourself, you cannot fail to inspire others. And if you aren't faithful to yourself, you'll never inspire others."
13 Mencius said: "Po Yi fled the tyrant Chou and settled on the shores of the North Sea. On hearing that Emperor Wen had come to power, he said _I hear Wen takes good care of the old, so why not go backand serve him?_ Duke T'ai fled the tyrant Chou and settled on the shores of the West Sea. On hearing that Emperor Wen had come to power, he said _I hear Wen takes good care of the old, so why not go back and serve him?_
"These two were the grandest old men in all beneath Heaven. When they returned to him, they were the fathers of all beneath Heaven returning. And when the fathers of all beneath Heaven return to him, where else would the children go? Now if one of our august lords governed the way Emperor Wen did, it wouldn't even be seven years before he governed all beneath Heaven."
14 Mencius said: "When Jan Ch'iu was governor for the Chi family, he wasn't able to raise their Integrity the least bit. Meanwhile, he managed to double the tax people had to pay. So Confucius said: _He's no follower of mine. If you sounded the drums and attacked him, my little ones, it wouldn't be such a bad thing._
"It's clear from this that Confucius deplored anyone enriching a ruler who didn't practice Humane government. And he deplored even more those who waged war for such a ruler. In wars for land, the dead crowd the countryside. In wars for cities, the dead fill the cities. This is called helping the land feed on human flesh. Death is not punishment enough for such acts.
"Hence, those who excel at war should receive the highest punishment. Next come those who form the august lords into alliances. And finally those who open up wild land hoping to increase profits."
15 Mencius said: "Nothing reflects the person so well as the eyes. The eyes won't hide the evil in a person. If a person's heart is noble, their eyes are bright and clear. If it is not, their eyes are dark and cloudy. To hear a person's words, look into their eyes – then they can hide nothing."
16 Mencius said: "The dignified never demean others. The thrifty never rob others. A ruler who demeans and robs others can only worry that the people might turn on him – so how can he be dignified or thrifty? Sweet words and smiling faces – how can that make them dignified or thrifty?"
17 Ch'un-yü K'un said: "When men and women give and receive, is it a violation of Ritual for them to touch?"
"It is," replied Mencius.
"If your sister-in-law was drowning, would you reach out your hand to rescue her?"
"If a sister-in-law was drowning, it would be vicious not to rescue her. When men and women give and receive, it's a violation of Ritual for them to touch. But reaching out your hand to rescue a drowning sister-in-law – it's the only choice you have."
"All beneath Heaven is drowning," continued Ch'un-yü K'un. "Why don't you reach out and rescue it?"
"To rescue all beneath Heaven from drowning, you need the Way. To rescue a sister-in-law, you need only a hand. Do you think a hand is enough to rescue all beneath Heaven?"
18 Kung-sun Ch'ou said: "Why is it the noble-minded never teach their own children?"
"The way people are, it's impossible," replied Mencius. "A teacher's task is to perfect the student, and if the student doesn't improve, the teacher gets angry. When the teacher gets angry, the student in turn feels hurt: _You demand perfection, but you're nowhere near perfect yourself._ So father and son would only hurt each other. And it's a tragedy when fathers and sons hurt each other.
"The ancients taught each other's children. That way father and son never demand perfect virtue of one another. If they demand perfect virtue of one another, they grow distant. And nothing is more ominous than fathers and sons grown distant from one another."
19 Mencius said: "Isn't family the most important thing to serve? And isn't character the most important thing to preserve? I've heard of refusing to squander your character in order to serve your family. But I've never heard of squandering your character in order to serve your family.
"There's no end to what we should serve, but serving family is the basis of all service. And there's no end to what we should preserve, but preserving character is the basis of all preservation.
"When Master Tseng was caring for his father, he always served wine and meat. When he cleared the table, he always asked who the food should be given to. And when his father asked if there were leftovers, he always said there were. His father died, and eventually Master Tseng was cared for by his son, Tseng Yüan. Tseng Yüan also served wine and meat, but when he cleared the table he never asked who the food should be given to. And when his father asked if there were leftovers, he always said there were none so that he could serve the food again. This is called caring for mouth and body alone. But Master Tseng's way is called caring for the essence. In serving family, Master Tseng should be your model."
20 Mencius said: "Admonitions aren't enough for them, and accusations aren't enough for their government. It takes a great man indeed to rectify the depravity in a sovereign's heart.
"When the sovereign is Humane, everyone is Humane. When the sovereign is Dutiful, everyone is Dutiful. And when the sovereign is principled, everyone is principled. Give it a principled sovereign and the nation is secure."
21 Mencius said: "There is the praise of those who demand little, and the derision of those who demand everything."
22 Mencius said: "Talk is easy when you don't have to get the job done."
23 Mencius said: "The trouble with people is that they fancy themselves great teachers."
24 Adept Yüeh-cheng went with Governor Wang Huan to Ch'i, and there he went to visit Mencius.
"So you've come to see me too?" wondered Mencius.
"Why do you ask that, Master?" replied Yüeh-cheng.
"How long have you been here?"
"I arrived yesterday."
"So is it surprising that I ask such a question?"
"But I haven't even found a place to stay yet."
"Is that what you've been taught – that you only visit your elders after finding a place to stay?"
"Yes, it was wrong of me," admitted Yüeh-cheng.
25 Mencius said to Adept Yüeh-cheng: "You've come with Wang Huan just to savor a little food and wine. All your studies of the ancient Way, and for what? A little food and wine?"
26 Mencius said: "There are three ways you can fail to honor your parents, and the worst is to have no heir. Shun married without telling his parents because he was afraid that he might have no heir. For the noble-minded, this is no different than telling them."
27 Mencius said: "The substance of Humanity is nothing other than serving your family, and the substance of Duty nothing other than obeying your elders. The substance of wisdom is to understand these two things and cleave to them always. The substance of Ritual is to shape and embellish these two things. And the substance of music is to infuse these two things with joy. Once joy wells up, how can it be stopped? And if joy can't be stopped, hands and feet soon strike up a dance of their own."
28 Mencius said: "Imagine all beneath Heaven turning to you with great delight. Now imagine seeing that happen and knowing it means nothing more than a wisp of straw: only Shun was capable of that.
"He knew that if you don't realize your parents you aren't a person, and that if you don't lead your parents to share your wisdom you aren't a child. He fulfilled the Way of serving parents completely until Blind Purblind, his depraved father, finally rejoiced in virtue. Once his father rejoiced in virtue, all beneath Heaven was transformed. Once his father rejoiced in virtue, the model for fathers and sons was set for all beneath Heaven. Such is the greatness of honoring parents."
VIII
Li Lou Book Two
1 Mencius said: "Emperor Shun was a barbarian from the east: he was born in Chu Feng, moved to Fu Hsia, and finally died in Ming T'iao. Emperor Wen was a barbarian from the west: he was born in Ch'i Chou and died in Pi Ying. They lived more than a thousand miles and a thousand years apart – but putting their principles into practice throughout the Middle Kingdom, they were like the matching halves of a jade seal. The first was a sage, and the second was a sage: their thoughts were identical."
2 Even though he was prime minister in Cheng, Lord Ch'an ferried people across the Chen and Wei himself.
"He was certainly kind," said Mencius, "but he didn't know how to govern. If he'd built footbridges every year in the tenth month and cart bridges every year in the eleventh month, the people could have avoided the ordeal of fording rivers. In governing, the noble-minded clear their way of people. How can they help people across rivers one by one? It's impossible to govern by making people happy one at a time: there aren't enough hours in the day."
3 Mencius said to Emperor Hsüan of Ch'i: "If a sovereign treats the people like his hands and feet, they'll treat him like their stomach and heart. If a sovereign treats the people like his dogs and horses, they'll treat him like a commoner. If a sovereign treats the people like weeds and dirt, they'll treat him like an enemy bandit."
"According to Ritual," said the emperor, "ministers wear mourning clothes when they leave the service of a sovereign. What must an emperor do so that his officials feel that way?"
"Act on their admonitions and listen to their words," replied Mencius, "so blessings rain down on the people. When a minister must travel, send people to escort him across the border and send emissaries ahead wherever he goes to prepare the way. Then give him three years to return before you seize his house and fields. These are called the three Ritual courtesies. If you follow them, your ministers will wear mourning clothes when they leave your service.
"These days a sovereign never acts on a minister's admonitions or listens to his words, and so blessings don't rain down on the people. If a minister must travel, the sovereign arrests him or makes things difficult for him wherever he goes. And the day the minister leaves, the sovereign takes back his house and fields. This is called being an enemy bandit. And why would anyone wear mourning clothes when leaving an enemy bandit?"
4 Mencius said: "When scholars are put to death for no reason, high ministers should resign their office and leave. When the people are slaughtered for no reason, scholars should resign their office and move away."
5 Mencius said: "When the sovereign is Humane, everyone is Humane. When the sovereign is Dutiful, everyone is Dutiful."
6 Mencius said: "Ritual empty of Ritual, Duty empty of Duty – great people never practice such things."
7 Mencius said: "Let the realized nurture the unrealized and the talented nurture the untalented, then people will rejoice in having worthy fathers and elders. If the realized abandon the unrealized and the talented abandon the untalented, there won't be the least difference between the worthy and the debased."
8 Mencius said: "Once there are things you refuse to do, you have things to do."
9 Mencius said: "When you speak of the virtues another lacks, think of the trials you may yet endure."
10 Mencius said: "Confucius was not a man of extremes."
11 Mencius said: "Great people's words need not be sincere, nor their actions fruitful. They need only abide in Duty."
12 Mencius said: "Great people never lose their child's heart."
13 Mencius said: "To nurture the living is not such a great thing. But to nurture them dead and gone – that is a great thing."
14 Mencius said: "To fathom great depths, the noble-minded realize themselves in the Way. Once they realize themselves in the Way, they dwell at ease in it. Once they dwell at ease in it, they trust themselves to it deeply. And once they trust themselves to it deeply, they find its origins all around them. This is why the noble-minded realize themselves in the Way."
15 Mencius said: "Make your learning abundant and speak of it with precision, then you will speak of essentials."
16 Mencius said: "If you use virtue to subdue others, you'll never subdue anyone. But if you use virtue to nurture others, you'll soon nurture all beneath Heaven. No one is emperor over all beneath Heaven unless it submits with subdued heart."
17 Mencius said: "Words that defy reality are ominous. And it's ominous reality that confronts those who would obscure the wise and worthy."
18 Master Hsü said: "Confucius often praised water, chanting _O water! O water!_ Why was it water that he praised?"
"Springs well up into streams," replied Mencius, "and cascade steadily down night and day, filling every hollow before flowing on to the four seas. Those rooted in a source are like this. That's why Confucius praised water.
"Those not rooted in a source are like water gathering during the autumn rains: ditches and gutters are quickly flooded, but they're always dry again in no time. So it is that renown beyond what they deserve makes the noble-minded uneasy."
19 Mencius said: "The difference between people and animals is slight indeed. Most people blur that difference: it's the noble-minded that preserve it.
"Shun understood the commonplace and looked deeply into human community. He never put Humanity and Duty into action, for Humanity and Duty were always there in his actions."
20 Mencius said: "Yü hated fine wine but loved good advice. T'ang kept to the middle way and didn't need rules when appointing worthy officials. Emperor Wen cared for the people as if they were invalids and gazed toward the Way as if he'd never seen it. Emperor Wu never slighted intimates and never forgot those far away.
"Duke Chou hoped to combine the methods of these dynastic founders in his rule. When he encountered some difficulty or contradiction, he turned to them and sat through the night deep in thought. If he was lucky enough to resolve the question, he would sit and await the dawn."
21 Mencius said: "When all trace of the sage emperors had vanished, the _Songs_ were no longer gathered from the people. After they stopped gathering the _Songs,_ the _Spring and Autumn_ was written.
"Such chronicles are all the same: for Chin the _Annals,_ for Ch'u the _Wooden Tiger_ and for Lu there is the _Spring and Autumn Annals._ It tells of such figures as Duke Huan of Ch'i and Duke Wen of Chin, and it's written in the historical style. Of it, Confucius said: _I've stolen all its lofty principles."_
22 Mencius said: "The influence of someone noble-minded lasts five generations, and the influence of someone small-minded also lasts five generations. I was never a disciple of Confucius: I'm schooled in the clarity he passed on to others."
23 Mencius said: "When you can choose to take or not take, taking offends humility. When you can choose to give or not give, giving offends generosity. When you can choose to die or not die, dying offends courage."
24 P'eng Meng studied archery under Yi. Once he had mastered Yi's Way, he thought Yi was the only archer in all beneath Heaven better than he. So he killed Yi.
"Yi was himself to blame for this," commented Mencius. "Kung-ming Yi said that Yi seemed blameless, but meant only that his blame was slight. How could he be completely blameless?
"Cheng once sent Master Cho Ju to invade Wei, and Wei sent Yü-kung Szu in pursuit. Master Cho Ju said: _I'm too sick: I can't pick up my bow. Today I'll die._ Then he asked his driver: _Who's coming in pursuit?_
_"Yü-kung Szu,_ replied the driver.
_"Then today I'll live._
_"But Yü-kung Szu is Wei's finest archer. Why do you say you'll live?_ asked the driver.
_"Yü-kung Szu studied archery under Yin-kung T'o,_ replied Master Cho Ju, _and Yin-kung T'o studied under me. Yin-kung T'o is a man of great dignity, and so only chooses friends of great dignity._
"Yü-kung Szu arrived and said _Why isn't your bow at the ready, Master?_
_"I'm too sick: I can't pick up my bow._
_"I studied archery under Yin-kung T'o, and Yin-kung T'o studied under you. How could I turn your own Way against you, Master? Still, I am here on my sovereign's business and dare not forsake it._
"Drawing four arrows, he struck them against the wheel of his chariot, breaking off their tips, then shot them into the air. Whereupon he turned and left."
25 Mencius said: "If the beautiful Lady Hsi wore filthy clothes, people would have held their noses and hurried past her. So it is that a man deformed by his depravity can fast and bathe himself so pure he's fit to perform sacrifices to the Celestial Lord."
26 Mencius said: "It's simple: To say anything about the nature of things, you must attend to the facts, facts in their original form. The trouble with knowledge is that it keeps chiseling things away. If intellectuals were like Yü draining floodwater into the sea, there'd be nothing wrong with knowing. Yü succeeded by letting water have its way, and if intellectuals just let things have their way, knowing would be great indeed.
"Heaven is high and the stars distant – but if you attend to the facts, you can calculate solstice for a thousand years without ever leaving your seat."
27 Lord Kung-hang's son had died. When Wang Huan arrived to offer his condolences, people hurried over to speak with him. And when he took his place as Counselor on the Right, others hurried over to speak with him. Seeing that Mencius made no attempt to speak with him, Wang Huan felt insulted and said: "Everyone here has had some words for me. Only Mencius has failed to do me that courtesy."
When Mencius heard about this, he said: "According to Ritual, you don't leave your position at court to speak with others, and you don't break ranks to bow to others. I was only observing Ritual. Isn't it strange Wang would consider that an insult?"
28 Mencius said: "What makes the noble-minded different is that they keep their hearts whole. And to do that, they depend on Humanity and Ritual. Those who practice Humanity love people, and those who observe Ritual honor people. If you love people that way, people will always love you faithfully. And if you honor people that way, people will always honor you faithfully.
"Now suppose someone is treating me poorly. If I'm noble-minded I'll turn to myself, thinking _I must be neglecting Humanity. I must be ignoring Ritual. Otherwise, how could such a thing happen?_ If I turn to myself and find that I am acting Humane and observing Ritual, but the poor treatment continues, I turn to myself again, thinking _I must be lacking in devotion._ If I turn to myself and find that I am indeed devoted, but the poor treatment still continues, I say: _This person is savage, absolutely savage: no different from an animal! Why should I keep troubling myself over such a creature?_
"This is how the noble-minded worry their whole lives through, and so never know unexpected disaster. They may have worries, but only worries like this: _Shun was a person, and I too am a person. Shun was an exemplar for all beneath Heaven, worthy to guide future generations, but I'm still nothing more than a common villager._ And that's a worthwhile worry, for what can you do about such worries? It's simple: be like Shun.
"The noble-minded never know disaster. If it isn't Humane, they don't do it. If it isn't according to Ritual, they don't do it. Therefore, an unexpected disaster is no disaster for the noble-minded."
29 In times of sage rule, Yü and Hou Chi passed by their own gates three times without entering. Confucius called them wise and worthy. In evil times, Yen Hui lived in a meager lane with nothing but some rice in a split-bamboo bowl and some water in a gourd cup. No one else could bear such misery. But it didn't even bother Hui. His joy never wavered. Confucius also called him wise and worthy.
Mencius said: "Yü, Hou Chi, Yen Hui – they all practiced the same Way. If anyone in all beneath Heaven drowned, Yü felt as if he himself had drowned them. If anyone in all beneath Heaven starved, Hou Chi felt as if he himself had starved them. And so they worked with fierce devotion. If the three of them had traded places, they would each have done as the other did.
"These days, if someone in your house gets in a fight, it's fine to rush out and rescue them with your hair hanging loose and your cap untied. But if it's someone from your village that's fighting, then it's wrong. In fact, it's perfectly fine if you just bolt your door and ignore it."
30 Adept Kung-tu said: "People all through the country talk about how poor a son K'uang Chang was. But you not only befriend him, Master, you treat him with gracious respect. How can that be?"
"It's common now for people to say there are five ways to be unfilial," replied Mencius. "Neglecting the care of parents because you're lazy – that is the first. Neglecting the care of parents because you love wine and _go_ – that is the second. Neglecting the care of parents because you love wealth and adore wife and children – that is the third. Disgracing parents because you can't resist beautiful sights and sounds – that is the fourth. Endangering parents because you love valor and conflict – that is the fifth. Does Chang do any of these things?
"Chang and his father had a falling out because they tried to reform each other. Between friends, reform is fine. But between fathers and sons, it's a great destroyer of love. Don't you think Chang longed for the affections of husband and wife, child and mother? Once his father was offended, he wouldn't let Chang come near him. That's why Chang sent his wife away, banished his children, and lived his whole life without their loving care. He was convinced that his offense would be even greater if he didn't do that. That's the kind of man K'uang Chang is."
31 Master Tseng was living in Wu Ch'eng when some bandits from Yüeh invaded. Someone cried out: "Bandits are coming! Run!"
"Don't let anyone stay in my house or harm the gardens," Tseng commanded his housekeeper. Then, when the bandits left, he sent word: "Get the house ready. I'll be back soon."
Once the bandits had left and Tseng returned, his disciples said: "The Master has been treated with such sincerity and honor here. But when the bandits came, he ran first for all the people to see, and then returned only after the bandits had left. Doesn't that seem wrong?"
"Understanding such things is beyond you," said Shen-yu Hsing. "I once had trouble with people stealing hay, but it didn't involve any of the master's seventy followers."
Master Szu was living in Wei when some bandits from Ch'i invaded. Someone cried out: "Bandits are coming! Run!"
"If I run," replied Master Szu, "who'll help our sovereign defend the country?"
Of these things, Mencius said: "Master Tseng and Master Szu – they both practiced the same Way. Master Tseng was a teacher and elder; Master Szu was a common citizen of no importance. If the two of them had traded places, they would each have done as the other did."
32 Lord Ch'u said: "The emperor sent spies to see if you're really different from other people."
"How would I be different from other people?" exclaimed Mencius. "Even Yao and Shun were just like everyone else."
33 There was a man in Ch'i who lived with his wife and mistress. When he went out, he always came home stuffed with wine and meat. One day his wife asked who his companions were, and he told her they were all men of wealth and renown. So she said to the mistress: "When he goes out, he always comes home stuffed with wine and meat. I ask who his companions are, and he says they're all men of wealth and renown. But we've never had such illustrious guests here in our house. I'm going to follow him and see where he goes."
She rose early the next morning and followed him everywhere he went. But no one in all the city even stopped to talk with him. Finally he went out to the graveyard east of the city, and there begged leftovers from someone performing sacrifices. He didn't get enough, so he went to beg from someone at another grave. That's how he stuffed himself full.
The wife returned home and told the mistress what she'd seen, then said: "A woman looks to her husband for direction and hope throughout life, and _this_ is what ours is like." Together they railed against their husband and wept in the courtyard. Later, knowing nothing of this, the husband came swaggering in to impress his women.
In the eyes of the noble-minded, when a man chases after wealth and renown, profit and position, it is rare that his women aren't disgraced and driven to tears.
IX
Wan Chang Book One
1 Wan Chang said: "When he was working the fields, Shun wept and cried out to the vast Heavens. Why did he weep and cry out?"
"He was full of resentment and longing," replied Mencius.
"If your parents love you, you rejoice and never forget them," said Wan Chang. "If your parents hate you, you suffer but never resent them. So what is it Shun resented so?"
Mencius said: _"Now I understand Shun working the fields. But weeping and crying out to his parents and the vast Heavens – that I don't understand._ When Ch'ang Hsi said this to Kung-ming Kao, Kung-ming Kao replied: _Understanding such things is beyond you._ So he certainly didn't believe a worthy child could be indifferent enough to think _I work hard plowing the fields. That's all parents can demand of a child. If they don't love me, how could it be my fault?_
"To help Shun in the fields, Yao sent his nine sons and two daughters, his hundred officials, cattle, sheep, provisions in plenty. Officials throughout all beneath Heaven turned to him. Yao was about to give all beneath Heaven over to his care. But not being in accord with his parents, Shun was like a man so poor he had no home to return to.
"Everyone wants to have officials throughout all beneath Heaven rejoice in them, but that wasn't enough to ease his worry. Everyone wants beautiful women, but even Yao's two daughters weren't enough to ease his worry. Everyone wants wealth, but even the wealth of all beneath Heaven wasn't enough to ease his worry. Everyone wants renown, but even the renown of being the Son of Heaven wasn't enough to ease his worry. People rejoicing in him, beautiful women, wealth, renown – all that wasn't enough to ease his worry. Being in accord with his parents – that was the one thing that could ease his worry.
"When we're young we long for our parents. When we begin thinking of beautiful women, we long for the young and beautiful. When we have a wife and family, we long for wife and family. When we're ready to serve, we long for a sovereign and burn with anxiety if we don't find one. Longing for your parents throughout life – that is the mark of a great child. To see a man who still longed for his parents at the age of fifty, I look to Shun."
2 Wan Chang said: "The _Songs_ say:
_How do you go about marrying a wife?_
_You first inform your parents._
No one should be a better example of this than Shun. How is it he married without first informing his parents?"
"If he'd told them, he wouldn't have married," replied Mencius. "A man and woman living together is a great bond of humankind. If he'd told his parents, he would have forsaken that great bond, and that would have been an act of hatred toward his parents. That's why he didn't tell them."
"Now I understand why Shun didn't tell his parents," said Wan Chang, "but how could Yao marry his two daughters to Shun without telling Shun's parents?"
"Yao also understood that if he told them there would be no marriage," replied Mencius.
"Shun's parents sent him to repair the granary," said Wan Chang, "then they pulled down the ladder and his depraved father set the granary on fire. They sent him to dredge the well, then followed him and sealed him in. His brother Hsiang said: _I'm the one who thought of a way to deal with my brother, the city-building sovereign. You can have his granaries, my parents, and his cattle and sheep. But his shield and spear are mine. His_ ch'in _and bow, are mine. And his two wives – they'll offer their comforts in my home now._
"Later Hsiang went to Shun's house and found him there, sitting on his bed playing the _ch'in._ Blushing, he said: _I was worried and thinking of you, that's all._
_"And I am thinking of my people,_ replied Shun. _Help me govern them._
"I wonder: didn't Shun realize that Hsiang was trying to kill him?"
"How could he not know?" responded Mencius. "But he was worried when Hsiang was worried, and pleased when Hsiang was pleased."
"So Shun was only pretending to be pleased?" asked Wan Chang.
"No," replied Mencius. "Someone gave a live fish to Lord Ch'an of Cheng. Lord Ch'an told his pond-keeper to put the fish in a pond and take care of it. The pond-keeper cooked the fish, then reported to Ch'an: _When I first let it go, it seemed confused by all that water. Before long it was savoring the vastness. And finally it disappeared into the distance._
_"It's in its element! It's in its element!_ exclaimed Ch'an.
"The pond-keeper left and said: _How can Lord Ch'an be called wise? I cooked his fish and ate it too, and he just says: 'It's in its element! It's in its element!'_
"So, to deceive the noble-minded, you must abide by their principles. It's impossible to trap them unless you use their own Way. Hsiang came in the same loving Way that Shun would have come, so Shun was truly pleased. Is that pretending?"
3 Wan Chang said: "Hsiang spent his days trying to kill Shun. So when Shun became the Son of Heaven, why did he only banish him?"
"He gave Hsiang a noble title and land," replied Mencius. "Some called it banishment."
"Shun sent Kung Kung to Yu Chou and banished Huan Tou to Ch'ung Mountain, executed San Miao at San Wei and imprisoned Kun at Yü Mountain," said Wan Chang, "and all beneath Heaven assented, knowing he was rooting out the Inhumane. Hsiang was brutally Inhumane, and yet Shun gave him a title and the lands of Yu Pi. What had the people of Yu Pi done to deserve that? How could a Humane man do such a thing: punishing innocent people so he could give his brother a noble title and land?"
"A Humane man never harbors anger or resentment toward a brother," replied Mencius. "He cherishes and loves him, that's all. Cherishing him, he wants him to enjoy renown; and loving him, he wants him to enjoy wealth. By giving Hsiang a title and the lands of Yu Pi, Shun let him enjoy wealth and renown. To be the Son of Heaven and let your brother live as a mere commoner – how could anyone call that cherishing and loving?"
"What did you mean when you said _Some called it banishment_?" asked Wan Chang.
"Hsiang had no power in his territory," said Mencius. "The Son of Heaven appointed others to govern and collect taxes there. That's why people called it banishment. Do you think Shun would allow him to abuse the people there? Shun still wanted to see him often, so he came to visit often. That's what is meant by:
_He didn't wait for times of tribute:_
_he welcomed him as the Lord of Yu Pi."_
4 Hsien-chiu Meng said: "There is a saying:
_Once rich in Integrity,_
_you're subject to no sovereign_
_and you're son to no father._
Shun stood facing south at court. Yao, leading the august lords, faced north and paid him homage. Blind Purblind, Shun's depraved father, also faced north in homage. When Shun saw his father there, a troubled look came over his face. Confucius said: _At that moment, all beneath Heaven was in such danger, such utter peril!_ I wonder about that – was it really true?"
"No," replied Mencius. "Those are not the words of a noble-minded man. They're the words of a villager from eastern Ch'i. When Yao grew old, Shun helped him govern. The _Record of Yao_ says:
_After twenty-eight years, Yao passed away. The people mourned three years as if they'd lost their mother and father. And no music was heard anywhere within the four seas._
And Confucius said: _The Heavens have not two suns, and the people have not two emperors._ If Shun had become the Son of Heaven and led the august lords of all beneath Heaven in their three years of mourning, there would have been two Sons of Heaven."
"Now I understand that Yao was never Shun's subject," said Hsien-chiu Meng. "But the _Songs_ say:
_Throughout all beneath Heaven_
_everything is the emperor's land,_
_and to the borders of this land_
_everyone is the emperor's subject._
And yet, after Shun became the Son of Heaven, how is it Blind Purblind wasn't his subject?"
"That isn't what this song is about. It's about people who neglect their parents because they're devoted to the concerns of an emperor's government, people who say: _Everything here is the emperor's concern, and am I alone capable of it?_
"Therefore, in speaking of a song, never let eloquence obscure words, and never let words obscure intent. Instead, let your thoughts inhabit the intention, then you'll understand. In the _Songs,_ "The Star River" says:
_Of those who survived in Chou,_
_there won't be half a person left._
If you just look at the words and trust what they say, there wasn't a single person left among all the people of Chou.
"For a worthy child, there's nothing greater than honoring parents; and for honoring parents, there's nothing greater than nurturing them with all beneath Heaven. To be the Son of Heaven's father – that is an honor indeed. And to nurture him with all beneath Heaven – that is nurturing indeed. That's what the _Songs_ mean when they say:
_Devoted always to his parents' care,_
_great exemplar of the devoted child_
And _The Book of History_ says:
_He went to see Blind Purblind full of respect, veneration, and_
_awe. And Blind Purblind finally understood._
That is to be _son to no father."_
5 Wan Chang said: "Is it true that Yao gave all beneath Heaven to Shun?"
"No," replied Mencius. "The Son of Heaven cannot give all beneath Heaven to another."
"Then who gave all beneath Heaven to Shun?"
"Heaven gave it to him."
"If Heaven gave it to him, did it also school him in the details of its mandate?"
"No. Heaven never speaks: it reveals itself only through actions and events."
"How does it reveal itself through actions and events?"
"The Son of Heaven can recommend someone to Heaven," replied Mencius, "but cannot compel Heaven to give all beneath Heaven over to that person. The august lords can recommend someone to the Son of Heaven, but cannot compel him to give that person a title. Ministers can recommend someone to an august lord, but cannot compel him to appoint that person a minister. In ancient times Yao recommended Shun to Heaven, and Heaven accepted him. Yao presented Shun to the people, and the people accepted him. That's why I say Heaven never speaks: it reveals itself only through actions and events."
"Yao recommended Shun to Heaven, and Heaven accepted him," repeated Wan Chang. "And Yao presented Shun to the people, and the people accepted him. But how did all this take place?"
"When he put Shun in charge of the sacrifices, the spirits welcomed them. This is how Heaven accepted him. When he put Shun in charge of the nation's affairs, they were well ordered and the people were at peace. This is how the people accepted him. So Heaven gave it to him, and the people gave it to him. This is what I mean when I say the Son of Heaven cannot give all beneath Heaven to another.
"Shun assisted Yao for twenty-eight years. People aren't capable of such things: only Heaven could have done it. And after Yao died and the three years of mourning had ended, Shun left for lands south of South River in deference to Yao's son. Even still, when the august lords of all beneath Heaven wanted an audience at court – they went to Shun, not Yao's son. When people had lawsuits to settle – they they went to Shun, not Yao's son. When choruses sang ballads of praise – they sang of Shun, not Yao's son. This is what I mean when I say it was Heaven. For only after all this happened did Shun return to the Middle Kingdom and take his place as the Son of Heaven. If he'd just moved into Yao's palace and driven Yao's son out, it would have been usurping the throne rather than receiving it from Heaven. That's why Emperor Wu says, in "The Great Declaration":
_Heaven sees through the eyes of the people. Heaven hears through the ears of the people._
6 Wan Chang asked: "People say Integrity began crumbling when Yü allowed his son to succeed him rather than choose someone wise and worthy. Is that true?"
"No," replied Mencius. "That isn't how it works. If Heaven wants to give all beneath Heaven to someone wise and worthy, Heaven gives it to someone wise and worthy. If Heaven wants to give it to a son, Heaven gives it to a son.
"In ancient times, Shun recommended Yü to Heaven. He died seventeen years later, and when the three years of mourning ended, Yü left for Yang Ch'eng in deference to Shun's son. The people throughout all beneath Heaven followed him the way they followed Shun after Yao's death, rather than follow Yao's son. Yü recommended Yi to Heaven. He died seven years later, and when the three years of mourning ended, Yi left for the north slope of Ch'i Mountain in deference to Yü's son. But when people wanted an audience at court or they had a lawsuit to settle, they didn't go to Yi, they went to Yü's son Ch'i. And they said: _He's the son of our sovereign._ When choruses sang ballads of praise, they sang of Ch'i, not Yi. And they said: _He's the son of our sovereign._
"Yao's son was depraved; so was Shun's. Meanwhile Shun was Yao's trusted assistant for many years, and Yü was Shun's, so their blessings had rained down on the people for a long time. Ch'i was wise and worthy, able to carry on Yü's Way and honor it. Meanwhile Yi was Yü's trusted assistant for only a few years, so his blessings hadn't rained down on the people for long. Yi was far from another Shun or Yü, and there was a great difference in how wise and worthy the emperor's sons were. Such circumstances are all acts of Heaven: people aren't capable of such things. When something's done, but no one does it, it's an act of Heaven. When something happens, but no one makes it happen, it's the Mandate of Heaven.
"For a common man to rule all beneath Heaven, he needs the Integrity of a Shun or Yü. But he also needs the Son of Heaven's recommendation. That's why Confucius never ruled all beneath Heaven. But if someone inherits all beneath Heaven, Heaven won't reject him unless he's a tyrant like Chieh or Chou. That's why Yi, Yi Yin and Duke Chou never ruled all beneath Heaven.
"Because Yi Yin was his trusted assistant, T'ang became emperor of all beneath Heaven. When T'ang died, T'ai Ting was no longer alive to succeed him. Wai Ping ruled for two years, and Chung Jen four. Then T'ai Chia overthrew the laws of T'ang, so Yi Yin banished him to T'ung. After three years, T'ai Chia began to regret his crimes. He reproached himself and changed. There in T'ung, he brought himself into Duty and dwelled in Humanity. After another three years, having taken Yi Yin's admonitions to heart, he returned to Po.
"Duke Chou never ruled all beneath Heaven in the Chou Dynasty, and it was for the same reason that Yi never ruled in the Hsia and Yi Yin never ruled in the Shang. Confucius said: _With Yao and Shun, succession was through abdication to their chosen successors. With the founders of the Hsia, Shang and Chou dynasties, succession was hereditary. But for all, the principle was the same."_
7 Wan Chang asked: "People say Yi Yin's cooking was marvelous and that he used it to impress T'ang. Is that true?"
"No," replied Mencius. "That isn't what happened. Yi Yin was farming in the countryside at Yu Hsin, delighting in the Way of Yao and Shun. He ignored anything that violated Duty or the Way, even if offered all beneath Heaven. He wouldn't even glance at it for a thousand teams of horses. If something violated Duty or the Way, he wouldn't offer or accept the merest trifle for it.
"T'ang sent lavish gifts, inviting Yi Yin to be his counselor, but Yi Yin was so perfectly content that he said: _What would I do with T'ang's lavish gifts? Why should I stop dwelling in these fields, delighting in the Way of Yao and Shun?_ Only after T'ang had sent three invitations did Yi Yin finally agree, saying: _I could go on dwelling in these fields, delighting in the Way of Yao and Shun, but wouldn't it be better to turn this sovereign into another Yao or Shun? Wouldn't it be better to turn our people into anothernation of Yao or Shun, to see this happen with my own eyes? Having brought this people into being, Heaven appointed the wise to awaken those who will be wise, appointed the awakened to awaken those who will be awakened. Of Heaven's people, I am one of the awakened, so I should use this Way to awaken the people. If I don't awaken them, who will?_
"If there were any peasants in all beneath Heaven not enjoying the blessings of Yao and Shun, Yi Yin felt as if he himself had thrown them into a ditch. That's how deeply responsible he felt for all beneath Heaven. So he went to T'ang and counseled him to invade Hsia and rescue its people.
"I've never heard of straightening others by bending yourself, let alone straightening all beneath Heaven by disgracing yourself. Sages all have their own methods: some are recluses and some statesmen, some leave and some stay. But these methods all return to the same place: keeping yourself pure.
"I've heard that Yi Yin used the Way of Yao and Shun to earn T'ang's admiration, not that he used his marvelous cooking. In "The Councils of Yi," Yi Yin says:
_Heaven's vengeance sprang from depravity in the Hsia palace._
_Our role sprang from nobility in our Shang palace."_
8 Wan Chang asked: "Some people say Confucius stayed with Yung Chü in Wei and the eunuch Chi Huan in Ch'i. Is that true?"
"No," replied Mencius. "That isn't what happened. Some busybody cooked that up. In Wei, Confucius stayed with Yen Ch'ou-yu. In fact, Lord Mi's wife and Adept Lu's wife were sisters, and Lord Mi said to Adept Lu: _If Confucius will stay at my home, I'll make him a minister here in Wei._ When Lu told him about this, Confucius said: _The Mandate of Heaven abides._ Confucius took office according to Ritual and renounced office according to Duty. Through both success and failure, he always said: _The Mandate of Heaven abides._ If he'd stayed with Yung Chü or Chi Huan, he would have violated both Duty and the Mandate of Heaven.
"Confucius left Lu and Wei in disgust. Huan T'ui, the Minister of War in Sung, wanted to kill him, so he had to travel through Sung in disguise. Then, when he was in such trouble, he stayed with the pure Mayor Chen and advised Chou, Lord of Ch'en.
"I have heard you can judge resident counselors by who stays in their homes, and you can judge visiting counselors by whose home they stay in. If Confucius had stayed with Yung Chü or Chi Huan, how could he be Confucius?"
9 Wan Chang asked: "Some people say Po-li Hsi bartered himself to a Ch'in herdsman for five sheep skins and tended this man's cattle – all to impress Duke Mu of Ch'in. Is it true?"
"No," replied Mencius. "That isn't what happened. Some busybody cooked that up. Po-li Hsi was a native of Yü. Chin offered jade from Ch'ui Chi and horses from Ch'ü, trying to buy safe passage through Yü so its armies could attack Kuo. Kung Ch'i advised against it, and Po-li Hsi said nothing. He knew that giving the Duke of Yü such advice was futile, so he left for Ch'in. He was already seventy when that happened. If he didn't know by then that it was vile to try impressing Duke Mu by tending cattle, how could he be called wise?
"But he knew advice was futile and so didn't offer any – wouldn't you call that wise? He knew the Duke of Yü was about to be destroyed and left before it happened – wouldn't you call that wise? He was appointed to high office in Ch'in, saw Duke Mu was capable of great things and so assisted him – wouldn't you call that wise? And as prime minister, he made Mu a beacon to all beneath Heaven, worthy of guiding future generations – who but a sage is capable of such things? To sell yourself in order to realize your sovereign – no self-respecting villager would do that. So how could a sage do such a thing?"
X
Wan Chang Book Two
1 Mencius said: "Po Yi wouldn't look at anything foul, and he wouldn't listen to anything foul. He never served a sovereign he disdained, and never governed a people he disdained. So he took office in times of wise rule, and he renounced office in times of chaos. He couldn't bear to live in a land where perverse government attracted perverse people, where living among villagers was like donning fine court robes to sit in mud and ash. So when the tyrant Chou came to power, Po Yi fled to the shores of the North Sea, where he awaited the return of purity to all beneath Heaven. That's why the greedy are cured of greed when they hear the legend of Po Yi, and the timid grow resolute.
"Yi Yin said:
_Any sovereign I serve is that much more worthy, and any people_
_I serve is that much more worthy. So I take office in times of_
_wise rule, and I take office in times of chaos. And he also said:_
_Having brought this people into being, Heaven appointed the wise_
_to awaken those who will be wise, appointed the awakened to_
_awaken those who will be awakened. Of Heaven's people, I am one_
_of the awakened, so I should use this Way to awaken the people._
If there were peasants anywhere in all beneath Heaven not enjoying the blessings of Yao and Shun, Yi Yin felt as if he himself had thrown them into a ditch. That's how deeply responsible he felt for all beneath Heaven.
"Liu-hsia Hui wasn't shamed by defiled rulers, nor did he consider common positions below him. When in office, he always depended on the Way and never hid his wisdom. When dismissed, he bore no resentment. And suffering adversity, he remained untroubled. Living among villagers, he was so content he couldn't bear to leave. He used to say: _You are you, and I am I. Even if you stripped naked and stood beside me, how could you ever tarnish me?_ That's why small minds grow broad when they hear the legend of Liu-hsia Hui, and the niggardly grow generous.
"When Confucius left Ch'i, he simply emptied his rice steamer and set out. But when he left Lu, he said: _There's no hurry, no hurry at all._ That's the Way to leave your parents' country. If it was wise to hurry away, he hurried away; and if it was wise to linger, he lingered. If it was wise to stay somewhere, he stayed; and if it was wise to take office, he took office. That was Confucius."
Then Mencius continued: "Po Yi was a sage of purity, Yi Yin a sage of deep responsibility, Liu-hsia Hui a sage of complaisance – but Confucius was a sage who understood for all things their proper time. You could say he gathered the great perfections into a single orchestra – everything from resounding bells to rustling chimes of jade. Resounding bells begin a performance, and rustling jade ends it. To begin a performance – that is the task of knowledge. And to end a performance – that is the task of a sage's wisdom. A good analogy for knowledge might be skill, and a good analogy for a sage's wisdom might be strength. When you're shooting from beyond a hundred paces and your arrow reaches the target, that is strength. But if it hits the mark, that is something else again."
2 Po-kung Ch'i asked: "How did the system of position and endowment work in the Chou Dynasty?"
"No one knows exactly how it worked," replied Mencius. "The august lords thought the system was hurting them, so they destroyed all the records. Still, I once heard a summary:
"The Son of Heaven held one rank, dukes another, lords another, marquises another, earls and barons together another: that's five grades in all. The sovereign held one rank, ministers another, counselors another, high officials another, middle officials another, low officials another: that's six grades in all. The Son of Heaven controlled a thousand square miles, dukes and lords controlled a hundred square miles, marquises seventy square miles, earls and barons fifty square miles: that's four grades in all. Whoever controlled less than fifty square miles had no relations with the Son of Heaven. They were attached to the august lords and called _dependents._
"The Son of Heaven's ministers were given the same amount of land as the august lords, his counselors the same as marquises, and his senior officials the same as earls and barons.
"There were a hundred square miles in a large nation, and its sovereign's endowment was ten times that of a minister. A minister's endowment was four times that of a counselor. A counselor's was double that of a high official, a high official's double that of a middle official, a middle official's double that of a low official, and a low official's equaled that of a commoner in government service, which was whatever he could have earned from farming.
"There were seventy square miles in a medium-sized nation, and its sovereign's endowment was ten times that of a minister. A minister's endowment was three times that of a counselor. A counselor's was double that of a high official, a high official's double that of a middle official, a middle official's double that of a low official, and a low official's equaled that of a commoner in government service, which was whatever he could have earned from farming.
"There were fifty square miles in a small nation, and its sovereign's endowment was ten times that of a minister. A minister's endowment was double that of a counselor. A counselor's was double that of a high official, a high official's double that of a middle official, a middle official's double that of a low official, and a low official's equaled that of a commoner in government service, which was whatever he could have earned from farming.
"As for the earnings of farmers: Each man had a hundred acres of land, and with that land an outstanding farmer could feed nine people and a superior farmer could feed eight, an average farmer could feed seven people, a fair farmer could feed six, and a poor farmer could feed five. In government service, the earnings of commoners was likewise calculated according to their different abilities."
3 Wan Chang asked: "May I ask about friendship?"
"Don't try to intimidate with age or position or powerful relations," replied Mencius. "In making friends, befriend a person's Integrity. Friendship isn't about intimidation. Lord Meng Hsien led a house of a hundred war-chariots, and he had five friends: Yüeh-cheng Ch'iu, Mu Chung, and three others whom I forget. They were only his friends because they weren't of a noble house: if they had been, they wouldn't have been his friends.
"This is true not only for someone who leads a house of a hundred war-chariots, but also for the sovereign of a small nation. Duke Hui of Pi said: _I've made Master Szu my teacher and Yen Pan my friend. But Wang Shun and Ch'ang Hsi – they attend me._ And it's true not only for the sovereign of a small nation, but also for the sovereign of a large nation. Think about Duke P'ing of Chin and the scholar Hai T'ang: Duke P'ing came to visit when Hai T'ang said _come,_ sat when he said _sit,_ and ate when he said _eat._ Even if it was only vegetables and broth, he ate until he was full. He didn't dare refuse. But nothing more ever came of it: Duke P'ing never shared the position Heaven gave him, never shared the responsibility Heaven gave him to govern, and never shared the endowment Heaven gave him. That's how a scholar should honor the wise and worthy, but not how a duke or emperor should honor the wise and worthy.
"When Shun went to see Emperor Yao, Yao offered him the reserve palace and entertained him lavishly. Sometimes he was Shun's host, and sometimes his guest. This is an instance of the Son of Heaven truly befriending a commoner.
"To revere a superior – that is called exalting the exalted. To revere an inferior – that is called honoring the wise and worthy. Exalting the exalted, honoring the wise and worthy – in principle they are one and the same."
4 Wan Chang asked: "In exchanging tokens of friendship, what is the proper frame of mind?"
"Reverence," replied Mencius.
"Why is it irreverent to refuse a gift?"
"If a superior presents you with a gift, it's irreverent to accept only after asking yourself _How did he come by this – was it honorable or dishonorable?_ So you certainly shouldn't refuse such a gift."
"What if you refuse in thought rather than word – so even though you're thinking _To get this, he did such dishonorable things to the people,_ you find some other excuse to decline the gift?"
"If he befriends you according to the Way and presents the gift according to Ritual, then even Confucius would accept the gift."
Wan Chang asked: "Suppose there was a bandit who robbed people outside the city gates. Would you accept his plunder as a gift just because he befriended you according to the Way and offered it to you according to Ritual?"
"No, of course not," replied Mencius. "In the 'Commission of K'ang,' Duke Chou says: _Everyone despises a person who murders and robs without any fear of death._ Such people are fit only for punishment: trying to reform them is pointless. This practice was handed down from the Hsia to the Shang, and from the Shang to the Chou. So by now, there should be no reason to make excuses. No, how can anyone accept a gift of plunder?"
"These days, the august lords extract wealth from the people just like thieving bandits," said Wan Chang. "Suppose they lend their gifts the virtue of Ritual occasion and the noble-minded accept: what would you say of that?"
"Do you imagine that these august lords would be punished if a true emperor appeared?" replied Mencius. "Do you imagine he would try to reform them, and then punish them when they don't change? To call anyone who takes something that isn't theirs a thief – that's pushing righteousness too far. When Confucius took office in Lu, people there fought over the kill after a sacrificial hunt, so Confucius did too. If there's nothing wrong with fighting over the kill, what could be wrong with accepting a gift?"
"He was like that?" said Wan Chang. "So he didn't take office to serve the Way?"
"He served the Way."
"If he served the Way, why did he fight over the kill?"
"Confucius tried to begin by rectifying the proper use of sacrificial vessels, and so put an end to loading them with such exotic foods."
"Why didn't he just leave?"
"He wanted to make a proposal that would indicate his method. His proposal was entirely practical, so when it wasn't put into practice he left. That's why he never served any sovereign for even three years. Confucius served when he thought his proposals would be put into practice, when he was invited earnestly, or when a duke offered to support him. Confucius served Lord Chi Huan because he thought his proposals would be put into practice, served Duke Ling of Wei because he was invited earnestly, and served Duke Hsiao of Wei because the duke offered to support him."
5 Mencius said: "You don't take office just to escape poverty, though there are times that is reason enough. And you don't marry a wife just for the sustenance, though there are times that too is reason enough. When escaping poverty, decline high positions and wealth in favor of common positions and poverty. What positions are fitting for those who would decline high positions and wealth in favor of common positions and poverty? Gatekeeper or night watchman.
"When Confucius was the officer in charge of grain warehouses, he said: _I keep accurate records, that's all._ And when he was in charge of flocks and fields, he said: _I make sure the cattle and sheep grow strong, that's all._ To hold a common position and spout lofty words – that is a crime. And to represent the people in their sovereign's court without putting the Way into practice – that is a disgrace."
6 Wan Chang said: "Why would a scholar refuse to be under an august lord's protectorate?"
"It would be too presumptuous," replied Mencius. "According to the rites, an august lord lives within another august lord's protectorate only after he has lost his nation. So for a scholar to live within an august lord's protectorate would violate Ritual."
"But if a sovereign presents him with grain, should he accept it?"
"Yes."
"How can it be right to accept?"
"The sovereign always provides for his people."
"If he's providing for you, you accept. But if he's offering you a gift, you refuse. How can that be?"
"It would be too presumptuous."
"Why isn't the other presumptuous?"
"When gatekeepers and night watchmen do their jobs, they're earning a salary. When they don't do their jobs, they're accepting gifts. And that is irreverent."
"Say a sovereign sends provisions and they are accepted," said Wan Chang. "Why shouldn't such gifts continue?"
"Duke Mu asked after Master Szu often, and often presented him with sacrificial meat. But Master Szu was insulted. He hustled the duke's envoy out the gate, made two deep bows facing north, then refused the duke's gifts, saying: _I can see this sovereign wants to tend me the way he tends his dogs and horses._ Perhaps that's when envoys stopped coming with gifts. And how could anyone say that a ruler is pleased with someone wise and worthy if he doesn't appoint him to high office or even support him?"
"What must a nation's sovereign do if he wants to earn a reputation for supporting the noble-minded," asked Wan Chang.
"The sovereign should send something first with his greetings," replied Mencius, "and it should be accepted with two deep bows. But from then on, the granaries and kitchens should send grain and meat without any mention of the sovereign. Being expected to break his back bowing over and over for a little sacrificial meat – that's what bothered Master Szu. He didn't think that was how you supported the noble-minded Way.
"Remember Yao's treatment of Shun? Yao sent his nine sons to serve him, gave his two daughters in marriage to him. He sent his hundred officials, cattle, sheep, provisions in plenty – all to support him as he worked the fields. Then he appointed him to the most exalted position. That's what I'm thinking about when I speak of _how a duke or emperor should honor the wise and worthy."_
7 Wan Chang said: "How can it be right to refuse a meeting with an august lord?"
"Scholars in the city are called _ministers of market and well,"_ replied Mencius, "and scholars in the country are called _ministers of forest and field._ But both are deemed commoners, and according to Ritual a commoner doesn't presume to meet with an august lord until he has presented his token of credentials and been appointed to office."
"When a commoner is summoned to war, he goes to war. So when the sovereign wants to see a scholar and summons him to a meeting, how can he refuse to go?"
"Going to war is proper. Going to such a meeting is not. And why does the sovereign want to see him anyway?"
"Because he's so renowned, so wise and worthy."
"If it's because he's so renowned – the Son of Heaven wouldn't presume to summon his teacher, so how could an august lord? If it's because he's so wise and worthy – I've never heard of summoning someone wise and worthy whenever you want to see him.
"Duke Mu went to see Master Szu often. Once he asked: _In an ancient nation of a thousand war-chariots, how would the sovereign befriend a scholar?_ Master Szu was insulted and said: _The ancients had a saying: 'Don't talk about making him your friend, just attend him.'_ Being insulted, Szu was blunt: _In terms of position – you are the sovereign and I the subject, so how could I presume to be your friend? In terms of Integrity – you should be attending me, so how could you be my friend?_ If that ruler of a thousand war-chariots couldn't even make a scholar his friend, how could he hope to summon such a man?
"Once when he was out hunting, Duke Ching of Ch'i summoned his gamekeeper with a plume-crested flag. The gamekeeper didn't come, so the duke wanted to have him executed, but Confucius said: _A man of great resolve never forgets that he could be abandoned to ditches and gutters, and a man of great valor never forgets that he could lose his head._ The gamekeeper wasn't entitled to such a lofty summons, so he didn't answer it – that's what Confucius admired."
"How should gamekeepers be summoned?" asked Wan Chang.
"With leather caps," replied Mencius. "Commoners should be summoned with plain banners on bent-top staffs, scholars with dragon banners, and high ministers with plume-crested flags. When the gamekeeper was summoned with the summons due a high minister, he preferred death to the presumption of answering. If a commoner is summoned with the summons due a scholar, how could he presume to answer? And that's nothing like a wise and worthy man being summoned with a summons due the unwise and unworthy.
"Wanting to see such a man while not abiding by the Way – that's like inviting someone in while closing the gate. Duty is the road, and Ritual the gate. Only the noble-minded can follow this road, going in and out the gate with ease. The _Songs_ say:
_Chou's Way is whetstone smooth,_
_and it's straight as an arrow:_
_the noble-minded travel upon it;_
_the small-minded gaze upon it."_
"When summoned by the sovereign," said Wan Chang, "Confucius didn't wait for a carriage to set out. Does that mean Confucius did wrong?"
"Confucius had taken office and so had responsibilities," replied Mencius. "And he was called with the summons due his position."
8 Speaking to Wan Chang, Mencius said: "Noble scholars in one village befriend noble scholars in another village. Noble scholars in one country befriend noble scholars in another country. Noble scholars throughout all beneath Heaven befriend noble scholars throughout all beneath Heaven. And when the friendship of noble scholars throughout all beneath Heaven isn't enough, we can also rise to converse with the lofty ancients. How can we fail to know them utterly by chanting their poems and reading their words? And we also converse with their age that way. That is lofty friendship."
9 Emperor Hsüan of Ch'i asked about ministers, and Mencius said: "What kind of minister are you asking about?"
"Is there more than one kind?" asked the emperor.
"Yes," replied Mencius. "There are ministers from royal families and there are ministers from common families."
"May I ask about ministers from royal families?"
"If the sovereign is making grave mistakes, they admonish him. If they have to admonish him over and over, and he still refuses to listen – they replace him."
The emperor blanched at this, so Mencius continued: "Why so surprised? You asked, and I wouldn't dare be less than honest and forthright with you."
After he'd recovered his color, the emperor asked about ministers from common families, and Mencius said: "If the sovereign is making mistakes, they admonish him. If they have to admonish him over and over, and he still refuses to listen – they resign and leave his country behind."
XI
Master Kao Book One
1 Master Kao said: "The nature of things is like willow wood, and Duty is like cups and bowls. Shaping human nature into Humanity and Duty is like shaping willow wood into cups and bowls."
"Do you follow the nature of willow wood to shape cups and bowls," replied Mencius, "or do you maul it? If you maul willow wood to make cups and bowls, then I guess you maul human nature to make Humanity and Duty. It's talk like yours that will lead people to ravage Humanity and Duty throughout all beneath Heaven."
2 Master Kao said: "The nature of things is like swirling water: channel it east and it flows east, channel it west and it flows west. And human nature too is like water: it doesn't choose between good and evil any more than water chooses between east and west."
"It's true that water doesn't choose between east and west," replied Mencius, "but doesn't it choose between high and low? Human nature is inherently good, just like water flows inherently downhill. There's no such thing as a person who isn't good, just as there's no water that doesn't flow downhill.
"Think about water: if you slap it, you can make it jump over your head; and if you push and shove, you can make it stay on a mountain. But what does this have to do with the nature of water? It's only responding to the forces around it. It's like that for people too: you can make them evil, but that says nothing about human nature."
3 Master Kao said: " _The nature of things_ means _that which is inborn_."
" _The nature of things_ means _that which is inborn_ ," repeated Mencius. "Just like _white_ means _that which is white?_ "
"Yes."
"So is the whiteness of a white feather the same as the whiteness of white snow? And is the whiteness of white snow the same as the whiteness of white jade?"
"Yes."
"Then is the nature of a dog the same as the nature of an ox? And is the nature of an ox the same as the nature of a human?"
4 Master Kao said: "Hunger for food and sex – that is nature. Then there's Humanity, which is internal not external; and Duty, which is external not internal."
"Why do you say Humanity is internal and Duty is external?" asked Mencius.
"Suppose there was an elder and I treated him with the honor due an elder," replied Master Kao, "it isn't because the honor due elders is somehow within me. It's like seeing something white as white: the whiteness is outside us. That's why I call Duty external."
"The whiteness of a white horse is no different from the whiteness of a white-haired person," said Mencius. "But doesn't the elderliness of an elderly horse mean something quite different to us than the elderliness of an elderly person? And which are you equating with Duty – the elder or the one who treats him with the honor due an elder?"
"I love my own brother, but not the brother of someone in Ch'in," said Master Kao, "so the reason lies within me, which is why I call Humanity internal. But I treat elders as elders, whether they're from Ch'u or my own family: so the reason lies within elderliness, which is why I call Duty external."
"But my enjoyment of roast meat is the same," countered Mencius, "whether I cooked it or someone from Ch'in cooked it. And it's like this for many things. So does that mean the enjoyment of roast meat is external?"
5 Adept Meng Chi asked Adept Kung-tu: "Why do you say Duty is internal?"
"I call it internal," replied Kung-tu, "because it's our reverence put into action."
"If someone in your village is a year older than your eldest brother, which do you revere?"
"My brother."
"In pouring wine, which do you serve first?"
"The village elder."
"First you treat this one with reverence, then you treat that one with the honor due an elder. So Duty derives from the external, not the internal."
Adept Kung-tu had no answer to this. Later, when he told Mencius what had happened, Mencius said: "Ask him which he reveres most, an uncle or a younger brother, and he'll say _An uncle._ Ask him which he reveres most, an uncle or a younger brother who's posing as the ancestral dead at a sacrifice, and he'll say _A younger brother._ Then ask what happened to his reverence for the uncle, and he'll say _It's because of the younger brother's position._ Then you can say: _If reverence is a matter of position, lasting reverence belongs to my elder brother, while fleeting reverence belongs to the village elder."_
When Adept Meng Chi heard this, he said: "I treat an uncle with reverence as reverence is due him, and I treat a younger brother with reverence as reverence is due him. So Duty derives from the external, not the internal."
"In winter we drink broth," commented Adept Kung-tu, "and in summer we drink water. Does that mean drinking and eating derive from the external?"
6 Adept Kung-tu said: "Master Kao says: _Human nature isn't good, and it isn't evil._ There are others who say: _Human nature can be made good, and it can be made evil. That's why the people loved goodnesswhen Wen and Wu ruled, and they loved cruelty when Yu and Li ruled._ And there are still others who say: _Human nature is inborn: some people are good and some evil. That's why a Hsiang could have Yao as his ruler, a Shun could have Blind Purblind as his father, a Lord Ch'i of Wei and Prince Pi Kan could have the tyrant Chou as their nephew and sovereign._
"But you say: _Human nature is good._ Does that mean all the others are wrong?"
"We are, by constitution, capable of being good," replied Mencius. "That's what I mean by good. If someone's evil, it can't be blamed on inborn capacities. We all have a heart of compassion and a heart of conscience, a heart of reverence and a heart of right and wrong. In a heart of compassion is Humanity, and in a heart of conscience is Duty. In a heart of reverence is Ritual, and in a heart of right and wrong is wisdom. Humanity, Duty, Ritual, wisdom – these are not external things we meld into us. They're part of us from the beginning, though we may not realize it. Hence the saying: _What you seek you will find, and what you ignore you will lose._ Some make more of themselves than others, maybe two or five or countless times more. But that's only because some people fail to realize their inborn capacities.
"The _Songs_ say:
_Heaven gave birth to humankind,_
_and whatever is has its own laws:_
_cleaving to what makes us human,_
_people delight in stately Integrity._
Of this, Confucius said: _Whoever wrote this song knew the Way well._ So whatever is must have its own laws, and whenever they cleave to what makes us human, the people must delight in stately Integrity."
7 Mencius said: "In good years, young men are mostly fine. In bad years, they're mostly cruel and violent. It isn't that Heaven endows them with such different capacities, only that their hearts are mired in such different situations. Think about barley: if you plant the seeds carefully at the same time and in same place, they'll all sprout and grow ripe by summer solstice. If they don't grow the same – it's because of inequities in richness of soil, amounts of rainfall, or the care given them by farmers. And so, all members belonging to a given species of thing are the same. Why should humans be the lone exception? The sage and I – surely we belong to the same species of thing.
"That's why Master Lung said: _Even if a cobbler makes a pair of sandals for feet he's never seen, he certainly won't make a pair of baskets._ Sandals are all alike because feet are the same throughout all beneath Heaven. And all tongues savor the same flavors. Yi Ya was just the first to discover what our tongues savor. If taste differed by nature from person to person, the way horses and dogs differ by species from me, then how is it people throughout all beneath Heaven savor the tastes Yi Ya savored? People throughout all beneath Heaven share Yi Ya's tastes, therefore people's tongues are alike throughout all beneath Heaven.
"It's true for the ear too: people throughout all beneath Heaven share Maestro K'uang's sense of music, therefore people's ears are alike thoughout all beneath Heaven. And it's no less true for the eye: no one throughout all beneath Heaven could fail to see the beauty of Lord Tu. If you can't see his beauty, you simply haven't eyes.
"Hence it is said: _All tongues savor the same flavors, all ears hear the same music, and all eyes see the same beauty._ Why should the heart alone not be alike in us all? But what is it about our hearts that is alike? Isn't it what we call reason and Duty? The sage is just the first to discover what is common to our hearts. Hence, reason and Duty please our hearts just like meat pleases our tongues."
8 Mencius said: "The forests were once lovely on Ox Mountain. But as they were near a great city, axes cleared them little by little. Now there's nothing left of their beauty. They rest day and night, rain and dew falling in plenty, and there's no lack of fresh sprouts. But people graze oxen and sheep there, so the mountain's stripped bare. When people see how bare it is, they think that's all the potential it has. But does that mean this is the nature of Ox Mountain?
"Without the heart of Humanity and Duty alive in us, how can we be human? When we abandon this noble heart, it's like cutting those forests: a few axe blows each day, and pretty soon there's nothing left. Then you can rest day and night, take in the clarity of morning's healing _ch'i –_ but the values that make you human keep thinning away. All day long, you're tangled in your life. If these tangles keep up day after day, even the clarity of night's healing _ch'i_ isn't enough to preserve you. And if the clarity of night's healing _ch'i_ isn't enough to preserve you, you aren't much different from an animal. When people see you're like an animal, they think that's all the potential you have. But does that mean this is the human constitution?
"With proper sustenance, anything will grow; and without proper sustenance, anything will fade away. Confucius said: _Embrace it and it endures. Forsake it and it dies. It comes and goes without warning, and no one knows its route._ He was speaking of the heart."
9 Mencius said: "Don't make the mistake of thinking the emperor lacks intelligence. Even the most vigorous plant in all beneath Heaven cannot grow if given sun for a day then left to freeze for ten. I very rarely see the emperor, and as soon as I leave, a crowd shows up to freeze him some more. So even if a new sprout appeared, what could I do?
_"Go_ is surely a minor art, but if you don't give it your single-minded devotion you'll never master it. GoAutumnal is the finest player in all the land. But suppose he tries to teach the game to two people. One listens intently, studying with single-minded devotion. The other listens, but he's dreaming of swans in flight, the heft of bow and tethered arrow, the shot. Although he studies beside the first, he'll never be anywhere near as good. Is that because he's less intelligent? Not at all."
10 Mencius said: "I want fish, and I also want bear paws. If I can't have both, I'll give up fish and take bear paws. I want life, and I also want Duty. If I can't have both, I'll give up life and take Duty. I want life – but there's something I want more than life, so I won't do something wrong just to stay alive. I loathe death – but there's something I loathe more than death, so there are disasters I won't avoid.
"If you want nothing more than life, you'll do anything to stay alive. If you loathe nothing more than death, then you'll do anything to avoid disasters. But there are things people won't do to stay alive, and there are things people won't do to avoid disasters. So there must be something we want more than life, and something we loathe more than death. And it isn't something that only a sage's heart possesses: everyone has it. It's just that a sage never loses it.
"A basket of rice, a bowl of soup: to take them means life, to leave them means death. If they're offered with threats and abuse, a wayfarer won't accept them. If they're trampled on, even a beggar won't bother with them. But people accept ten thousand measures of grain as salary without even asking if they're violating Ritual or Duty. What could ten thousand measures of grain mean to me? A beautiful house? The esteem of wife and mistress? The gratitude of friends in need? If I refused to accept something even to save my life, am I now to accept it for a beautiful house, for the esteem of wife and mistress, for the gratitude of friends in need? Can't these people stop themselves? They're throwing away their original heart. There's no other way to describe it."
11 Mencius said: "Humanity is the heart, and Duty the road. To stop following the road and abandon it, to let the heart wander away and not know enough to search for it – what a sad sad thing. When chickens or dogs wander away, people know enough to search for them, but when their heart wanders away they don't. The Way of learning is nothing other than this: searching for the heart that's wandered away."
12 Mencius said: "Suppose your fourth finger were gnarled and crooked, though not lame or painful. If there was someone who could straighten it, you'd think nothing of traveling all the way from Ch'in to Ch'u. That's because your finger isn't as good as other people's fingers.
"When your finger isn't as good as other people's fingers, you know enough to resent it. But when your heart isn't as good, you don't know enough to resent it. That's what I call _not knowing what is what."_
13 Mencius said: "Consider a young tree, an _wu-t'ung_ or _tzu:_ anyone who wants to keep it alive knows how to nurture it. Meanwhile they don't know how to nurture themselves. How can they love a tree more than themselves? This is thoughtlessness at its worst."
14 Mencius said: "People love all aspects of themselves equally. Loving them all equally, people nurture them all equally. When there isn't an inch of their flesh that they don't love, there isn't an inch they don't nurture. There's only one way to know if people are good or evil: look at the choices they make. We each contain precious and worthless, great and small. Never injure the great for the sake of the small, or the precious for the sake of the worthless. Small people nurture what is small in them; great people nurture what is great in them.
"Consider a gardener who nurtures the scraggly sour-plum and date-bramble, but neglects the magnificent _wu-t'ung_ and _chia_ – that's a worthless gardener indeed. If you neglect shoulder and back to nurture a finger, and don't even realize what you're doing, you're nothing but a reckless wolf. And if you're obsessed with food and drink, you'll be scorned as worthless because you're nurturing the small and neglecting the great. Even if you neglect nothing else in your obsession with food and drink, you've let your mouth and belly become so much more than just another inch of flesh."
15 Adept Kung-tu asked: "If we're all equally human, how is it some are great and some small?"
"Great people abide by what is great in them;" replied Mencius, "small people abide by what is small in them."
"If we're all equally human, how is it some abide by what is great in them and some abide by what is small in them?"
"The senses cannot think, and so ear and eye are easily deceived by things. And things interact together, which only makes it worse. It is the heart which thinks, and so understands. Without thought there is no understanding. Heaven has given us these two things: heart and senses. If you insist from the beginning on what is great in you, what is small cannot steal it away. This is what makes a person great without fail."
16 Mencius said: "There is the nobility of Heaven on the one hand, and human nobility on the other. Humanity, Duty, loyalty, sincerity, tireless delight in the virtuous – such is the nobility of Heaven. Duke, counselor, minister – such is human nobility.
"The ancients cultivated the nobility of Heaven, and human nobility followed naturally. Today people cultivate the nobility of Heaven only out of desire for human nobility. And once they win human nobility, they abandon the nobility of Heaven. This is delusion at its worst, and such people come to nothing but ruin in the end. "
17 Mencius said: "The heart we all share longs to be exalted. But the exalted is already there in us, though we may not realize it. What people exalt is not the truly exalted. What some mighty lord exalts today, he may scorn as worthless tomorrow.
"The _Songs_ say
_we've drunk deep your wine_
_and feasted on your Integrity,_
meaning that if you feast on Humanity and Duty, you don't long for the lavish flavors of sumptuous meat and millet. And if you're renowned far and wide, you don't long for robes of elegant embroidery."
18 Mencius said: "Humanity overcomes Inhumanity the way water overcomes fire. But when people wield Humanity these days, it's like they're throwing a cup of water on a cartload of burning firewood. When the fire keeps burning, they claim water can't overcome fire. This is the promotion of Inhumanity at its worst, and such people come to nothing but ruin in the end."
19 Mencius said: "The five grains are the finest of all plants. But if they don't ripen, they aren't even as good as wild rice-grass. For Humanity too – the essential thing is that it ripens well."
20 Mencius said: "Yi always shot from a full draw when teaching archery, and his students also shot from a full draw. A master carpenter always uses a compass and square when he teaches, and his students also use a compass and square."
XII
Master Kao Book Two
1 Someone from Jen asked Adept Wu-lu: "Which is most important, Ritual or food?"
"Ritual," replied Wu-lu.
"Which is most important, Ritual or sex?
"Ritual"
"What if using food for the Ritual sacrifice meant starving to death, and not using it meant having something to eat – would you insist on using it for the sacrifice? And what if observing the Ritual of claiming the bride in her home meant not marrying, and not observing it meant marrying – would you insist on claiming your bride?"
Adept Wu-lu had no answer. The next day he went to Chou and told Mencius what had happened. Mencius said: "It's easy. If you compare the tops without checking the bottoms, you can make an inch-long twig taller than a lofty tower. And if you say gold is heavier than feathers, you certainly aren't comparing a wisp of gold to a cartload of feathers. It's pointless to compare food and Ritual at a moment when food is vital and Ritual isn't: you can make lots of things seem more important that way, not just food. And it's pointless to compare sex and Ritual at a moment when sex is vital and Ritual isn't: you can make lots of things seem more important that way, not just sex.
"Go say this to him: _Suppose the only way you could get food was by twisting your brother's arm behind his back and stealing his food. Would you do it? And suppose the only way you could get a wife was by climbing over your east wall and dragging off the neighbor's daughter. Would you do that?"_
2 Lord Chiao of Ts'ao asked: "Is it true anyone can be a Yao or Shun?"
"Yes," replied Mencius.
"I've heard that Emperor Wen was ten feet tall," said Chiao, "and T'ang was nine feet tall. I'm nine feet four inches, but I have nothing but grain to eat. What shall I do?"
"Isn't it easy?" said Mencius. "Just act like Yao and Shun. If you can't lift a baby chicken, you are weak indeed. If you can lift three thousand pounds, you are strong indeed. And if you can lift as much as Wu Huo, you're an Wu Huo. Why do people agonize over what they cannot do? They simply aren't trying.
"If you follow your elders, walking with dignity and respect, you can be called a younger brother. If you hurry ahead of your elders, you cannot be called a younger brother. How can anyone say they haven't the capacity to walk slowly behind? They just aren't trying. The Way of Yao and Shun is simple: act with the respect proper to a son and younger brother. If you dress the way Yao dressed, speak the way Yao spoke, and act the way Yao acted – then you're a Yao. And if you dress the way Shun dressed, speak the way Shun spoke, and act the way Shun acted – then you're a Shun. It's that simple."
"The Chou sovereign would listen to me and give me a place to live," said Chiao, "but I want to stay here, receiving your beautiful teachings with the other disciples."
"The Way is like a great highway," replied Mencius. "It's easy to find. People just don't bother to look. Go back to your home. Look for it there, and you'll find teachers aplenty."
3 Kung-sun Ch'ou said: "Master Kao claims 'Tiny Wingbeats' is the poem of a little person."
"Why did he say that?" asked Mencius.
"Because it's so full of resentment."
"Old Kao was awfully dogmatic about the _Songs,"_ said Mencius. "Suppose a man from Yüeh drew his bow and shot someone: I might tell the story with a smile because the man's a stranger to me. But suppose my brother drew his bow and shot someone: then I'd be in tears when I told the story because he's my own flesh and blood. The resentment of 'Tiny Wingbeats' comes from the close bonds of family, for those bonds are themselves Humanity. Old Kao was impossibly dogmatic about the _Songs."_
"Why is there no resentment in 'Gentle Wind'?
"In 'Gentle Wind' the parent's fault is slight, but in 'Tiny Wingbeats' the parent's fault is great. If you don't resent a parent's fault when it's serious, you're treating parents like strangers. And if you resent a parent's fault when it's slight, you're treating parents with abandon. Treating them like strangers, treating them with abandon – either is no way for a child to honor parents. Confucius said:
_Shun was masterful in honoring his parents: at fifty, he was still longing for them."_
4 Sung K'eng was traveling to Ch'u. Meeting him at Chih Ch'iu, Mencius said: "Where are you going?"
"I've heard that war has broken out between Ch'u and Ch'in," replied Sung K'eng, "so I'm going to see the Ch'u emperor. I'll try to convince him to end the fighting. If I can't convince him, I'll go see the Ch'in emperor. I hope one of them will listen."
"I won't ask about the details, if you don't mind," said Mencius, "but I would like to ask about the essence of your plan, and how you intend to convince these emperors to act on it."
"I'll show them how there's no profit in it."
"Your intent is noble, but your appeal misguided. If you talk to these emperors about profit, and in their love of profit they stop their armies – their armies will rejoice in peace and delight in profit. Soon ministers will embrace profit in serving their sovereign, sons will embrace profit in serving their fathers, younger brothers will embrace profit in serving their elder brothers – and all of them will have abandoned Humanity and Duty. When these relationships become a matter of profit, the nation is doomed to ruin.
"But if you talk to these emperors about Humanity and Duty, and in their love of Humanity and Duty they stop their armies – their armies will rejoice in peace and delight in Humanity and Duty. Soon ministers will embrace Humanity and Duty in serving their sovereign, sons will embrace Humanity and Duty in serving their fathers, younger brothers will embrace Humanity and Duty in serving their elder brothers – and all of them will have abandoned profit. When these relationships become a matter of Humanity and Duty, then the sovereign is sure to be a true emperor. So why mention profit?"
5 When Mencius was living in Chou, Chi Jen was the governor of Jen. As a token of friendship and respect, he sent Mencius a gift. Mencius accepted it, but without any show of gratitude. When Mencius was living in P'ing Lu, Lord Ch'u was the prime minister in Ch'i. As a token of friendship and respect, he too sent Mencius a gift. Mencius accepted it, but again without any show of gratitude.
Later, when he traveled from Chou to Jen, Mencius went to visit Lord Chi Jen. But when he traveled from P'ing Lu to Ch'i, he didn't visit Lord Ch'u. Adept Wu-lu was overjoyed at this, and said: "Now I see!"
"You visited Lord Chi Jen when you went to Jen," he said to Mencius, "but you didn't visit Lord Ch'u when you went to Ch'i. Is this because Lord Ch'u is a prime minister?"
"No," replied Mencius. _"The Book of History_ says:
_The gift is in the giving. If the giving isn't equal to the gift, it's like no gift at all, for the gift isn't invested with your good will._
That is, it isn't a true gift at all."
Adept Wu-lu was delighted at this. When someone asked why, he said: "Lord Chi Jen couldn't leave his responsibilities and go to Chou, but Lord Ch'u could have gone to P'ing Lu."
6 Ch'un-yü K'un said: "If you consider fame and achievement primary, you serve the people. If you consider fame and achievement secondary, you serve yourself. You were one of the three high ministers, but you left before your fame and achievement had spread to sovereign and people. Is that really how the Humane act?"
"Po Yi lived in a humble position," said Mencius, "and refused to put his wisdom in the service of an unworthy ruler. Yi Yin approached both the noble T'ang and the tyrant Chieh five times. And Liu Hsia-hui didn't despise defiled rulers and didn't reject common positions. Each of these masters had his own Way, but they all shared the same goal."
"What was it?"
"Humanity. The noble-minded are Humane, so why must they share anything else?"
"Lord Kung-yi was prime minister in Duke Mu's time, Master Liu and Master Szu were counselors – but Lu lost territory faster than ever. Does this mean the wise and worthy can do nothing for a country?"
"When the nation of Yü ignored Po-li Hsi," replied Mencius, "it perished. When Duke Mu employed him well in Ch'in, the duke became the finest of august lords. Whenever countries ignore the wise and worthy, they don't just lose a little territory: they perish entirely."
"In ancient times," said Ch'un-yü K'un, "when Wang Pao settled at the Ch'i River, people west of the Yellow River became eloquent carolers. When Mien Chü settled in Kao T'ang, people in Ch'i's right-hand regions became eloquent singers. And the wives of Hua Chou and Ch'i Liang wept so eloquently for their husbands that they transformed the country's mourning traditions.
"What lies within reveals itself without. No one's ever been devoted to a purpose and had no achievements for the world to see. So there cannot be anyone wise and worthy among us: if there were, I would know of them."
"When Confucius was justice minister in Lu," said Mencius, "he was ignored. He took part in the sacrifices, but received no sacrificial meat, so he left Lu without even taking off his ceremonial cap. Those who didn't understand him thought he left because of the meat. But those who did understand him knew it was because Lu was violating Ritual. Confucius preferred to leave over a slight offense rather than wait for a grievous wrong. Commoners never understand the ways of the noble-minded."
7 Mencius said: "The five chiefs of the august lords were offenders against the three emperors. The august lords of today are offenders against the five chiefs. And the high ministers of today are offenders against our august lords.
"When the Son of Heaven visited the august lords, it was called an Inspection Tour. And when the august lords went to the Son of Heaven's court, it was called a Duty Report. In spring, the purpose was to inspect the planting and provide whatever the farmers lacked. And in autumn, it was to inspect the harvest and help whoever didn't bring in enough. An august lord was rewarded with more territory if the Son of Heaven came to his domain and found the land opened up and the fields cultivated well, the old nurtured, the wise and worthy honored, and the distinguished serving in office. An august lord was reprimanded if the Son of Heaven came and found the land overgrown, the old abandoned, the wise and worthy neglected, and oppressors serving in office. The first time an august lord failed to appear at court, his rank was reduced. The second time, his territory was reduced. And if he failed to appear a third time, the Son of Heaven's armies removed him from power. Hence the Son of Heaven disciplined but never attacked. The august lords, on the other hand, attacked but never disciplined. Indeed, the five chiefs of the august lords often coerced august lords into attacking other august lords. That's why I say: _The five chiefs of the august lords were offenders against the three emperors._
Duke Huan was the most illustrious of the five chiefs. When he called the august lords together at K'uei Ch'iu, they bound a sacrificial animal and recorded their covenant, but they didn't trace their mouths with blood to consummate the covenant. Their first article stated: _Children who don't honor their parents shall be punished. Descendants shall not be set aside. Mistresses shall not be given the status of wives._ The second article stated: _Let Integrity shine forth by honoring the wise and nurturing the talented._ The third article stated: _Show reverence for elders, gentleness for children, and never forget the traveler and guest._ The fourth article stated: _Let no one hold office by hereditary privilege, and let no one hold more than one office at a time. In selecting officials, select only the most qualified. No ruler shall have sole authority to execute a high minister._ The fifth article stated: _Let no one build threatening earthworks. Let no one ban the sale of grain. And let no one confer land and title without the proper announcements._ The agreement also stated: _All who are united in this covenant shall hereafter live in harmony._ The august lords of today all violate these five precepts. That's why I say: _The august lords of today are offenders against the five chiefs._
"Encouraging a sovereign's evil is nothing compared to the high crime of collusion in a sovereign's evil. The high ministers of today are all colluding in their sovereign's evil. That's why I say: _The high ministers of today are offenders against our august lords."_
8 When the Lu sovereign wanted to make Lord Shen commander of his armies, Mencius said: "Sending the people to war without training – that is called ravaging the people. In the time of Yao and Shun, there was no toleration for a person who ravaged the people. It would be wrong even if Ch'i could be defeated and Nan-yang reclaimed, all in a single battle."
Lord Shen's face darkened, and he said: "I don't understand this at all."
"Let me explain it to you clearly," responded Mencius. "The Son of Heaven's territory covers a thousand square miles. If it's any less than a thousand square miles, he doesn't have enough to provide hospitality for the august lords. An august lord's territory covers a hundred square miles. If it's any less than a hundred square miles, he doesn't have enough to keep the canons of the ancestral temple.
"When Duke Chou was given Lu to rule, he had a hundred square miles. Still, it was plenty because he used it wisely. When Duke T'ai was given Ch'i to rule, he too had a hundred square miles. Again, it was plenty because he used it wisely. Today, Lu is five times a hundred square miles. If a true emperor arose, do you think Lu is one of those states he would pare down or one he would enlarge? A Humane person wouldn't even take what belongs to one state and give it to another, let alone kill people in his pursuit of land. The noble-minded address fundamentals when they serve a sovereign: they make the Way his guide and Humanity his resolve."
9 Mencius said: "In serving their sovereign, people these days all say: _I'm expanding his territory and filling his treasury._ But what the world now calls a distinguished minister, the ancients called a plunderer of the people. To enrich a sovereign when he doesn't make the Way his purpose and Humanity his resolve – that is to enrich another tyrant Chieh.
"They say: _I'm forming alliances and winning wars for him._ But what the world now calls a distinguished minister, the ancients called a plunderer of the people. To strengthen a sovereign for war when he doesn't make the Way his purpose and Humanity his resolve – that is to empower another tyrant Chieh.
"When you abide by the Way of our times, leaving the practices of this world unchanged, then even if you're given all beneath Heaven, you won't keep it for a single morning."
10 Po Kuei said: "I'd like to see people taxed one part in twenty. What would you think of that?"
"Your Way is the Way of northern barbarians," replied Mencius. "In a nation of ten thousand families, would a single potter be sufficient?"
"No, there wouldn't be enough pottery."
"Northern barbarians don't grow the five grains, only millet. They have no city walls or buildings, no ancestral temples, no sacrificial rituals. They have no august lords, no diplomatic hospitality or gifts. And they don't have the hundred government offices and officials. That's why one part in twenty is enough tax for them. But here in the Middle Kingdom, how can we do without noble-minded leaders and the bonds of human community? If a country is crippled without potters, what happens without noble-minded leaders? If our rulers levy tax rates below that prescribed by the Way of Yao and Shun, they'll be nothing but barbarians great and small. And if our rulers levy tax rates above that prescribed by the Way of Yao and Shun, they'll be nothing but tyrant Chiehs great and small."
11 Po Kuei said: "I can manage high waters better even than Yü."
"You're wrong," replied Mencius. "Yü's management of water is the very Way of water. And so he used the four seas as valleys to drain the floodwaters away. But you use neighboring countries. When you force water out of its natural course, it becomes a flood. And a flood is nothing less than a deluge, which is something the Humane despise. No, you're quite wrong."
12 Mencius said: "If the noble-minded are not faithful and sincere, how can they take command of a situation?"
13 The Lu sovereign wanted Adept Yüeh-cheng to preside over his government.
"When I heard this," said Mencius, "I was so happy I couldn't sleep."
"Is Yüeh-cheng a man of great strength?" asked Kung-sun Ch'ou.
"No."
"Is he a man of wisdom and foresight?"
"No."
"Is he a man of broad learning?"
"No."
"Then why were you so happy you couldn't sleep?"
"Because he's one of those men who loves virtue and benevolence."
"Is loving virtue and benevolence sufficient?"
"Loving virtue and benevolence is enough to govern all beneath Heaven," replied Mencius, "and what is Lu compared to that? If you love virtue and benevolence, people everywhere within the four seas will think nothing of a thousand miles: they'll come share their thoughts about virtue and benevolence. If you don't love virtue and benevolence, people will think your smug and arrogant manner says _I understand all things._ The tone and bearing of such smug arrogance – that alone will keep people a thousand miles away. And when worthy scholars stay a thousand miles away, people with flattering smiles and pleasing tongues come crowding around. Once that happens, how could anyone govern a country well?"
14 Adept Ch'en said: "In ancient times, when would a noble-minded man take office?"
"There were three situations where a noble-minded man would take office," replied Mencius, "and three where he would renounce office. First – he would take office when invited with reverence, according to Ritual, and told that his counsels would be put into practice. Then he would renounce office if his counsels were not put into practice, even if the Ritual courtesies hadn't been violated. Second – he would take office when invited with reverence, according to Ritual, even if his counsels weren't put into practice. Then he would renounce office if the Ritual courtesies were neglected. Third – if he had no food morning or night, and so lived in such hunger that he couldn't walk out his gate, he would accept office if the sovereign heard about his plight and offered assistance, saying: _I've failed in the great work of putting his Wayinto practice, and I've failed to follow his counsels. Now if I let him starve to death in my domain, how could I live with the shame?_ But in such a case, he accepts only to escape starvation."
15 Mencius said: "Shun issued forth from farmlands. Fu Yüeh rose from builders, Chiao Ko from salt and fish, Kuan Chung from jails, Sun Shu-ao from the sea, and Po-li Hsi from markets. So it is that whenever Heaven invests a person with great responsibilities, it first tries his resolve, exhausts his muscles and bones, starves his body, leaves him destitute, and confounds his every endeavor. In this way his patience and endurance are developed, and his weaknesses are overcome.
"We change and grow only when we make mistakes. We realize what to do only when we work through worry and confusion. And we gain people's trust and understanding only when our inner thoughts are revealed clearly in our faces and words. When it has no lawful families or wise officials within and no enemy threats without, a nation will surely come to ruin. Then its people will understand that through calamity and grief we flourish, and through peace and joy we perish."
16 Mencius said: "There are many ways to teach. I don't bother with teaching and instructing, but that's just another way of teaching and instructing."
XIII
To Fathom the Mind Book One
1 Mencius said: "To fathom the mind is to understand your nature. And when you understand your nature, you understand Heaven. Foster your mind, nurture your nature – then you are serving Heaven.
"Don't worry about dying young or living long. What will come will come. Cultivate yourself well – and patient in that perfection, let it come. Then you will stand firm in your fate."
2 Mencius said: "Whatever happens is destiny, but we should accept only what is truly fated. Hence, one who understands destiny won't stand beneath a wall teetering on the verge of collapse.
"To fathom the Way in life, and then die – that is our true fate. To live tangled in fetters, and then die – that is no one's true fate."
3 Mencius said: _"What you seek you will find, and what you ignore you will lose._ Where this saying is right, and to seek means to find, we're seeking something within ourselves.
_"To seek is a question of the Way, and to find is a question of destiny._ Where this is right, and to seek doesn't necessarily mean to find, we're seeking something outside ourselves."
4 Mencius said: "The ten thousand things are all there in me. And there's no joy greater than looking within and finding myself faithful to them. Treat others as you would be treated. Devote yourself to that, for there's no more direct approach to Humanity."
5 Mencius said: "To enact it without making it clear, to enact it over and over without inquiring into it, to enact it for a lifetime without ever understanding its Way – that's how it is for nearly everyone."
6 Mencius said: "It's impossible to be shameless. The shame of being shameless – that is shameless indeed."
7 Mencius said: "Shame is a great thing for people. Crafty schemers have no use for shame. And if you aren't ashamed of being inhuman, what will ever make you human?"
8 Mencius said: "In their love of virtue and benevolence, sage emperors of ancient times forgot about their exalted position. How could sage scholars of ancient times be any different? Delighting in the Way, they too forgot about exalted positions. So unless emperors and dukes came in reverence and according to Ritual, they were rarely admitted to see such scholars. And if it was nearly impossible to see them, how could those rulers ever convince them to take office?"
9 Mencius said to Sung Kou-chien: "You love to travel, offering your counsel to leaders, so I'll tell you something about such things: Know contentment when your counsel is valued, and contentment when it's ignored."
"What must a person be to know such contentment?" asked Sung Kou-chien.
"If you honor Integrity and delight in Duty you can know such contentment," replied Mencius. "The worthy never forget Duty when destitute, and never abandon the Way when they succeed. Not forgetting Duty when destitute, the worthy realize themselves. And when they succeed without abandoning the Way, the people's faith in them never falters.
"When the ancients fulfilled their ambitions, bounty rained down on the people. When they failed, they were still worthy exemplars for all the world to see. Cultivate virtue and benevolence in yourself when destitute and alone. And when you succeed, share that virtue and benevolence with all beneath Heaven."
10 Mencius said: "A commoner only feels called to great work when an Emperor Wen appears. But a great man sets to work even when there's no sign of an Emperor Wen."
11 Mencius said: "To live humble and dissatisfied with yourself, even if all the wealth of Han and Wei were added to your own – that is the mark of a person beyond compare."
12 Mencius said: "If your Way is making life easier for them, the people won't resent hard work. And if your Way is helping them live, the people won't resent being led to their death."
13 Mencius said: "Under the finest of august lords, the people seem peaceful and happy. Under a true emperor, they seem utterly content. They neither resent him when put to death, nor praise him when richly rewarded. They grow more virtuous and benevolent every day, without ever realizing who makes this happen.
"So it is that when the noble-minded pass through a place, they leave transformations behind. And when they dwell in a place, they work miracles. They grace the same stream as Heaven above and earth below: who can doubt their healing power?"
14 Mencius said: "It's Humane music that goes deep inside people, not Humane words. And it's virtuous teaching that wins people over, not virtuous government. The people fear virtuous government, but they love virtuous teaching. Virtuous government can win people's wealth, but virtuous teaching can win their hearts."
15 Mencius said: "To have an ability without being taught – that is true ability. To know without struggling to know – that is true knowing.
"Young children all know love for their parents. And when they grow up, they all know respect for their elders. Loving parents is Humanity, and respecting elders is Duty. That's the secret. Just extend it throughout all beneath Heaven."
16 Mencius said: "When Shun dwelled deep in the mountains, he dwelled among trees and stones, roamed with boar and deer. The difference between him and the other mountain people was slight indeed. But then he heard a single word of virtue, saw a single act of virtue, and it was like a great river breaking through its banks: nothing could stop it."
17 Mencius said: "Don't do what should not be done, and don't desire what should not be desired. Abide by this one precept, and everything else will follow."
18 Mencius said: "Integrity, wisdom, skill, intelligence – such things are forged in adversity. Like the son of a common mistress, a forsaken minister is ever cautious, ever watchful. That's how he avoids danger and succeeds."
19 Mencius said: "There are people who find satisfaction in serving a sovereign. There are ministers who find satisfaction in keeping the gods of grain content. There are the denizens of Heaven who learn what will benefit all beneath Heaven and put it into practice. And then there are the truly great: they can rectify all things by rectifying themselves."
20 Mencius said: "The noble-minded have three great joys, and ruling all beneath Heaven is not one of them. To have parents alive and brothers well – that is the first joy. To face Heaven above and people below without any shame – that is the second joy. To attract the finest students in all beneath Heaven, and to teach and nurture them – that is the third joy. The noble-minded have three great joys, and ruling all beneath Heaven is not one of them."
21 Mencius said: "The noble-minded may want a large country and vast population, but that isn't what fills them with joy. To stand at the center of all beneath Heaven and bring contentment to people everywhere within the four seas – that's what fills the noble-minded with joy. But it isn't what answers to their nature. Their nature gains nothing if they manage the great affairs of state, and it loses nothing if they live in destitute obscurity. This is because the noble-minded know their given nature to be complete in itself.
"Humanity, Duty, Ritual, wisdom – such aspects of their nature take root in mind, flourish in appearance. There's a calmness in the face of the noble-minded, a calmness that also graces their back, radiates through their four limbs. And so the body of someone noble-minded speaks a parable without words."
22 Mencius said: "Po Yi fled the tyrant Chou and settled on the shores of the North Sea. On hearing Emperor Wen had come to power, he said _I hear Wen takes good care of the old, so why not go back and serve him?_ Duke T'ai fled the tyrant Chou and settled on the shores of the West Sea. On hearing Emperor Wen had come to power, he said _I hear Wen takes good care of the old, so why not go back and serve him?_ When there's a ruler somewhere in all beneath Heaven who takes good care of the old, the Humane flock to serve him.
"When every five-acre farm has mulberry trees along the walls and a woman to raise silkworms, the old can wear silk. And when there are five hens and two sows, and their proper seasons aren't neglected, the old need not go without meat. When every hundred-acre farm has a man to till the fields, even large families don't go hungry.
"This is what they meant by _Wen takes good care of the old._ He organized farmlands and villages, taught people to plant mulberries and raise livestock, showed the women how to care for the aged. Without silk at fifty, people can't keep warm. And without meat at seventy, they can't get full. Not warm and not full – that is called freezing and starving. Among Emperor Wen's people, the old never froze or starved. That's what Po Yi and Duke T'ai were saying."
23 Mencius said: "If you expand their fields and reduce their taxes, you'll make the people rich. And if they use food according to season and wares according to Ritual, they'll never exhaust their wealth.
"People can't live without fire and water. But if you go knocking on gates at nightfall, asking for fire and water, no one will refuse you. That's because fire and water are so plentiful. In ruling all beneath Heaven, the sage makes beans and millet as plentiful as fire and water. When beans and millet are as plentiful as fire and water, how can any of the people be Inhumane?"
24 Mencius said: "When Confucius climbed Tung Mountain, he realized how tiny Lu is. And when he climbed T'ai Mountain, he realized how tiny all beneath Heaven is. So it is that once you've seen oceans, water seems petty. And once you've entered the gate of a sage, words seem petty.
"But there's an art to seeing water: look at its ripples, for the brilliance of sun and moon ignite anything that will hold light. And when water flows, it fills every hollow before moving on. It's like this for the noble-minded in the Way: they succeed only if the pattern they make is beautiful."
25 Mencius said: "To rise at the cock's cry and practice virtue and benevolence with untiring diligence – that is to be a follower of Shun. To rise at the cock's cry and chase profits with untiring diligence – that is to be a follower of Chih the bandit. There's nothing more to the difference between Shun and Chih than this: the distinction between virtue and profit."
26 Mencius said: "Yang Chu valued self above all: even if it would bring great profit to all beneath Heaven, he wouldn't pluck a single hair from his head. Mo Tzu proposed universal love: if it would bring any profit to all beneath Heaven, he would toil long and hard, wearing every hair from his body.
"Now we have Master Mo who clings to the middle ground. The middle ground is closer to the mark, but unless he allows for the complexity of circumstance he's still clinging to a single doctrine. The problem with clinging to a single doctrine is that it plunders the Way: to glorify the one, you cast out a hundred."
27 Mencius said: "The hungry savor any food. The thirsty savor any drink. They have no discrimination in food and drink: hunger and thirst has ruined it. And hunger and thirst can ruin more than people's tongues: it can also ruin their minds. Once you free your mind from the ruin of hunger and thirst, you no longer worry about failing to equal the great sages."
28 Mencius said: "All the wealth of three dukes couldn't make Liu-hsia Hui waver in his resolve."
29 Mencius said: "Getting something done is like digging a well. You can dig a well seventy feet deep, but if you don't hit water it's just an abandoned well."
30 Mencius said: "Yao and Shun possessed it by nature. T'ang and Wu embodied it. And the five chiefs of the august lords borrowed it. But if you borrow something long enough, who would know it isn't yours?"
31 Kung-sun Ch'ou said: "Yi Yin banished T'ai Chia to T'ung, saying: _I can't be so intimately involved with someone who is so contrary._ The people were greatly pleased. And when T'ai Chia returned to Yi Yin a sage, the people were again greatly pleased. When a sage serves as minister under a sovereign who is not a sage, can he banish the sovereign?"
"He can if his motives are like Yi Yin's," replied Mencius. "But if his motives aren't like Yi Yin's, it's usurping the throne."
32 Kung-sun Ch'ou said: "The _Songs_ say the noble-minded _never eat the food of idleness._ What do you think of the noble-minded living on food they haven't grown themselves?"
"When a noble-minded man lives in a country and the sovereign values him," replied Mencius, "the sovereign gains peace and wealth, honor and glory. When disciples follow him, they learn to honor parents and elders, to earn trust and stand by their words. If there's anyone who _never eats the food of idleness,_ surely it's him."
33 Prince T'ien asked: "What is the task of a worthy official?"
"To cultivate the highest of purposes," replied Mencius.
"What do you mean by _the highest of purposes_?"
"It's simple: Humanity and Duty. You defy Humanity if you cause the death of a single innocent person, and you defy Duty if you take what is not yours. What is our dwelling-place if not Humanity? And what is our road if not Duty? To dwell in Humanity and follow Duty – that is the perfection of a great person's task."
34 Mencius said: "If he were offered the state of Ch'i in violation of Duty, everyone believes Master Chung would refuse. But this is only the Duty that refuses a basket of rice and a bowl of soup.
"There's nothing great about abandoning your place in the bonds of parent and family, sovereign and minister, leader and citizen. How is it people see something so small and believe it to be great?"
35 T'ao Ying asked: "When Shun was the Son of Heaven and Kao Yao was the justice minister, what would have happened if Blind Purblind killed someone?"
"Kao Yao would have arrested him," replied Mencius.
"But wouldn't Shun have forbidden it?"
"How could he forbid it? Kao Yao had been given authority."
"Then what would Shun have done?"
"Casting all beneath Heaven aside meant no more to Shun than casting aside an old sandal," said Mencius. "He would have stolen away with his father on his back, and gone to live beside the sea. He would have lived out his life happily there, forgetting all beneath Heaven entirely."
36 When Mencius was traveling from Fan to Ch'i, he saw the Ch'i prince and said with a sigh: "A dwelling-place transforms the _ch'i,_ just as food transforms the body. Great indeed is the influence of a dwelling-place – for aren't we all alike born of humankind?"
Then he continued: "This prince's house, carriage, and clothes aren't much different from other people's. And yet he's so different. If his dwelling-place can do that, imagine dwelling in the most boundless dwelling-place of all beneath Heaven.
"The sovereign of Lu once went to Sung and called out at Tieh-tse Gate. Hearing him, the gatekeeper said: _This isn't my sovereign. How is it he sounds so much like my sovereign?_ The reason is simple: their dwelling-places were so much alike."
37 Mencius said: "To feed people without showing them love – that is to treat them like pigs. To love people without showing them reverence – that is to keep them like pets. But honor and reverence are gifts not yet given. Honor and reverence without substance – you can't lure the noble-minded with such empty gestures."
38 Mencius said: "Our appearance belongs to the nature of Heaven. Only as a true sage can you abide by your appearance."
39 When Emperor Hsüan of Ch'i wanted to shorten his mourning period, Kung-sun Ch'ou said: "A year of mourning is better than none at all, isn't it?"
"That's like watching someone twist an elder's arm and saying: _Gently. Do it gently,"_ replied Mencius. "What you should do is teach him how to honor parents and elders."
At the same time, there was a prince whose mother had died. On the prince's behalf, his teacher asked that he be allowed a mourning period of several months. "What do you think of that?" asked Kung-sun Ch'ou.
"The prince wants to observe the full mourning period," replied Mencius, "but he cannot. In this case, even a single day is better than nothing. There was nothing preventing Emperor Hsüan from mourning: he just wanted to avoid it."
40 Mencius said: "The noble-minded teach in five ways. They transform like rain coming in its season. They realize Integrity. They perfect talents. They answer questions. They cultivate themselves and so stand apart as examples. These five ways are how the noble-minded teach."
41 Kung-sun Ch'ou said: "The Way is lofty and beautiful indeed, but it's like climbing to Heaven: it seems impossible to reach. Why not offer something people can hope to reach, something they can work at day after day with untiring diligence?"
"A great carpenter doesn't abandon the measuring string to make woodwork easy for inept apprentices," replied Mencius. "And Yi didn't give up a strong full draw to make archery easy for inept students. The noble-minded draw the bow and hold it. Then it seems they've leapt into the center of the Way, letting whoever is able follow them there."
42 Mencius said: "When all beneath Heaven abides in the Way, people use the Way to find themselves. When all beneath Heaven ignores the Way, people use themselves to find the Way. I never hear of using the Way to find the human anymore."
43 Adept Kung-tu said: "When T'eng Keng was your disciple, he seemed a man deserving of the Ritual respect, but you refused to answer his questions. Why?"
"When people wield such privileged positions as renown or wisdom, age or merit or friendship," replied Mencius, "I never answer them. And T'eng Keng wielded two of them."
44 Mencius said: "If someone stops where they should not, they'll stop anywhere. If someone slights a person they should treat generously, they'll slight anyone. And if someone races ahead, they retreat in a hurry."
45 Mencius said: "The noble-minded love things, but don't treat them with Humanity. They treat the people with Humanity, but don't treat them as kindred. Once you treat kindred as kindred, you treat the people with Humanity. And once you treat the people with Humanity, you love things."
46 Mencius said: "The wise understand all things, and so devote themselves to the essentials. The Humane love all things, and so consider kindred devotion to the sages essential. The wisdom of Yao and Shun was that they didn't treat all things alike: they devoted themselves to essentials first. And the Humanity of Yao and Shun was that they didn't love all people alike: they devoted themselves to kindred affection for the sages.
"To be meticulous about mourning for a few months while declining to mourn the full three years, to ask about the etiquette of dining while swilling soup and wolfing down food – such things are called not understanding the essentials."
XIV
To Fathom the Mind Book Two
1 Mencius said: "Emperor Hui of Liang was utterly Inhumane. The Humane extend their love to those they hate. The Inhumane inflict their hatred on those they love."
"What do you mean by that?" asked Kung-sun Ch'ou.
"In his passion for more territory, Emperor Hui sent his people to war, tearing them asunder and suffering disastrous defeats. Soon he wanted to return to the battlefield, but was afraid he couldn't win. So he sent his beloved son to the grave too. This is what I mean by _inflicting their hatred on those they love."_
2 Mencius said: "There were no just wars in _The Spring and Autumn Annals._ Some were better than others, but that's all. A sovereign may discipline his august lords by attacking them. But one country should never discipline another in such a way."
3 Mencius said: "If people believe everything in _The Book of History,_ it's worse than having no _Book of History_ at all. In the entire 'War Successfully Completed' chapter, I accept no more than two or three strips.
"The Humane have no match in all beneath Heaven. If a Humane ruler attacks an Inhumane one, how could _blood flow so deep fulling sticks begin floating away_?"
4 Mencius said: "There are people who say: _I am an expert in war and tactics._ But they're just common criminals. If the ruler of a country loves Humanity, he will have no match in all beneath Heaven. When he marches south, the northern tribes will complain: _Why does heleave us for last?_ And when he marches east, the western tribes will complain: _Why does he leave us for last?_
"When Emperor Wu marched against Shang with three hundred war-chariots and three thousand illustrious warriors, he said: _Have no fear: I bring you peace. The Shang people are not my enemy._ At this, the Shang people bowed to the ground like animals shaking their horns loose. Hence, to invade was to rectify. People all want to rectify themselves, so what's the use of war?"
5 Mencius said: "A master carpenter or carriage-maker can hand down compass and square to his followers, but he cannot make them skillful."
6 Mencius said: "When Shun was eating cracked rice and wild greens, he lived as if he would spend his whole life like that. And when he was the Son of Heaven, wearing embroidered robes and playing his _ch'in_ in the company of Yao's two daughters, he lived as if he'd always enjoyed such things."
7 Mencius said: "Only now have I realized the true gravity of killing a man's family members. If you kill his father, he'll kill your father. If you kill his brother, he'll kill your brother. There's precious little difference between that and killing your father or brother with your own hands."
8 Mencius said: "In ancient times, border stations were set up to resist attacks. Now they're set up to launch attacks."
9 Mencius said: "If you don't practice the Way yourself, how will you ever get your wife and child to practice it? And if you don't employ people according to the Way, how can you ever get your wife and child to practice it?"
10 Mencius said: "If you're always cultivating profit, you'll avoid death in bad years. If you're always cultivating Integrity, you'll avoid confusion in evil times."
11 Mencius said: "If you love renown, you can give away a nation of a thousand war-chariots. If you don't, you can't give away a basket of rice or bowl of soup without looking pained."
12 Mencius said: "If the worthy and Humane are not trusted, the country is an empty shell. If Ritual and Duty are ignored, leaders and citizens are confounded. And if the work of government is ignored, no amount of wealth will satisfy a country's needs."
13 Mencius said: "It has happened that Inhumane tyrants have gained control of a country. But such men have never ruled all beneath Heaven."
14 Mencius said: "The people are the most precious of all things. Next come the gods of soil and grain. The sovereign matters least.
"That's why a person must win over the people to become the Son of Heaven, win over the Son of Heaven to become an august lord, and win over an august lord to become a high minister.
"When an august lord neglects the gods of soil and grain, he should be replaced. When the sacrificial animals are perfect, the vessels of grain pure, the sacrifices observed in their proper seasons, and still drought and flood plague the land, then the gods of soil and grain should be replaced."
15 Mencius said: "A sage is teacher to the hundred generations. Po Yi and Liu-hsia Hui are such men. That's why the greedy are cured of greed when they hear the legend of Po Yi, and the timid grow resolute; why the niggardly grow generous when they hear the legend of Liu-hsia Hui, and small minds grow broad. They arose a hundred generations ago, but a hundred generations from now they'll still inspire all who hear of them. If they weren't sages, how could this happen? And imagine what they meant to the people who knew them!"
16 Mencius said: "Humanity is the human. Put them together and you have the Way."
17 Mencius said: "When Confucius left Lu, he said: _There's no hurry, no hurry at all._ That's the Way to leave your parents' country. When he left Ch'i, he simply emptied his rice steamer and set out. That's the Way to leave a foreign land."
18 Mencius said: "When Confucius suffered such hardship in Ch'en and Ts'ai, it was because he had no friends among rulers and ministers."
19 Mo Chi said: "I've never been much good at talk."
"There's no harm in that," replied Mencius. "Thoughtful people despise those who talk too much. The _Songs_ say:
_My troubled heart is grief-stricken_
_at this small-minded world's hatred._
Confucius was like that. And Emperor Wen was like this:
_Though he couldn't ease their hatred,_
_his renown never faltered among them."_
20 Mencius said: "The wise and worthy used their bright insight to open bright insight in people. Now pundits use blind ignorance to open bright insight in people."
21 Mencius said to Adept Kao: "If a footpath in the mountains suddenly gets a lot of use, it becomes a road. And if it's never used, it's soon choked with underbrush. That's how it is with your heart: choked with underbrush."
22 Adept Kao said: "Yü's music was much finer than Emperor Wen's."
"Why do you say that?" asked Mencius.
"Because the bell-pivots in his orchestra were nearly worn through."
"That's hardly proof. Do the deep ruts passing through a city gate come from the power of a single team of horses?"
23 When there was famine in Ch'i, Adept Ch'en said: "The Ch'i people are hoping you can get T'ang to open its granaries for them again. But you can't do that, can you?"
"If I did," replied Mencius, "I'd be another Feng Fu. Feng Fu was a man in Chin who was good at seizing tigers, but eventually became a good official. Many years later he went out into the country and found a crowd of people chasing a tiger. They cornered the tiger against some cliffs, but no one dared tangle with it. When they saw Feng Fu, they ran to greet him. And seeing him boldly roll up his sleeves and climb out of his carriage, they were delighted. But the other scholars there only laughed."
24 Mencius said: "The mouth's relation to flavor, the eye's to color, the ear's to sound, the nose's to fragrance, the four limbs' to ease – these are human nature. But they're also the Mandate of Heaven, so the noble-minded never call them human nature.
"Humanity's relation to father and son, Duty's to sovereign and minister, Ritual's to guest and host, understanding's to the wise and worthy, the sage's to Heaven's Way – these are the Mandate of Heaven. But they're also human nature, so the noble-minded never call them the Mandate of Heaven."
25 Hao-sheng Pu-hai asked: "What kind of man is Adept Yüeh-cheng?"
"A man of virtue and sincerity," replied Mencius.
"What do you mean by _virtue_ and _sincerity_?"
"What we aspire to is called _virtue,_ and to possess it within us is called _sincerity_ ," began Mencius. "To possess it in rich abundance is called _beauty,_ and to be ablaze with that rich abundance is called _great._ Someone transformed by that greatness is a _sage,_ and to be a sage beyond all knowing – that is called _divinity._ Yüeh-cheng has mastered the first two, but the last four are still beyond him."
26 Mencius said: "When people abandon the school of Mo Tzu, they turn to Yang Chu. And when they abandon the school of Yang Chu, they turn to Confucius. When they turn to our Confucian school, we should take them in. That's all.
"But these days, people debate the followers of Mo Tzu and Yang Chu, and it's like they're chasing stray pigs. First they herd them back into the pen, then they tie up their legs."
27 Mencius said: "There are three forms of taxation: cloth, grain, and labor. The noble-minded levy one, and relax the other two. If you levy two at once, the people starve and die. If you levy all three at once, father and son are torn asunder."
28 Mencius said: "An august lord has three treasures: land, people, and government. If they treasure pearls and jade, they're destined for ruin."
29 When P'en-ch'eng K'uo took office in Ch'i, Mencius said: "He's as good as dead."
Eventually P'en-ch'eng K'uo was put to death, and the disciples asked: "How did you know he'd be put to death?"
"He was a man of little talent," replied Mencius, "and he'd never learned the great noble-minded Way. That's all it took to kill him."
30 When Mencius went to T'eng and stayed in the Upper Palace, there was a half-finished pair of sandals on the windowsill. At some point, the palace servants came looking for them but couldn't find them. So someone asked: "Can your followers really be so shameless?"
"Do you think we came all this way just to steal sandals?" replied Mencius.
"I wouldn't think so. But as a teacher, you don't chase after students who leave and you don't refuse students who come. If they come to you with an earnest mind, you accept them without any question."
31 Mencius said: "There are things people find unbearable. To see that and use it to understand what makes life bearable – that is Humanity. There are things people will not do. To see that and use it to understand what people should do – that is Duty.
"The heart detests harming others. If you apply that everywhere, you'll never exhaust Humanity. The heart detests peeking through holes and stealing over walls. If you apply that everywhere, you'll never exhaust Duty. People resent condescension. If you apply that everywhere, you can practice Duty wherever you go.
"To say what you should not say – that is to use words as a ploy. Not to say what you should say – that is to use silence as a ploy. Either way, it's no different from peeking through holes and stealing over walls."
32 Mencius said: "Words that speak of things close at hand and carry far-reaching implications – those are the good words. Guarding the essentials and applying them broadly – that is the good Way.
"The noble-minded always use forthright words, so the Way endures in them. And they cultivate themselves tenaciously, so all beneath Heaven is at peace.
"People keep leaving their own fields to weed the fields of others. It's a sickness. They demand everything of others, and nothing of themselves."
33 Mencius said: "For Yao and Shun, it was their very nature. And T'ang and Wu – they returned to it.
"When every movement of mind and body is in accord with Ritual – that is the fullest form of Integrity. When you mourn the dead utterly, it isn't to impress the living. When you abide by Integrity without swerving, it isn't to earn a fat salary. And when you speak with true sincerity, always standing by your word, it isn't to justify your actions. The noble-minded simply put the law into action, then await their fate."
34 Mencius said: "When you counsel great figures, do it with disdain. Don't let their majesty impress you. Ceilings thirty feet high and rafter-beams a yard across – if I realized my every dream, I wouldn't have such things. Serving girls by the hundred and tables ten feet wide spread with food – if I realized my every dream, I wouldn't have such things. Great fun drinking, riding, and hunting, always a retinue of a thousand carriages following behind – if I realized my every dream, I wouldn't have such things.
"The things they do are all things I would never do. And the things I do are all in accordance with the ancient precepts. So why should I cower before them?"
35 Mencius said: "For nurturing the mind, there's nothing like paring your desires away to a very few. If you have few desires, there may still be some capricious whims in your mind, but they'll be few. If you have many desires, there may still be some enduring principles in your mind, but they'll be few indeed."
36 Tseng Hsi loved sheep-dates. But his son, Master Tseng, couldn't bear to eat them.
"Which tastes better – roast mincemeat or sheep-dates?" asked Kung-sun Ch'ou.
"Roast mincemeat, of course," replied Mencius.
"Then why did Master Tseng eat roast mincemeat and not sheep-dates?"
"Roast mincemeat is a taste shared by many, but a taste for sheep-dates is unique. It's forbidden to use someone's personal name, but not their family name. This is because a family name is shared by many, while a personal name is unique."
37 Adept Wan Chang asked: "When he was in Ch'en, Confucius said: _Let's go back home. The young in our villages are full of impetuous ambition. They forge ahead but cannot forget their childish ways._ But he was in Ch'en, so what made him think of the impetuous young scholars in Lu?"
Mencius replied: "Confucius said: _I can't find students who steer the middle Way, so I turn to the impetuous and the timid. The impetuous forge ahead, and the timid know what to avoid._ Obviously, Confucius wanted to find students who steer the middle Way. But since he couldn't find such people, he started thinking about the best alternatives."
"What sort of person did he mean by _impetuous?"_ asked Wan Chang.
"People like Ch'in Chang, Tseng Hsi, and Mu P'i."
"Why did he call them impetuous?"
"They were full of ambition," said Mencius, "and grand boasting about _The ancients! The ancients!_ But if you examine their actions, you see they often violated the ancient precepts.
"And when he couldn't find the impetuous for students, all Confucius could do is look for arrogant scholars who wouldn't condescend to anything the least bit impure. These are the timid, and they are the next best alternative."
Wan Chang continued: "Confucius said: _I regret all those who pass by my gate without entering to become students – all but the righteous villager. Arighteous villager is the thief of Integrity._ What sort of person did he mean by _righteous villager?"_
"All that grand boasting of the impetuous is senseless," replied Mencius. "Their words ignore their actions; their actions ignore their words. And still they bluster about _The ancients! The ancients!_ And how can the timid walk around so cold and self-contained? They live in this world, so they should act like they're a part of it. But if these two only act with virtue and benevolence, they're alright.
"As for those righteous villagers: they enfeeble themselves fawning all over this world."
"If a whole village praises someone as righteous," said Adept Wan, "then they'd be called righteous wherever they went. So why did Confucius call such a person _the thief of Integrity?"_
"If you want to accuse such a person, there's no place to begin," replied Mencius. "If you want to criticize, there's nothing to criticize. They do what everyone else does, in perfect harmony with this sordid world. They live that way, and yet seem loyal and sincere. They act that way, and yet seem pure and honest. They please everyone and believe they're always right. But it's impossible to enter the Way of Yao and Shun with them. That's why Confucius called such a person _the thief of Integrity._
"Confucius said:
_I hate things that are not what they appear. I hate weeds for fear they'll be confused with young rice. I hate sweet talk for fear it will be confused with eloquence. I hate calculating tongues for fear they'll be confused with sincerity. I hate the dissolute songs of Cheng for fear they'll be confused with music. I hate purple for fear it will be confused with the purity of vermilion. And I hate righteous villagers for fear they'll be confused with people of Integrity._
"The noble-minded simply return to the changeless principle. When the changeless principle is established, the people flourish. And when the people flourish, the twisty ways of evil are unknown."
38 Mencius said: "It was over five hundred years from Yao and Shun to T'ang. People like Yü and Kao Yao understood because they knew Yao and Shun, and people like T'ang understood through learning. It was over five hundred years from T'ang to Emperor Wen. People like Yi Yin and Lai Chu understood because they knew T'ang, and people like Emperor Wen understood through learning. It was over five hundred years from Emperor Wen to Confucius. People like Duke T'ai and San-yi Sheng understood because they knew Wen, and people like Confucius understood through learning.
"Now it's hardly been a hundred years from Confucius to our own age. We aren't far from his time, and we're so near his home. But if no one here's gleaned anything from that great sage, then no one here's gleaned anything."
Notes
I. Emperor Hui of Liang, Book One
**miles:** The Chinese mile _(li)_ is much shorter than our own, the ratio being 3 _li_ per mile.
**Humanity:** See Key Terms: _Jen._
**Duty:** See Key Terms: _Yi._
**Emperor Wen:** Father of Wu, the founder of the Chou Dynasty, Wen was considered responsible for the resplendent culture of the Chou Dynasty, hence his name, which means "culture." See Historical Table.
**Way:** See Key Terms: _Tao._
**acre:** The Chinese acre _(mu)_ is much smaller than our own, the ratio being 6.6 _mu_ per acre or less.
**square miles:** In ancient China this form of measurement seems to have meant something different than it does for us. Seven hundred square miles apparently means an area of land seven hundred miles on each side. Still, such measurements don't seem consistent, and seem more figurative than literal.
**Emperor Hsiang:** Emperor Hui died, and Hsiang was the son who became his successor.
**Duke Huan:** Most illustrious of the noble lords in the earlier years of the Chou Dynasty (reigned 685–643). See note III.2.
**Integrity:** See Key Terms: _Te_.
**Middle Kingdom:** Ancient heartland in the north inhabited by fully civilized Chinese, as opposed to the southern and other outlying regions, which were "barbarian" or only partially civilized. As those regions became fully Chinese, this term ( _Chung Kuo_ ) extended to mean all of China.
**Ritual:** See Key Terms: _Li_.
II. Emperor Hui of Liang, Book Two
**Way:** See Key Terms: _Tao._
**Emperor T'ai:** Chou sovereign who preceded King Wen. See Historical Table.
**Celestial Lord:** Shang Ti, the Shang Dynasty's supreme deity: see Introduction p. 12 f.
**Emperor Wu:** Chou Emperor who conquered the last Shang emperor and replaced the Shang Dynasty with the Chou Dynasty. Hence his name, which means "martial." See Historical Table.
**Ch'i:** Different from the Ch'i ruled by King Hsüan.
**Emperor Kung Liu:** Chou sovereign in a time well before the Chou state conquered the Shang Dynasty, when the semi-barbarian Chou was being forced east toward Shang by western tribes.
**Tyrant Chieh . . . Tyrant Chou:** Chieh and Chou were the last, debased rulers of the Hsia and Shang dynasties respectively. In overthrowing them, T'ang and Wu founded new and noble dynasties: the Shang and Chou, respectively.
**Ch'i invaded the nation of Yen:** Trying to make himself look like the sage-emperor Yao, who passed over his own son and bequeathed the throne to the most worthy successor, Emperor K'uai of Yen abdicated in favor of his prime minister, Lord Chih, in 315 B.C.E. The prime minister was expected to decline, but instead accepted. This sparked a very destructive civil war led by the rightful heir, and King Hsüan of Ch'i finally intervened. See also IV.8–9.
**Master Tseng:** Disciple of Confucius who became an influential teacher.
**Ch'i Mountain:** See next section for the entire story.
III. Kung-Sun Ch'ou, Book One
**Kung-sun Chou:** Disciple of Mencius.
**successes of Kuan Chung:** Duke Huan became sovereign in Ch'i by killing his brother Chiu. Kuan Chung was initially Chiu's advisor, but afterwards became a sage prime minister under Duke Huan. His talents turned Ch'i into a powerful and rich state, and made Huan first among the august lords.
**Duke Chou:** A cultural hero much admired by Confucius and Mencius, Duke Chou helped his brother, Wu, found the Chou Dynasty. He was also a major intellectual figure, another in legend at least of a good share of The Book of Songs ( _Shih Ching_ ) and The Book of Change ( _I Ching_ ). As the primary architect of the Chou political system, he set up the institutions of sagely government and is traditionally credited with developing the doctrine of the Mandate of Heaven, which introduced ethics into government (see Historical Table and Introduction, pp. 13 f).
**Mind:** The word _hsin,_ which recurs throughout this section, means both "heart" and "mind." The Chinese made no fundamental distinction between the two.
**Meng Pin:** Courageous warrior of antiquity.
**Master Kao:** Philosopher contemporary with Mencius. See XI.1–6 for their dialogues on human nature.
**ch'i:** See Key Terms: _Ch'i._
**Tsai Yü, Adept Kung . . . Jan Po-niu, Min Tzu-ch'ien, and Yen Hui:** These five were disciples of Confucius.
**Po Yi:** Po Yi and his brother Shu Ch'i (twelfth century B.C.E.) were heir to the throne, but they felt it would be wrong to accept it, so they refused. As a result, they lived in great poverty, finally dying of cold and hunger in the mountains.
**Yi Yin:** The great minister who helped T'ang found the Shang Dynasty. See Historical Table.
**Yao . . . Shun:** Two mythic sage-emperors from legendary prehistory. See Historical Table.
**disparage me:** _Songs_ 155. A bird is speaking.
**"T'ai Chia":** The _Analects_ IV.1.
**Liu-hsia Hui:** Sage governor in Lu (7th–6th century).
IV. Kung-Sun Ch'ou, Book Two
**Shen T'ung:** For an explanation of the events referred to in this and the following section, see note II.7.
**Ch'en Chia:** One of the Ch'i emperor's counselors.
**Master Szu:** The celebrated grandson of Confucius and reputed author of _The Doctrine of the Mean,_ one of the Confucian classics. Mencius is said to have studied under one of Master Szu's disciples.
V. Duke Wen of T'eng, Book One
**Yen Hui:** Perhaps the most able of Confucius' disciples. Confucius admired his wisdom and ability above all others and grieved deeply when he died young.
**mutual assistance:** In the personal system _(kung),_ each family cultivated its own land and paid ten percent of the produce as a tax. In the mutual system _(chu),_ each family cultivated its own land, and also cultivated public land jointly with other families. The produce of the public land was paid as a tax. This is essentially the well-field system described below. In the communal system _(ch'e),_ families cultivated land communally, dividing the produce between them and paying ten percent to the government.
**well-field system:** Under this system, each parcel of land is divided into nine plots and so looks like the character _(ching)_ meaning _well:_ . The eight outer plots in this configuration are each cultivated by one family. In addition to cultivating their own plot, the eight families cultivate the center plot jointly. This is public land, and its produce is given to the government as a tax.
**Shen Nung:** literally: "Divine Farmer," a mythic emperor believed to have reigned from 2838 to 2698 B.C.E., is credited with the invention of the plow and the agricultural arts. He also discovered the medicinal uses of plants, and began the practice of trading in markets.
**Kao Yao:** Shun's sage justice minister.
**Mo Tzu:** Mo Tzu (5th c. B.C.E.), who lived in the century between Confucius and Mencius, was the founder of a major school of social philosophy that competed with the Confucian school. He is most famously associated with the idea that social ills can be resolved if we each love all others equally, rather than loving some (family, e.g.) more than others.
VI. Duke Wen of T'eng, Book Two
**Ch'en Tai:** Disciple of Mencius.
**summons:** See X.7 for a fuller version of this story.
**Ching Ch'un:** Politician in the time of Mencius.
**Kung-sun Yen and Chang Yi:** Itinerant scholars who were very influential as advisors of rulers.
**boundless dwelling-place:** That is: Humanity. See XIII.33 and 36.
**token of credentials:** Each government rank had its own prescribed token. Itinerant scholars wanting a position would present this token to a sovereign as a way of proving their qualifications.
**P'eng Keng:** Disciple of Mencius.
**Wan Chang:** Disciple of Mencius.
**K'uang Chang:** High official in Ch'i.
VII. Li Lou, Book One
**Three Dynasties:** Hsia, Shang, Chou.
**I rinse my feet clean:** This song also appears in "The Fisherman," part of the ancient _Ch'u Tz'u_ anthology _(The Songs of Ch'u)._
**Duke T'ai:** Duke T'ai became a great counselor to Emperors Wen and Wu, helping them to overcome the Shang tyrant and found the Chou Dynasty.
**Jan Ch'iu:** Disciple of Confucius.
**Chun-yü K'un:** Scholar who rose to high position from humble origins.
VIII. Li Lou, Book Two
**Lord Ch'an:** Wise and worthy prime minister of Cheng much admired by Confucius.
**from the people:** The poems in the _Book of Songs_ were folk songs gathered by emperors wanting to know how the people felt about their rule.
**without entering:** See V.4.
**wise and worthy:** See the _Analects_ VI.10.
IX. Wan Chang, Book One
**ch'in:** An ancient stringed instrument played by all intellectuals in ancient China, ancestor to the more familiar Japanese koto.
**Hsien-chiu Meng:** Disciple of Mencius.
**half a person left:** There is nothing in the language itself to show that this is describing a future possibility, so it could literally be read in the present: "there _isn't_ half a person left."
**T'ai Chia:** Son who suceeded T'ang after his death.
XII. Master Kao, Book Two
**Wu Huo:** A legendary strongman.
**better even than Yü:** For Yü managing floodwaters, see V.4 and VI.9.
XIII. To Fathom the Mind, Book One
**Yi Yin banished T'ai Chia:** See IX.6.
XIV. To Fathom the Mind, Book Two
**beloved son to the grave:** See also I.5.
**two or three strips:** Books were written on bamboo strips, which were tied together with leather string.
**fulling sticks:** Used by women as they prepared heavy winter clothes. In literary use, it usually implies the men have been conscripted and are far away at war.
**hardship in Ch'en and Ts'ai:** See the _Analects_ XI.2 and XV.2.
**childish ways:** Cf. the _Analects_ V.21.
**what to avoid:** The _Analects_ XIII.21.
**thief of Integrity:** This sentence is the _Analects_ XVII.11.
Historical Table
Key Terms
_An Outline of Mencius' Though_ t
Li: | Ritual
---|---
|
A religious concept associated with the worship of gods and spirits prior to Confucius, Ritual was reconfigured by Confucius to mean the web of social responsibilities that bind a society together. These include the proprieties in virtually all social interactions, and are determined by the individual's position within the structure of society. By calling these secular acts "Ritual," Confucius makes everyday experience itself a sacred realm. This Ritual structure of society is part of a vast cosmological weave: the Ritual structure of natural process as the ten thousand things emerge from the primal emptiness.
Jen: | Humanity (Humane)
|
The character for _jen_ is formed by a combination of the characters for "human being" and "two," and it means all of the moral qualities expressed in the behavior of ideal human beings toward one another. _Jen_ is the internalization of _li_ , and _li_ is the codified external expression of _jen_. So, to be Humane means to master a kind of selflessness by which we dwell as an integral part of the Ritual weave. Or, more simply: to act with a selfless and reverent concern for the well-being of others. Jen is the touchstone of Confucian sagehood, a kind of _enlightenment_ which Confucius claimed was beyond even him.
Yi: | Duty
|
The prescriptions of Ritual are general in nature. The ability to apply them in specific situations is Duty, and so Duty is the particular ethical expression of Humanity.
Tao: | Way
|
The effortless process of human society functioning according to its natural Ritual structure. It can be expanded to cover Ritual's cosmological dimensions, making it comparable to the more familiar Taoist Tao. Hence: the effortless process of the cosmos functioning according to its natural Ritual structure. The cosmos always abides by the Tao, with the frequent exception of human societies.
Te: | Integrity
|
The ability to act according to the Tao (Way). Or more precisely, the embodiment of the Tao in the sage, where it becomes a kind of power through which the sage can transform others "by example." This concept is deepened by _Te_ 's etymological meaning at the level of pictographic imagery: "heart-sight clarity."
T'ien: | Heaven
|
Natural process. Or, more descriptively, the inevitable unfolding of things in the cosmological process. Hence, Heaven appears as a kind of immanent fate in the human realm – and as Ritual is its organizing principle, it becomes a kind of moral force encouraging societies to abide by Ritual and the Tao.
Ch'i: | Ch'i
|
The universal breath, vital energy, or cosmic life-force. It is the breath-force that pulses through the Cosmos as both matter and energy simultaneously, giving form and life to the ten thousand things and driving their perpetual transformations. And so it is the tissue of which the Cosmos is made. In its originary form, it is primal- _ch'i_ ( _yüan-ch'i_ ), which is present in Absence and is perhaps the aspect that gives the primordial emptiness of Absence pregnant with possibility. Primal _-ch'i_ is made up of _yin_ and _yang_ completely intermingled and indistinguishable. Once primal _-ch'i_ separates out into _yin_ and _yang, yang_ rose up to become sky and _yin_ sunk down to form earth. As the universal breath, _ch'i_ is in constant motion, animating all things, and so is a kind of tissue that connects us always to the empty source.
Further Reading
Chan Wing-tsit. _A Source Book of Chinese Philosophy._ New York: Columbia University Press, 1969.
DeBary, William T., Wing-tsit Chan, and Burton Watson, eds. _Sources of Chinese Tradition._ 2 vols. New York: Columbia University Press, 1960.
Eno, Robert. _The Confucian Creation of Heaven._ Buffalo: SUNY Press, 1990.
Fingarette, Herbert. _Confucius: The Secular As Sacred._ New York: Harper & Row, 1972.
Fung Yu-lan. _A History of Chinese Philosophy._ Translated by Derk Bodde. Princeton: Princeton University Press, 1952–53.
Graham, A. C. _Disputers of the Tao._ LaSalle, Ill.: Open Court, 1989.
Hughes, E.R. _The Great Learning and the Mean in Action._ London: Dent, 1942.
Mencius. _Mencius._ Translated by D. C. Lau. London: Penguin, 1970.
———. _Mencius, Vol. 1, The Chinese Classics._ Translated by James Legge. 1861–73. Reprint Hong Kong: University of Hong Kong Press, 1960.
Mote, Frederick. _Intellectual Foundations of China._ New York: Alfred A. Knopf, 1971.
Ropp, Paul, ed. _Heritage of China._ Berkeley: University of California Press, 1990.
Schwartz, Benjamin. _The World of Thought in Ancient China._ Cambridge: Harvard University Press, 1985.
Shun Kwong-Loi. _Mencius and Early Chinese Thought._ Palo Alto, Calif.: Stanford University Press, 1997.
Tu Wei-ming. _Humanity and Self-Cultivation: Essays in Confucian Thought._ Berkeley: Asian Humanities Press, 1979.
| {
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using Nager.Date.Contract;
using Nager.Date.Extensions;
using Nager.Date.Model;
using System;
using System.Collections.Generic;
using System.Linq;
namespace Nager.Date.PublicHolidays
{
/// <summary>
/// Monaco
/// </summary>
public class MonacoProvider : IPublicHolidayProvider
{
private readonly ICatholicProvider _catholicProvider;
/// <summary>
/// MonacoProvider
/// </summary>
/// <param name="catholicProvider"></param>
public MonacoProvider(ICatholicProvider catholicProvider)
{
this._catholicProvider = catholicProvider;
}
///<inheritdoc/>
public IEnumerable<PublicHoliday> Get(int year)
{
var countryCode = CountryCode.MC;
var items = new List<PublicHoliday>();
items.Add(new PublicHoliday(year, 1, 27, "La Sainte Dévote", "Saint Devota's Day", countryCode));
items.Add(this._catholicProvider.EasterMonday("Easter Monday", year, countryCode));
items.Add(new PublicHoliday(year, 5, 1, "Le 1er mai", "May Day", countryCode));
items.Add(this._catholicProvider.AscensionDay("L'Ascension", year, countryCode));
items.Add(this._catholicProvider.WhitMonday("Le lundi de Pentecôte", year, countryCode));
items.Add(this._catholicProvider.CorpusChristi("La Fête Dieu", year, countryCode));
items.Add(new PublicHoliday(year, 8, 15, "L'Assomption de Marie", "Assumption Day", countryCode));
items.Add(new PublicHoliday(year, 12, 8, "L'Immaculée Conception", "The Immaculate Conception", countryCode));
#region New Year's Day
var newYearsDay = new DateTime(year, 1, 1).Shift(saturday => saturday, sunday => sunday.AddDays(1));
items.Add(new PublicHoliday(newYearsDay, "Le jour de l'An", "New Year's Day", countryCode));
#endregion
#region All Saints Day
var allSaintsDay = new DateTime(year, 11, 1).Shift(saturday => saturday, sunday => sunday.AddDays(1));
items.Add(new PublicHoliday(allSaintsDay, "La Toussaint", "All Saints Day", countryCode));
#endregion
#region National Day / La Fête du Prince
var nationalDay = new DateTime(year, 11, 19).Shift(saturday => saturday, sunday => sunday.AddDays(1));
items.Add(new PublicHoliday(nationalDay, "La Fête du Prince", "National Day", countryCode));
#endregion
#region Christmas Day
var christmasDay = new DateTime(year, 12, 25).Shift(saturday => saturday, sunday => sunday.AddDays(1));
items.Add(new PublicHoliday(christmasDay, "Noël", "Christmas Day", countryCode));
#endregion
return items.OrderBy(o => o.Date);
}
///<inheritdoc/>
public IEnumerable<string> GetSources()
{
return new string[]
{
"https://en.wikipedia.org/wiki/Public_holidays_in_Monaco"
};
}
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 8,693 |
Q: Given is a set of clauses. Find a logic formula in CNF such that..
Given is the set of clauses $$\tau_1 := \left\{\left\{P, \neg
S\right\}, \left\{S\right\},\left\{S,R\right\},\left\{\neg S, \neg
P\right\}\right\}$$
For this set of clauses, find a logic formula $\varphi_1$ in CNF such
that for all interpretations $I$ you have that $$I \models \varphi_1
\Leftrightarrow I \models \tau_1$$
I start with change the set of clauses to CNF formula.
How?
In reading they say example:
The CNF formula $$\varphi = A_1 \wedge (\neg A_2 \vee A_1) \wedge (A_3
> \vee \neg A_2 \vee \neg A_1)$$
is represented by the finite set of clauses
$$\left\{\left\{A_1\right\}, \left\{\neg A_2, A_1\right\}, \left\{A_3,
> \neg A_2, \neg A_1\right\}\right\}$$
So in this case the formula is:
$$\varphi_1 := (P \vee \neg S) \wedge (S) \wedge (S \vee R) \wedge (\neg S \vee \neg P)$$
But I don't know it also satisfy the condition in task? I mean $$I \models \varphi_1 \Leftrightarrow I \models \tau_1$$
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 2,522 |
{"url":"https:\/\/labs.idsucla.org\/unit_3\/lab3c\/lab3c.html","text":"# Random Sampling\n\nLab 3C\n\n### Learning by sampling\n\n\u2022 In many circumstances, there's simply no feasible way to gather data about everyone in a population.\n\n\u2022 For example, the Department of Water & Power (DWP) wants to determine how much water people in Los Angeles use to take a shower. They've created a survey to pass out to collect this information.\n\u2022 Write down two reasons why getting everyone in Los Angeles to fill out the survey would be difficult. Also, write a sentence why the DWP might consider using a sample of households instead.\n\u2022 In this lab, we'll learn how sampling methods affect how representative a sample is of a population.\n\n\u2022 In previous labs, we used the cdc data as a sample for young people in the United States.\n\u2022 In this lab, we'll consider these survey respondents to be our population.\n\u2022 Load the cdc data into R and fill in the blanks to take a convenience sample of the first 50 people in the data:\ns1 <- slice(____, 1:____)\n\n\u2022 Why do you think we call this method a convenience sample?\n\n\u2022 A convenience sample is a sample from a population where we collect data on subjects because they're easy-to-find.\n\u2022 Using your convenience sample, create a bargraph for the number of people in each grade.\n\u2022 Do you think the distribution of grade for your sample would look similar when compared to the whole cdc data?\n\u2022 Which groups of people do you think are over or under represented in your convenience sample? Why?\n\u2022 Create a bargraph for grade using the cdc data.\n\u2022 Compare the distributions of the cdc data and your convenience sample and write down how they differ.\n\n### Using randomness\n\n\u2022 Fill in the blanks below to create a sample by randomly selecting 50 people in the cdc data, without replacement. Call this new sample s2:\n___ <- sample(___, size = ___, replace = ___)\n\n\u2022 Write a sentence that explains why you think the distribution of grade for this random sample will look more or less similar to the distribution from the whole cdc data.\n\u2022 Create a bargraph for grade based on this random sample to check your prediction.\n\n### Increasing sample size\n\n\u2022 Create bargraphs for grade based on each of the following sample sizes: 10, 100, 1,000, 10,000.\n\u2022 Compare each distribution to that of the population.\n\u2022 How do the distributions change as the size of the sample increases? Why do you think this occurs?\n\u2022 tally() the proportion of grades for your convenience sample and all your random samples.\n\u2022 Which set of proportions looks most similar to the proportions of the population?\n\n### Lessons learned\n\n\u2022 The mean, or proportion, from a random sample might not always be closer to that of the true population when compared to a convenience sample.\n\u2022 However, as sample sizes get larger:\n\u2022 Random samples will tend to be better estimates for the population.\n\u2022 With convenience samples, this might not be the case.\n\u2022 Write down a reason why estimates based on convenience samples might not improve even as sample size increases.","date":"2021-03-03 05:33:00","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\": 0.30905967950820923, \"perplexity\": 1245.6590417772613}, \"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-2021-10\/segments\/1614178365454.63\/warc\/CC-MAIN-20210303042832-20210303072832-00271.warc.gz\"}"} | null | null |
2020-THE GAME
21/01/2021 | Written by:Penny | Blogs
Why Adventure Board Games Are Worth Playing?
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Introducing 2020 – The Game!
2020-The Game is an exhilarating board game where the players struggle to collect 270 electoral votes and win the White House, all while navigating the challenges of the year 2020. | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 8,891 |
The best time to prepare for raising a child, on your own or together, is in the months before the baby is born.
Many of us take courses to prepare for childbirth. Most hospitals offer guidance on the physical care of your infant. But what about preparation for parenthood itself.
know your own areas of confidence and areas of vulnerability, and those of your partner.
New parents benefit immeasurably from the chance to examine, explore, and discuss the many unspoken assumptions and feelings about parenthood that they bring with them from their own childhoods and life experiences.
I can give you a heads-up about some of the most common issues that take new parents by surprise. I can help you to explore ahead of time how you might want to approach these issues in your changing family. I can help partners to meld their wishes together to create an effective working partnership.
I can help you to give your baby, and your new family, the best start possible! | {
"redpajama_set_name": "RedPajamaC4"
} | 8,730 |
Rituals of Life è il secondo album in studio della band hardcore punk Stretch Arm Strong, pubblicato nel 1999 dalla Solid State Records.
Tracce
When Sorrow Falls
Outside Looking in
Second Chances
All We've Lost
Try to Forget
For Now
Pursuit of Happiness
Reach Out
Set Free
Through My Actions
To a Friend
I Melt With You (Modern English cover) (traccia nascosta)
Formazione
Chris McLane - voce
Scott Dempsey - chitarra
David Sease - chitarra
Jeremy Jeffers - basso
John Barry - batteria
Note
Collegamenti esterni
Album del 1998 | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 9,902 |
\section{\label{sec:Intro}Introduction}
Low-dimensional systems are model materials in which intertwined electronic degrees of freedom lead to strongly correlated ground states. Experimental realizations includes fabrication of quantum/nano dots \cite{Daniel1998, Li2012}, thin films \cite{Venables2000, Geim2010} and even bulk samples \cite{Kimura2008, Forslund2019}, for which the crystal structure may facilitate low dimensional character. These systems where superconductivity \cite{Lange2003}, metal-insulator transition \cite{Mott1968, Kobayashi2019}, spin liquids \cite{Zhou2017} are only a few of many phenomena reported, which have raised the interest of scientists from both fundamental and applied sciences.
Cr$X_3$ ($X =$ I, Cl) are a series of compounds exhibiting low dimensionality. These materials have a rhombohedral symmetry, consisting of 2D Cr layers arranged in a honeycomb web fashion, surrounded by octahedrally coordinated $X$ ions. Many studies on Cr$X_3$ ($X =$ I, Cl) were performed back when the Beatles or ABBA were still on tour \cite{Hansen1958, Cable1961, Narath1964, Kuhlow1982}, but the materials have regained attention due to current topical interest in 2D layered materials \cite{Balleste2011}. Notably, a recent study has shown that monolayers may be obtained via exfoliation \cite{Huang2017}. The interest is driven by the possibility to study low dimensional magnetism, and prospects of electrical control of magnetism for future functional devices \cite{Matsukura2015, Jiang2018}.
Neutron diffraction measurements at low temperatures revealed that the Cr ions in CrCl$_3$ are ferromagnetically (FM) coupled in the plane and antiferromagnetically (AF) along the c-axis (Fig.~\ref{fig:ZFSpec}(c)) \cite{Cable1961}. A Faraday rotation study \cite{Kuhlow1982} as a function of temperature suggested a rather bold yet fascinating ordering phenomena. On cooling from the paramagnetic state, a first magnetic transition occurs at 16.8~K, at which the Cr spins order ferromagnetically (FM) in a quasi-2-dimensional fashion but they remain disordered in-between the layers. Upon further cooling, the FM structure is rearranged such that an interlayer antiferromagnetic (AF) coupling is stabilised at 15.5~K (AF - quasi-2D FM - PM transition). \cite{Kuhlow1982} This cascade of transitions was also studied by SQUID \cite{Bykovetz2019} and heat capacity \cite{McGuire2017} measurements. The studies support the two transitions scenario but without fully able to experimentally disregard the quasi-2D FM scenario. While the SQUID study hinted at a third possible transition (at 16.8~K, 16.0~K and 14.3~K), such picture was only supported in the low field SQUID measurements suggesting that the magnetism of CrCl$_3$ is sensitive to externally applied magnetic field. This suggests that studies in zero field (ZF) are imperative and relevant for the title compound.
\begin{figure*}[ht]
\begin{center}
\includegraphics[keepaspectratio=true,width=160 mm]{Fig_1_ZF_Spec_V2_MM.pdf}
\end{center}
\caption{(a) Zero field (ZF) $\mu^+$SR spectra for selected temperatures ($T = 2$, 14, 15, 16, 17, 19, 24 and 44 K) for the CrCl$_3$ compound. (b) The FFT of the ZF time spectrum as a function of selected temperature. Solid lines represent the best fit using Eq.~(\ref{eq:ZF}). The temperature dependencies of $f^{\rm AF}_1$, $f^{\rm AF}_2$ and $f^{\rm AF}_3$ are highlighted as dashed lines for guide to the eyes. (c) The magnetic structure of CrCl$_3$ drawn within the crystal unit cell, where the ordered moments are shown as black arrows. The predicted muon sites are included as purple ($\mu1$ = (0, 0, 0.15)), red ($\mu2$ = (0, 0, 0)) and orange ($\mu3$ = (0, 0, 0.5)) spheres.}
\label{fig:ZFSpec}
\end{figure*}
In this letter, we report the results of a muon spin rotation, relaxation and resonance ($\mu^+$SR) study of CrCl$_3$. The internal magnetic field distribution at the muon site is measured in ZF and compared with the expected one for the reported magnetic structure \cite{Cable1961}. The low temperature out of plane fluctuations are suppressed above above 9.5~K, which seem to alter the magnetic structure. Moreover, transverse field (TF) measurements highlight that a significant local spin density compared with the paramagnetic (PM) state is not established in the intermediate quasi-2D FM state, questioning the previous assessments. Instead of quasi-2D FM, our results point toward the formation of ferromagnetic short range order (FM-SRO), settling the debate.
Chemical vapor transport (CVT) method was used to prepare single crystals of CrCl$_3$, which were later crushed into a powder form since each individual crystals were not large enough for the experiment. The quality of the sample was checked with basic characterisations prior to the $\mu^+$SR measurements. Details regarding the synthesis is found in SM. The $\mu^+$SR measurements were performed at the surface muon beamline GPS \cite{GPS} at PSI (Switzerland) whereas the DFT calculation were performed using the pseudopotential-based plane-wave method as implemented in $Quantum~Espresso$ \cite{QE-2009, QE-2017}. Details of sample synthesis and experimental setup is found in Ref.~\onlinecite{McGuire2017} and Supplementary materials (SM).
The collected zero field (ZF) time spectra for selected temperatures, and the corresponding Fourier transform frequency spectra, are shown in Fig.~\ref{fig:ZFSpec}. In order to account for all processes described in the whole measured temperature range, the ZF time spectra were fitted using a combination of oscillations, a stretched exponential, and an exponentially relaxing static Gaussian Kubo-Toyabe (KT) function:
\begin{eqnarray}
A_0 \, P_{\rm ZF}(t) &=&
\sum_{i}^{3} A^{\rm AF}_i \cos(f^{\rm AF}_i 2\pi t+\phi^{\rm AF}_i)e^{-\lambda^{\rm AF}_i t}\cr &+& A_{\rm tail} e^{-(\lambda_{\rm tail}t)^{\beta_{\rm tail}}} + A_{\rm KT}G^{\rm SGKT}(\Delta_{\rm KT}, t)e^{-\lambda_{\rm KT} t},
\label{eq:ZF}
\end{eqnarray}
where $A_{0}$ is the initial asymmetry determined by the instrument and $P_{\rm ZF}$ is the muon spin polarization function in ZF configuration. $A^{\rm AF}_{i}$, $f^{\rm AF}_{i}$, $\phi^{\rm AF}_{i}$ and $\lambda^{\rm AF}_{i}$ are the asymmetry, frequency, phase and depolarization rate resulting from the internal magnetic field components that are perpendicular with respect to the initial muon spin polarisation. $A_{\rm tail}$, $\lambda_{\rm tail}$ and $\beta_{\rm tail}$ on the other hand are the asymmetry, the relaxation rate and the stretched exponent originating from internal magnetic field components that are parallel with respect to the initial muon polarisation. This form is selected to represent three tail components for $A^{\rm AF}_1$, $A^{\rm AF}_2$, and $A^{\rm AF}_3$ by one term. In a perfect powder, on average, in a perfect powder, on average, 2/3 of the internal fields are oriented perpendicular to the initial muon spin while 1/3 are oriented along the initial muon spin. Indeed, $A_{\rm tail}\simeq \sum A^{\rm AF}_{i}/2$, justifying the usage of a stretched exponential as the tail. $A_{\rm KT}$ and $\lambda_{\rm KT}$ are the asymmetry and the relaxation rate of the KT. The static Gaussian KT is represented by $G^{\rm SGKT}(\Delta_{\rm KT}, t)$ where $\Delta_{\rm KT}$ is related to the second moment of the (Gaussian) field distribution created by the nuclear magnetic moments, considered static in the time window of the experiment. The detailed fitting procedure is outlined and justified in SM.
\begin{figure}[ht]
\begin{center}
\includegraphics[keepaspectratio=true,width=85 mm]{Fig_2_ZF_Para_V3_MM2.pdf}
\end{center}
\caption{Temperature dependencies of Zero field (ZF) fit parameters, obtained using Eq.~(\ref{eq:ZF}): (a) precession frequencies ($f^{\rm AF}_1$, $f^{\rm AF}_2$ and $f^{\rm AF}_3$), (b) relaxation rates (right: $\lambda_{\rm tail}$ and $\lambda_{\rm KT}$) and left: $\lambda^{\rm AF}_{1}$. The inset in (a) is the stretched exponent ($\beta_{\rm tail}$). The solid lines in (a) represents the best fit using $f=f_0(1-\frac{T}{T^{\rm ZF}_{\rm N}})^{\alpha}$: $\alpha_1=0.43(14)$, $T^{\rm ZF}_{\rm N}=14.2(4)$ and $f_0=25(3)$ for the signal $f^{\rm AF}_1$ and $\alpha_2=0.36(1)$, $T^{\rm ZF}_{\rm N}=14.32(6)$ and $f_0=42.9(4)$ for the signal $f^{\rm AF}_2$. The dashed lines are guide to the eyes. For clarity, $\lambda^{\rm AF}_2$ and $\lambda^{\rm AF}_3$ are omitted in Fig.~\ref{fig:ZFPara} and presented in SM instead.}
\label{fig:ZFPara}
\end{figure}
Temperature dependencies of the precession frequencies are shown in Fig.~\ref{fig:ZFPara}(a). Order parameter-like behaviour is observed for $f_{1}$ and $f_{2}$ up to $T^{\rm ZF}_{\rm N}$. In fact, $f_{1}(T)$ and $f_{2}(T)$ can be fitted in accordance with mean field theory: $f=f_0(1-\frac{T}{T^{\rm ZF}_{\rm N}})^{\alpha}$, where $\alpha_1=0.43(14)$, $T^{\rm ZF}_{\rm N}=14.2(4)$~K and $f_0=25(3)$~MHz for the signal $f^{\rm AF}_1$ and $\alpha_2=0.36(1)$, $T^{\rm ZF}_{\rm N}=14.32(6)~$K and $f_0=42.9(4)$~MHz for the signal $f^{\rm AF}_2$. Restricting the fit to closer to $T^{\rm ZF}_{\rm N}$ does not significantly modify the obtained parameters. While both signals are within the error bars of each other, the larger error bars for the $f^{\rm AF}_1$ component is due to the very large value of $\lambda^{\rm AF}_1$, suggesting that the values obtained for $f_2$ are more accurate and we shall define $T_{\rm N}=T^{\rm ZF}_{\rm N}=14.32(6)$. Interestingly, a third frequency component, $f^{\rm AF}_{3}$ presents itself above 9.5~K, which may or may not be present already at 2~K (Fig.~\ref{fig:ZFSpec}(b)). Although, a deviation in the temperature dependence is observed in the $f^{\rm AF}_{3}$ component above 9.5~K and exhibits a rather abrupt change at $T^{\rm ZF}_{\rm N}$. This may suggests that the magnetic structure is altered such that the crystalline moun site is split magnetically above 9.5~K.
The temperature dependencies of the relaxation rates for the slower components ($\lambda_{\rm tail}$ and $\lambda_{\rm KT}$) are shown in Fig.~\ref{fig:ZFPara}(b). $\lambda_{\rm tail}$ corresponds to the spin-lattice relaxation rate and is therefore a measure on how dynamic the system is. A peak like feature is observed between 2 and 9.5~K and is most likely related to difficulty in fitting the $A^{\rm AF}_1$ component, given the high value of $\lambda^{\rm AF}_1$. Instead of a peak feature, one would expect the relaxation rates to increase monotonically with decreasing temperature (see guide to the eyes in Fig.~\ref{fig:ZFPara}(b)). It should be noted that a similar peak behaviour, but less pronounced, is also obtained if two exponentials are used for the tail instead of a streached one. The striking feature is however that the dynamics seems to decrease with increasing temperature, on the contrary to most compounds. Therefore, the internal field dynamics is a driver and an important factor for the system to change its magnetic structure, such that the new magnetic structure splits the crystalline $\mu1$ site into two magnetically different sites, yielding one low frequency and one high frequency precessions. A change in the magnetic structure has not been reported in previous studies \cite{Cable1961, McGuire2017, Bykovetz2019}, suggesting that the change is very subtle. Similarly, a change in the crystal structure has not been reported as well \cite{Cable1961, Morosin1964, McGuire2017}.
Above $T^{\rm ZF}_{\rm N}$, $\lambda_{\rm KT}$ exhibits a maximum value and rapidly decreases with increasing temperature. The increase at $T^{\rm ZF}_{\rm N}$ corresponds to critical spin fluctuation slowing down, and the decrease with higher temperature suggests an increase in internal magnetic field fluctuations. This temperature dependence is similar to what is found in TF configuration ($\lambda_{\rm TF}$, SM). This behaviour demonstrates spin-spin dynamical correlations in the magnetically non ordered state and is thus expected to follow the temperature dependence of the Curie-Weiss law. Finally, the temperature dependence of the stretched exponent, $\beta_{\rm tail}$, is shown in inset of Fig.~\ref{fig:ZFPara}(a). In this case, $\beta_{\rm tail}\simeq0.6$ at 2~K and increases with increasing temperature. Typically, $\beta$ exhibits values close to 1 at higher temperature and decreases as the temperature is lowered towards 0.3 \cite{Ogielski1985, Campbell1994, Amit1996}.
Before addressing the quasi-2D FM state, the recorded $\mu^+$SR time spectrum collected at 2~K is reproduced in order to confirm both the proposed magnetic structure and the predicted muon sites. In our past treatment \cite{Forslund2020_Na}, it was shown that the hyperfine contact field is neglectable in an AF, even for an A-type AF. This behaviour is naturally different from that of a FM \cite{Forslund2021_La}. Therefore, the current system shall be modeled assuming only dipolar fields. Based on the magnetic structure of Ref.~\onlinecite{Cable1961}, the internal magnetic field at the considered muon sites can be calculated. Each site yield one single presession frequency. In fact, $\mu1$ and $\mu2$ explain the observed ZF time spectrum collected at 2~K: $\mu1=12.73\simeq17.6(1.7)=f^{\rm AF}_1(2~$K$)$ and $\mu2=39.37\simeq40.64(4)=f^{\rm AF}_2(2~$K$)$. A rather large discrepency is observed for site $\mu1$. The very large field distribution width ($\lambda^{\rm AF}_1$ in Fig.~\ref{fig:ZFPara}(b)) at this temperature is making an exact estimate of the frequency difficult. Expected results are obtained for the $\mu2$ site even without the inclusion of hyperfine contact field. The third component, $f^{\rm AF}_3$, is not reproduced in this calculation. This is explained by; (1) the DFT fails to predict all sites, (2) the determined magnetic structure is not complete or (3) the $f^{\rm AF}_3$ is not present below 9.5~K (Fig.~\ref{fig:ZFSpec}(b)). We further discuss the implications of $f^{\rm AF}_3$ below.
While $\mu1$ and $\mu2$ explains the main frequencies observed in the data, it does not provide an adequate answer to why the field distribution width of the site $\mu1$ is large ($\lambda^{\rm AF}_1$ in Fig.~\ref{fig:ZFPara}(b)) at low temperatures, and why it becomes structured as the third $f_3$ component becomes significant around 9.5~K. The answer is most likely related to internal magnetic field fluctuations, that seems to be especially active below 9.5~K. Let us first remind ourselves that $\lambda_{\rm tail}$ corresponds to the spin-lattice relaxation rate. This rate corresponds to the rate in which the muon relaxes between the two Zeeman state present for the spin-1/2 particle.
Now, $\lambda_{\rm tail}(2~$K$)\neq0~\mu$s$^{-1}$ was obtained irrespective of fitting function, $i.e.$ a stretched tail or two separate exponential tail, confirming that the ground state is indeed very dynamical.
Suppose now that the local moments are fluctuating within the a/b plane, given the crystal symmetry and the positions of the muon sites, such fluctuation does not result in significant change in the local field at the $\mu1$ and $\mu2$ sites. However, if the fluctuation are out of plane, the local field at the moun sites changes more dramatically for the $\mu1$ site while this change is not significant for the $\mu2$ site. Therefore, an out of plane fluctuation would explain why $\lambda^{\rm AF}_1$ is large but not $\lambda^{\rm AF}_2$. It seem as these out of plane fluctuations are suppressed as $T_{\rm N}$ is approached and lead to a more static new magnetic structure above 9.5~K.
The detailed magnetic structure can be deduced from the presented data and model. There are many possible magnetic structure and we have selected few relevant ones. First of, canting the in-plane moments out of plane may result in a more defined internal field at $\mu_1$ site with internal field values closer to experimentally obtained ones. Although, a simple canting does not split the sites magnetically. Similarly, an A-type AF with moments aligned parallel to c-axis provide somewhat reasonable results but it does not split the sites either. In fact, many simple structure results in none split $\mu1$ site. Therefore, if $f^{\rm AF}_3$ is a result of a split of the known crystalline moun sites ($\mu1$ and $\mu2$), the magnetic structure above 9.5~K is most likely a little more complicated. If on the other hand $f^{\rm AF}_3$ is from a separate crystalline muon site not predicted with DFT, we may conclude that the reported magnetic structure \cite{Cable1961} is consistent with the presented data but with a potential canting present below 9.5~K. In this case, the degree of the canting is likely to decrease with increasing temperature as the out of plane fluctuations are suppressed. Either case, the detailed magnetic structure is ideally re-investigated in a detailed neutron diffraction study.
While the system is generally considered as a 2D system, mean field fits of the order parameters (Fig.~\ref{fig:ZFPara}(a)) yielded exponents $>0.36$, suggesting 3D like fluctuations below $T_{\rm N}$ \cite{Blundell2003, Taroni2008}. In fact, neutron diffraction \cite{Cable1961}, spin wave analysis \cite{Narath1965}, heat capacity \cite{McGuire2017} and magnetisation \cite{Bykovetz2019} measurements suggest very weak anisotropy. Relatively weak field is able to spin polarise the low temperature AF phase. Moreover, the obtained effective moment from magnetisation measurements is consistent with a value expected for spin only Cr$^{3+}$. In other words, the orbital contribution is suppressed and anisotropy is thus expected to be small. This assessment is also supported by the TF measurements presented below, as small values of TF easily polarises the system.
Now, lets turn our focus onto the proposed quasi-2D FM phase. Faraday rotation measurements \cite{Kuhlow1982} showed that the sample undergoes two transitions, one at 16.8~K and one around 15.5~K: from a high temperature paramagnetic (PM) phase, to a quasi-2D ferromagnetic (FM) phase that is disordered in three dimensions to finally a 3D antiferromagnetic (AF) phase. While studies so far has not manage to neither confirm or reject the quasi-2D FM scenario, we shall now present microscopic evidence for the absence of a quasi-2D FM order.
A clear microscopic evidence of this quasi-2D order can be obtained by measuring the local spin density at the muon site. Therefore, TF as a function of temperature was measured and Fig.~\ref{fig:TFSpec} shows the collected TF $(= 50$~G $\simeq0.6871$~MHz) time spectra for selected temperatures. Two oscillations are needed in order to fit the collected data, due to the presence of the two muon sites ($\mu1$ and $\mu2$). As the temperature is lowered, the frequency is shifted towards higher values, accompanied by a suppression in the amplitude of the oscillation. Therefore, the TF contributions to the time spectra were fitted with three exponentially relaxing oscillations
\begin{eqnarray}
A_0 \, P_{\rm TF}(t) &=&
\sum_{i}^{2} A^{\rm TF}_{i} \cos(f^{\rm TF}_{i}2\pi t+\phi^{\rm TF}_{i})e^{-\lambda^{\rm TF}_{i}t}\cr &+&A^{\rm TF}_{\rm imp} \cos(f^{\rm TF}_{\rm imp}2\pi t+\phi^{\rm TF}_{\rm imp})e^{-\lambda^{\rm TF}_{\rm imp}t},
\label{eq:TF}
\end{eqnarray}
where $A_{0}$ is the initial asymmetry determined by the instrument and $P_{\rm TF}$ is the muon spin polarization function in TF configuration. $A^{\rm TF}$, $f^{\rm TF}$, $\phi^{\rm TF}$ and $\lambda^{\rm TF}$ are the asymmetry, frequency, phase and depolarization rate resulting from the applied TF, where the superscripts $i$ and imp represent the contributions from the sample and impurity phase ($<3\%$). The asymmetry of the impurity contribution was fixed throughout the whole measured temperature range, a value estimated at 2~K. The internal magnetic field contribution present below $T^{\rm TF}_{\rm N}$ were fitted with a combination of exponentials and is further explained in SM, together with the the detailed fitting procedure.
\begin{figure}[ht]
\begin{center}
\includegraphics[keepaspectratio=true,width=65 mm]{Fig_3_TF_MM.pdf}
\end{center}
\caption{(a) Transverse field (TF) $\mu^+$SR spectra for selected temperatures ($T=2$, 14, 15, 16, 17, 18 and 38~K) for the CrCl$_{3}$ compound. Solid lines represent the best fit using Eq.~(\ref{eq:TF}).
}
\label{fig:TFSpec}
\end{figure}
Temperature dependence of muon Knight shift for each site can be obtained from fitting the data using Eq.~\ref{eq:TF}, and is defined as
\begin{eqnarray}
K_{\mu,i}=\frac{\bm B_{\rm ext} \cdot (\bm B_{\rm loc}- \bm B_{\rm ext})}{B_{\rm ext}^2}=\frac{f^{\rm TF}_i-f_{\rm ref}}{f_{\rm ref}}
\label{eq:Knight}
\end{eqnarray}
where the value of the precession frequency obtained at highest measured temperature, $f_{\rm ref}=0.6871$~MHz, was used. Naturally, this results in $K=0$ at the highest measured temperature. The applied field yields positive muonic knight shift as $T^{\rm TF}_{\rm N}$ is approached, despite a TF of 50~G. This suggest that the compound is indeed quite susceptible to externally applied magnetic field, and is consistent with previously reported magnetic field dependent studies \cite{Cable1961, McGuire2017, Bykovetz2019}. The positive shift suggest that the local field aligns with the applied field, and a paramagnetic like state is thus expected.
\begin{figure}[ht]
\begin{center}
\includegraphics[keepaspectratio=true,width=80 mm]{Fig_4_Knight_MM.pdf}
\end{center}
\caption{Muon Knight shift ($K_{\mu,i}$) and the bulk magnetic susceptibility ($\chi$) is plotted with temperature as an implicit parameter. The solid lines represents best linear fits, where the dotted parts are extrapolated. The vertical dashed lines indicted the phase temperature boundaries of the sample: antiferromagnetic (AF), short range order (SRO) and paramagnetic (PM) phases. The AF-SRO transition temperature boundary is around $T=14$~K, while SRO-PM transition temperature is around 17-18~K. The $\chi$ was extracted from a DC-magnetisation measurement under zero field cooling protocol, with an applied of $B=1000$~G.
}
\label{fig:KnightX}
\end{figure}
The microscopic origin to the local field, $\bm B_{\rm loc}$, consists of dipolar field, hyperfine contact field and a temperature independent component. Therefore, the temperature dependence can be attributed to coupling between the muon and polarised localised and intenerant electrons. Given that the dipolar and hyperfine contact field contribution is related to the local magnetic susceptibility, the Knight shift is expected to follow a linear behaviour when plotted against the bulk magnetic susceptibility with temperature as an intrinsic parameter, as shown in Fig.~\ref{fig:KnightX}, where linear behaviours are observed for both sites. The linearity is present from higher temperature (PM phase) down to $T^{\rm ZF}_{\rm N}$, the AF-SRO boundary. At this point however, the derivative changes and is most likely attributed to an increase in the hyperfine coupling constant, as the sample forms an AF order. Of course, the increase can be attributed due to the fact that fitting weak-TF becomes difficult close to $T^{\rm TF}_{\rm N}$ because the TF asymmetry decreases (SM). More importantly though, a change in shape is not present between the PM-SRO phases (around $17-18$~K). This suggests that the local field does not ordered in such a way that the local spin density modifies. For a fully ordered quasi-2D FM, one would expect a significant change in the hyperfine coupling, even if it is just ordered in 2D. These results represent clear microscopic evidence for the absence of "quasi-2D FM" in this compound, as proposed by Ref.~\cite{Kuhlow1982}. Instead of "quasi-2D FM", it is more natural to assign this phase to SRO. While our data cannot determine the detailed interaction, previous studies \cite{Kuhlow1982, McGuire2017} have suggested this phase to be FM like in nature and we may thus assign it to FM-SRO.
Recently, topological spin excitations were observed in the related compound, CrI$_3$ \cite{Chen2018}, given the 2D honeycomb structure of the Cr. A similar behavior may be expected in CrCl$_3$ as well, provided the similar arrangement of 2D honeycomb Cr layers, surrounded by octahedrally coordinated $X$ ion. Compounds with a nontrivial topological magnon edge states are highly attractive for future dissipationless and highly efficient spintronic applications. Naturally, unveiling the details as presented is imperative before undertaking a detailed study of bulk and/or thin films.
In summary, the two dimensional Van der waals magnet, CrCl$_3$, was investigated by muon spin rotation, relaxation and resonance ($\mu^+$SR). This study clarified the magnetic phases present in the compound as a function of temperature: an antiferromagnetic state (AF) for $T\leq T_{\rm N}=14.32(6)$~K, a ferromagnetic short range ordered state (FM - SRO) for $T_{\rm N}<T<\sim18$~K and a paramagnetic phase (PM) for $T\geq\sim18$~K. Zero field (ZF) measurements, complemented by local field calculations, confirmed the magnetic order proposed by neutron diffraction. However, the ground state is found to be highly dynamic, which decreases with increasing temperature, evidenced by the temperature dependence of the spin-lattice relaxation rate. ZF data suggested that the local magnetic structure is changed above 9.5~K, driven by out of plane fluctuations. Knight shifts measurements on the other hand provided with microscopic evidence for the absence of a quasi-2D FM order, which was previously proposed by Faraday measurements. Instead, a ferromagnetic short range order (FM - SRO) is stabilised just above $T_{\rm N}$, for which a paramagnetic phase is recovered above $\sim18$~K.
\begin{acknowledgments}
We thank the staff of PSI for help with the $\mu^+$SR experiments. This research was supported by the Swedish Research Council (VR) (Dnr. 2016-06955) as well as the Swedish Foundation for Strategic Research (SSF) within the Swedish national graduate school in neutron scattering (SwedNess). Y.S. is funded by the Swedish Research Council (VR) through a Starting Grant (Dnr. 2017-05078). Y.S. and K.P. acknowledge funding a funding from the Area of Advance- Material Sciences from Chalmers University of Technology. D.A. acknowledges partial financial support from the Romanian UEFISCDI Project No. PN-III-P4-ID-PCCF-2016-0112. M.A.H. acknowledges financial support from the Swedish Research Council (VR) under project No. 2018-05393. Support by the P220 program of Government of Russia through the project 075-15-2021-604 is acknowledged. J.S. acknowledge support from the Ministry of Education, Culture, Sports, Science and Technology (MEXT) of Japan, KAKENHI Grant No.23108003 and Japan Society for the Promotion Science (JSPS) KAKENHI Grant No. P18H01863 and JP20K21149. The data was analysed with software package musrfit \cite{musrfit}. The crystal figure was drawn using VESTA \cite{Momma2008}.
\end{acknowledgments}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 3,794 |
Q: How to detect a window has been maximized? Does anyone know the WM_MESSAGE that is sent when a window has been maximized (either by the maximize button being pressed in the title bar, or by double clicking the title bar?)
Is there a windows message for the maximize button being pressed?
Win32/C++, thanks.
A: You get the WM_SIZE message with the value SIZE_MAXIMIZED in wParam
Edit
The @jamesdlin comment bellow called my atention to WM_WINDOWPOSCHANGED documentation, which states (emphasis mine):
Remarks
By default, the DefWindowProc function sends the WM_SIZE and WM_MOVE messages to the window. The WM_SIZE and WM_MOVE messages are not sent if an application handles the WM_WINDOWPOSCHANGED message without calling DefWindowProc. It is more efficient to perform any move or size change processing during the WM_WINDOWPOSCHANGED message without calling DefWindowProc.
Thanks james!
A: I dealt with this recently, and the approach I settled on was to check IsZoomed in response to WM_WINDOWPOSCHANGED, comparing its result to the previous one to detect when a transition occurs, and then to forward WM_WINDOWPOSCHANGED to the default window procedure.
If you have complete control over the message handling in your application and know that there isn't (and won't ever be) a WM_WINDOWPOSCHANGED handler that suppresses WM_MOVE/WM_SIZE, then you should be able to handle it directly in a WM_SIZE handler as described in jachguate's answer.
| {
"redpajama_set_name": "RedPajamaStackExchange"
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Gains and losses in Phila. region's population
by Erin Arvedlund, Inquirer Staff Writer, Posted: May 23, 2014
A number of communities in the region's Pennsylvania suburbs, notably in Chester and Montgomery Counties, grew substantially between April 2010 and July 2013, Census Bureau population estimates released Thursday show.
In Chester County, there were noteworthy upticks in municipalities such as Malvern, West Chester, East Brandywine, and West Goshen, and the same was true in Chester/Delaware County border towns such as Bethel and Chadds Ford. In central Montgomery County, Upper Hanover, Towamencin, and Salford were among the burgeoning towns.
Camden County population falls
Meanwhile, Philadelphia remained the fifth-largest U.S. city, with a population estimated at 1.553 million through July 2013, an increase of just over 27,000 from April 2010. It was the seventh year in a row of population growth, the census data showed.
(Population estimates for neighborhoods within the city limits will not be available until December.)
In New Jersey, some towns continued to slowly lose population, though there were notable exceptions on that side of the Delaware River, as well, the estimates indicated.
Seven of the eight counties in the region grew in population. Only Camden County shrank over the three-year period, down 0.2 percent, according to the Census Bureau, which on Thursday released 2013 population estimates for the region's 340 municipalities in Pennsylvania and southern New Jersey.
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Much of that loss was in the city of Camden (0.6 percent), Gloucester Township (0.5 percent), and Winslow (0.8 percent), the numbers showed.
The Census Bureau offered little analysis of the data it released. But, in general, observers of the region's demographic and housing trends said, the data seem consistent.
"The pattern here is one of continued momentum. Townships with good fundamentals remain good places to live," said Kevin C. Gillen, an economist at the University of Pennsylvania's Fels Institute of Government who tracks housing in the region. "But the spike in energy costs is a short-run factor in play behind the numbers. Since the recession, towns that have done well are accessible to public transit and to highways."
Conversely, Gillen said, some locales that have not "are far-flung townships, with no public transport and not near major highways."
New construction lures new residents, and construction in towns like Montgomery Township accounted for three-quarters of the growth, the Census Bureau said in a news release accompanying the data.
Suburban populations will likely keep growing as people young and old seek out new homes and apartments, said economist Joel L. Naroff, of Naroff Economic Advisors in Holland, Bucks County.
"Some second-ring suburbs, like central Bucks County, are catering to baby boomers moving into higher-density housing," Naroff said. "Remember, a few hundred people can be accounted for by just one big housing development."
Closer to the Mason-Dixon Line, he said, the outer ring of Philadelphia suburbs represents "the next logical place to live with buildable land." In addition, Naroff noted, more commuters are living in Delaware and Chester County towns like Avondale and working in Maryland and Delaware, where wages may be higher.
In the inner-ring suburbs, population remained relatively flat between 2010 and 2013, the census data showed, and towns farther out, such as East Brandywine, London Grove, and Montgomery Township led in new residents. But this period of outward population movement doesn't seem as significant as the one that occurred during the prerecession housing bubble.
"Around the country, there are a number of major cities that have been growing faster than their suburbs in recent years, and for the most part that is true in . . . Philadelphia," said Larry Eichel, project director of the Philadelphia Research Initiative at the Pew Charitable Trusts.
"This phenomenon appears to be fueled by three factors: foreign immigration; the preference of the millennial generation for urban life, and baby boomers leaving the suburbs after their children are out of the house," Eichel said.
Some observers cautioned against jumping to conclusions about individual municipalities. For example, a prison (Graterford) in Skippack, Montgomery County, could account for a population increase there, said Susan Copella, director of the Pennsylvania State Data Center at Penn State Harrisburg in Middletown.
"Cities have been witnessing growth for the past few years. Younger people moving in, and not just in Philly," Copella said. But across Pennsylvania, "the majority of the growth we saw is in townships - they grew 78 percent over the three-year period."
That's chiefly due to the fact that smaller boroughs are more often fully built out, she said.
Some Bucks County locales, such as Falls Township, continued to lose residents. River towns nearby such as Bristol have been declining since the steel industry closed down in the 1980s.
In New Jersey, a ribbon of towns along the Delaware in Gloucester, Camden, and Burlington Counties lost residents, the census numbers showed. But some towns, such as Cinnaminson and Woolwich, defied the trend, gaining 7.7 percent and 10.4 percent in the three-year period.
Cinnaminson boasts new housing developments and access to the Camden-Trenton River Line, Gillen said. "That goes to the transit story and the cost of energy."
With $4-a-gallon gasoline, he said, "heating and cooling a 6,000 [square] foot home plus driving a 110-minute commute is very expensive these days."
In southern Gloucester County's boomtowns, growth and building permits go hand-in-hand.
"There have been substantial permits issued in East Greenwich and Woolwich. It's been growing for more than three years," said Sen-Yuan Wu, a research economist at the New Jersey Department of Labor & Workforce Development in Trenton.
Older housing stock is behind population loss in many South Jersey towns, said Noemi Mendez Eliasen, information-services specialist with the Census Bureau's Philadelphia regional office.
"Magnolia and Runnemede . . . have old houses, and that influences whether people want to live there or escape an older home," she said.
earvedlund@phillynews.com
@erinarvedlund
Posted: May 23, 2014 - 3:01 AM
Erin Arvedlund, Inquirer Staff Writer
Even taking the low-price road, the 2021 Lexus IS 300 reaches the highs
Scott Sturgis
Andrew Maykuth
Affordable Care Act open enrollment ends Friday in Pennsylvania
Harold Brubaker
COVID-19 vaccines starting to reach Philly area's intellectually disabled community
U.S. weekly unemployment claims jump to 965,000 as coronavirus takes toll
Christopher Rugaber, Associated Press | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 8,532 |
\section{Conclusion}
\label{sec:conclusion}
Successful application of hybrid-quantum classical algorithms, with the
classical step involving an optimizer, on current hardware, requires the
classical optimizer to be noise-aware.
We have collected a suite of optimizers in {\sc scikit-quant} that we have
found to work particularly well, easily outperforming optimizers available
through the widely used standard SciPy software.
We have focused on VQE, but we expect the results to be generally
applicable: by providing a suite of optimizers with consistent programming
interfaces, it is possible to easily apply combinations of optimizers,
playing into their respective strengths.
Our studies indicate that with these optimizers, the classical step is no
longer the weakest link on NISQ-era hardware.
\section{Discussion}
\label{sec:discusion}
Much work is being dedicated to improving the VQE quantum circuits (depth,
CNOT count, ansatz etc.) and to demonstrate science results on NISQ hardware.
The need for noise-aware minimizers has been previously acknowledged, but
its magnitude may have been understated.
In fact, our study indicates that using a classical optimizer that is not
noise-aware would make it the weakest link in the VQE chain: {\it use
of specialized noise robust optimizers is essential on NISQ hardware}.
Our evaluations of the noise-aware optimizers we collected (and rewrote in
some cases) into {\sc scikit-quant} indicate that:
\begin{itemize}[leftmargin=*]
\item When solving noise-free optimization problems, SciPy optimizers such
as BFGS or Cobyla are fastest by far.
They do fail in the presence of even small noise, to the point of becoming
unusable.
\item When decent parameter bounds are available, ImFil is preferable,
followed by NOMAD.
When tight bounds are available, SnobFit should be considered.
A composition of optimizers works best for final solution quality,
e.g.\ running ImFil first to derive tight bounds for SnobFit.
\item When high quality initial parameters are available, trust region
methods such as PyBobyqa are fastest and preferable, followed by NOMAD and
to a lesser extent SnobFit.
ImFil is not sensitive to the value of the initial solution.
\item Taking performance data into account does not change the above
recommendations.
We do note that some optimizers are adaptive and properly reduce the number
of evaluations in the presence of noise, e.g.\ ImFil and NOMAD.
\item When examining control over the number of iterations and search
strategy (balancing solution quality, execution time, and premature
convergence), ImFil provides direct control over scales and searches.
For the others, only limited control is possible by tweaking the
convergence criteria, (attenuated) step sizes, points in the local model,
or overall budget.
\end{itemize}
Given our collection of optimizers, we wanted to know which method best
handles the combination of optimization surfaces generated by the science
problems and noise caused by the quantum hardware.
Since the ansatz in VQE directly drives the former, and influences the latter
(e.g.\ through circuit depth), this provides important feedback for practical
ansatz design.
There are strong convergence requirements on the minimizer in terms of
distance to the global minimum~\cite{McClean2015}, but also constraints on the
number of evaluations possible before convergence as e.g.\ calibrations may
drift over the duration of the experiment.
To make progress, the optimizer may need to find gradients on a surface with
many local minima due to the noise, and do so with the least number of
iterations possible.
Our results support the following conjectures:
\begin{itemize}[leftmargin=*]
\item There is no free lunch: a {\em suite} of minimizers is needed to match
specific strengths to specific problems, making use of available domain
science information such as a high quality initial parameters, knowledge of
local minima, or the need to search around inaccessible regions.
\item Circuit level noise redistributes counts in the output bit string
probability distributions, from which the objective is calculated.
This redistribution affects the latter in a non-linear way and thus does
not simply average out.
With large noise, it may thus be impossible to retrieve the actual global
minimum value, but by searching for a robust minimum, the correct optimal
parameters may still be found.
\item For complex surfaces with local minima close to the global minima,
noise can prevent the optimizer from distinguishing local from global.
An understanding of the science is then needed to provide more
constraints, e.g.\ in subdividing the problem and studying the minimum
found in each with higher statistics.
\item Most of the methods can scale up to hundreds of parameters.
On NISQ hardware, with the minimizers provided, we expect the performance
of hybrid approaches to be limited by the quantum part of the algorithms.
The optimizers can easily execute on a single node server systems, no
distributed memory parallelization is required yet.
\end{itemize}
Overall, this study indicates that the success of VQE on NISQ devices is
contingent on the availability of classical optimizers that handle noisy
outputs well at the scale of the ``necessary'' qubit concurrency.
As of yet, this is a largely open research area, where our study details some
of the challenges to be expected.
Our software optimizers toolkit is directly useful to VQE Quantum Information
Science practitioners, as well as a good starting point for mathematicians in
search of better optimization methods tailored to VQE and other hybrid
quantum-classical algorithms.
\section{Hybrid Quantum-Classical Algorithms}
\label{sec:hqca}
The hybrid quantum-classical algorithms we consider iteratively alternate
between a classical numerical optimizer and a quantum algorithm that
evaluates some objective to be minimized.
The classical optimizer varies a set of parameters that determine the input
state for the quantum processor to prepare.
The quantum side then executes an algorithm resulting in measurement and
some output distribution of probabilities.
This distribution is mapped into an objective function value that the classical optimizer
can handle, such as a single floating point number, e.g., one representing
the expected energy of a physical system (see Figure~\ref{fig:vqe}).
\begin{figure}[ht]
\begin{minipage}{\columnwidth}
\centering
\includegraphics[width=\columnwidth]{vqeaps}
\caption{\it \small VQE algorithm schematic.
The goal of the algorithm is to find
$\mathrm{E_0(\theta) = min_{\theta}(\langle\psi(\theta)|\mathcal{H}|\psi(\theta)\rangle/\langle\psi(\theta)\psi(\theta))}$
with the classical optimizer changing the input by varying optimization
parameters $\theta$ and the quantum chip calculating the expectation value
of $\mathcal{H}$.}
\label{fig:vqe}
\end{minipage}
\end{figure}
In the Variational Quantum Eigensolver approach for solving chemistry and
physics problems, the objective function calculates the expectation value
of the Hamiltonian $\mathcal{H}$ associated with a configuration of the
simulated physical system.
Without noise, the optimization surface is expected to be smooth and convex
around the global minimum.
Bounds and constraints to help the optimizer and analysis are often
straightforward to obtain from physical laws, e.g.\ there should be no loss
of particles.
In Quantum Approximate Optimization Algorithms, the state is prepared
by a {\it p}-level circuit specified by {\it 2p} variational
parameters. Even at the lowest circuit depth (p=1), QAOA has
non-trivial provable performance guarantees. Initial QAOA exemplars
have been selected from the domain of graph optimization problems such
as MaxCut. The optimization surfaces generated by QAOA problems can be
arbitrarily complex and bounds and constraints are harder to define as they
need not be physical.
Because of these last differences, understanding the impact of noise on the
behavior of hybrid algorithms is more straightforward for VQE and we will
concentrate our study on its behavior.
However, since we do not restrict the study to realistic noise levels only,
but push the optimizers to their breaking point, we believe that our
findings are directly applicable to the higher complexity in QAOA algorithms
as well.
For more details, see Section~\ref{sec:related}.
\subsection{Role of the Ansatz in VQE}
The classical optimizer is not free to choose input states for VQE, but
constrained by a parametrized {\em ansatz}, which describes the range of
valid physical systems and thus determines the optimization surface.
A good ansatz provides a balance between a simple representation (and
thus simple operators in the quantum circuit), efficient use of available
native hardware gates, and sufficient sensitivity of the objective with the
input parameters.
An effective ansatz can greatly reduce circuit depth, search space, and the
number of steps necessary to convergence.
For now, ansatz design is still an art that requires detailed insights from
the domain science to uncover symmetries and to decide which simplifications
are acceptable.
However, our main interest is to push the optimizers.
Since a better ansatz will simply allow the domain scientist to work on
larger, more complex, problems that equally push the optimizer harder, we
will restrict ourselves to the commonly used, and practical, {\em unitary
coupled cluster} ansatz (UCC ansatz) for all studies.
For physical systems, the UCC ansatz can be thought of as describing the
movements of individual particles (linear terms) and those of interacting
(e.g.\ through electric charge) pairs of particles (quadratic terms).
It is simple to map and, because particles such as electrons are
indistinguishable, easy to find symmetries to reduce the number of
parameters needed to describe all valid configurations.
Besides the number of parameters, the choice of ansatz also affects the
number of qubits used.
For example, the UCC ansatz provides for simple physical interpretations,
such as `1' meaning that a site or orbital is occupied by an electron, and
`0' meaning that it is unoccupied.
Add a second qubit for spin up and down, and two qubits can fully describe a
site or orbital.\footnote{It is still completely up to the domain scientist to
determine which and thus how many sites are relevant for the problem they are
trying to solve, which is the most important driver of the number of qubits
needed.}
However, there is a clear inefficiency here: it is unnecessary to describe
the spin of an unoccupied site.
But changing to a more compact representation requires changing the ansatz
and the operators, which can actually make the problem harder to solve.
Published results~\cite{Li_2017,Temme_2017,Dumitrescu_2018} comprise only two
and four qubit experiments with two parameters.
In our studies we have used 4 and 8 qubit problems, with the number of
parameters ranging from 2 to 14.
\subsection{VQE Quantum Processor Step}
The quantum circuit consists of two parts: a state preparation and an
evolution.
The state preparation takes the chip from its computational ground state to
the intended initial state as set by the classical optimizer.
The evolution works by computing successive steps in ``imaginary time''
($e^{-i\mathcal{H}\tau}$ with $\tau = it$).
This process attenuates the contributions of the eigenvectors of the
Hamiltonian proportional to the exponent of their respective eigenvalues.
Thus, after a sufficient number of steps, only the component of the smallest
eigenvalue is left.
The chip readout is then a probability distribution of bit strings that
represents the estimated ground energy eigenstate, from which the estimated
energy is then calculated classically using the Hamiltonian.
The mapping of the measured probability distribution to a single number (the
energy) is non-linear because the input is constrained to be physical and
sum to 1.
It is thus not possible to make any general inference about the uncertainty
distribution of the estimated energy from the expected errors in the
probability distribution, but only about specific problem instances.
\section{Introduction}
\label{sec:intro}
Hybrid quantum-classical algorithms are promising candidates to exploit the
potential advantages of quantum computing over classical computing on
current quantum hardware.
Target application domains include the computation of physical and chemical
properties of atoms and molecules~\cite{feynman1982}, as well as optimization
problems~\cite{farhi2014quantum,Wang_2018} such as graph MaxCut.
These hybrid algorithms execute a classical optimizer that iteratively queries
a quantum algorithm that evaluates the optimization objective.
An example is the Variational Quantum Eigensolver (VQE)
algorithm~\cite{McClean2015} applied in chemistry, where the objective
function calculates the expectation value of a Hamiltonian $\mathcal{H}$
given an input configuration of a simulated physical system.
The Hamiltonian describes the energy evolution of the system, thus the global
minimum represents the ground level energy.
The classical side variationally changes the parametrized input configuration
until convergence is reached, thereby finding the eigenvalue and eigenstate
of the ground energy of $\mathcal{H}$.
Quantum Approximate Optimization
Algorithms~(QAOA)~\cite{farhi2014quantum,Wang_2018} employ a similar
approach.
For the foreseeable future, quantum algorithms will have to run on Noisy
Intermediate-Scale Quantum (NISQ) devices which are characterized by a small
number of noisy, uncorrected qubits.
Hybrid methods are considered auspicious on such devices due to:
\begin{enumerate}[leftmargin=*]
\item the expectation that their iterative nature makes them robust to
noise; and
\item reduced chip coherence time requirements because of the single
Hamiltonian evaluation per circuit execution.
\end{enumerate}
However, these considerations relate to the quantum side of the hybrid
approach.
Rather, as we will show in this paper, the impact of noise on {\em both} the
classical and quantum parts needs to be taken into account.
In particular, the performance and mathematical guarantees, regarding
convergence and optimality in the number of iterations, of commonly used
classical optimizers rest on premises that are broken by the existence of
noise in the objective function.
Consequently, they may converge too early, not finding the global minimum,
get stuck in a noise-induced local minimum, or even fail to converge at
all.
For chemistry, the necessity of developing robust classical
optimizers for VQE in the presence of hardware noise has already been
recognized~\cite{McClean2015}.
However, the first published hardware studies side-stepped optimizers by
performing a full phase space
exploration~\cite{Li_2017,Temme_2017,Dumitrescu_2018} and backfitting the
solution to zero noise.
This works for low qubit count and few minimization parameters, but is not
tractable at the $\mathcal{O}(100)$ qubit concurrency soon expected on
NISQ-era devices, nor for the number of parameters needed for realistic
problems.
To our knowledge, QAOA studies also ignore the effects of the noise on the
classical optimizers.
In this study, we want to understand the requirements on classical
optimizers for hybrid algorithms running on NISQ hardware and which
optimization methods best fulfill them.
We use VQE as the testing vehicle, but expect the findings to be readily
applicable to QAOA and other hybrid quantum-classical methods which employ
similar numerical optimization.
The goals and contributions of our empirical study are twofold:
\begin{itemize}[leftmargin=*]
\item A practical software suite of classical optimizers, directly usable
from Python-based quantum software stacks, together with a tuning guide.
We consider factors such as the quality of the initial solution and
availability of bounds, and we test problems with increasing number of
parameters to understand scalability of the selected methods.
\item A study of the optimizers' sensitivity to different types of noise,
together with an analysis of the impact on the full VQE algorithm.
We consider the domain science perspective: some level of experimental
error is expected and acceptable, as long as the result is accurate and
the errors can be estimated.
We run simulations at different noise levels and scale, for several
science problems with different optimization surfaces, finding the
breaking points of the minimizers and the algorithm for each.
\end{itemize}
We have taken a very practical tack and first evaluated the minimizers from
SciPy~\cite{scipy_web}.
These include methods such as the quasi-Newton BFGS~\cite{NoceWrig06}
algorithm, and are the default choice of many practitioners.
Most optimization tools in standard Python and MATLAB software are not
noise-aware and, as we have found in our evaluations, actually fail in the
presence of quantum noise.
Some optimizers are more robust due to the smoothing effect of the underlying
methods used (e.g.\ modeling in trust region methods), but that is seldom by
design.
Fortunately, applied mathematicians in the optimization community have long
been working on this type of problem and have provided high quality, open
source, software.
Based on their recommendation, our final selection contains representative
methods of (hybrid) mesh (ImFil~\cite{ImFil11}, NOMAD~\cite{nomad}); local
fit (SnobFit~\cite{snobfit}); and trust regions
(PyBobyqa~\cite{pybobyqa1, pybobyqa2}).
Python and C++ are far more widely used in quantum computing than MATLAB.
Thus, we have rewritten optimizers where necessary from MATLAB into Python,
while ensuring, through a suite of unit tests, reproducible deterministic
behavior after porting, and provided consistent interfaces and plugins for
high level quantum frameworks such as Qiskit~\cite{qiskit} and
Cirq~\cite{cirq}.
These products have been packaged into {\sc scikit-quant}~\cite{urlsciq}.
The optimization package in {\sc scikit-quant} also provides tutorial
notebooks with tips and hints for hyper-parameter optimization, and an
evaluation harness to quickly assess applicability to new problems.
{\sc scikit-quant} has been evaluated on three VQE problems (ethylene
$C_2H_6$ rotation and bond stretching, and Hubbard model simulation), each
with different optimization requirements.
The results indicate that a {\em suite} of minimizers is needed to match
specific strengths to specific problems.
Achieving high quality solutions is aided by domain science information, if
available, such as a good initial parameters, knowledge of local minima, or
the need to search around inaccessible regions.
Such information is problem specific and in practice we observe different
performance benefits with different optimizers from its inclusion.
Where this information is {\em not} available, our study indicates that the
best results are obtained by composing local and global optimizers,
leveraging their respective strengths, during the VQE algorithm run.
The organization of this paper is as follows.
In Section~\ref{sec:numopt_background}, we give a brief background on numerical
optimization and our requirements on optimizers.
In Section~\ref{sec:scq} we describe the optimizers available in
{\sc scikit-quant} in more detail.
We provide the necessary background on hybrid quantum-classical algorithms in
Section~\ref{sec:hqca} and we describe the impact of noise in
Section~\ref{sec:noise_impact}.
Our numerical experiments are presented in Section~\ref{sec:results} and
discussed in Section~\ref{sec:discusion}.
We compare our work with related studies in Section~\ref{sec:related} and
finally summarize the main conclusions in Section~\ref{sec:conclusion}.
\section{Impact of Noise}
\label{sec:noise_impact}
VQE is considered to have some robustness against noise due to its iterative
nature and hence is expected to be well suited for upcoming NISQ devices.
Nevertheless, the need for studying the dynamics of the full hybrid VQE
algorithm has been identified early on~\cite{McClean2015} as a prerequisite
for successfully running it on NISQ hardware.
There are two components to this problem: 1) understanding how well
optimizers handle noisy data; and 2) understanding how well the full
quantum-classical algorithm handles noise.
\subsection{Accounting for Noise Sources}
There are a range of ways that noise enters the final result: from electronic
noise and quantum crosstalk, to decoherence and calibration inaccuracies.
How the output of a quantum circuit is affected by noise is an open research
problem, with no accurate predictive models available, even when restricted
to a specific chip instance.
Our main concerns, however, are about overall magnitude of noise and the
effects on the shape of the optimization surface.
In our study, we provide coverage of the problem domain by varying the
magnitude of the noise in simulation by a wide range, and by studying
different problems with a priori different optimization surfaces.
The actual noise impact for a given hardware instance is likely to be
captured within our parameter sweep.
The upshot is that we study a wide range of noisy profiles across different
optimizers to arrive at a {\em map and guidance} for actual experiments.
The goal is explicitly not to find and describe \textit{the} single way, if any such
exists, of how VQE behaves with a given noise model, nor to find the one
optimizer that should be used for all VQE problems.
It is, after all, well known in the applied math community that there is no
such thing as a ``free lunch,'' meaning that each optimizer has specific
strengths, none are best in all instances, and each problem needs to be
individually matched to the appropriate optimizer(s).
To account for the impact of noise sources, we consider an empirical
approach where we inject noise as Gaussian-distributed over-/under-rotations
with an added orthogonal component onto the circuit gates.
This ensures several realistic properties: noise increases with circuit depth
and complexity, and two-qubit gates have larger contributions than one-qubit
gates.
\begin{figure}[ht]
\begin{tabular}{cc}
\begin{minipage}{0.46\columnwidth}
\includegraphics[width=\textwidth]{figures/effect_systematic}
\end{minipage}
&
\begin{minipage}{0.46\columnwidth}
\centering
\includegraphics[width=\textwidth]{figures/effect_stochastic}
\end{minipage}
\\
\end{tabular}
\caption{\it \small Impact of noise types.
The optimizer can ``compensate'' in the choice of input for the predictable
effects of systematic/coherent noise (left) and thus still find the global
minimum.
But stochastic noise leads to a ``random walk'' away from the intended output
state (right), resulting in an increasingly diminished likelihood of the
objective function returning the global minimum.}
\label{fig:noise_impact}
\end{figure}
We do not add coherent or correlated noise sources, for the reasons
explained below.
The measurement result is a probability distribution of bit strings, and any
stochastic noise behaves on it in a similar way: it redistributes relative
counts with rates proportional to the content and with the same equilibrium
in the limit, namely a uniform distribution.
Coherent and correlated noise sources can, on the other hand, potentially
result in {\em any biased distribution}, making their study meaningless,
unless taken from the behavior of actual hardware.
But that would, of course, limit their relevance to that specific hardware.
Further, as detailed below, VQE has more ``builtin'' robustness against
coherent than against stochastic noise.
Coherent noise can also be expected to more easily produce non-physical
outcomes (e.g.\ fewer or more particles in the final than in the input
states); those measurements can be filtered out and discarded.
Last but not least, orthogonal error mitigation techniques such as Randomized
Compiling~\cite{PhysRevA.94.052325} have been shown to alleviate coherent
errors by making them stochastic.
We do not factor in an additional noise contribution from measurement errors:
shot noise is expected to be unbiased (i.e.\ it can be averaged out to zero
noise in the limit by taking a large number of measurements).
In other words, it affects the overall magnitude of stochastic noise sources,
which we already sweep, not what we most care about: the shape changes in the
optimization surface.
\subsection{Interplay with Minimizer}
Some general observations can be made about the different impacts of coherent
and stochastic errors, and why the distinction matters on hybrid
quantum-classical algorithms that involve a classical optimizer, such as VQE.
Quantum computing is very sensitive to noise, because a noisy execution is just
as valid as a noise-free one: without error correction codes, there is no
distinguishing between valid and erroneous states.
Therefore, if a circuit is intended to simulate the evolution of some
Hamiltonian $\mathcal{H}$, then a single noisy run can be seen as the
evolution of some other Hamiltonian $\mathcal{H}'$.
As long as the noise level is ``small enough,'' the eigenstates\footnote{And
eigenvalues, but that is irrelevant, because these are calculated classically
based on the output distribution.}
of $\mathcal{H}$ and $\mathcal{H}'$ will be close.
\textbf{The algorithm is somewhat robust to coherent errors.}
By definition, changes around the output state that represents the global
minimum are, to first order, zero for small linear changes in the input
state.
With a systematic difference between $\mathcal{H}'$ and $\mathcal{H}$,
the global minimum is still found by the optimizer compensating accordingly
in the input state, see Figure~\ref{fig:noise_impact} (left).
Thus, even as the calculated minimum energy may still be very close, the
optimal parameters found are likely to be systematically off.
There is a further twist here for VQE: the ansatz restricts the input states
that can be chosen, thus VQE will be more quickly affected by coherent errors
than hybrid algorithms in general.
\textbf{The algorithm has challenges with stochastic noise.}
The picture changes significantly with stochastic noise: each execution of
the circuit is in effect a different $\mathcal{H}'$.
Once close to the global minimum, the minimizer will not be able to distinguish
the outputs of runs with different inputs, as the changes get washed out in
the noise (as shown earlier in Figure~\ref{fig:hubbardnoise}).
\begin{figure}[h]
\centering
\includegraphics[height=2in]{ethylene8}
\vspace{-0.1in}
\caption{\it \small Objective function evaluation at the optimal parameters
for ethylene bond breaking simulation under increasing stochastic errors.
Energy estimates broaden in distribution and the average lifts. Eventually,
with increasing noise, the true global minimum is never returned.}
\label{fig:objnoise}
\end{figure}
With sufficient symmetry in the optimization profile or a functional
description based on the domain science, the optimizer can still find the
correct optimal parameters by searching for a {\em robust} global minimum or
doing a local fit.
However, any execution at the optimal parameters will calculate an output
distribution that is some random walk away from the intended state, as the
errors (in particular those on the control qubit of CNOTs) do not commute
with the circuit as a whole, see Figure~\ref{fig:noise_impact} (right).
When calculating the energy objective from any of these noisy outputs that
are close to, but not at, the global minimum, the results will by definition
be higher than the ground state energy\footnote{Unless the noise is so large
that the output state no longer represents the initial physical system: then
all bets are off.}.
With increasing noise, the likelihood of the true global minimum energy
being returned by the objective function goes to zero, as shown in
Figure~\ref{fig:objnoise}.
\comment{
\begin{figure}
\tiny
\bgroup
\def1.1{1.1}
\begin{tabular}{ c c | c | c | c }
\multirow{12}{*}{
\begin{minipage}{0.35\columnwidth}
\centering
\includegraphics[width=\textwidth]{figures/effect_systematic}
\end{minipage}}
& \multicolumn{4}{c}{4-qubit VQE, ethylene rotation simulation} \\
& \multicolumn{4}{c}{2 parameters; ``science cut-off" at -77.93318 ha} \\
& {\bf $\mu_{noise}$} {\bf (rad.)} & {\bf $\theta_{0}$} & {\bf
$\theta_{1}$}
& {\bf energy (ha)} \\[1ex]
\cline{2-5}
& 0.0001 & 9.46E-7 & 0.1778 & -77.93478 \\
& 0.0005 & 1.47E-6 & 0.1778 & -77.93477 \\
& 0.001 & 4.08E-6 & 0.1778 & -77.93476 \\
& 0.005 & 8.81E-5 & 0.1779 & -77.93442 \\
& 0.007 & 1.73E-4 & 0.1779 & -77.93389 \\
& 0.01 & 4.55E-4 & 0.1780 & -77.93338 \\
\cline{2-5}
\cline{2-5}
& 0.02 & 1.47E-3 & 0.1785 & -77.92924 \\
& 0.03 & 3.48E-2 & 0.1793 & -77.92247 \\
\end{tabular}
\egroup
\caption{\it \small Effect of systematic errors.
The end result is the same for the same input parameters, thus if the error
is small, the global minimum can still be reached by the minimizer adjusting
the input to counter the systematic error.
The end results are incorrect parameters, but a correct minimum value.}
\label{fig:systematic_err1}
\end{figure}
}
\comment{
\begin{figure}
\tiny
\begin{tabular}{ l l }
\begin{minipage}{0.35\columnwidth}
\centering
\includegraphics[width=\textwidth]{figures/effect_stochastic}
\end{minipage}
&
\begin{minipage}{0.6\columnwidth}
\centering
\includegraphics[width=\textwidth]{figures/ethylene8}
\end{minipage}
\\
\end{tabular}
\caption{\it \small Effect of stochastic errors.
The end result will vary even when given the same input parameters, and the
average result is a ``random walk" away of the error-free result.
Energy estimates broaden in distribution and the average lifts.
Eventually, with increasing noise, the true global minimum is never
returned.}
\label{fig:stochastic_err1}
\end{figure}
}
\section{Numerical Optimization}
\label{sec:numopt_background}
In variational hybrid quantum-classical algorithms, such as VQE, the
execution on the quantum processor evaluates the objective function to be
optimized classically.
In most cases, it is not possible to calculate gradients directly, thus
derivative-free optimization methods are required.
For a deterministic function
$f:\Omega\subset {\rm I\!R}^n \rightarrow {\rm I\!R}$
over a domain $\Omega$ of interest that has lower and upper bounds on the
problem variables, derivative-free algorithms require only evaluations of
$f$ but no derivative information.
They assume that the derivatives of $f$ are neither symbolically nor
numerically available, and that bounds, such as Lipschitz constants, for the
derivatives of $f$ are also unavailable.
Optimizers are judged on the quality of the solution and on their speed and
scalability.
A good solution has a short distance to the true global optimum, high
accuracy of the optimal parameters found, or both.
A good overview and thorough evaluation of derivative-free algorithms can be
found in Rios et al.~\cite{Rios2013}.
The main criteria for matching an optimizer to a problem are the convexity
and the smoothness of the optimization surfaces.
Convexity has the familiar meaning; smoothness in our context requires
that the function is ``sufficiently often differentiable''.
In VQE, the shape of the optimization surface is determined by the ansatz, and although
typical surfaces are smooth, noise can change this considerably.
\begin{figure*}
\begin{minipage}[l]{1.0\columnwidth}
\centering
\includegraphics[height=2.5in]{ethynoise}
\caption{\it \small Evolution of the
optimization surface in the main parameter for ethylene rotation simulation
as a function of Gaussian gate noise.
The surface goes from convex and smooth to non-convex, non-smooth as noise
increases.}
\label{fig:ethynoise}
\end{minipage}
\hfill{}
\begin{minipage}[r]{1.0\columnwidth}
\centering
\includegraphics[height=2.5in]{hubbardnoise}
\caption{\label{fig:hubbardnoise}\it \small Optimization surfaces of
all 14 parameters with Gaussian gate noise of
$\sigma = 0.01 \mathrm{rad.}$ in a Hubbard model simulation of 4 sites
with 4 electrons (see Section~\ref{sec:results} for full details).}
\end{minipage}
\end{figure*}
Figure~\ref{fig:ethynoise} shows the evolution of the optimization surface
for a single parameter in a simple VQE problem (rotation/torsion of an
ethylene molecule; 4 qubits, 2 parameters) for increasing levels of Gaussian
gate noise (detailed background on this and other studies is provided in
Sections~\ref{sec:hqca}~and~\ref{sec:noise_impact}).
For low noise, the optimization surface is convex around the global minimum
and smooth.
For increasing levels of noise, the optimization surface becomes both
non-convex and non-smooth.
It gets substantially worse for more complex problems: because circuit depth
increases, because the number of parameters increases the likelihood of
noise-induced local minima, and because entanglement over many qubits means
that the effects of gate noise become non-local.
This can be seen in Figure~\ref{fig:hubbardnoise}, which displays the effect
of noise on an 8 qubit Hubbard model simulation, with 14 parameters at a
moderate level of gate noise of $\sigma = 0.01 \mathrm{rad.}$ (cf.\ the
mid-range in the ethylene figure).
We are thus interested in optimizers that perform well across the whole range
of behaviors: convex and non-convex surfaces, smooth and non-smooth surfaces.
\subsection{Optimizer Selection Criteria}
The criteria for selecting optimizers that we considered are:
\begin{enumerate}[leftmargin=*]
\item Ability to find a good solution in the presence of noise, potentially
using different methods for different types of surfaces.
\item Scalability with the number of parameters, as this determines the
asymptotic behavior on future quantum hardware that allows the simulation of
larger problems.
\item Number of samples (queries to the objective function) required and precision needed, which affects scaling
and wall-clock time spent on the quantum chip.
\item Implementation performance and ability to parallelize, as these affect
scaling and wall-clock time spent on the classical side.
\end{enumerate}
There are two common strategies for optimizing noisy outcomes: optimize
for the expected value of the response, or for the worst
case~\cite{Powell2014}.
Quantum simulations, being probabilistic in nature, fit the former: many
runs (``shots'') of a circuit are required to obtain the output distribution,
which is then inclusively averaged over local noise sources.
\subsection{Baseline Optimizers}
\label{sec:baseline}
Under the assumption that the objective function is still continuously
differentiable, quasi-Newton methods can be used.
These approximate the first (and often the second) derivative from the
evaluations at different points.
Such methods work better if a detailed understanding of the noise is
available, allowing selection of good step sizes and properly weigh
evaluations when incorporating them into the approximation of the derivatives.
In the case of BFGS, which has been used by VQE developers for algorithm
development on quantum simulators\footnote{As opposed to real hardware.}, each
new evaluation is instead added to the current derivative estimate with equal
weight to all points collected so far combined.
This means that BFGS is easily thrown off when function values are noisy.
Given that it is still a common first choice, we retain BFGS as a baseline for
comparisons for our initial experiments and candidate optimizer selection for
{\sc scikit-quant}.
We use the SciPy~\cite{scipy_web} BFGS implementation and tune it for all input
problems.
We have also evaluated a range of other methods for which implementations are
readily available in Python, such as the Nelder-Mead simplex
method~\cite{nelder-mead} (considered by McClean et al.~\cite{McClean2015} in
their initial VQE analysis paper), RBFOpt~\cite{rbfopt}, Cobyla~\cite{cobyla},
DYCORS\cite{dycors}, and CMA-ES~\cite{cmaes,cmapy}.
These methods do not make the hard assumptions about data quality that BFGS
does, leaving them somewhat more robust to noise.
Based on our evaluation, we find Cobyla to outperform and thus we use it as a
second baseline for subsequent comparisons.
\comment{A different type of minimizers that focuses on derivative-free methods are
so-called ``blackbox optimizers").
These employ sampling techniques, possibly combined with local models, to
and do not impose any requirements on the
objective function. For example, the Nelder-Mead simplex method~\cite{nelder-mead} is
considered by McClean et al~\cite{mcclean} in their initial VQE
analysis paper.
There are two common strategies (which can be intermixed within the same
minimizer) sampling based on meshes and based on local fitting.
The former requires that the parameter space that is searched is bounded, the
latter requires some functional description of the local optimization surface.
}
\section{{\sc scikit-quant} Optimizers}
\label{sec:scq}
The initial selection of optimizers packaged in {\sc scikit-quant} consists
of NOMAD, ImFil, SnobFit, and BOBYQA; each detailed in the rest of this
section.
This choice is motivated by the evaluation of Rios et al.~\cite{Rios2013}
combined with open-source availability and ease of porting\footnote{Note
that while we ported the same algorithms, they evaluated different
implementations, which may affect some of the total running time.}
to Python.
Rios et al.~\cite{Rios2013} indicate the following trends:
\begin{itemize}[leftmargin=*]
\item In terms of scalability, SnobFit and NOMAD may have scalability
challenges with the number of parameters (tested up to 300).
ImFil and BOBYQA are among the fastest optimizers.
\item For convex optimization surfaces, BOBYQA and SnobFit perform well
for smooth surfaces, while NOMAD and ImFil perform better for non-smooth
surfaces.
\item For non-convex optimization surfaces, SnobFit and NOMAD are good
for smooth surfaces, while ImFil and NOMAD are good for non-smooth
surfaces.
\end{itemize}
In the rest of this section we give a short description of each algorithm
together with their tunable knobs that affect their performance and solution
quality.
As common characteristics we note that all derivative-free optimizers employ
sampling strategies and require a minimum number of samples to get started.
This allows a common interface to employ parallelization of the quantum step,
even if the original codes do not support this directly.
Sampling requires that the parameter space is bounded, or that search vectors
are provided.
Most optimizers can make use of further detailed science domain information,
such as the magnitude and shape of uncertainties, local functional descriptions,
inaccessible regions, etc.
If no such information is provided or available, they will choose reasonable
defaults, e.g.\ assumption of homogeneous, symmetric, uncertainties; and
qubic or quadratic local functional behavior on a small enough region.
Inaccessible regions can simply be communicated by returning $\mathrm{NaN}$
from the objective function.
\subsection{NOMAD}
\label{ssec:nomad}
NOMAD, or {\em Nonlinear Optimization by Mesh Adaptive Direct
Search (MADS)}~\cite{nomad} is a C++ implementation of the MADS
algorithm~\cite{abramson2009, audet2006, audet2009}.
MADS searches the parameter space by iteratively generating a new sample
point from a mesh that is adaptively adjusted based on the progress
of the search. If the newly selected sample point does not improve the current
best point, the mesh is refined. NOMAD uses two steps ({\em search} and
{\em poll}) alternately until some preset stopping criterion (such
as minimum mesh size, maximum number of failed consecutive trials, or maximum
number of steps) is met.
The search step can return any point on the current mesh, and therefore offers no
convergence guarantees.
If the search step fails to find an improved solution, the poll step is used to
explore the neighborhood of the current best
solution. The poll step is central to the convergence analysis of NOMAD, and
therefore any hyperparameter optimization or other tuning to make progress should
focus on the poll step.
Options include: poll direction type (local model, random, uniform angles,
etc.), poll size, and number of polling points.
The use of meshes means that the number of evaluations needed scales at least
geometrically with the number of parameters to be optimized.
It is therefore important to restrict the search space as much as possible
using bounds and, if the science of the problem so indicates, give preference
to polling directions of the more important parameters.
In {\sc scikit-quant} we incorporate the published open-source NOMAD code
through a modified Python interface.
\subsection{ImFil}
\label{ssec:imfil}
Implicit Filtering (ImFil~\cite{ImFil11}) is an algorithm designed for problems
with local minima caused by high-frequency, low-amplitude noise and with an
underlying large scale structure that is easily optimized.
ImFil uses difference gradients during the search and can be considered as an
extension of coordinate search.
In ImFil, the optimization is controlled by evaluating the objective function
at a cluster (or stencil) of points within the given bounds.
The minimum of those evaluations then drives the next cluster of points,
using first-order interpolation to estimate the derivative, and aided by
user-provided exploration directions, if any.
Convergence is reached if the ``budget'' for objective function evaluations is
spent, if the smallest cluster size has been reached, or if incremental
improvement drops below a preset threshold.
The initial clusters of points are almost completely determined by the
problem boundaries, making ImFil relatively insensitive to the initial
solution and allows it to easily escape from local minima.
Conversely, this means that if the initial point is known to be of high
quality, ImFil must be provided with tight bounds around this point, or it
will unnecessarily evaluate points in regions that do not contain the global
minimum.
As a practical matter, for the noisy objective functions we studied, we find
that the total number of evaluations is driven almost completely by the
requested step sizes between successive clusters, rather than finding
convergence explicitly.
For {\sc scikit-quant} we have rewritten in Python the original ImFil MATLAB
implementation available.
\subsection{SnobFit}
\label{ssec:SnobFit}
Stable Noisy Optimization by Branch and FIT (SnobFit)~\cite{snobfit} is an
optimizer developed specifically for optimization problems with noisy and
expensive to compute objective functions.
SnobFit iteratively selects a set of new evaluation points such that a balance
between global and local search is achieved, and thus the algorithm can escape
from local optima.
Each call to SnobFit requires the input of a set of evaluation points and
their corresponding function values and SnobFit returns a new set of points to
be evaluated, which is used as input for the next call of SnobFit.
Therefore, in a single optimization, SnobFit is called several times.
The initial set of points is provided by the user and should contain as many
expertly chosen points as possible (if too few are given, the choice is a
uniformly random set of points, and thus providing good bounds becomes important).
In addition to these points, the user can also specify the uncertainties
associated with each function value.
We have not exploited this feature in our test cases, because although we know
the actual noise values from the simulation, properly estimating whole-circuit
systematic errors from real hardware is an open problem.
As the name implies, SnobFit uses a branching algorithm that recursively
subdivides the search space into smaller subregions from which evaluation
points are chosen.
In order to search locally, SnobFit builds a local quadratic model around the
current best point and minimizes it to select one new evaluation point.
Other local search points are chosen as approximate minimizers within a trust
region defined by safeguarded nearest neighbors.
Finally, SnobFit also generates points in unexplored regions of the parameter
space and this represents the more global search aspect.
For {\sc scikit-quant} we have rewritten in Python the original SnobFit MATLAB
implementation available.
\subsection{BOBYQA}
\label{ssec:BOBYQA}
BOBYQA (Bound Optimization BY Quadratic Approximation)~\cite{bobyqa} has been
designed to minimize bound constrained black-box optimization problems.
BOBYQA employs a trust region method and builds a quadratic approximation in
each iteration that is based on a set of automatically chosen and adjusted
interpolation points.
New sample points are iteratively created by either a ``trust region'' or an
``alternative iterations'' step.
In both methods, a vector (step) is chosen and added to the current iterate to
obtain the new point.
In the trust region step, the vector is determined such that it minimizes the
quadratic model around the current iterate and lies within the trust region.
It is also ensured that the new point (the sum of the vector and the current
iterate) lies within the parameter upper and lower bounds.
BOBYQA uses the alternative iteration step whenever the norm of the vector is
too small, and would therefore reduce the accuracy of the quadratic model.
In that case, the vector is chosen such that good linear independence of the
interpolation points is obtained.
The current best point is updated with the new point if the new function value
is better than the current best function value.
Note that there are some restrictions for the choice of the initial point due
to the requirements for constructing the quadratic model.
BOBYQA may thus adjust the initial automatically if needed.
Although it is not intuitively obvious that BOBYQA would work well on noisy
problems, we find that it performs well in practice if the initial parameters
are quite close to optimal and the minimum and maximum sizes of the trust
region are properly set.
This is rather straightforward to do for the specific case of VQE, where a
good initial guess can be obtained relatively cheaply from classical simulation.
For Hubbard model problems, which have many (shallow) local minima, BOBYQA
does not perform nearly as well.
In {\sc skikit-quant}, we use the existing PyBobyqa implementation~\cite{pybobyqa1, pybobyqa2}
directly.
\subsection{Validation and Tuning}
\label{sec:validation}
We have validated the {\sc scikit-quant} implementations for correctness and
performance using a suite of unit tests.
For ImFil and SnobFit, which have been ported from MATLAB, we have thoroughly
tested correctness, using their original tests as well as our own.
For NOMAD and PyBobyqa we invoke the original implementations, limiting the
need for testing beyond the application programming interface.
All tests have been included in the {\sc scikit-quant} repository.
We have chosen defaults for each optimizer that should work best for the
type of optimization surfaces and noise behavior observed in the problems
considered.
Several of these choices are different from the original defaults, and in all
cases involved at least an increase of the number of samples per iteration
(BOBYQA and NOMAD in particular benefit here) or a tightening of the
convergence criteria (important for SnobFit).
This trades wall clock performance with science performance.
In the case of ImFil, a functional change was needed: without a reduction in
the smallest step scales, chemical accuracy could not be achieved.
We balanced this cost with a reduction in the allowed number of internal
iterations in the interpolation on a stencil.
We consider good default values extremely important: as a practical matter,
domain scientists tend to judge optimizers based on trial runs on their
problem at hand, rather than first studying their problem's mathematical properties and only then searching for an optimizer to match, with
different tuning as needed.
That (faulty) approach may well cause them to miss out on the best choice.
Good domain-specific defaults ameliorate this practical issue somewhat.
\section*{Acknowledgment}
This work was supported by the DOE under contract DE-5AC02-05CH11231,
through the Office of Advanced Scientific Computing Research (ASCR) Quantum
Algorithms Team and Accelerated Research in Quantum Computing programs.
{\footnotesize
\bibliographystyle{abbrv}
\section{Related Work}
\label{sec:related}
Hybrid quantum-classical algorithms such as VQE and QAOA employ
optimizers in the classical part of the computation. For VQE, an
initial discussion about optimization challenges in the presence of
noise is provided by McClean et al.~\cite{McClean2015}.
They study a unitary coupled cluster wavefunction for $H_2$, encoded
into 4 qubits and with optimization over a single parameter. In the
experiments, simulated measurement estimator noise is added to the
objective function at a specified variance ${\epsilon }^{2}$. They
compare Nelder-Mead with TOMLAB/GLCLUSTER, TOMLAB/LGO, and
TOMLAB/MULTIMIN. The choice of TOMLAB is motivated by the optimization study by Rios et
al.~\cite{Rios2013}, which reports a good combination of scalability and
quality of solution. Even for this single parameter problem, these
optimizers face challenges in the presence of noisy
output. Current QAOA~\cite{zhou2018quantum} studies still use BFGS and
Nelder-Mead, as they still concentrate mostly on the quantum
algorithm part of the problem. While the VQE result (system energy) is
subject to physical or chemical laws which constrain its values,
there is no such equivalent for most QAOA approaches.
Thus, it is our expectation they will need to be supplemented with
optimizers robust in the presence of noise.
An orthogonal approach in the realm of hybrid-algorithm design for
short-depth circuits is the
incorporation of error mitigation techniques.
The proposed zero-noise extrapolation techniques~\cite{Li_2017,Temme_2017}
seem to impose no constraints on optimizers and just run in the first
step the full VQE algorithm. An additional step calibrates the impact
of system noise, followed by an offline procedure to extrapolate
results to the ideal regimen of zero-noise. While the IBM
studies~\cite{Li_2017,Temme_2017} insert noise at the pulse level,
Dumitrescu et al.~\cite{Dumitrescu_2018} insert noise using additional
CNOT gates and describe a zero-noise extrapolation procedure.
Current results are for small circuits with few parameters (two) involved in
the optimization.
Their applicability to higher dimensional problems on complex optimization
surfaces remains to be seen and whether they relax the requirements on robust
optimizers.
Another area of interest is the work in the numerical optimization
realm. Rios et al.~\cite{Rios2013} provide a comprehensive evaluation
of derivative-free numerical optimizers along multiple dimensions including
scalability and quality of solution, for convex and non-convex, smooth
and non-smooth surfaces. Overall, they recommend the
commercial TOMLAB~\cite{tomlab} implementations of GLCLUSTER, LGO and
MULTIMIN. Each is best for a given combination of surface convexity
and smoothness. Also note that all the algorithms included in {\sc
scikit-quant} are very close to any of the TOMLAB implementations
for some type of surface.
\section{Results}
\label{sec:results}
As study cases, we used the C-C axis rotation and bond stretching and
breaking of the ethylene ($C_{2}H_{6}$) molecule (see
Figure~\ref{fig:ethybench}), representing two different chemical
transformation processes.
\begin{figure}[h]
\centering
\includegraphics[height=1.5in]{ethylene}
\caption{\it \small Illustration of the ethylene rotation/torsion and bond
stretching/breaking simulations.}
\label{fig:ethybench}
\vspace{-0.08in}
\end{figure}
In the rotation and bonding processes, the character of the wave function
changes drastically.
For example, in the C-C axis rotation $\Pi-\Pi$ bonds are broken/formed.
We also used a Hubbard simulation of 4 sites, occupied with either 4 or 2
electrons (see Figure~\ref{fig:hubbbench}).
In the Hubbard simulations, we use a hopping term of $1.0$, a Coulomb term of
$2.0$, and in the 4 electron case add a chemical potential of $0.25$.
The electrons have spins in all cases.
In all cases, OpenFermion~\cite{openfermion} is used to generate the
circuits.
With a Unitary Coupled Cluster ansatz (see Section~\ref{sec:hqca}), the
minimal representation needs to describe the rotation consisting of 4 qubits
(representing 4 orbitals) and 2 terms in the wave function expansion that
need to be optimized.
Similarly, the bond breaking process requires 8 qubits and uses a wave
function expansion with 14 parameters, the 4 sites Hubbard model requires
8 qubits and 9 parameters for a 2 electron occupancy; and 8 qubits with 14
parameters when simulating 4 electrons.
\begin{figure}[h]
\centering
\includegraphics[height=1.5in]{hubbard}
\caption{\it \small Illustration of the 4-site Hubbard model simulation for
electrons with spins, using hopping term $t$ and Coulomb term $U$.}
\label{fig:hubbbench}
\vspace{-0.08in}
\end{figure}
\subsection{Experimental Setup}
{\bf Noise Injection:}
We extended the ProjectQ~\cite{projq} quantum simulation infrastructure with
noise injection capabilities.
For each gate in the circuit circuit ($R_{X}(\theta)$, $R_{Y}(\theta)$, $H$,
$CNOT$\footnote{We do not add noise to $R_{Z}(\theta)$ as these are purely
mathematical, thus noise-free.}), we add an operator in the form of rotations
whose angles are independently sampled from a distribution: systematic
over/under rotation (along the same axis) and noise drawn from a Gaussian
probability distribution (main component along same axis, small orthogonal
component).
The noise operator for each gate is sampled independently of the others.
For each scenario we perform sweeps with increasing noise strength until it
breaks the minimizers.
In the rest of this paper, numerical values for noise magnitude refer to the
standard deviation ($\sigma$) of the Gaussian noise probability distribution.
{\bf Methodology:}
In each study, the minimizer is given an appropriate budget (maximum number
of invocations of the objective function) and convergence criteria are
adjusted in favor of using up the budget.
The minimizers are run until any convergence criteria are met or the budget
is used up.
We repeat the full algorithm several times and report the average and
overall minimum across all runs, as well as the average result when running
the simulation at the optimal parameters found.
The results are compared to the results of classical ab-initio calculations.
{\bf Optimizer Baseline:}
The optimizers included in {\sc scikit-quant} have been described in
Section~\ref{sec:scq}.
Each optimizer has been individually tuned with good settings for the type
of problems generated by our VQE test circuits, see
Section~\ref{sec:validation}.
As baseline comparison, we choose BFGS and Cobyla, both from
SciPy~\cite{scipy_web}, because they are well known and widely used, as
explained in Section~\ref{sec:baseline}.
{\bf Hardware:}
The simulations were small enough, memory-wise, to run on a standard server.
We note that for this study simulating the quantum circuit constitutes the
main bottleneck; optimizers can run well and handle a large number of
parameters when using just a single server.
\subsection{Optimization Solution Quality}
\label{sec:optreq}
\begin{figure*}
\begin{tabular}{cc}
\begin{minipage}{\columnwidth}
\includegraphics[width=\columnwidth,height=1.8in]{ethyrot4}
\end{minipage} &
\begin{minipage}{\columnwidth}
\includegraphics[width=\columnwidth,height=1.8in]{ethybond8}
\end{minipage} \\
\end{tabular}
\vspace{-0.06in}
\caption{\label{fig:ethy_results}\it \small Average calculated energy
of the full VQE algorithm for the ethylene rotation (left) and bond breaking
simulation (right).
Lowest noise level is $10^{-4}$.
The cut-off for chemical accuracy is shown by the straight, dashed, black
line.
With increasing noise, the result from the objective function is increasingly
moved away from the global minimum.
The lowest value that the objective function could return at a given noise
level is estimated by the dashed yellow line.}
\vspace{0.05in}
\end{figure*}
\begin{figure*}
\begin{tabular}{cc}
\begin{minipage}{\columnwidth}
\includegraphics[width=\columnwidth,height=1.9in]{hubbard_4s4e}
\end{minipage} &
\begin{minipage}{\columnwidth}
\includegraphics[width=\columnwidth,height=1.9in]{snobfil}
\end{minipage}\\
\end{tabular}
\vspace{-0.06in}
\caption{\label{fig:hubb_results}\it \small Full VQE results of a 4
site Hubbard model simulation with 4 electrons for individual optimizers
(left); and results when combining ImFil and SnobFit for 2 (dashed lines)
and 4 (solid) electrons (right).
The ground energy is recalculated at the optimal parameters found using a
noise-free simulation.}
\vspace{0.05in}
\end{figure*}
\begin{figure*}
\begin{tabular}{cc}
\begin{minipage}{\columnwidth}
\includegraphics[width=\columnwidth,height=1.9in]{ety_iters}
\end{minipage} &
\begin{minipage}{\columnwidth}
\includegraphics[width=\columnwidth,height=1.9in]{hubb_iters}
\end{minipage} \\
\end{tabular}
\vspace{-0.06in}
\caption{\label{fig:iterations}\it \small Number of objective
function calls used for each of the optimizers as a function of the
noise level.
Ethylene rotation simulation (left; budget of 50) and Hubbard Hubbard
model simulation with 4 electrons (right; budget of 1000).}
\vspace{0.05in}
\end{figure*}
\begin{figure*}
\begin{tabular}{cccc}
\begin{minipage}{0.55\columnwidth}
\hspace{-0.1in}
\includegraphics[width=\columnwidth]{imfil_good}
\end{minipage} &
\begin{minipage}{0.55\columnwidth}
\hspace{-0.3in}
\includegraphics[width=\columnwidth]{imfil_bad}
\end{minipage} &
\begin{minipage}{0.55\columnwidth}
\hspace{-0.5in}
\includegraphics[width=\columnwidth]{bobyqa_good}
\end{minipage} &
\begin{minipage}{0.55\columnwidth}
\hspace{-0.7in}
\includegraphics[width=\columnwidth]{bobyqa_bad}
\end{minipage} \\
\end{tabular}
\vspace{-0.1in}
\caption{\label{fig:search}\it \small Effect of the quality of the
initial on the overall solution for the ethylene rotation simulation.
Shown are parameters chosen by the optimizer to evaluate: ImFil with good (A)
and with bad initial (B); PyBobyqa with good (C) and bad initial (D).
The good initial is at $(0.1, 0.1)$, the bad at $(0.3, -0.3)$, and the global
optimum is at $(0.00012, 0.04)$.}
\end{figure*}
One of the effects of stochastic noise is to lift the results returned from
the objective function as explained in Section~\ref{sec:noise_impact}
and shown in Figures~\ref{fig:ethynoise}~and~\ref{fig:objnoise}.
There are two ways to evaluate the optimizers: 1) by the minimum energy they
actually find relative to what was possible given the response limitations of
the objective function; or 2) by the quality of the optimal parameters found,
evaluated by calculating the expected energy from a noise-free simulation run
at those parameters.
Which quality measure is most relevant will depend on the application and
science goals at hand, so we provide examples of both.
For example, in the case of chemistry studies, quantum subspace
expansion~\cite{McClean_2020} requires accurate parameters.
\textbf{Distance to minimum energy.}
Figure~\ref{fig:ethy_results} shows the average calculated energy of the full
VQE algorithm for the ethylene rotation (left) and bond breaking simulation
(right), for 100 runs at each noise level for the former and 10 each for the
latter.\footnote{The larger 8-qubit circuits took about two orders of
magnitude more time to run.}
The straight, dashed, black lines show the chemical accuracy ($0.00159$
hartrees): a solution closer to the exact value than this cut-off
(i.e.\ results below this line) are scientifically useful.
The dashed yellow lines show the lowest value the objective function returned
across all runs, i.e.\ the lowest value any of the minimizers could
theoretically have found.
Where this line is above the chemical accuracy, {\em the optimizer is not the
weak link of the algorithm, the quantum processor is the limiting component.}
The larger, deeper, 8-qubit circuit clearly suffers more from noise: even at
moderate levels, a chip with such gate noise would be the weak link in the
full algorithm.
Considering the minimizers, BFGS can not find the global minimum even with
small levels of noise (lowest level shown is $10^{-4}$), because it treats
any gradients seen as real, including fakes due to noise, and gets stuck.
It works, however, fine on a noise-free run (not plotted).
The other baseline, Cobyla, performs quite well at low levels of noise, but
clearly underperforms as noise increases.
The optimizers designed to handle noise well outperform across the full
range, with some stratification only happening at the highest noise levels
and ImFil yielding the overall best results.
In the low noise regime, however, where all optimizers perform similarly,
other considerations, such as the total number of iterations, come into play
to determine which is ``best.''
Cobyla would then most likely be preferred
(see Section~\ref{sec:perf_considerations} for a detailed discussion).
\textbf{Parameter quality.}
Figure~\ref{fig:hubb_results} (left) shows the results for the full VQE
algorithm Hubbard model simulations, with the energy recalculated at the
optimal parameters using a noise-free run.
With the Hubbard model, the region of the optimization surface around the
global minimum is rather shallow (see also Figure~\ref{fig:hubbardnoise}),
which clearly stresses the optimizers a lot more.
The behavior of BFGS and Cobyla mimics the results from the ethylene
studies, but this time both NOMAD and especially SnobFit also underperform
or even fail.
A detailed analysis shows that this weakness is exposed by bounds that are
too large for either optimizer to handle: reducing the bounds greatly
improves their performance (whereas it does not for BFGS and Cobyla).
\subsection{Leveraging Domain Science Constraints and Optimizer Knowledge}
From the discussion above, it is already apparent that different methods
perform best for different problems as optimization surfaces vary.
Furthermore, the quality of the solution may be improved by exploiting a
combination of domain science and optimizer knowledge.
For our VQE examples, the most obvious and realistically actionable
parameters are: 1) quality of initial solution; and 2) good parameter
bounds.
\textbf{Impact of initial solution quality.}
VQE for chemical problems has the advantage that a good initial can often
be obtained from approximate classical calculations.
To understand the impact of initial solution quality we consider a
comparison of ImFil and PyBobyqa for the ethylene rotation simulation.
In Figure~\ref{fig:search} we plot the evaluation points chosen by each
optimizer: using a good initial at $(0.1, 0.1)$ and a bad one at
$(0.3, -0.3)$.
The global optimum is at $(0.00012, 0.04)$.
Whether it receives a good (A) or bad (B) initial, ImFil will use the given
bounds to determine its first stencil, doing a mostly global search.
Although the initial drives the first few iterations, it quickly moves away
from the bad initial, to converge at the optimum.
PyBobyqa starts by considering only points within its trust region around
the initial point.
If the initial is close enough to make the global optimum fall within that
region, it will find it quickly (C).
However, if the initial is near a pronounced local minimum, in $(0.5, -0.5)$
in this case, it will get stuck (D), never finding the global minimum.
Overall, this analysis indicates that if good initials are available
with low computational overhead, they can improve both the quality and
speed to solution.
{\it \bf Impact of bounds.}
Some optimization methods, such as SnobFit, benefit greatly from having the
search space (and thus the needed number of evaluations, alleviating scaling
issues) reduced by tight bounds on the optimization variables.
When possible, such bounds should be provided from the domain science.
When bounds derived from first principles are unavailable, an automatic way
of finding tighter bounds can be had by running a composition of optimizers.
To illustrate this principle we show the effect of optimizer composition by
using ImFil to derive tight bounds for SnobFit.
ImFil uses progressively smaller stencils in its search for the global
minimum (see Section~\ref{ssec:imfil}).
Once close enough, the combination of high noise levels and a shallow
optimization surface means that no further progress can be made on the
stencil, which ImFil then labels as ``failed.''
The last good stencil provides the necessary bounds for SnobFit to proceed
and find a robust minimum.
The results of this approach are shown in Figure~\ref{fig:hubb_results}
(right) for Hubbard simulations with occupancies of 2 and 4 electrons.
In all cases, ImFil already outperforms the other optimizers, but SnobFit is
still able to improve from the point where ImFil fails.
Crucially, ImFil fails much earlier when noise levels are high
(see Section~\ref{sec:perf_considerations}), allowing the combined run of
ImFil+SnobFit to stay within budget.
\subsection{Performance Considerations}
\label{sec:perf_considerations}
Besides finding a good solution, optimizer quality is also quantified by its
total execution time.
First, we note that for hybrid algorithms the wall time is completely
dominated\footnote{The true ratio depends on the quantum hardware
chosen and the server CPU running the classical optimizer. We estimate
the time spent in the classical step to be about 1\% of the total.
Furthermore, several of the optimizers are in pure Python and their wall
clock performance could be greatly improved with a rewrite in C++ if
necessary.}
by the quantum chip for current devices.
When considering the optimizer in isolation the number of objective function
evaluations is thus a good proxy for wall clock performance.
Most optimizers provide control over the number of evaluations per iteration,
thus determining single iteration overhead.
We find in practice that the defaults work best: a certain minimum number of
evaluations is always necessary to fill out a stencil, local model, or map a
trust region.
{\it The incremental improvement from adding more points to the current
iteration is, however, less than the improvement obtained from spending that
budget on an extra iteration.}
Convergence criteria provide control over the total number of iterations.
Most optimizers define convergence as improvement between consecutive steps
falling below a threshold, or failing altogether a given number of times.
The lack of local improvement need not stop the search, e.g.\ for NOMAD and
SnobFit it can be chosen to initiate more {\em global} searches, and
subsequently use up the whole budget.
Whether those global searches are useful depends on the quality of the
initial and on the presence of local minima.
The setup of the science problem at hand matters greatly as well: tighter
bounds and a higher quality initial reduce the number of iterations needed,
as was already seen in Figure~\ref{fig:search}.
An efficient ansatz with fewer parameters, for example through exploitation
of symmetries, and an optimization surface with steep gradients near the
global minimum, can also have a big impact.
Finally, there are differences intrinsic to the optimization methods.
Figure~\ref{fig:iterations} shows the number of objective function
evaluations for increasing levels of noise, for both the ethylene rotation
simulation (left) and the Hubbard model with 4 electrons (right).
There is little sensitivity to noise in the much simpler rotation simulation,
except for BFGS which falls apart at high noise levels.
A clearer picture emerges in the Hubbard simulation: convergence criteria
that take into account the observed level of noise in their definition of
``no improvement'' work best.
E.g.\ PyBobyqa, which uses a fixed threshold, fails to converge, because
noise causes sufficient differences between iterations to remain above
threshold, so it continues, using up the full budget.
The other optimizers, which either track overall improvement or improvement
within an iteration given the noise, stop much earlier as noise
increases.
This is especially beneficial when conserving budget is important to allow
switching of optimizers, e.g.\ from ImFil to SnobFit as shown in the
previous section, while remaining within the budget overall.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 4,568 |
{"url":"http:\/\/tug.org\/pipermail\/tex-live\/2007-February\/012855.html","text":"# [tex-live] [tlpmgui] Re: [tlpmgui] tlpmgui starts in the wrong mode under Win32\n\nMon Feb 5 11:40:12 CET 2007\n\n2007\/2\/4, Karl Berry <karl at freefriends.org>:\nSTASZEK> Well, tlpmgui v. 1.69 introduces --install-mode option to force\n>\n> Thanks.\n>\nSTASZEK> we have to think about ordinary, not so advanced users and\nSTASZEK> they rarely have many TeX installations.\n>\n> It seems to me the new option is helpful *exactly* for the ordinary users\n> who already have some version of TeX installed. This way, they can try\n> out the new version without uninstalling the old one.\n> --install_mode is a lot less obscure way of doing that than something\n> like \"rename c:\\myoldtex\\bin\\win32\\tex c:\\myoldtex\\bin\\win32\\tex.skip\",\n> which seemed like the only available workaround.\n>\n> I understand that the installer will change PATH and environment\n> variables, so it's not seamless to get back to the existing system after\n> the new installation. But at least it is possible.\n>\n> Thanks again,\n> Karl\n>\nThank you very much, too, Staszek, for the \"--install-mode\" option for tlpmgui!\n\nI understand and accept the argument that an ordinary Windows user\nwant things to be preconfigured in a way he have only to start the\nsetup program and get the stuff smoothly installed. To ease many\nthings for non-expert users seems a feature of Windows (ans some Linux\ndistributions) attracting many non-geek users. But there are at least\n2 things of the strategy puzzling me:\n(1)\nYou are in big trouble when something does _not_ automagically work.\nEither things are done very easily or can not be done at all.\n(2)\nThe easy-use-strategy seems to tend to exclude more experienced users.\nThis was my main point in the discussion here. I do not see any\ncompelling reason why ease for more unexperienced or 'lazy' users does\nnecessarily conflict which the _possibility_ to customize all\nparameters _on my own risk_. The more I work with some tool the more I\ntend shape my preferences concerning this tool. Thus in this way my\ndesire to customize aspects of the tool accordingly.\n(And TeX is such a tool for me.) This seems an important point I miss\nin many usability discussions.\n\nAt the moment I am about to test the new tlpmgui (vers. 1.72) under\nWin32. When finished I will post a report.\n\nThanks again, Staszek\nDirk","date":"2019-01-18 13:30:45","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\": 0.9041962623596191, \"perplexity\": 6757.103965337946}, \"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-2019-04\/segments\/1547583660139.37\/warc\/CC-MAIN-20190118131222-20190118153222-00264.warc.gz\"}"} | null | null |
Lispe apicalis är en tvåvingeart som beskrevs av Josef Mik 1869. Lispe apicalis ingår i släktet Lispe och familjen husflugor. Inga underarter finns listade i Catalogue of Life.
Källor
Husflugor
apicalis | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 2,523 |
\section{Introduction}
\label{sec:intro}
Accreting compact objects radiate brightly in X-rays, enabling a view
of the region close to the horizon in the case of black holes (BHs),
or the surface in the case of neutron stars (NSs). Accretion occurs
through a geometrically thin disk, which emits a thermalised spectrum
(\citealt{Novikov1973,Shakura1973}), and a hot cloud of electrons
located close to the compact object, in which photons are Compton
up-scattered into a cut-off power-law spectrum
(\citealt{Thorne1975,Eardley1975}). The exact geometry of this
electron cloud is still debated, with candidate models including
evaporation of the inner disk into a large scale-height accretion flow
(\citealt{Eardley1975}), the base of a jet (\citealt{Markoff2005}),
and a coronal layer held above the disk by magnetic reconnection
(\citealt{Galeev1979,Haardt1991}). In the case of NSs, additional
radiation is associated with the surface of the compact star.
Since the region of interest closest to the compact object
cannot be directly imaged, the accretion geometry there can only be
inferred by analysing the properties of the X-ray signal. For the past
$\sim 40$ years this has been limited to analysis of the spectral and
variability properties, with particular success resulting from
combining the two disciplines
(e.g. \citealt{Miyamoto1988,Maccarone2002,Skipper2013}). Such
`spectral-timing' techniques allow, for instance, analysis of
propagating accretion rate fluctuations
(e.g. \citealt{Ingram2013,Rapisarda2017}) and reverberation mapping
(e.g. \citealt{Uttley2014}). Soon with the (proposed late 2020) launch
of the \textit{Imaging X-ray Polarimetry Explorer} (\textit{IXPE}:
\citealt{Weisskopf2016}), it will also be possible, for the first time
since \textit{OSO 8} was switched off in 1978, to observe the X-ray
polarisation of these sources. Polarimetry provides two extra
properties: the polarisation degree and angle. Analysis of these
properties as a function of energy (spectral-polarimetry) will provide
a powerful new lever arm to determine the geometry of the system and
measure parameters of the compact object
(e.g. \citealt{Stark1977,Schnittman2010,Dovciak2011}). Analysis of the
rapid variability of the polarisation degree and angle will provide
similarly powerful diagnostics. For instance, this will allow us to
track propagation of accretion rate fluctuations from strongly to
weakly polarised regions of the accretion flow and vice versa, and
will provide a new way to disentangle scattered from directly observed
photons for the purposes of reverberation mapping.
Accreting stellar-mass BHs and NSs display a rich phenomenology of
X-ray variability properties on timescales ranging from milliseconds
to hundreds of seconds (e.g. \citealt{VDK2006}). In particular,
quasi-periodic oscillations (QPOs) are often observed. These signals
can be classified depending on the fundamental frequency of the
oscillation. Low frequency (LF) QPOs are routinely observed from both
BHs and NSs, often with a large amplitude. The observed frequency
range for BHs is $\sim 0.1-30$ Hz, with the higher frequencies
observed from NSs consistent with simple mass scaling
(\citealt{Wijnands1999,vanderKlis2005,Belloni2010}). BHs occasionally
display high frequency (HF) QPOs, with frequencies $\gtrsim 100$ Hz
(e.g. \citealt{Morgan1997,Remillard1999,Homan2001}).
Even though these features are extremely rare and
weak, they command significant theoretical interest because their
frequencies are commensurate with the orbital frequency at the
innermost stable circular orbit (\citealt{Stella1999,Motta2014}). NSs on the
other hand display kHz QPOs which are common and often strong features
(\citealt{Strohmayer1996,vanderKlis1996}). Although it is tempting to
interpret HF QPOs as the BH equivalent of kHz QPOs, this comparison
is challenging on closer inspection (\citealt{Motta2017}).
All of these
classes of QPO are often interpreted as a geometrical effect, giving
rise to the possibility of detecting a QPO in the polarisation degree
and/or angle with a sufficiently sensitive X-ray polarimeter. In
particular, there is now mounting evidence that LF QPOs in BHs (or at
least the `Type C' subclass of LF QPOs; see
e.g. \citealt{Casella2005}) result from Lense-Thirring precession of
the inner accretion flow (\citealt{Stella1998,Ingram2009}). This is a
relativistic effect in which a spinning compact object twists up the
surrounding spacetime, inducing nodal precession in nearby orbits
inclined to the BH equatorial plane
(\citealt{Lense1918}). \cite{Ingram2016} recently discovered that the
iron K$\alpha$ fluorescence line in the spectrum of the accreting BH H
1743$-$322 rocks from red to blue shifted over the course of a QPO
cycle, confirming a distinctive prediction of the precession model
(\citealt{Schnittman2006,Ingram2012}). This model also predicts a QPO
in both the polarisation angle, resulting from the changing projected
orientation of the accretion flow, and in polarisation degree,
resulting from the expected angular dependence of Compton scattering
(\citealt{Ingram2015a}). Confirmation of these predictions would not
only provide smoking gun evidence for the precession hypothesis, but
would also provide tight geometrical constraints, particularly in
combination with QPO phase-resolved iron line modeling
(i.e. tomography: \citealt{Ingram2017}).
Detection of rapid variability of the polarisation degree and/or angle
would therefore provide a valuable probe of these systems. However,
the polarisation properties cannot be directly measured on
arbitrarily short timescales due to Poisson counting statistics. For
the count rates to be expected ($\sim$tens to hundreds of c/s), the
polarisation properties cannot be constrained directly with sub-minute
timescale resolution. Coherent pulsations can be studied simply by
folding the light curve, but folding is not appropriate for stochastic
variability (including QPOs; e.g. \citealt{Ingram2015}). Here, we
present a simple and robust general method for detecting rapid
variability in X-ray polarisation properties, circumventing the
technical challenges associated with stochastic variability. We focus
our analysis mainly on QPOs, but the method can also be used for broad
band variability. In Section \ref{sec:method}, we present our
method. In Section \ref{sec:sims}, we run simulations to determine the
expected signal to noise of the QPOs in polarisation degree and angle
predicted by the precession model. In Section \ref{sec:errors}, we
analyse the improvement in signal to noise that can be achieved by
cross correlating the polarimeter signal with a reference light curve
collected with a large area X-ray detector, before summarising our
results in Section \ref{sec:conc}.
\section{The Method}
\label{sec:method}
In this Section, we first outline why a special method is required for
fast X-ray polarimetry-timing before presenting our method.
\begin{figure*}
\includegraphics[angle=0,width=\columnwidth]{i70_IXPE_rms.ps} ~~~~
\includegraphics[angle=0,width=\columnwidth]{i70_IXPE_lag.ps}
\vspace{-5mm}
\caption{Fractional variability amplitude (left) and phase lag
(right) as a function of modulation angle, $\psi$, for the QPO
fundamental frequency. The red solid lines assume the oscillations
in flux, polarisation degree and polarisation angle calculated for the
high inclination ($i=70^\circ$) model shown in Fig 6 of
\citet{Ingram2015a} (solid lines therein). The blue dashed lines result
from assuming the same QPO in the flux, but constant polarisation
degree and angle. Sinusoidal modulations such as those depicted by
the red lines therefore provide a robust diagnostic of variability
in polarisation properties. The black points are a simulation of a
200 ks \textit{IXPE}~exposure, assuming the red lines as the input model.}
\label{fig:i70}
\end{figure*}
\begin{figure*}
\includegraphics[angle=0,width=\columnwidth]{i30_IXPE_rms.ps} ~~~~
\includegraphics[angle=0,width=\columnwidth]{i30_IXPE_lag.ps}
\vspace{-5mm}
\caption{The same as for Fig. \ref{fig:i70}, except we now use as
input the low inclination ($i=30^\circ$) model shown in Fig 8 of
\citet{Ingram2015a} (solid lines therein).}
\label{fig:i30}
\end{figure*}
\subsection{The Problem}
\label{sec:problem}
We wish to detect fast ($<10$ s) variability of the
polarisation degree $p_0$ and angle $\psi_0$. This is not trivial,
since we measure these parameters in a statistical
sense by detecting many photons. For each photon, a \textit{modulation
angle}, $\psi$, is measured, which is effectively an estimate for
the instantaneous polarisation angle of the population of photons. For a
photoelectric effect polarimeter such as the gas pixel detectors
(GPDs) used on \textit{IXPE}, this measurement of $\psi$ is obtained from the
orientation of the electron tracks on the
detector. Similar GPD detectors are also planned to be onboard the
proposed missions \textit{The X-ray Imaging Polarimetry Explorer}
(\textit{XIPE}; \citealt{Soffitta2016}) and \textit{the Extended X-ray Timing
and Polarimetry mission} (\textit{eXTP}; \citealt{Zhang2016}). For a Thomson
scattering polarimeter such as the balloon experiment
\textit{X-Calibur} (\citealt{Guo2013}), the measurement is
instead obtained from the position on the detector where the photon
lands. After enough photons have been collected, the polarisation
properties can be measured from a histogram of photon counts versus
modulation angle $\psi$. Specifically, the detected counts as a
function of $\psi$ will be proportional to the modulation function
\begin{equation}
f(\psi|\psi_0,p_0,\mu) = \frac{1}{2\pi} \bigg\{ 1 + \mu ~ p_0
\cos[2(\psi_0-\psi)] \bigg\},
\label{eqn:fpsi}
\end{equation}
where $\mu$ is the modulation factor of the polarimeter, defined by
the detector's response to a $100\%$ polarised signal. Throughout this
paper, we assume a modulation factor of $\mu=0.3$, which is expected
for \textit{IXPE}~(\citealt{Weisskopf2016})\footnote{Also see the
\textit{IXPE}~\textit{WebPIMMS}:
\url{https://wwwastro.msfc.nasa.gov/ixpe/for_scientists/pimms/}
}. The polarisation degree $p_0$ can therefore be measured from the
amplitude of the modulation function, and the polarisation angle
$\psi_0$ can be measured from the location of the peak of the
modulation function. Alternatively Stokes parameters can be used,
which is essentially equivalent to measuring the shape of the
modulation function. Note that the modulation function is cyclical on
the interval $\psi=0$ to $\psi=180^\circ$, and therefore $\psi_0$ is
only usefully defined on the interval $0$ to $180^\circ$ (or any
interval spanning $180^\circ$). This is because a wave with a
polarization angle of $\psi_0$ is indistinguishable from a wave with a
polarization angle of $\psi_0+180^\circ$. For example, rotating a
vertically polarised wave by $180^\circ$ leaves another vertically
polarised wave. The modulation angle $\psi$, however, is defined on
the interval $0$ to $360^\circ$ (or any interval spanning
$360^\circ$). For photoelectric effect polarimeters, this is because
the electron track caused by an incoming photon \textit{does} have a
direction since the starting point of the track can be determined, and
$\psi$ is the angle between the electron track and the projection of
north on the sky. For Thompson scattering polarimeters, $\psi$ also
spans the full $360^\circ$ interval, since it is determined from the
position on the detector where the photon is detected.
The simplest way to measure variability in $p_0$ and $\psi_0$ is of
course to measure both properties directly for many time
intervals. However, detection of polarisation requires a lot of
photons. The minimum detectable polarisation (MDP) is the minimum
polarisation degree that can be detected with statistical confidence
$\mathcal{L}$. This is given by (\citealt{Weisskopf2010})
\begin{equation}
{\rm MDP} = \frac{-\ln(1-\mathcal{L})}{\mu \langle s \rangle }
\sqrt{\frac{\langle s \rangle + \langle b \rangle } {T} },
\end{equation}
where $\langle s \rangle$ and $\langle b \rangle$ represent mean
source and background count rate respectively, and $T$ is the exposure
time. Therefore, for a source with a mean polarisation degree of
$\langle p_0 \rangle = 5\%$, a count rate of $\langle s \rangle =100$
c/s and a negligible background, achieving a statistical confidence of
$\mathcal{L}=99\%$ requires a $T\approx 15$ minute
exposure. For a higher intrinsic polarisation of $\langle p_0 \rangle
= 10\%$, this is still $T \approx 4$ minutes. Therefore, with the
expected count rates and reasonable assumptions about the polarisation
degree, it is not possible to probe sub-minute timescales by directly
calculating time series of $p_0$ and $\psi_0$. To probe faster
timescales, we need a statistical method. For broad band variability
and even QPOs, phase-folding is not a viable method. This is because
the phase of the oscillation does not evolve with time in a
predictable manner.
\subsection{The Solution}
\label{sec:solution}
We can instead consider the variability patterns that will be created
in the modulation function from variability in the count rate,
polarisation angle and polarisation degree. That is, we can make light
curves selected by the modulation angle $\psi$ of each incoming
photon, such that the count rate in the $i^{\rm th}$ $\psi$ bin at
time $t$ is
\begin{equation}
s(\psi_i,t) = s(t) f(\psi_i|\psi_0(t),p_0(t),\mu) \Delta\psi_i,
\label{eqn:tmod}
\end{equation}
where $\Delta\psi_i$ is the width of the $\psi$ bin, $s(t)$ is the
total polarimeter count rate, and the modulation function, $f$, is
given by Equation (\ref{eqn:fpsi}). From Equations (\ref{eqn:tmod})
and (\ref{eqn:fpsi}), it is clear that, if only the total count rate
is varying, and $p_0$ and $\psi_0$ are constant in time, then the
light curves $s(\psi_i,t)$ selected for each $\psi$ bin will all have
the same fractional rms as one another, and will all vary in phase
with one another. This is because the shape of the modulation function
does not vary if $p_0$ and $\psi_0$ remain constant. In contrast, if
only $p_0$ is varying (with $s$ and
$\psi_0$ now constant), this will cause a stretching and squeezing of
the modulation function as $p_0$ respectively increases and
decreases. This will lead to a peak in fractional rms at $\psi=\psi_0$
and a minimum at $\psi=\psi_0+90^\circ$, with all the light curves
varying in phase with one another as in the previous example. Finally,
if we imagine only $\psi_0$ is varying (with $s$ and $p_0$ constant),
the resulting rocking of the distribution peak will lead to light curves
for $\psi_i > \langle \psi_0 \rangle$ varying in anti-phase with light
curves for $\psi_i < \langle \psi_0 \rangle$. For a more general (and
realistic) situation, with $s$, $p_0$ and $\psi_0$ all varying, an
intuition is harder to form and calculations are required. However, it
is possible to appreciate that variability of polarisation properties
is encoded in the $\psi$ dependent variability properties of the
signal, which can be probed using standard cross-spectral techniques
developed for the purposes of spectral-timing.
We can therefore define a reference time series, $r(t)$, that is highly
correlated with all the $s(\psi_i,t)$ light curves and define a set of
cross-spectra
\begin{equation}
C(\psi_i,\nu,\Delta) = \langle S(\psi_i,\nu) R^*(\nu) \rangle,
\label{eqn:cross}
\end{equation}
where an uppercase letter represents the Fourier transform (FT) of the
corresponding lowercase letter and a star denotes a complex
conjugate. The angle brackets denote averaging, which is over an
ensemble of different realisations (i.e. the light curves are split
into many segments) and also over the Fourier frequency range
$\nu-\Delta/2$ to $\nu+\Delta/2$ (\citealt{vanderKlis1987}). We see
that the only difference with more familiar spectral-timing analyses,
is that we are selecting light curves based on modulation angle rather
than energy. Everything else is, in principle, entirely equivalent. The
reference light curve may be provided by a second detector on the same
satellite as the polarimeter, such as the $\sim 3 {\rm m}^2$
\textit{Large Area Detector} (LAD) of \textit{eXTP}. Alternatively, it could
be provided by a simultaneous pointing from another observatory, such
as \textit{AstroSat}~(\citealt{Singh2014}) which is likely to still be in
operation during the \textit{IXPE}~mission lifetime, or \textit{The
Spectroscopic Time-Resolving Observatory for Broadband Energy
X-rays} (\textit{STROBE-X}; \citealt{WilsonHodge2017}) which is
proposed to include an $\sim 8 {\rm m}^2$ version of the LAD. In the
absence of another instrument, the total polarimeter count rate
(i.e. summed over all $\psi$) could be used. It is convenient if the
reference time series is statistically independent from the other
light curves. This property is automatically satisfied by the use of a
second instrument\footnote{Although in practice electronic issues, such
as very large events that are picked up by more than one detector, can
lead to statistical independence of detectors being lost.}, and can
be ensured by using, for example, the total
polarimeter count rate minus the currently considered $\psi$ bin in
the absence of a second instrument\footnote{Alternatively, one could
use e.g. even energy
channels for the reference time series and odd energy channels for
the other light curves, or simply deal with the mathematics of not
having statistical independence.} (in direct
analogy to spectral-timing techniques;
e.g. \citealt{Uttley2014}). From the cross-spectrum for a given
Fourier frequency range, we can calculate the fractional rms as a
function of $\psi$, and also the phase lag as a function of $\psi$
with respect to the reference time series (See Appendix \ref{sec:bbn}
for more details).
The red solid lines in Fig \ref{fig:i70} and \ref{fig:i30} show the
fractional rms and phase lags as a function of $\psi$ calculated by
inputing the (LF) QPOs in polarimeter count rate, polarisation degree and
angle predicted by \cite{Ingram2015a}. In that paper, the authors ray
trace radiation from a precessing torus to a distant observer using
the Kerr metric, and calculate the resulting polarisation properties
as a function of precession phase. Two parameter combinations are
featured, referred to here as the high inclination model ($i=70^\circ$,
$\Phi=110^\circ$, $\beta=10^\circ$; see Fig 6 in
\citealt{Ingram2015a}) and the low inclination model ($i=30^\circ$,
$\Phi=180^\circ$, $\beta=10^\circ$; see Fig 8 in
\citealt{Ingram2015a}). Note that \citet{Ingram2015a} used the symbol
$\chi$ for the polarisation angle, whereas here we use the symbol $\psi_0$
- reserving $\chi$ for the $\chi^2$ fit statistic. Figs \ref{fig:i70}
and \ref{fig:i30} correspond to the high and low inclination model
respectively. We consider the rms and phase lags at the QPO
fundamental frequency, and we also take onto account the broad band
noise that is observed coincident with Type C QPOs. The details of our
calculation are presented in Appendix \ref{sec:bbn}. The figures show
approximately sinusoidal modulations in both the amplitude and phase
resulting from $p_0$ and $\psi_0$ varying with QPO phase. The blue
dashed lines show an alternative, null-hypothesis, model, in which
only the count rate varies and $p_0$ and $\psi_0$ stay constant with
QPO phase. As expected, we see no modulations in either the amplitude
or phase for this null-hypothesis model. We therefore have a simple
and statistically robust way to detect variability in the polarisation
properties: simply by looking for these $\sim$sinusoidal modulations
in the rms and phase lags as a function of $\psi$. We note that just
detecting these modulations does not automatically tell us about
whether it is $p_0$, $\psi_0$ or both varying. This requires a more
detailed analysis (see Section \ref{sec:polang}). There is one
exception however. If $\psi_0$ is constant and $p_0$ varies in phase
with the total count rate, then there will be a sinusoidal modulation
in the amplitude but not in the phase lags. We finally note that the
rms and phase are both cyclical on the interval $0$ to
$180^\circ$, which is because $\psi_0$ is only defined on an interval
of $180^\circ$ (see Section \ref{sec:problem}).
\section{Simulations}
\label{sec:sims}
In this section, we present methods to detect $p_0$ and $\psi_0$
oscillations in noisy data, with null-hypothesis significance
testing. Throughout, we consider a $200$ ks exposure of a bright
source (absorbed power-law spectrum with index $\Gamma=2$,
normalisation $=3$ photons/s/cm$^{2}$/keV, hydrogen column density
$n_h=10^{22}$ cm$^{-1}$) with negligible background, comparable to
e.g. GX 339-4 in a bright hard state or intermediate state. We first
describe our simulation method, focusing on \textit{IXPE}. We then introduce a
simple null-hypothesis test, which compares a sinusoidal model for the
rms and phase lag modulations as a function of $\psi$ to a
null-hypothesis model with constant rms and phase lag. This determines
the statistical confidence with which we prefer a model with variable
polarisation properties over a null-hypothesis model with constant
polarisation properties. We then specifically consider how to
constrain an oscillation in polarisation angle, which is the most
interesting quantity, offering a `smoking gun' detection of
precession.
The null-hypothesis tests presented here additionally allow us to
properly explore trade-offs when deciding whether to target high or
low inclination sources to search for an oscillation in polarisation
angle. In the precession model (and in the
observational data: \citealt{Schnittman2006,Motta2015,Heil2015}), the
oscillation in the flux has a larger amplitude for higher
inclinations (i.e. systems viewed more edge-on), since there is more
variability in solid angle and Doppler boosting over each precession
cycle. The mean polarisation degree is also expected to increase with
inclination angle (\citealt{Chandrasekhar1960,Sunyaev1985}). However,
the oscillation in polarisation angle has a greater amplitude for the
low inclination model, since a precessing vector traces out a cone
when viewed from the side and a full circle when viewed from the
top. We therefore consider both the high and low inclination model in
this Section.
\subsection{Simulation setup}
We present details of our simulations in Appendix
\ref{sec:simdet}. Here we summarise the general scheme. We calculate
our model for the fractional rms and phase lag corresponding to each
QPO harmonic as a function of $\psi$ as described in Appendix
\ref{sec:bbn}. We generate synthetic data by calculating $1~\sigma$
errors on the model (the expression for which we present and discuss
in Appendix \ref{sec:simdet}) and selecting Gaussian random
variables. With real data, we would measure the rms and phase lags
by calculating the cross-spectrum for many segments, each of length
$T_{\rm seg}$ seconds, and averaging. We would also average over all
the frequency bins lying in the frequency range $\Delta$ Hz. Since
there are a total of $T/T_{\rm seg}$ segments (where $T$ is the total
exposure time), and the frequency resolution is $d\nu=1/T_{\rm seg}$
(\citealt{vanderKlis1989}), the averaging is over $T \Delta$
realisations of the cross-spectrum. Therefore $T$ and $\Delta$ are
important parameters for calculating the error on the rms and phase
lags. For a QPO, it is appropriate to average over the frequency range
$\nu_k - \Delta_k/2$ to $\nu_k + \Delta_k/2$, where $\nu_k$ and
$\Delta_k$ are respectively the centroid frequency and full width at
half maximum (FWHM) of the $k^{\rm th}$ QPO harmonic. These two
parameters are related by the quality factor, $Q=\nu_k/\Delta_k$,
which is generally observed to be $Q\sim 8-10$ for most Type C LF QPOs
(note that the quality factor is generally equal for all detected
harmonics). The remaining inputs required to calculate the errors are
the mean polarimeter and reference time series count rates, $\langle s
\rangle$ and $\langle r \rangle$. These parameters determine the
Poisson noise level.
The black points in Fig \ref{fig:i70} and \ref{fig:i30} show our
simulation results for a $T=200$ ks simulated exposure with only \textit{IXPE},
using the red solid lines as the input model. The polarimeter
mean count rate is $\langle s \rangle =100$ c/s, calculated assuming
the spectral parameters defined at the start of this Section and
folding around the \textit{IXPE}~response matrix. We set the reference time
series count rate to $\langle r \rangle = \langle s \rangle$, assuming
that we can use the total \textit{IXPE}~count rate as the reference time
series. We set $\Delta =0.2$ Hz, which is appropriate for a QPO with
centroid frequency $\nu=1.6$ Hz and quality factor $Q = 8$. For the
high inclination model (Fig \ref{fig:i70}), the predicted modulations
in both fractional rms and phase lag are clearly visible. For the low
inclination model (Fig \ref{fig:i30}), the modulations are less clear
in the rms, but can be seen in the larger amplitude phase lag
modulations (resulting from the larger amplitude oscillations in
polarisation angle in the low inclination model). We only plot the
results for the QPO fundamental here. The modulations are not
detectable in the synthetic data for higher harmonics.
\subsection{Null-hypothesis testing}
\label{sec:null}
We now formally test the confidence with which we can rule out a
null-hypothesis of constant $p_0$ and $\psi_0$ for the synthetic data
points in Fig \ref{fig:i70} and \ref{fig:i30}. For this
null-hypothesis, the fractional rms and phase would not depend on
$\psi$. Alternatively, for a model in which $p_0$ and/or $\psi_0$ are
varying, the fractional rms and phase would have an approximately
sinusoidal dependence on $\psi$. We can therefore fit two models to
the data and, since one model is a `nested' version of the other,
compare the goodness of fit using an F-test. For the null-hypothesis,
we simply calculate the error weighted mean fractional amplitude and
phase lag from the data (this is identical finding a best-fitting
constant by minimising $\chi^2$). For the `full' model, we fit a
sinusoid function to both fractional rms and phase lag
\begin{equation}
y(\psi) = A + B \cos[ 2 ( \psi - C ) ],
\end{equation}
where $A$, $B$ and $C$ are free parameters in each of the two fits
(i.e. one fit to the rms and the other to the lags).
For the high
inclination simulation shown in Fig \ref{fig:i70}, the best fitting
null-hypothesis model has a reduced $\chi^2$ of
$\chi^2_\nu=234.6/98$. This is calculated for both rms and phase over
a total of 100 data points (50 rms points and 50 lag points), with
only two free parameters (the mean rms and the mean phase lag),
resulting in 98 degrees of freedom. The sinusoidal model has a much
better reduced $\chi^2$ of $98.6/94$. Here, there are the same number
of data points but now there are 6 free parameters ($A$, $B$ and $C$
for rms and phase lag), giving 94 degrees of freedom. An F-test
returns an F statistic of $F=32.4$, which corresponds to a null-hypothesis
p-value far lower than the threshold for $5 \sigma$ confidence
($p=6\times 10^{-17}$). For the low inclination simulation shown in
Fig \ref{fig:i30}, the reduced $\chi^2$ values for null-hypothesis and
sinusoidal models are instead $\chi^2_\nu=158.2/98$ and
$\chi^2_\nu=85.8/94$ respectively. This again gives a p-value
corresponding to $>5\sigma$ confidence ($F=19.8$, $p=7\times
10^{-12}$). As a final check, we also compare the input model with
the data, to get $\chi^2_\nu=104.9/100$ and $\chi^2_\nu=90.0/100$ for the high and
low inclination models respectively, indicating good fits.
We note that $\chi^2$ statistics are only appropriate for the case of
Gaussian errors. This is clearly the case for our simulation, since we
select Gaussian random variables. In practice however, the
cross-spectra must be averaged over a suitably large number of
realisations for the Gaussian limit to be reached (i.e. the central
limit theorem). This requires $T\Delta \gtrsim 400$
(\citealt{Vaughan2003}), which is comfortably the case for our chosen
parameters ($T\Delta = 2\times10^4$).
Thus, we expect to be able to detect the
oscillations predicted by \cite{Ingram2015a}, even for low inclination
sources. However, there is of course some uncertainty over what we
expect theoretically for the $p_0$ and $\psi_0$ oscillations. It is
therefore worth exploring parameter space with our new simple
hypothesis testing tool. The most robust prediction of the precession
model is the $\psi_0$ oscillation, since this largely depends on
geometry alone. The modulation in $p_0$ is much more uncertain, since
it depends on the angular dependence of emergent radiation, which in
turn depends on the details of the Comptonisation process that drives
the hard X-ray radiation. A key uncertainty is the average
polarisation degree, $\langle p_0 \rangle$. In particular, the
calculations of \cite{Sunyaev1985} used by \cite{Ingram2015a} may
over-estimate $\langle p_0 \rangle$, since they only consider photons
that have had `many scatterings'. More detailed calculations have
since predicted lower polarisation from Comptonisation
(e.g. \citealt{Schnittman2010}), particularly in the $2-8$ keV range
that the GPD detectors are sensitive to. This is largely because
photons with energies of $2-8$ keV often do not fulfil the
aforementioned criterion of having been scattered many times. It is
worth mentioning that polarimeters sensitive to harder X-rays are
therefore desirable, since more $\sim 10-50$ keV photons will have
undergone many scatterings and are therefore expected to be more
highly polarised (also the LF QPO fractional amplitude is often observed
to increase with energy). Thomson scattering polarimeters such as the
\textit{Polarization Spectroscopic Telescope Array} (\textit{PolSTAR}:
\citealt{Henric2016}), the proposed satellite version of
\textit{X-Callibur}, are therefore promising prospects for the future.
\begin{figure*}
\includegraphics[angle=0,width=\columnwidth]{linesi70Fversuspav.ps} ~~~~
\includegraphics[angle=0,width=\columnwidth]{linesi30Fversuspav.ps}
\vspace{-7mm}
\caption{The curves show the $F$ statistic calculated by
comparing the best-fitting sinusoid model with a null-hypothesis
corresponding to constant polarisation properties (see text
for further details) as a function of mean polarisation
degree. The left and right plots are for the simulations
corresponding to the high and low inclination models
respectively. Each curve represents a different combination of mean
count rate in the polarimeter $\langle s \rangle$ and mean count rate in
the reference time series, $\langle r \rangle$. From bottom to top,
they represent $\langle s \rangle =100$ c/s, $\langle r
\rangle=100$ c/s (black solid), $\langle s \rangle=100$, $\langle r
\rangle=5000$ (red dashed), $\langle s \rangle =200$, $\langle r
\rangle=38,000$ (green dot-dashed) and $\langle s \rangle=500$, $\langle r
\rangle =38,000$ (blue dotted). These cases are respectively relevant for
\textit{IXPE}~alone, \textit{IXPE}+\textit{AstroSat}, \textit{eXTP}~baseline and \textit{eXTP}~goal. The
grey dashed lines show $3 \sigma$ and $5 \sigma$ values. We see that,
for the high inclination model, a $5 \sigma$ detection is possible
for $\langle p_0 \rangle \gtrsim 5.5 \%$ with \textit{IXPE}~alone, or
$\langle p_0 \rangle \gtrsim 2.3 \%$ with the \textit{eXTP}~goal
configuration. Smaller polarisation degrees are required for the
low inclination model, but we do expect low inclination sources to
be less polarised.}
\label{fig:X2}
\end{figure*}
In Fig. \ref{fig:X2}, we therefore explore a range of $\langle p_0
\rangle$ values, again considering a $200$ ks exposure and
$\Delta=0.2$ Hz. We use the same high (left) and (low) inclination
input models as before for $s$, $p_0$ and $\psi_0$ as a function of QPO
phase, except we re-scale the $p_0$ oscillation by the new mean.
The curves show the $F$ statistic resulting from comparing
a null-hypothesis and a sinusoidal model to synthetic data for
different polarimeter and reference time series count rates. In order
to smooth out noise, we average $\chi^2$ values over $10,000$
realisations of synthetic data before doing the F-test. From
bottom to top, the curves represent: only \textit{IXPE}~(black solid),
\textit{IXPE}~with \textit{AstroSat}~recording the reference time series (red dashed),
\textit{eXTP}~`requirement' specifications with the reference time series
recorded by the $\sim 3$ m$^2$ LAD (green dot-dashed) \footnote{Here,
the requirement specifications of the \textit{eXTP}~polarimeter are assumed
to be the same as the \textit{XIPE}~specifications. Therefore the green
dot-dashed line could also represent \textit{XIPE}~plus the $\sim 3$ m$^2$ LAD.}, and \textit{eXTP}~`goal'
specifications (blue dotted). The grey dashed lines represent $3$ and $5~\sigma$
confidence. As expected, the oscillations in $p_0$ and $\psi_0$ are
harder to detect when the mean polarisation degree is low. Also, for
lower inclination angles, the minimum degree of polarisation required
for a significant detection of polarisation variability is
smaller. This is because the swings in polarisation angle are
predicted to have a larger amplitude for the low inclination
model. However, we \textit{do} expect a lower mean
polarisation degree for lower inclinations, so it is likely still best
to target high inclination sources. We see that sensitivity is
improved by using configurations that increase the mean polarimeter
count rate $\langle s \rangle$ and the mean reference time series
count rate $\langle r \rangle$. Therefore, for a given polarimeter, we
can increase signal to noise simply by observing simultaneously with
another observatory with greater collecting area than the
polarimeter. We will discuss the relative importance of high reference
and polarimeter count rates in Section \ref{sec:errors}.
\subsection{Measuring an oscillation in polarisation angle}
\label{sec:polang}
\begin{figure*}
\includegraphics[angle=0,width=\columnwidth]{i70_contour.ps} ~~~~
\includegraphics[angle=0,width=\columnwidth]{i30_contour.ps}
\vspace{-5mm}
\caption{Plot of minimum $\chi^2$ against the parameter $A_{1\psi}$
(black solid line) for fits to synthesised \textit{IXPE}~data. A non-zero
value of this parameter indicates that the polarisation angle is modulated on the
QPO fundamental. The left and right hand panels correspond to the
high and low inclination models respectively. The red crosses show
the input value of $A_{1\psi}$ for each simulation and the blue
dashed lines show the $5 \sigma$ confidence contour. For both input
models the null-hypothesis of $A_{1\psi}=0$ can be strongly ruled out.}
\label{fig:contour}
\end{figure*}
We have shown that it is simple to measure variability in polarisation
properties with an X-ray polarimeter. However, determining if
specifically the polarisation angle is oscillating, and/or if the
polarisation degree is oscillating, and moreover measuring the
amplitude and phase of those oscillations, requires further work. In
this section, we show that a method entirely analogous to the
\cite{Ingram2016} QPO phase-resolving method can be employed to do
just this. We start by representing the oscillations in count rate,
polarisation degree and angle as a simple phenomenological function of
QPO phase, $\omega$. For example, the $\psi_0$ oscillation is given by
\begin{equation}
\psi_0(\omega) = \langle \psi_0 \rangle + A_{1\psi_0}
\sin[\omega - \phi_{1\psi_0}] + A_{2\psi_0}
\sin[2(\omega - \phi_{2\psi_0})],
\end{equation}
and we use equivalent expressions for $p_0(\omega)$ and
$s(\omega)$. This is simply a sum of harmonics, where we only
consider two harmonics (since in most cases only two QPO harmonics
can be detected). Here, $A_{1\psi_0}$ and $A_{2\psi_0}$ are the
amplitudes of respectively the first and second harmonics of the
$\psi_0$ oscillation, and $\phi_{1\psi_0}$ and $\phi_{2\psi_0}$ are
the phases. Including the 3 mean parameters ($\langle s \rangle$,
$\langle p_0 \rangle$ and $\langle \psi_0 \rangle$), 6 amplitude
parameters [i.e. $A_{1\psi_0}$, $A_{2\psi_0}$ and the equivalents for
$p_0(\omega)$ and $s(\omega)$], and 6 phase parameters, there are 15
model parameters altogether. We simultaneously fit this model to the
synthetic data of the mean count rate vs $\psi$, the fractional rms vs
$\psi$ for two QPO harmonics, and the phase lag vs $\psi$ for two QPO
harmonics. The simultaneous fit is therefore performed over a total of
five datasets. We use \textsc{xspec} v 12.9 (\citealt{Arnaud1996}).
We use the same two simulations shown in Figs. \ref{fig:i70} and
\ref{fig:i30}. Although these figures only show the rms and phase for
the QPO fundamental (i.e. first harmonic), we also consider the second
harmonic and the mean count rate in our fit. Even though the synthetic
data for the second harmonic are very noisy, they still constrain our
model since they rule out parameter combinations that predict very
large rms and lag modulations in the second harmonic that are not
present in the synthetic data. Fig. \ref{fig:contour} shows the
minimum $\chi^2$ as a function of the parameter $A_{1\psi_0}$ (black
solid line) for the high (left) and low (right) inclination models. In
both cases, the red cross depicts the exact answer calculated directly
from the input model for the simulation, which is clearly consistent
with the best fit value. The blue dashed line depicts the $5~\sigma$
confidence contour. We see that the QPO in $\psi_0$ is detected with
$> 5 \sigma$ confidence in both cases, with the significance being
greater for the high inclination model. We note that the simulation
includes the effect of broad band noise, but our simple model fitting
in this Section does not. The fact that we recover the input
polarisation angle oscillation accurately gives us confidence that the
method is fairly robust to biases introduced by the broad band noise
signal. Clearly, it is also possible to use the same method presented
here to measure the oscillation in polarisation degree.
\begin{figure*}
\includegraphics[angle=0,width=\columnwidth]{i70_pdetvsr.ps} ~~~~
\includegraphics[angle=0,width=\columnwidth]{i30_pdetvsr.ps}
\vspace{-5mm}
\caption{Mean polarisation degree required in order to make a
$5\sigma$ detection of the oscillations in polarisation properties
predicted by \citet{Ingram2015a} for a high (left) and low (right)
inclination object, plotted against mean count rate of the reference
time series. We assume a 200 ks exposure and consider three
different specifications of polarimeter, assuming mean polarimeter
count rates of $\langle s \rangle = 100$ c/s (black: \textit{IXPE}),
$\langle s \rangle = 200$ c/s (red: \textit{XIPE}~/ \textit{eXTP}~baseline) and
$\langle s \rangle = 500$ c/s (blue: \textit{eXTP}~goal). We see that
increasing the polarimeter count rate increases sensitivity, as
does increasing the reference count rate. We can therefore
increase the sensitivity of a given polarimeter by using a large
area instrument to collect the reference time series. There is
however a saturation point (here at $\sim 5000$ c/s) beyond which
increasing the reference count rate provides no further advantage.}
\label{fig:pdet}
\end{figure*}
\begin{figure*}
\includegraphics[angle=0,width=\columnwidth]{lagerr_mue3.ps} ~~~~~
\includegraphics[angle=0,width=\columnwidth]{zoomin.ps}
\vspace{-5mm}
\caption{Square of the 1 $\sigma$ error on the phase lag (in radians)
between a $\psi$ bin with a count rate of 3 c/s and a reference
time series, plotted against the count rate of the reference time
series, $\langle r \rangle$. The magenta solid line depicts the
total error and the other lines in the left hand plot show the 4
separate terms in the formula for the error (see Equation
\ref{eqn:fracerr}). The right hand plot is a zoom in of the
left. The grey dashed vertical line depicts the `saturation count
rate' at which the error transitions from a very steep function of
$\langle r \rangle$ to a more shallow dependence (see Equation
\ref{eqn:sat}).}
\label{fig:errors}
\end{figure*}
\section{The importance of a high count rate reference
time series}
\label{sec:errors}
It is clear from Fig. \ref{fig:X2} that the reference count rate
is important for detection. In this Section we explore the importance
of the reference time series count rate, to assess how much of an advantage
can be gained simply by using an instrument with higher effective area
than the polarimeter to collect the reference time series. We first
note that the most important property of the reference time series is
that it is highly correlated with the polarimeter light curve. This is
guaranteed if instruments with a similar spectral response are used to
measure the polarimeter and reference time series. Therefore,
instruments sensitive to the same $\sim 2-8$ keV band as the GPDs,
such as the \textit{Neutron star Interior Composition ExploreR}
(\textit{NICER}: \citealt{Gendreau2016}), the X-Ray Concentrator Array
(XRCA) of \textit{STROBE-X} and the Spectroscopic Focusing Array (SFA) of
\textit{eXTP}~will provide an advantage in this respect. In practice though,
hard and soft X-rays tend to be highly correlated for the case of
accreting compact objects (e.g. \citealt{Nowak1999}), and so the
harder response of the LAD is unlikely to be a problem. We therefore
assume unity coherence throughout this paper.
\subsection{The polarisation degree required for detection}
Fig \ref{fig:pdet} shows the mean polarisation degree required to
detect polarisation variability with $5 \sigma$ confidence plotted
against mean reference time series count rate. Again, results for the
high and low inclination models are plotted on the left and right
respectively. To calculate the `detection polarisation degree',
$p_{\rm det}$, plotted on the y-axis, we find the $\langle p_0
\rangle$ value for which the $F$ statistic for the simulation
corresponds to $5 \sigma$ confidence. For example, the solid
black line in Fig \ref{fig:X2} (left), representing $\langle s \rangle
= \langle r \rangle =100$ c/s, crosses the $5 \sigma$ level
(upper dashed line) for $\langle p_0 \rangle \approx 5.5
\%$. Therefore, $p_{\rm det}\approx 5.5\%$ for \textit{IXPE}~($\langle s
\rangle=100$ c/s) when the reference time series mean count rate is
$\langle r \rangle =100$ c/s.
We show results for three different polarimeters: \textit{IXPE}~(black),
\textit{XIPE}~(which is the same as the baseline \textit{eXTP}~polarimeter; red) and
\textit{eXTP}~goal (blue). For each line, we only consider $\langle r \rangle
\geq \langle s \rangle$, since in practice there is no need to use a
reference time series with a lower mean count rate than can be
provided by the polarimeter itself. We again assume a $200$ ks
exposure. We see that increasing the area of the polarimeter (from
\textit{IXPE}~to \textit{XIPE}~to \textit{eXTP}~goal) has a large impact on
sensitivity. Increasing the reference count rate also has a
significant effect up until $\sim 5000$ c/s where the sensitivity
starts to saturate. This is interesting, since \textit{AstroSat}~can achieve
count rates of $\sim 5000$ c/s for a bright source as specified at the
start of Section \ref{sec:sims}. Therefore, for the simulation
parameters considered, \textit{AstroSat}~would perform comparably to the
\textit{eXTP}~or \textit{STROBE-X} versions of the LAD over a 200 ks exposure
(that is, if the coherence between the LAD and GPD energy bands is
high as assumed, otherwise \textit{NICER} or the XRCA of
\textit{STROBE-X} may provide an advantage). We show below, however,
that there are other parameter combinations for which the LAD gives a
large advantage. It is also important to note that a $200$ ks exposure
on a low Earth orbit satellite will take $\sim 5$ days to collect,
over which time the QPO frequency will change fairly
significantly. This would therefore need to be accounted for in the
analysis [e.g. using techniques similar to the \cite{Mendez1998}
`shift and add' technique employed for kHz QPOs, or the
\cite{Tomsick2001} `stretch and bin' technique employed for LF
QPOs]. Finally, the detection polarisation degree is related very
simply to the modulation factor, $\mu$. Doubling $\mu$ would half
$p_{\rm det}$, and so polarimeter designs with larger $\mu$ are
unsurprisingly more sensitive.
\subsection{The `saturation count rate'}
We can further understand the role of the reference time series by
exploring the error on the phase lag. From Equation \ref{eqn:error},
the squared error is
\begin{equation}
\left[ d\phi(\psi_i,\nu) \right]^2 \propto
1 + \frac{P_{\rm noise}(\psi_i)}{P(\psi_i,\nu)} + \frac{P_{\rm noise} }{ P(\nu)} +
\frac{P_{\rm noise} P_{\rm noise}(\psi_i) }{ P(\nu) P(\psi_i,\nu) }.
\label{eqn:fracerr}
\end{equation}
Here, $P(\nu)$ and $P(\psi_i\nu)$ are respectively the intrinsic
(i.e. no Poisson noise) power spectra of the reference time series and
the light curve for the $i^{\rm th}$ $\psi$ bin. $P_{\rm noise}$ and
$P_{\rm noise}(\psi_i)$ are respectively the Poisson noise
contribution for the reference time series and the light curve for the
$i^{\rm th}$ $\psi$ bin. Fig. \ref{fig:errors} (left) shows this
squared error for a $\psi$ bin with mean count rate $3$ c/s, as a
function of reference band count rate, $\langle r \rangle$. We assume
a QPO with $10\%$ fractional rms (consistent with the high inclination
model), $T=200$ ks and $\Delta=0.2$ Hz. The solid magenta line shows
the total, whereas the black dashed line, the red dot-dashed line, the
green dotted line and the blue triple dot dashed line depict
respectively the first, second, third and fourth terms on the right
hand side of Equation \ref{eqn:fracerr}. We see that the first two
terms do not depend on $\langle r \rangle$, whereas the third and
fourth terms reduce with $\langle r \rangle$. We also see that the
second and fourth terms dominate over the others for this example,
which turns out to be generally the case for the set of observed LF
QPO properties.
Therefore, in the regime in which the fourth term dominates, we gain
an enormous advantage by increasing the area used to collect our
reference time series. If instead the second term dominates, any
further increase in $\langle r \rangle$ gives a more incremental
improvement. We can estimate this `saturation count rate' by setting
the second and fourth terms equal to one another to obtain
\begin{equation}
r_{\rm sat} = \frac{2(1+\langle b \rangle / \langle s \rangle)\Delta}{
{\rm rms}^2 },
\label{eqn:sat}
\end{equation}
where $\langle b \rangle / \langle s \rangle$ is the fractional
contribution of the polarimeter background (in this discussion we only
consider $b=0$). We see that $r_{\rm sat}=40$ c/s for the parameters used in
Fig. \ref{fig:errors}. It is important to note that $r_{\rm sat}$
marks only a change in regime. It is still possible to get an
improvement in signal to noise by increasing $\langle r \rangle$, even
for $\langle r \rangle >r_{\rm sat}$. Fig \ref{fig:errors} (right) - a
zoom in of Fig \ref{fig:errors} (left) - demonstrates this. The error
is still decreasing for $\langle r \rangle >r_{\rm sat}$ (grey dashed
line), until $\langle r \rangle >>r_{\rm sat}$. We also see this in
Fig \ref{fig:pdet}, where the sensitivity still improves until
$\langle r \rangle \sim 5000$ c/s, even though the saturation count
rate is $r_{\rm sat}=40$ c/s.
Nonetheless, Equation \ref{eqn:sat} shows that a high count rate
reference time series is most important for low rms, high $\Delta$
QPOs. Since LF QPOs have a roughly constant quality factor of $Q\sim
8$, high $\Delta$ translates to high $\nu_{qpo}$. Therefore, if we
wish to observe QPOs with \textit{IXPE}~alone, we should target the lowest
frequency, highest rms QPOs. For a fractional rms of $10\%$, we
calculate that this transition in regime occurs at $\nu_{ qpo} \sim 4$
Hz (by setting $r_{\rm sat}=100$ c/s, since this is the count rate
achievable by \textit{IXPE}~alone).
For $\nu_{qpo} \gtrsim 4$ Hz a high count rate reference time series
will vastly improve signal to noise, much more so than shown in Fig.
\ref{fig:pdet}. We do however need to keep in mind time lost to lining
up orbits of two observatories, except for \textit{eXTP}, which has both the
polarimeter and the LAD onboard. It is clear from our discussion in
this section that the biggest advantage afforded by a high count rate
reference time series is for high frequency (HF) QPOs, or indeed kHz
QPOs in NSs, which may display modulations in polarisation
properties if they are due to e.g. orbiting hot spots on the disc
(\citealt{Beheshtipour2016}). Taking the upper HF QPO from the triplet
of QPOs measured in GRO J1655-40 by \cite{Motta2014} ($\Delta=30$ Hz,
rms=$4.5\%$), gives $r_{\rm sat} \approx 29,630$ c/s. This count rate
is not achievable with current instrumentation, but the count rate for
both the \textit{STROBE-X} and \textit{eXTP}~versions of the LAD will be
higher than this for a bright source. These next-generation detectors
will therefore provide an enormous advantage over current
instrumentation.
\section{Discussion \& Conclusions}
\label{sec:conc}
We present a simple and robust method for detecting fast stochastic
variability in the polarisation properties of an X-ray source. Whereas
coherent oscillations can be detected using phase-folding, this is not
the case for broad band noise or even QPOs - for which the phase of
the oscillation does not increase predictably with time. We
demonstrate that, with our method, ruling out constant polarisation
degree and angle is simple for any kind of stochastic variability. If
we see sinusoidal modulations in the fractional rms and phase as a
function of modulation angle $\psi$ for any frequency range, we can
conclude that there is variability in the polarisation
properties. We also introduce a method to measure the amplitude and
phase of the individual oscillations in polarisation degree and angle
for the case of QPOs, which is analogous to the spectral-timing method
used in \cite{Ingram2016,Ingram2017}. However, also taking this extra
step for the case of broad band variability is more difficult. This is
because the bi-spectrum of the variability may mean that contamination
from other frequencies becomes important (\citealt{Kim1979}). QPOs
present a special limit of the bi-spectrum for which the phases of
different QPO harmonics are strongly coupled to one another
(\citealt{Ingram2015}; or in other words the bi-coherence is high
between different QPO harmonics: \citealt{Maccarone2011}), and the rms
near the centroid frequency of a given QPO harmonic is dominated by
that harmonic. We will consider broad band variability more closely in
a later work.
We note that the method explored here does not take account of the
phase difference between the QPO harmonics, since the phase of the
cross-spectrum is relative to a reference
time series. It is however simple to include this extra detail in the
analysis using the method of \cite{Ingram2015}, which will provide
further information on the physics of the system. We also note that it
is possible to use an equivalent method using Stokes parameters, which
we will explore in a future work.
We use our new method to investigate the detectability of the QPOs in
polarisation degree and angle predicted by the Lense-Thirring
precession model (\citealt{Ingram2015a}). We consider the predictions
for a high (more edge-on) inclination ($i=70^\circ$) and low
inclination ($i=30^\circ$) object, and vary the mean polarisation
degree of the source, which is critical for detectability and a key
model uncertainty. We find that \textit{IXPE}~will be able to detect the
oscillations in a $200$ ks exposure, providing the mean polarisation
degree is $\langle p_0 \rangle \gtrsim 5.5\%$ and $\langle p_0 \rangle
\gtrsim 2.6\%$ for the high and low inclination models
respectively. The difference between models results from the swings in
polarisation angle being greater for a precessing vector being viewed
from above as opposed to from the side. The mean polarisation degree
is however \textit{predicted} to be lower for low inclination objects,
so high inclination objects will still likely be better targets
(\citealt{Chandrasekhar1960,Sunyaev1985}). Utilising a simultaneous
exposure with a larger area detector such as \textit{AstroSat} or
\textit{NICER} reduces the required polarisation degree down to
$\langle p_0 \rangle \gtrsim 4.7\%$ and $\langle p_0 \rangle \gtrsim
1.7\%$ for high and low inclination objects respectively. This is
encouraging, since the existing \textit{OSO 8} polarisation
measurements for Cygnus X-1, a low inclination ($i \approx 30^\circ$;
\citealt{Orosz2011a}) source, are $\langle p_0 \rangle = 2.4 \pm 1.1
\%$ and $\langle p_0 \rangle = 5.3 \pm 2.5 \%$ at $\sim 2.6$ keV and
$\sim 5.2$ keV respectively (\citealt{Long1980}). It is debatable
whether or not Cygnus X-1 displays QPOs in its flux at all
(\citealt{Axelsson2013}; Rapisarda et al submitted), but if there is
indeed precession in this source, the apparent lack of QPOs could be
due to the high amplitude broadband variability dominating over a low
amplitude QPO (consistent with the low measured inclination angle). In
this case, we would expect to see QPOs in the polarisation properties
using \textit{IXPE}~and \textit{AstroSat}. We also expect to detect these QPOs in the
higher inclination sources, if they do indeed have a larger mean
polarisation degree than Cygnus X-1 as predicted.
Interestingly for the prospect of polarimetry-timing, recent general
relativistic magnetohydrodynamic simulations show that the jet is
expected to precess in step with a precessing accretion flow (Liska et
al in prep). If optically thin synchrotron emission from the jet also
contributes significantly to the X-ray flux for some states, we would
expect still a higher polarisation degree for such states
(e.g. \citealt{Rybicki1979}), and therefore would expect detection of
of polarisation variability to be easier than we estimate here. For the hard
state, a dominant jet contribution to the X-rays has been argued
against on the basis of e.g. X-ray/radio scaling relations and
energetics (\citealt{Maccarone2005,Malzac2009}). In addition,
\cite{Heil2015} find that higher inclination sources
have harder X-ray spectra, which is not expected for emission from an
outflowing jet. Indeed, a precessing jet cannot explain Type-C
QPOs, at least in the X-rays, since their amplitude increases with
inclination angle. The trend should be the opposite for a precessing
jet, which would produce QPOs with amplitude roughly $\propto [1-
(v/c) \cos i]^{-2}$, where $v$ is the speed of the outflow.
However, it is possible that jet emission becomes more important in
the soft intermediate state (SIMS) when the source starts to display
Type-B QPOs. The amplitude of Type-B QPOs is higher for \textit{lower}
inclination sources (\citealt{Motta2015}), and jet precession has
previously been suggested as an origin (\citealt{Stevens2016}). Such a
switch in the X-ray
luminosity of the jet predicts that the ratio of power-law flux to
disk flux in the SIMs should be higher for lower inclination objects
due to beaming. This does not appear to be the case in the data (see
Fig 4 in \citealt{Gao2017}), in fact there are even hints of the
opposite trend, although the number of data points are too few to be
conclusive. Still, the relative importance of optically thin
synchrotron emission in the X-rays will be easy to test with \textit{IXPE},
through simply measuring the polarisation degree. Jet precession has
also been suggested to explain observed infrared QPOs
(\citealt{Kalamkar2016}), which would predict a QPO in the infrared
polarisation angle. Finally, \textit{INTEGRAL} observations suggest
that the $\gamma$-ray ($0.4-2$ MeV) emission from Cygnus X-1 is highly
polarised (\citealt{Laurent2011}). It would be very interesting to
search for variability in this polarised $\gamma$-ray emission, but
the count rate achievable with \textit{INTEGRAL} ($\sim 0.03$ c/s) is
too low.
Although simultaneous observation with a large area detector improves
statistics, we caution that in practice much time will be lost to
lining up the orbits of two satellites, particularly for low Earth
orbits. A huge advantage will therefore be gained by use of a
satellite such as \textit{eXTP}, which is proposed to have a large area
detector and a polarimeter in the same payload. Higher signal to noise
can of course be achieved with longer exposure times, although the
drift in QPO frequency over timescales of $\sim$days will need to be
taken into account. We also show that the impact of using a large area
to collect the reference time series is maximised for higher
frequency QPOs. In particular, the study of polarisation in HF QPOs
will be inaccessible to \textit{IXPE}~but may be possible if a very large area
detector such as the LAD on \textit{eXTP}/\textit{STROBE-X} is used to collect
the reference time series.
The source code used to make some of the plots in this paper can be
downloaded from
\url{https://bitbucket.org/adingram/polarimetry-timing}. At the time
of writing, the repository contains the code used to create
Figs. \ref{fig:i70} and \ref{fig:i30} from this paper. In addition, we
plan to further develop this repository over time, with the ambition
of developing public software compatible with the eventual
\textit{IXPE}~pipeline.
\section*{Acknowledgements}
A. I. acknowledges support from the Netherlands Organisation for
Scientific Research (NWO) Veni Fellowship, grant number
639.041.437.
\bibliographystyle{/Users/adamingram/Dropbox/bibmaster/mnras}
| {
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Skuru IK är en idrottsklubb i Skuru i Nacka kommun, bildad 22 oktober 1922. Klubben bedriver basket, handboll och simsport, tidigare även gymnastik, bowling och ishockey. Klubben började spela handboll 1950 och damlaget blev svenska inomhusmästarinnor 2001, 2004, 2005 och 2021.
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\section{Introduction}
In this paper, for a positive integer $n$, $N$ denotes the set $\{1,2,\cdots,n\}$. $\mathbb{R}^{n\times n}$ denotes the set of all $n\times n$ real matrices and the set of all $n\times n$ complex
matrices is denoted by $\mathbb{C}^{n\times n}$. Let $A = (a_{ij})$ and $B = (b_{ij})$ be two real $n\times n$ matrices. We write $A\geq B (> B)$ if $a_{ij} \geq b_{ij} (> b_{ij})$ for all $i,j\in N$. If $A\geq 0(> 0)$, we say that $A$ is a nonnegative (positive) matrix. The spectral radius of $A$ is denoted by $\rho(A)$. If $A$ is a nonnegative matrix, the Perron-Frobenius theorem guarantees that $\rho(A)\in \sigma(A)$, where $\sigma(A)$ is the set of all eigenvalues of $A$. In addition, define
$\tau(A)\triangleq min\{\lambda|\lambda\in\sigma(A)\}$, and denote by $\mathcal{M}_{n}$ the set of nonsingular $M$-matrices
(see \cite{QG}).
For $n\geqslant 2$, an $n\times n$ matrix $A$ is said to be
reducible if there exists a permutation matrix $P$ such that
$$
\mathop {\mathop {P^{T}AP = \left( {\begin{array}{*{20}c}
{B} & {C} \\
{0} & {D} \\
\end{array}} \right)}\limits_{} },
$$
where $B$ and $D$ are square matrices of order at least one. If no
such permutation matrix exists, then A is called irreducible. If $A$
is a $1\times1$ complex matrix, then $A$ is irreducible if and only
if its single entry is nonzero (see \cite{GQ}).
According to Ref. \cite{GQ}, a matrix $A$ is called an $M$-matrix,
if there exists an $n\times n$ nonnegative real matrix $P$ and a
nonnegative real number $\alpha$ such that $A=\alpha I-P$, and
$\alpha\geq\rho(P)$, where $\rho(P)$ denotes the spectral radius of
$P$ and $I$ is the identity matrix. Moreover, if $\alpha>\rho(P)$,
$A$ is called a nonsingular $M$-matrix; if $\alpha=\rho(P)$, we call
$A$ a singular $M$-matrix.
In addition, a matrix $A=(a_{ij})\in \mathbb{R}^{n\times n}$ is
called $Z$-matrix if all of whose off-diagonal entries are negative,
and denoted by $A\in \mathcal{Z}_{n}$. For convenience, the following simple
facts are needed (see Problems 16, 19 and 28 in Section 2.5 of
\cite{R.C}):
\begin{enumerate}
\item $\tau(A)\in\sigma(A)$;
\item If $A, B\in \mathcal{M}_{n}$, and $A\geq B$, then $\tau(A)\geq\tau(B)$;
\item If $A\in \mathcal{M}_{n}$, then $\rho(A^{-1})$ is the Perron eigenvalue of the nonnegative matrix $A^{-1}$, and $\tau(A)=\frac{1}{\rho(A^{-1})}$ is a positive real eigenvalue of $A$.
\end{enumerate}
Let $A$ be an irreducible nonsingular $M$-matrix. It is well known
that there exist positive vectors $u$ and $v$ such that
$Au=\tau(A)u$ and $v^{T}A=\tau(A)v^{T}$, where $u$ and $v$ are right
and left Perron eigenvectors of $A$, respectively.
The Hadamard product of $A=(a_{ij})\in \mathbb{C}^{n\times n}$ and $B=(b_{ij})\in \mathbb{C}^{n\times n}$ is defined by
$A\circ B=(a_{ij}b_{ij})\in \mathbb{C}^{n\times n}$.
For two real matrices $A, B\in \mathcal{M}_{n}$, the Fan product of $A$ and $B$ is denoted by $A\star B=C=[c_{ij}]\in \mathcal{M}_{n}$ and is defined by
$$
c_{ij}=\left\{{\begin{array}{ll}
-a_{ij}b_{ij},&{\rm if}\;\;i\neq j,\\
a_{ii}b_{ii},&{\rm if}\;\;i=j.
\end{array}}\right.
$$
We define: for any $i,j,l\in N$,
$$r_{li}=\frac{|a_{li}|}{|a_{ll}|-\sum\limits_{k\neq l,i}|a_{lk}|},~~l\neq i;~~~~r_{i}=\max_{l\neq i}\{r_{li}\},~~i\in N,
$$
$$
s_{ji}=\frac{|a_{ji}|+\sum\limits_{k\neq j,i}|a_{jk}|r_{k}}{|a_{jj}|},~~j\neq i;~~~~s_{i}=\max\limits_{j\neq i}\{s_{ji}\}, ~~i\in N,
$$
throughout the paper.
For two nonnegative matrices $A, B$, we will exhibit a new upper bound for $\rho(A\circ B)$, a new lower bound on the eigenvalue $\tau(A\star B)$ for the Fan product and a new lower bound on the eigenvalue $\tau(A\circ B^{-1})$ for the hadamard product in this paper.
\setcounter{equation}{0}
\renewcommand{\theequation}{2.\arabic{equation}}
\section{An upper bound for the spectral radius of the Hadamard product of two nonnegtive matrices}\label{sec2}
In (\cite{R.C}, p. 358), there is a simple estimate for $\rho(A\circ B)$: if $A, B\in \mathbb{R}^{n\times n}$, $A\geq 0$, and $B\geq 0$, then
\begin{equation}\label{eq:2.1}
\rho(A\circ B)\leq \rho(A)\rho(B).
\end{equation}
Fang \cite{MF} gave an upper bound for $\rho(A\circ B)$, that is,
\begin{equation}\label{eq:2.2}
\rho(A\circ B)\leq \max_{1\leq i\leq n}\Big\{2a_{ii}b_{ii}+\rho(A)\rho(B)-b_{ii}\rho(A)-a_{ii}\rho(B)\Big\},
\end{equation}
which is shaper than the bound $\rho(A)\rho(B)$ in (\cite{R.C}, p. 358).
Recently, Liu \cite{QG} improved the above results, have
\begin{equation}\label{eq:2.3}
\begin{array}{lll}
\rho(A\circ B)\leq \max\limits_{i\neq j}\frac{1}{2}\Big\{a_{ii}b_{ii}+a_{jj}b_{jj}+[(a_{ii}b_{ii}-a_{jj}b_{jj})^{2}\\
~~~~~~~~~~~~~~+4(\rho(A)-a_{ii})(\rho(B)-b_{ii})(\rho(A)-a_{jj})(\rho(B)-b_{jj})]^{\frac{1}{2}}\Big\}.
\end{array}
\end{equation}
Firstly, we give some lemmas in this section.
\begin{lemma}\label{lem:2.1}(Perron-Frobenius theorem)(\cite{R.C}).
If $A$ is an irreducible nonnegative matrix, there exist positive vectors $u$, such that $Au=\rho(A)u$.
\end{lemma}
\begin{lemma}\label{lem:2.2}(\cite{R.C}).
If $A, B\in \mathbb{C}^{n\times n}$, $D$ and $E$ are positive diagonal matrices, then $$D(A\circ B)E=(DAE)\circ B=(DA)\circ (BE)=(AE)\circ (DB)=A\circ (DBE).$$
\end{lemma}
\begin{lemma}\label{lem:2.3}(Brauer's theorem).
Let $A=(a_{ij})\in\mathbb{C}^{n\times n}$ $(n\geq2)$,
then all the eigenvalues of $A$ lie inside the union of $\frac{n(n-1)}{2}$ ovals of Cassini, i.e.,
\begin{equation}\label{eq:2.4}
B(A)=\bigcup^{n}_{i,j=1;i\neq j}\Big\{z\in
\mathbb{C}:|z-a_{ii}||z-a_{jj}|\leq (\sum\limits_{k\neq
i}|a_{ki}|)(\sum\limits_{k\neq
j}|a_{kj}|)\Big\},
\end{equation}
\end{lemma}
Obviously, if we denote $C=D^{-1}AD$, $D=diag(d_{1},d_{2},\cdots,d_{n}), d_{i}>0$, then $C$ and $A$ have the same eigenvalues, we obtain that all the eigenvalues of $A$ lie in the region:
\begin{equation}\label{eq:2.5}
\bigcup^{n}_{i,j=1;i\neq j}\Big\{z\in
\mathbb{C}:|z-a_{ii}||z-a_{jj}|\leq (\sum\limits_{k\neq
i}\frac{d_{k}}{d_{i}}|a_{ik}|)(\sum\limits_{k\neq
j}\frac{d_{l}}{d_{j}}|a_{jl}|)\Big\}.
\end{equation}
Next, we present a new estimating formula on the upper bound of $\rho(A\circ B)$.
\begin{theorem}\label{th:2.1}
If $A=(a_{ij})$ and $B=(b_{ij})$ are nonnegative matrices, $s_{i}=\max\limits_{j\neq i}\{a_{ij}\}$, $t_{i}=\max\limits_{j\neq i}\{b_{ij}\}$, then
\begin{equation}\label{eq:2.6}
\begin{array}{lll}
\rho(A\circ B)\leq \max \limits_{i\neq j} \frac{1}{2}\Big\{a_{ii}b_{ii}+a_{jj}b_{jj}+[(a_{ii}b_{ii}-a_{jj}b_{jj})^{2}\\
~~~~~~~~~~~~~~~~~~+4t_{i}s_{j}(\rho(A)-a_{ii})(\rho (B)-b_{jj})]^{\frac{1}{2}}\Big\}.
\end{array}
\end{equation}
\end{theorem}
\textbf{Proof.} It is evident that the inequality (\ref{eq:2.6})
holds with the equality for $n=1$. Therefore, we assume that $n\geq 2$
and divide two cases to prove this problem.
\textbf{Case 1}. Suppose that $A\circ B$ is irreducible. Obviously
$A$ and $B$ are also irreducible. By Lemma \ref{lem:2.1}, there
exists positive vectors $u=(u_{1},u_{2},\cdots,u_{n})$ and have $$(D^{-1}AD)u=\rho(D^{-1}AD)u=\rho(A)u,$$ where $D=diag(d_{1},d_{2},\cdots,d_{n}), d_{i}>0$, then $$\sum\limits_{j\neq i}\frac{a_{ij}d_{j}u_{j}}{d_{i}u_{i}}=\rho(A)-a_{ii}.$$
Define $U=diag(u_{1},u_{2},\cdots,u_{n})$, $C=(DU)^{-1}A(DU)$, then we have that
$$
\mathop {\mathop {C=\left( {\begin{array}{*{20}c}
a_{11}&\frac{d_{2}u_{2}}{d_{1}u_{1}}a_{12}&\cdots&\frac{d_{n}u_{n}}{d_{1}u_{1}}a_{1n}\\
\frac{d_{1}u_{1}}{d_{2}u_{2}}a_{21}&a_{22}&\cdots&\frac{d_{n}u_{n}}{d_{2}u_{2}}a_{2n}\\
\vdots&\vdots&\ddots&\vdots\\
\frac{d_{1}u_{1}}{d_{n}u_{n}}a_{n1}&\frac{d_{2}u_{2}}{d_{n}u_{n}}a_{n2}&\cdots&a_{nn}\\
\end{array}} \right)}\limits_{} }
$$
is an irreducible nonnegative matrix and
$$
\mathop {\mathop {C\circ B=(m_{ij})=\left( {\begin{array}{*{20}c}
a_{11}b_{11}&\frac{d_{2}u_{2}}{d_{1}u_{1}}a_{12}b_{12}&\cdots&\frac{d_{n}u_{n}}{d_{1}u_{1}}a_{1n}b_{1n}\\
\frac{d_{1}u_{1}}{d_{2}u_{2}}a_{21}b_{21}&a_{22}b_{22}&\cdots&\frac{d_{n}u_{n}}{d_{2}u_{2}}a_{2n}b_{2n}\\
\vdots&\vdots&\ddots&\vdots\\
\frac{d_{1}u_{1}}{d_{n}u_{n}}a_{n1}b_{n1}&\frac{d_{2}u_{2}}{d_{n}u_{n}}a_{n2}b_{n2}&\cdots&a_{nn}b_{nn}\\
\end{array}} \right)}\limits_{} }.
$$
By Lemma \ref{lem:2.2},
$$(DU)^{-1}(A\circ B)(DU)=(DU)^{-1}A(DU)\circ B=C\circ B,$$ i.e., $\rho (A\circ B)=\rho (C\circ B)$.
By the inequality (\ref{eq:2.4}) and $\rho(A\circ B)\geq a_{ii}b_{ii}$ (see \cite{A.R}), $\mathrm{for ~any} ~j\neq i\in N$,
we have
\begin{equation}
\begin{array}{lll}\label{eq:2.7}
(\rho(A\circ B)-a_{ii}b_{ii})(\rho(A\circ B))-a_{jj}b_{jj})
\leq \sum\limits_{ k\neq i}|m_{ik}|\sum\limits_{l\neq j}|m_{jl}|\\
~~~~~~~~~~~~~~~~~~~~~~~=\sum\limits_{k\neq i}\frac{d_{k}u_{k}a_{ik}b_{ik}}{d_{i}u_{i}}\sum\limits_{l\neq j}\frac{d_{l}u_{l}a_{jl}b_{jl}}{d_{j}u_{j}}\\
~~~~~~~~~~~~~~~~~~~~~~~\leq \Big(\max\limits_{k\neq i}\{b_{ik}\}\sum\limits_{k\neq i}\frac{d_{k}u_{k}a_{ik}}{d_{i}u_{i}}\Big)\Big(\max\limits_{l\neq j}\{a_{jl}\}\sum\limits_{l\neq j}\frac{d_{l}u_{l}b_{jl}}{d_{j}u_{j}}\Big)\\
~~~~~~~~~~~~~~~~~~~~~~~\leq\max\limits_{k\neq i}\{b_{ik}\}(\rho (A)-a_{ii})\max\limits_{l\neq j}\{a_{jl}\}(\rho (B)-b_{jj})\\
~~~~~~~~~~~~~~~~~~~~~~~=t_{i}s_{j}\Big(\rho (A)-a_{ii}\Big)\Big(\rho (B)-b_{jj}\Big).\\
\end{array}
\end{equation}
Thus, by solving the quadratic inequality (\ref{eq:2.7}), we have that
$$
\begin{array}{lll}
\rho(A\circ B)\leq \frac{1}{2} \Big\{a_{ii}b_{ii}+a_{jj}b_{jj}+[(a_{ii}b_{ii}-a_{jj}b_{jj})^{2}
+4t_{i}s_{j}(\rho (A)-a_{ii})(\rho (B)-b_{jj})]^{\frac{1}{2}}\Big\}\\
~~~~~~~~~~~\leq\max\limits_{i\neq
j}\frac{1}{2} \Big\{a_{ii}b_{ii}+a_{jj}b_{jj}+[(a_{ii}b_{ii}-a_{jj}b_{jj})^{2}
+4t_{i}s_{j}(\rho (A)-a_{ii})(\rho (B)-b_{jj})]^{\frac{1}{2}}\Big\}.
\end{array}
$$
i.e., the conclusion (\ref{eq:2.6}) holds.
\textbf{Case 2}. If $A\circ B$ is reducible. We may denote by $P=(p_{ij})$ the
$n\times n$ permutation matrix $(p_{ij})$ with
$$p_{12}=p_{23}=\cdots=p_{n-1,n}=p_{n,1}=1,$$ the remaining $p_{ij}$ zero, then both $A+\varepsilon P$ and $B+\varepsilon P$ are nonnegative irreducible matrices for any sufficiently small positive real number $\varepsilon$. Now we substitute $A+\varepsilon P$ and $B+\varepsilon P$
for $A$ and $B$, respectively in the previous Case 1, and then
letting $\varepsilon\rightarrow 0$, the result (\ref{eq:2.6})
follows by continuity. $\Box$
\textbf{Remark 2.1.}\label{re:2.1} Next, we give a comparison between
the upper bound in the inequality (\ref{eq:2.3}) and the upper bound in
the inequality (\ref{eq:2.6}). Without loss of generality, if $t_{i}+b_{ii}\geq\rho(B)$, $s_{j}+a_{jj}\geq\rho(A)$, $i,j=1,\cdots,n$, then we have $t_{i}s_{j}\geq(\rho(B)-b_{ii})(\rho(A)-a_{jj})$.
Thus, the upper bound in the inequality (\ref{eq:2.6}) is better than the upper bound in the inequality (\ref{eq:2.3}).
\begin{example}\label{ex:2.1}.
Let A and B be the same as in Example 1 from \cite{QG}:
\end{example}
$$
\mathop {\mathop {A=(a_{ij})=\left( {\begin{array}{*{20}c}
{4}&{1}&{0}&{2}\\
{1}&{0.05}&{1}&{1}\\
{0}&{1}&{4}&{0.5}\\
{1}&{0.5}&{0}&{4}
\end{array}} \right)}\limits_{} }, ~~
\mathop {\mathop {B=(b_{ij})=\left( {\begin{array}{*{20}c}
{1}&{1}&{1}&{1}\\
{1}&{1}&{1}&{1}\\
{1}&{1}&{1}&{1}\\
{1}&{1}&{1}&{1}
\end{array}} \right).}\limits_{} }
$$
By direct calculation, $\rho(A\circ B)=5.7339$.
According to (\ref{eq:2.1}), we have
$$\rho(A\circ B)\leq \rho(A)\rho(B)=22.9336.$$
If we apply (\ref{eq:2.2}) and (\ref{eq:2.3}), we get
$$\rho(A\circ B)\leq \max\limits_{1\leq i\leq 4}\Big\{2a_{ii}b_{ii}+\rho(A)\rho(B)-a_{ii}\rho(B)-b_{ii}\rho(A)\Big\}=17.1017,$$
and
$$
\begin{array}{lll}
\rho(A\circ B)\leq \max\limits_{i\neq j}\frac{1}{2}\Big\{a_{ii}b_{ii}+a_{jj}b_{jj}+[(a_{ii}b_{ii}-a_{jj}b_{jj})^{2}\\
~~~~~~~~~~~~~~+4(\rho(A)-a_{ii})(\rho(B)-b_{ii})(\rho(A)-a_{jj})(\rho(B)-b_{jj})]^{\frac{1}{2}}\Big\}=11.6478.
\end{array}
$$
If we apply Theorem \ref{th:2.1}, we obtain that
$$
\begin{array}{lll}
\rho(A\circ B)\leq \max \limits_{i\neq j} \frac{1}{2}\Big\{a_{ii}b_{ii}+a_{jj}b_{jj}+[(a_{ii}b_{ii}-a_{jj}b_{jj})^{2}\\
~~~~~~~~~~~~~~~~~~+4t_{i}s_{j}(\rho(A)-a_{ii})(\rho (B)-b_{jj})]^{\frac{1}{2}}\Big\}=8.1897.
\end{array}
$$
The example shows that the bound in Theorem \ref{th:2.1} is better than the existing bounds.
In addition, by the Theorem \ref{th:2.1} and \cite{QG}, we also have the following corollary:
\begin{corollary}\label{cor:2.1}
Let A and B be nonnegative matrices, then
\end{corollary}
$$
\begin{array}{lll}
|det(A\circ B)|\leq \Big(\rho(A\circ B)\Big)^{n}\\
~~~~~~~~~~~~~~~~\leq\max\limits_{i\neq j} \frac{1}{2^{n}}\Big\{a_{ii}b_{ii}+a_{jj}b_{jj}+[(a_{ii}b_{ii}-a_{jj}b_{jj})^{2}\\
~~~~~~~~~~~~~~~~~~~~~~+4t_{i}s_{j}(\rho(A)-a_{ii})(\rho (B)-b_{jj})]^{\frac{1}{2}}\Big\}^{n} \\
~~~~~~~~~~~~~~~~~\leq\max \limits_{i\neq j} \frac{1}{2^{n}}\Big\{a_{ii}b_{ii}+a_{jj}b_{jj}+[(a_{ii}b_{ii}-a_{jj}b_{jj})^{2}\\
~~~~~~~~~~~~~~~~~~~~~~+4(\rho(A)-a_{ii})(\rho (B)-b_{ii})(\rho(A)-a_{jj})(\rho (B)-b_{jj})]^{\frac{1}{2}}\Big\}^{n}.
\end{array}
$$
\setcounter{equation}{0}
\renewcommand{\theequation}{3.\arabic{equation}}
\section{Inequalities for the Fan product of two $M$-matrices}\label{sec3}
It is known (p.359, \cite{R.C}) that the following classical result
is given: if $A,B\in \mathbb{R}^{n\times n}$ are $M$-matrices, then
\begin{equation}\label{eq:3.1}
\tau(A\star B)\geq\tau(A)\tau(B).
\end{equation}
In 2007, Fang improved (\ref{eq:3.1}) in the Remark 3 of Ref.
\cite{MF} and gave a new lower bound for
$\tau(A\star B)$, that is
\begin{equation}\label{eq:3.2}
\tau(A\star B)\geq \min_{1\leq i\leq n}\Big\{b_{ii}\tau(A)+a_{ii}\tau(B)-\tau(A)\tau(B)\Big\}.
\end{equation}
Subsequently, Liu et al.\cite{QG} gave a sharper bound than
(\ref{eq:3.2}), i.e.,
\begin{equation}
\begin{array}{lll}\label{eq:3.3}
\tau(A\star B)\geq \frac{1}{2} \min \limits_{i\ne j}\Big\{a_{ii}b_{ii}+a_{jj}b_{jj}-[(a_{ii}b_{ii}-a_{jj}b_{jj})^{2}\\
~~~~~~~~~~~~~~+4(b_{ii}-\tau(B))(a_{ii}-\tau(A))(b_{jj}-\tau(B))(a_{jj}-\tau(A))]^{\frac{1}{2}}\Big\}.
\end{array}
\end{equation}
In addition, by the definition of Fan product, the following lemma holds:
\begin{lemma}\label{lem:3.1}(\cite{QG}).
If $A, B\in \mathbb{C}^{n\times n}$ be nonsingular $M$-matrices, $D$ and $E$ are positive diagonal matrices, then $$D(A\star B)E=(DAE)\star B=(DA)\star (BE)=(AE)\star (DB)=A\star (DBE).$$
\end{lemma}
Next, we give a new lower bound on the minimum eigenvalue $\tau(A\star B)$ of the Fan product of nonsingular $M$-matrices.
\begin{theorem}\label{th:3.1}
If $A=(a_{ij})$ and $B=(b_{ij})$ are nonsingular $M$-matrices, $s_{i}=\max\limits_{j\neq i}|a_{ij}|$, $t_{i}=\max\limits_{j\neq i}|b_{ij}|$, then
\begin{equation}\label{eq:3.4}
\begin{array}{lll}
\tau(A\star B)\geq \min \limits_{i\neq j}\frac{1}{2}\Big\{a_{ii}b_{ii}+a_{jj}b_{jj}-[(a_{ii}b_{ii}-a_{jj}b_{jj})^{2}\\
~~~~~~~~~~~~~~~~~~+4t_{i}s_{j}(a_{ii}-\tau (A))(b_{jj}-\tau (B))]^{\frac{1}{2}}\Big\}.
\end{array}
\end{equation}
\end{theorem}
\textbf{Proof.} It is clear that the (\ref{eq:3.4})
holds with the equality for $n=1$.
We next assume $n\geq 2$ and divide two cases to prove this problem.
\textbf{Case 1}. Suppose that $A\star B$ is irreducible. Obviously
$A$ and $B$ are also irreducible. By \cite{A.R}, there
exists positive vectors $u=(u_{1},u_{2},\cdots,u_{n})$ such that $$(D^{-1}AD)u=\tau(D^{-1}AD)u=\tau(A)u,$$ where $D=diag(d_{1},d_{2},\cdots,d_{n}), d_{i}>0$,
and then $$a_{ii}-\sum\limits_{j\neq i}\frac{|a_{ij}|d_{j}u_{j}}{d_{i}u_{i}}=\tau(A).$$
Define $U=diag(u_{1},u_{2},\cdots,u_{n})$, $C=(DU)^{-1}A(DU)$, we have that
$$
\mathop {\mathop {C=\left( {\begin{array}{*{20}c}
a_{11}&\frac{d_{2}u_{2}}{d_{1}u_{1}}a_{12}&\cdots&\frac{d_{n}u_{n}}{d_{1}u_{1}}a_{1n}\\
\frac{d_{1}u_{1}}{d_{2}u_{2}}a_{21}&a_{22}&\cdots&\frac{d_{n}u_{n}}{d_{2}u_{2}}a_{2n}\\
\vdots&\vdots&\ddots&\vdots\\
\frac{d_{1}u_{1}}{d_{n}u_{n}}a_{n1}&\frac{d_{2}u_{2}}{d_{n}u_{n}}a_{n2}&\cdots&a_{nn}\\
\end{array}} \right)}\limits_{} }
$$
is an irreducible nonsingular $M$- matrix, then
$$
\mathop {\mathop {C\star B=(m_{ij})=\left( {\begin{array}{*{20}c}
a_{11}b_{11}&\frac{d_{2}u_{2}}{d_{1}u_{1}}a_{12}b_{12}&\cdots&\frac{d_{n}u_{n}}{d_{1}u_{1}}a_{1n}b_{1n}\\
\frac{d_{1}u_{1}}{d_{2}u_{2}}a_{21}b_{21}&a_{22}b_{22}&\cdots&\frac{d_{n}u_{n}}{d_{2}u_{2}}a_{2n}b_{2n}\\
\vdots&\vdots&\ddots&\vdots\\
\frac{d_{1}u_{1}}{d_{n}u_{n}}a_{n1}b_{n1}&\frac{d_{2}u_{2}}{d_{n}u_{n}}a_{n2}b_{n2}&\cdots&a_{nn}b_{nn}\\
\end{array}} \right)}\limits_{} }.
$$
By the Lemma \ref{lem:3.1},
$$(DU)^{-1}(A\star B)(DU)=(DU)^{-1}A(DU)\star B=C\star B,$$ i.e., $\tau (A\star B)=\tau (C\star B)$.
In addition, by the inequality (\ref{eq:2.4}) and $0\leq\tau(A\star B)\leq a_{ii}b_{ii}$ (see \cite{A.R}), $\mathrm{for ~any} ~j\neq i\in N$, we have
\begin{equation}
\begin{array}{lll}\label{eq:3.5}
|\tau(A\star B)-a_{ii}b_{ii}||\tau(A\star B)-a_{jj}b_{jj}|
\leq \sum\limits_{ k\neq i}|m_{ik}|\sum\limits_{l\neq j}|m_{jl}|\\
~~~~~~~~~~~~~~~~~~~~~~~=\sum\limits_{k\neq i}|\frac{d_{k}u_{k}a_{ik}b_{ik}}{d_{i}u_{i}}|\sum\limits_{l\neq j}|\frac{d_{l}u_{l}a_{jl}b_{jl}}{d_{j}u_{j}}|\\
~~~~~~~~~~~~~~~~~~~~~~~\leq \Big(\max\limits_{k\neq i}|b_{ik}|\sum\limits_{k\neq i}|\frac{d_{k}u_{k}a_{ik}}{d_{i}u_{i}}|\Big)\Big(\max\limits_{l\neq j}|a_{jl}|\sum\limits_{l\neq j}|\frac{d_{l}u_{l}b_{jl}}{d_{j}u_{j}}|\Big)\\
~~~~~~~~~~~~~~~~~~~~~~~\leq\max\limits_{k\neq i}|b_{ik}|(a_{ii}-\tau (A))\max\limits_{l\neq j}|a_{jl}|(b_{jj}-\tau (B))\\
~~~~~~~~~~~~~~~~~~~~~~~=t_{i}s_{j}(a_{ii}-\tau (A))(b_{jj}-\tau (B)).\\
\end{array}
\end{equation}
Thus, by solving the quadratic inequality (\ref{eq:3.5}), we have that
$$
\begin{array}{lll}
\tau(A\star B)\geq \frac{1}{2} \Big\{a_{ii}b_{ii}+a_{jj}b_{jj}-[(a_{ii}b_{ii}-a_{jj}b_{jj})^{2}
+4t_{i}s_{j}(a_{ii}-\tau (A))(b_{jj}-\tau (B))]^{\frac{1}{2}}\Big\}\\
~~~~~~~~~~~\geq\min\limits_{i\neq
j}\frac{1}{2} \Big\{a_{ii}b_{ii}+a_{jj}b_{jj}-[(a_{ii}b_{ii}-a_{jj}b_{jj})^{2}
+4t_{i}s_{j}(a_{ii}-\tau (A))(b_{jj}-\tau (B))]^{\frac{1}{2}}\Big\}.
\end{array}
$$
i.e., the conclusion (\ref{eq:3.4}) holds.
\textbf{Case 2}. If $A\star B$ is reducible. It is well known that a matrix in $\mathcal{Z}_{n}$ is a nonsingular $M$-matrix if and only if all its leading principal minors are positive (see condition (E17) of Theorem 6.2.3 of \cite{A.R}). We denote by $P=(p_{ij})$ the $n\times n$ permutation matrix $(p_{ij})$ with
$$p_{12}=p_{23}=\cdots=p_{n-1,n}=p_{n,1}=1,$$ the remaining $p_{ij}$ zero, then both $A-\varepsilon P$ and $B-\varepsilon P$ are irreducible nonsingular $M$-matrices for any sufficiently small positive real number $\varepsilon$. Now we substitute $A-\varepsilon P$ and $B-\varepsilon P$ for $A$ and $B$, respectively in the previous Case 1, and then letting $\varepsilon\rightarrow 0$, the result (\ref{eq:3.4}) follows by continuity. $\Box$
\textbf{Remark 3.1.}\label{re:3.1} Similarly, we give a comparison between
the lower bound in the inequality (\ref{eq:3.3}) and the lower bound in
the inequality (\ref{eq:3.4}).
If $a_{jj}\geq\tau(A)+s_{j}$, $b_{ii}\geq\tau(B)+t_{i}$, $i,j=1,\cdots,n$, then $(a_{jj}-\tau(A))(b_{ii}-\tau(B))\geq s_{j}t_{i}$ for all $i\neq j$.
Thus, the lower bound in the inequality (\ref{eq:3.4}) is better than the lower bound in the inequality (\ref{eq:3.3}).
In addition, from Theorem \ref{th:3.1} and \cite{A.R}, we may get the following corollary.
\begin{corollary}\label{cor:3.1}.
If $A$, $B$ are nonsingular $M$-matrices, then
\end{corollary}
$$
\begin{array}{lll}
|det(A\star B)|\geq \Big(\tau(A\star B)\Big)^{n}\\
~~~~~~~~~~~~~~~~\geq\min \limits_{i\neq j}\frac{1}{2^{n}}\Big\{a_{ii}b_{ii}+a_{jj}b_{jj}-[(a_{ii}b_{ii}-a_{jj}b_{jj})^{2}\\
~~~~~~~~~~~~~~~~~~+4t_{i}s_{j}(a_{ii}-\tau (A))(b_{jj}-\tau (B))]^{\frac{1}{2}}\Big\}^{n} \\
~~~~~~~~~~~~~~~~~\geq\min \limits_{i\neq j}\frac{1}{2^{n}}\Big\{a_{ii}b_{ii}+a_{jj}b_{jj}-[(a_{ii}b_{ii}-a_{jj}b_{jj})^{2}\\
~~~~~~~~~~~~~~~~~~+4(a_{ii}-\tau (A))(b_{ii}-\tau (B))(a_{jj}-\tau (A))(b_{jj}-\tau (B))]^{\frac{1}{2}}\Big\}^{n}.
\end{array}
$$
\begin{example}\label{ex:3.1}(\cite{QG}).
Let A and B be the nonsingular $M$-matrices:
\end{example}
$$
\mathop {\mathop {A=(a_{ij})=\left( {\begin{array}{*{20}c}
{2}&{-1}&{0}\\
{0}&{1}&{-0.5}\\
{-0.5}&{-1}&{2}
\end{array}} \right)}\limits_{} }, ~~
\mathop {\mathop {B=(b_{ij})=\left( {\begin{array}{*{20}c}
{1}&{-0.25}&{-0.25}\\
{-0.5}&{1}&{-0.25}\\
{-0.25}&{-0.5}&{1}
\end{array}} \right).}\limits_{} }
$$
By (\ref{eq:3.1}), we have
$$\tau(A\star B)\geq \tau(A)\tau(B)=0.1854.$$
If we use the inequalities (\ref{eq:3.2}) and (\ref{eq:3.3}), then we get
$$\tau(A\star B)\geq \min\limits_{1\leq i\leq 3}\Big\{a_{ii}\tau(B)+b_{ii}\tau(A)-\tau(A)\tau(B)\Big\}=0.6980,$$
and
$$
\begin{array}{lll}
\tau(A\star B)\geq \min\limits_{i\neq j}\frac{1}{2}\Big\{a_{ii}b_{ii}+a_{jj}b_{jj}-[(a_{ii}b_{ii}-a_{jj}b_{jj})^{2}\\
~~~~~~~~~~~~~~+4(a_{ii}-\tau(A))(b_{ii}-\tau(B))(a_{jj}-\tau(A))(b_{jj}-\tau(B))]^{\frac{1}{2}}\Big\}=0.7655.
\end{array}
$$
If we apply Theorem \ref{th:3.1}, we obtain that
$$
\begin{array}{lll}
\tau(A\star B)\geq \min \limits_{i\neq j}\frac{1}{2}\Big\{a_{ii}b_{ii}+a_{jj}b_{jj}-[(a_{ii}b_{ii}-a_{jj}b_{jj})^{2}\\
~~~~~~~~~~~~~~~+4t_{i}s_{j}(a_{ii}-\tau(A))(b_{jj}-\tau(B))]^{\frac{1}{2}}\Big\}=0.8002.
\end{array}
$$
In fact, $\tau(A\star B)=0.8819$. The example shows that the bound in Theorem \ref{th:3.1} is better than the existing bounds.
\setcounter{equation}{0}
\renewcommand{\theequation}{4.\arabic{equation}}
\section{A bound for the Hadamard product of $M$-matrix and an inverse $M$-matrix}\label{sec4}
Now, we consider the lower bound of $\tau(A\circ B^{-1})$, for $A=(a_{ij}),B=(b_{ij})\in \mathcal{M}_{n}$ and $B^{-1}=(\beta_{ij})$.
Firstly, in \cite{R.C}, Horn and Johnson gave the classical results
\begin{equation}\label{eq:4.1}
\tau(A\circ B^{-1})\geq\tau(A)\min\limits_{1\leq i\leq n}\beta_{ii}.
\end{equation}
Subsequently, Huang \cite{HR} gave new bound for $\tau(A\circ B^{-1})$, that is,
\begin{equation}\label{eq:4.2}
\tau(A\circ B^{-1})\geq \frac{1-\rho(J_{A})\rho(J_{B})}{1+\rho^{2}(J_{B})}\min\limits_{1\leq i\leq n}\frac{a_{ii}}{b_{ii}},
\end{equation}
where $\rho(J_{A})$ and $\rho(J_{B})$ are the spectral radius of the Jacobi iterative matrices $J_{A}$ and $J_{B}$, respectively.
In 2008, Li \cite{LYT} improved the above results as follows.
\begin{equation}\label{eq:4.3}
\tau(A\circ B^{-1})\geq\min\limits_{i}\frac{b_{ii}-s_{i}\sum\limits_{j\neq i}|b_{ji}|}{a_{ii}}.
\end{equation}
Recently, Chen \cite{CFB} improved the result and gave a new lower bound for $\tau(A\circ B^{-1})$:
\begin{equation}\label{eq:4.4}
\begin{array}{lll}
\tau(A\circ B^{-1})\geq \min \limits_{i\neq j} \frac{1}{2}\Big\{a_{ii}\beta_{ii}+a_{jj}\beta_{jj}-[(a_{ii}\beta_{ii}-a_{jj}\beta_{jj})^{2}\\
~~~~~~~~~~~~~~~~~~+4a_{ii}a_{jj}\beta_{ii}\beta_{jj}\rho^{2}(J_{A})\rho^{2}(J_{B})]^{\frac{1}{2}}\Big\}.
\end{array}
\end{equation}
In this section, we give a lower bound of $\tau(A\circ B^{-1})$ for $M$-matrix and inverse $M$-matrix, which improves the above bounds.
\begin{lemma}\label{lem:4.1}(\cite{CJL}).
If $A=(a_{ij})\in\mathcal{M}_{n}$, there exists a positive diagonal matrix $D$ such that $D^{-1}AD$ is a strictly row diagonally dominant matrix.
\end{lemma}
\begin{lemma}\label{lem:4.2}(\cite{CJL}).
If $A=(a_{ij})\in\mathcal{M}_{n}$, and $D=diag(d_{1},d_{2},\cdots,d_{n})$, $d_{i}>0 ~~(i\in N)$, then $D^{-1}AD$ is also an $M$-matrix.
\end{lemma}
\begin{lemma}\label{lem:4.3}(\cite{CJL}).
If $A, B\in\mathcal{M}_{n}$, then $B\circ A^{-1}$ is also an $M$-matrix.
\end{lemma}
\begin{lemma}\label{lem:4.4}(\cite{LYT}).
If $A=(a_{ij})$ be a strictly diagonally dominant $M$-matrix by rows, then for $A^{-1}=(\alpha_{ij})$, we have $$\alpha_{ji}\leq\frac{|a_{ji}|+\sum\limits_{k\neq j,i}|a_{jk}|r_{k}}{a_{jj}}\alpha_{ii}, ~~~~\mathrm{for ~all} ~~j\neq i.$$
\end{lemma}
\begin{theorem}\label{th:4.1}
If $A=(a_{ij})$ and $B=(b_{ij})$ are two nonsingular $M$-matrices and $B^{-1}=(\beta_{ij})$, $s_{i}=\max\limits_{j\neq i}|a_{ij}|$, then
\begin{equation}\label{eq:4.5}
\begin{array}{lll}
\tau(A\circ B^{-1})\geq \min \limits_{i\neq j} \frac{1}{2}\Big\{a_{ii}\beta_{ii}+a_{jj}\beta_{jj}-[(a_{ii}\beta_{ii}-a_{jj}\beta_{jj})^{2}\\
~~~~~~~~~~~~~~~~~~+4s_{i}s_{j}\beta_{ii}\beta_{jj}(a_{ii}-\tau(A))(b_{jj}-\tau (B))]^{\frac{1}{2}}\Big\}.
\end{array}
\end{equation}
\end{theorem}
\textbf{Proof.} If $A$ is an $M$-matrix, by Lemmas (\ref{lem:4.1}-\ref{lem:4.2}), there exists a positive diagonal matrix $D$ such that
$D^{-1}AD$ is a strictly diagonally dominant $M$-matrix by rows.
\textbf{Case 1}. Suppose that $A\circ B^{-1}$ is irreducible. Obviously
$A$ and $B$ are also irreducible. Since $A-\tau(A)I$ is an irreducible nonsingular $M$-matrix, then $a_{ii}-\tau(A)>0$, $\forall i\in N$, and there exists a positive vector
$u=(u_{1},u_{2},\cdots,u_{n})$ such that $$Au=\tau(A)u, $$ where $u=diag(u_{1},u_{2},\cdots,u_{n}), u_{i}>0$, and then $$a_{ii}+\sum\limits_{j\neq i}\frac{a_{ji}u_{j}}{u_{i}}=\tau(A).$$
Define $U=diag(u_{1},u_{2},\cdots,u_{n})$, $C=U^{-1}AU$, then we have that
$$
\mathop {\mathop {C=(\tilde{a}_{ij})=U^{-1}AU=\left( {\begin{array}{*{20}c}
a_{11}&\frac{a_{12}u_{1}}{u_{2}}&\cdots&\frac{a_{1n}u_{1}}{u_{n}}\\
\frac{a_{21}u_{2}}{u_{1}}&a_{22}&\cdots&\frac{a_{2n}u_{2}}{u_{n}}\\
\vdots&\vdots&\ddots&\vdots\\
\frac{a_{n1}u_{n}}{u_{1}}&\frac{a_{n2}u_{n}}{u_{2}}&\cdots&a_{nn}\\
\end{array}} \right)}\limits_{} }
$$
is an irreducible nonsingular $M$-matrix.
By Lemma \ref{lem:2.2},
$$U^{-1}(A\circ B^{-1})U=(U^{-1}AU)\circ B^{-1}=C\circ B^{-1},$$ i.e., $\tau (A\circ B^{-1})=\tau (C\circ B^{-1})$.
By the inequality (\ref{eq:2.4}) and $0\leq\tau(A\star B)\leq a_{ii}b_{ii}$ (see \cite{A.R}), $\mathrm{for ~any} ~j\neq i\in N$,
we have
\begin{equation}
\begin{array}{lll}\label{eq:4.6}
|\tau(A\circ B^{-1})-a_{ii}\beta_{ii}||\tau(A\circ B^{-1})-a_{jj}\beta_{jj}|
\leq \sum\limits_{ k\neq i}|\tilde{a}_{ki}|\beta_{ki}\sum\limits_{l\neq j}|\tilde{a}_{lj}|\beta_{lj}\\
~~~~~~~~~~~~~~~~~~~~~~~\leq\sum\limits_{k\neq i}|\tilde{a}_{ki}|\frac{b_{ki}+\sum\limits_{u\neq k,i}|b_{ku}|r_{u}}{b_{kk}}\beta_{ii}\sum\limits_{l\neq j}|\tilde{a}_{lj}|\frac{b_{lj}+\sum\limits_{v\neq l,j}|b_{lv}|r_{v}}{b_{ll}}\beta_{jj}\\
~~~~~~~~~~~~~~~~~~~~~~~=\sum\limits_{k\neq i}|\tilde{a}_{ki}|s_{ki}\beta_{ii}\sum\limits_{l\neq j}|\tilde{a}_{lj}|s_{lj}\beta_{jj}\\
~~~~~~~~~~~~~~~~~~~~~~~\leq \sum\limits_{k\neq i}|\tilde{a}_{ki}|s_{i}\beta_{ii}\sum\limits_{l\neq j}|\tilde{a}_{lj}|s_{j}\beta_{jj}\\
~~~~~~~~~~~~~~~~~~~~~~~=\sum\limits_{k\neq i}\frac{|a_{ki}|u_{k}}{u_{j}}s_{i}\beta_{ii}\sum\limits_{l\neq j}\frac{|a_{jl}|u_{j}}{u_{l}}s_{j}\beta_{jj}\\
~~~~~~~~~~~~~~~~~~~~~~~=s_{i}s_{j}\beta_{ii}\beta_{jj}(a_{ii}-\tau (A))(a_{jj}-\tau (A)).\\
\end{array}
\end{equation}
Thus, by solving the quadratic inequality (\ref{eq:4.6}), we obtain that
$$
\begin{array}{lll}
\tau(A\circ B^{-1})\geq \frac{1}{2} \Big\{a_{ii}\beta_{ii}+a_{jj}\beta_{jj}-[(a_{ii}\beta_{ii}-a_{jj}\beta_{jj})^{2}
+4s_{i}s_{j}\beta_{ii}\beta_{jj}(a_{ii}-\tau (A))(a_{jj}-\tau (A))]^{\frac{1}{2}}\Big\}\\
~~~~~~~~~~~\geq\min\limits_{i\neq
j}\frac{1}{2} \Big\{a_{ii}\beta_{ii}+a_{jj}\beta_{jj}-[(a_{ii}\beta_{ii}-a_{jj}\beta_{jj})^{2}
+4s_{i}s_{j}\beta_{ii}\beta_{jj}(a_{ii}-\tau (A))(a_{jj}-\tau (A))]^{\frac{1}{2}}\Big\}.
\end{array}
$$
i.e., the conclusion (\ref{eq:4.5}) holds.
\textbf{Case 2}. If $A\circ B^{-1}$ is reducible, then one denotes by $P=(p_{ij})$ the
$n\times n$ permutation matrix with $$p_{12}=p_{23}=\cdots=p_{n-1,n}=p_{n,1}=1,$$ the remaining $p_{ij}$ zero, then both $A-\varepsilon P$ and $B-\varepsilon P$ are irreducible nonsingular $M$-matrices for any sufficiently small positive real number $\varepsilon$. Now we substitute $A-\varepsilon P$ and $B-\varepsilon P$
for $A$ and $B$, respectively from the previous Case, and then letting $\varepsilon\rightarrow 0$, the result (\ref{eq:2.6}) follows by continuity. $\Box$
\begin{example}\label{ex:4.1}(\cite{CFB}).
Let A and B be nonsingular $M$-matrices:
\end{example}
$$
\mathop {\mathop {A=(a_{ij})=\left( {\begin{array}{*{20}c}
{1}&{-0.5}&{0}&{0}\\
{-0.5}&{1}&{-0.5}&{0}\\
{0}&{-0.5}&{1}&{-0.5}\\
{0}&{0}&{-0.5}&{1}
\end{array}} \right)}\limits_{} }, ~~
\mathop {\mathop {B=(b_{ij})=\left( {\begin{array}{*{20}c}
{4}&{-1}&{-1}&{-1}\\
{-2}&{5}&{-1}&{-1}\\
{0}&{-2}&{4}&{-1}\\
{-1}&{-1}&{-1}&{4}
\end{array}} \right).}\limits_{} }
$$
By direct calculation, $\tau(A\circ B^{-1})=0.2148$.
According to (\ref{eq:4.1}), we have
$$\tau(A\circ B^{-1})\geq\tau(A)\min\limits_{1\leq i\leq n}\beta_{ii}=0.07.$$
If we apply (\ref{eq:4.2}) and (\ref{eq:4.3}), we get
$$\tau(A\circ B^{-1})\geq\frac{1-\rho(J_{A}\rho(J_{B}))}{1+\rho^{2}(J_{B})}\min\limits_{i}\frac{b_{ii}}{a_{ii}}=0.0707,$$
and
$$\tau(A\circ B^{-1})\geq\min\limits_{i}\frac{b_{ii}-s_{i}\sum\limits_{j\neq i}|b_{ji}|}{a_{ii}}=0.08.$$
According to (\ref{eq:4.4})
$$
\begin{array}{lll}
\tau(A\circ B^{-1})\geq \min \limits_{i\neq j} \frac{1}{2}\Big\{a_{ii}\beta_{ii}+a_{jj}\beta_{jj}-[(a_{ii}\beta_{ii}-a_{jj}\beta_{jj})^{2}\\
~~~~~~~~~~~~~~~~~~+4a_{ii}a_{jj}\beta_{ii}\beta_{jj}\rho^{2}(J_{A})\rho^{2}(J_{B})]^{\frac{1}{2}}\Big\}=0.1524.
\end{array}
$$
If we apply Theorem \ref{th:4.1}, we obtain that
$$
\begin{array}{lll}
\tau(A\circ B^{-1})\geq\min\limits_{i\neq
j}\frac{1}{2} \Big\{a_{ii}\beta_{ii}+a_{jj}\beta_{jj}+[(a_{ii}\beta_{ii}-a_{jj}\beta_{jj})^{2}\\
~~~~~~~~~~~~~~~~+4s_{i}s_{j}\beta_{ii}\beta_{jj}(a_{ii}-\tau (A))(a_{jj}-\tau (A))]^{\frac{1}{2}}\Big\}=0.1929.
\end{array}
$$
The example shows that the bound in Theorem \ref{th:4.1} is better than the existing bounds.
\setcounter{equation}{0}
\renewcommand{\theequation}{5.\arabic{equation}}
\section{Inequalities for the Fan product of several $M$-matrices}\label{sec5}
Firstly, let us recall the following lemmas.
\begin{lemma}\label{lem:5.1}(\cite{LHB}).
Let $A$ be an irreducible nonsingular $M$-matrix, if $AZ\geq kZ$ for a nonegative nonzero vector $Z$, then $k\leq\tau(A)$.
\end{lemma}
\begin{lemma}\label{lem:5.2}(\cite{HL}).
Let $x_{j}=(x_{j}(1),\cdots,x_{j}(n))^{T}\geq0$, $j\in\{1,2\cdots,m\}$, if $P_{j}>0$ and $\sum^{m}_{k=1}\frac{1}{P_{k}}\geq 1$, then we have
\begin{equation}\label{eq:5.1}
\sum\limits_{i=1}^{n}\prod_{j=1}^{m}x_{j}(i)\leq\prod_{j=1}^{m}\Big\{\sum\limits_{i=1}^{n}[x_{j}(i)]^{P_{j}}\Big\}^{\frac{1}{P_{j}}}.
\end{equation}
\end{lemma}
Next, according to these results, we expand the inequality
(\ref{eq:3.2}) of the Fan product of two matrices to the Fan product
of several matrices. One can obtain the following result:
\begin{theorem}\label{th:5.1}
For any matrices $A_{k}\in M_{n}$, and positive integers $P_{k}$
with $\sum^{m}_{k=1}\frac{1}{P_{k}}\geq 1$, $k\in\{1,2,\cdots,m\}$,
we have that
\begin{equation}\label{eq:5.2}
\tau(A_{1}\star A_{2}\cdots\star A_{m})\geq \min_{1\leq i\leq
n}\Big\{\prod^{m}_{k=1}A_{k}(i,i)-\prod^{m}_{k=1}[A_{k}(i,i)^{P_{k}}-\tau(A_{k}^{(P_{k})})]^\frac{1}{P_{k}}\Big\}.
\end{equation}
\end{theorem}
\textbf{Proof.} It is quite evident that the (\ref{eq:5.2}) holds with
the equality for $n=1$. Below we assume that $n\geq 2$.
\textbf{Case 1}. Let $A_{1}\star A_{2}\cdots\star A_{m}$ be an
irreducible nonsingular $M$-matrix, thus $A_{k}$ is irreducible,
$k\in\{1,2,\cdots,m\}$, we can obtain that $A_{k}^{(P_{k})}$ is also
irreducible. Let
$u_{k}^{(P_{k})}=(u_{k}(1)^{P_{k}},\cdots,u_{k}(n)^{P_{k}})^T>0$ be
a right Perron eigenvector of $A_{k}^{(P_{k})}$, and
$u_{k}=(u_{k}(1),\cdots,u_{k}(n))^T>0$, thus for any $i\in N$, we
have that
$$
A_{k}^{(P_{k})}u_{k}^{(P_{k})}=\tau (A_{k}^{(P_{k})})u_{k}^{(P_{k})},
$$
$$
A_{k}(i,i)^{P_{k}}u_{k}(i)^{P_{k}}-\sum\limits_{j\neq
i}|A_{k}(i,j)^{P_{k}}|u_{k}(j)^{P_{k}}=\tau
(A_{k}^{(P_{k})})u_{k}(i)^{(P_{k})},
$$
and
\begin{equation}\label{eq:5.3}
\sum\limits_{j\neq
i}|A_{k}(i,j)^{P_{k}}|u_{k}(j)^{P_{k}}=\Big(A_{k}(i,i)^{P_{k}}-\tau
(A_{k}^{(P_{k})})\Big)u_{k}(i)^{P_{k}}.
\end{equation}
Denote $C=A_{1}\star A_{2}\cdots\star A_{m}$, $Z=u_{1}\star
u_{2}\cdots\star u_{m}=(Z(1),\cdots,Z(n))^{T}>0$, thus
$Z(i)=\prod^{m}_{k=1}u_{k}(i)$. By the Lemma \ref{lem:5.2}
and (\ref{eq:5.3}), we get that
$$
\begin{array}{lll}
(CZ)_{i}=\Big(\prod^{m}_{k=1}A_{k}(i,i)\Big)Z(i)-\Big(\sum\limits_{j\neq
i}\prod^{m}_{k=1}|A_{k}(i,j)|\Big)Z(j)\\~~~~~~~~~
=\Big(\prod^{m}_{k=1}A_{k}(i,i)\Big)Z(i)-\sum\limits_{j\neq
i}\prod^{m}_{k=1}\Big(|A_{k}(i,j)|u_{k}(j)\Big)\\~~~~~~~~~
\geq\Big(\prod^{m}_{k=1}A_{k}(i,i)\Big)Z(i)-\prod^{m}_{k=1}\Big\{\sum\limits_{j\neq
i}[|A_{k}(i,j)|u_{k}(j)]^{(P_{k})}\Big\}^\frac{1}{P_{k}}~~\mathrm{(by~the~
equality~ (\ref{eq:5.3}))}\\~~~~~~~~~
=\Big(\prod^{m}_{k=1}A_{k}(i,i)\Big)Z(i)-\prod^{m}_{k=1}\Big\{[A_{k}(i,i)^{P_{k}}-\tau
(A_{k}^{(P_{k})})]u_{k}(i)^{P_{k}}\Big\}^\frac{1}{P_{k}}\\~~~~~~~~~
=\Big\{\prod^{m}_{k=1}A_{k}(i,i)-\prod^{m}_{k=1}[A_{k}(i,i)^{P_{k}}-\tau
(A_{k}^{(P_{k})})]\Big\}^\frac{1}{P_{k}}Z(i).
\end{array}
$$
According to the Lemma \ref{lem:5.1}, we obtain that
$$
\tau(A_{1}\star A_{2}\cdots\star A_{m})\geq \min_{1\leq i\leq
n}\Big\{\prod^{m}_{k=1}A_{k}(i,i)-\prod^{m}_{k=1}[A_{k}(i,i)^{P_{k}}-\tau(A_{k}^{(P_{k})})]^\frac{1}{P_{k}}\Big\}.
$$
\textbf{Case 2}. If $A_{1}\star A_{2}\cdots\star A_{m}$ is
reducible, where $A_{i}~(i=1,2,\cdots,m)$ are nonsingular
$M$-matrices. Similarly, let $P=(p_{ij})$ be the $n\times n$
permutation matrix with $p_{12}=p_{23}=\cdots=p_{n-1,n}=p_{n,1}=1$,
the remaining $p_{ij}$ zero, then $A_{k}-\varepsilon P$ is an
irreducible nonsingular $M$-matrix for any chosen positive real
number $\varepsilon$. Note that $A_{k}-\varepsilon P$ is a
continuous function on $\varepsilon$. Now we substitute
$A_{k}-\varepsilon P$ for $A_{k}$, in the previous Case 1, and then
letting $\varepsilon\rightarrow 0$, the result (\ref{eq:5.2})
follows by continuity. $\Box$
\textbf{Remark 4.1.}\label{re:5.1} If we take $m=2$ in Theorem
\ref{th:4.1}, one can obtain the following results:
\begin{itemize}
\item If $p_{1}=p_{2}=1$, $A_{1}=A=(a_{ij})$, $A_{2}=B=(b_{ij})$,
we have that
$$
\tau(A\star B)\geq \min_{1\leq i\leq
n}\Big\{a_{ii}b_{ii}-(a_{ii}-\tau(A))(b_{ii}-\tau(B))\Big\},
$$
which is just the inequality (\ref{eq:3.2}).
\item If $p_{1}=p_{2}=2$, $A_{1}=A=(a_{ij})$, $A_{2}=B=(b_{ij})$, then
\begin{equation}\label{eq:5.4}
\tau(A\star B)\geq \min_{1\leq i\leq
n}\Big\{a_{ii}b_{ii}-[a_{ii}^{2}-\tau(A\star
A)]^{\frac{1}{2}}[b_{ii}^{2}-\tau(B\star B)]^{\frac{1}{2}}\Big\}.
\end{equation}
In addition, by using the inequalities of arithmetic
and geometric means, we may obtain that
\[
a_{ii}^{2}\tau(B\star B)+b_{ii}^{2}\tau(A\star A)\geq
2a_{ii}b_{ii}[\tau(A\star A)\tau(B\star B)]^{\frac{1}{2}},
\]
so
\begin{equation}\label{eq:5.5}
(a_{ii}^{2}-\tau(A\star A))(b_{ii}^{2}-\tau(B\star B))\leq
\Big\{a_{ii}b_{ii}-[\tau(A\star A)\tau(B\star B)]^{\frac{1}{2}}\Big\}^{2}.
\end{equation}
Since for any $A,B\in M_n$, $\tau(A\star B)\geq \tau(A) \tau(B)$
(see \cite{QG} or (\ref{eq:3.1})), then, by (\ref{eq:5.5}), we have
that
$$
a_{ii}b_{ii}-\Big[(a_{ii}^{2}-\tau(A\star A))(b_{ii}^{2}-\tau(B\star
B))\Big]^{\frac{1}{2}}\geq[\tau(A\star A)\tau(B\star
B)]^{\frac{1}{2}}\geq\tau(A)\tau(B).
$$
That is, the bound in (\ref{eq:5.2}) is better than the bound in
(\ref{eq:3.1}).
\item If $p_{1}=1, p_{2}=2, A_{1}=A=(a_{ij}), A_{2}=B=(b_{ij})$,
then we get
$$
\tau(A\star B)\geq \min_{1\leq i\leq
n}\Big\{a_{ii}b_{ii}-[a_{ii}-\tau(A)][b_{ii}^{2}-\tau(B\star
B)]^{\frac{1}{2}}\Big\}.
$$
\end{itemize}
\textbf{Acknowledgements}. \emph{The authors sincerely thank Prof.
Julio Moro and the reviewers and editor for their valuable and
detailed comments and suggestions on the manuscript of this paper,
which led to a substantial improvement on the presentation and
contents of this paper.}
{\small | {
"redpajama_set_name": "RedPajamaArXiv"
} | 9,574 |
According to a report from Eurogamer's Digital Foundry, a smaller version of the Xbox One core processor is in development. The information comes not via Microsoft but from the LinkedIn profile of an AMD senior manager of the company's System On a Chip physical design.
The manager's profile says that he "successfully planned and executed the first APU for Microsoft's Xbox One Game Console in 28nm technology and a cost-reduced derivative in 20nm technology."
While a revised Xbox One console is, at minimum, a year away – more likely two or three – this shows that they're already working on designing it. The smaller chip would be nearly two times as dense with semiconductors and consume 25 percent less power than the current processor. It's even possible that they could eke a bit more power out of the chip, though it's not likely that we'd see that on the consumer side.
Digital Foundry notes that shrinking the processor benefits Microsoft in a surprising number of ways. A cooler, smaller system means more working chips for the amount of material it takes to create the chips as well as less materials required for things like cooling, while a smaller system means smaller packaging and easier shipping.
Check out Digital Foundry's article for the full story. | {
"redpajama_set_name": "RedPajamaC4"
} | 9,554 |
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